Math Homework Questions & Answers Archive

Consider the following functions. f(x) = sqrt(x-4) and g(x) = sqrt[3]x Find the formula for (f+g)(x) and simplify your answer. Then find the domain for (f+g)(x). Round your answer to two decimal places, if necessary.

Find the common logarithm of 0.0352 log 0.0352= (Round to four decimal places as needed.)

Use a half-angle formula to evaluate the expression without using a calculator. csc (15π/8) a. What is the measure of the half-angle α/2 ? α/2= (Type an exact answer in terms of π. Use integers or fractions for any numbers in the expression.)

f: R^2 -> R^2, f(x, y) = (ax-2, by+3b) fonksiyonu sabit fonksiyon olduğuna göre a+b toplamı kaçtır? A) 5 B) 2 C) 1 D) -1 E) -3

The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 19500. (a) Find a function that models the population t years after 2000 ( t=0 for 2000). Your answer is P(t)=

Find the derivative of the function. Do not find the product before finding the derivative. y=5 x^2(4 x^4-3 x^2) Choose the correct answer below. A. y'=(4 x^4-3 x^2)(16 x^3-6 x)+(10 x)(5 x^2) B. y'=(5 x^2)(4 x^4-3 x^2)+(16 x^3-6 x)(10 x) C. y'=(5 x^2)(16 x^3-6 x)+(4 x^4-3 x^2)(10 x) D. y'=(4 x)(5 x^2)+(4 x^4-3 x^2)(16 x^3-6 x)

Use the Squeeze Theorem to find the limit as x approaches 7 of f(x), given that 6 - x - 7 ≤ f(x) ≤ 6 + x - 7.

Solve the equation on the interval (0 leq theta<2 pi). [ 8 sin ^2 theta-17 sin theta+9=0 ] What is the solution in the interval (0 leq theta<2 pi) ? Select the correct choice and fill in any answer boxes in your choice below. A. The solution set is (square) (Simplify your answer. Type an exact answer, using (pi) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.

Consider the following functions. f(x) = x and g(x) = x Step 1 of 4 : Find (f+g)(-2).

If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker.

For a segment of a radio show, a disc jockey can play 7 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged? ways

Solve the inequality. Write the solution set in interval notation if possible. Simplify your answer, if necessary. d^4 - 37d^2 + 36 ≤ 0 Part 1 of 4 The inequality is already in the form F(d) ≤ 0. Now, find the real solutions to the related equation F(d) = 0. (d^2 □)(d^2 □) = 0

Determine whether the given statement is true or false. 9 not in 1,2,3, ..., 24 Choose the correct answer below. True False

Find the critical value for a left-tailed test using the F distribution with α=0.025, degrees of freedom in the numerator =20, and degrees of freedom in the denominator =50. A portion of the table of critical values of the F-distribution is provided. What is the critical value? (Round to two decimal places as needed.)

Time Magazine reports the "Divorce" rate has dropped to a 40-year low. Time's estimate is that 1.69% of married women get "Divorced" each year. We will take a sample of n=700 married women and model the proportion who got "Divorced" last year. (You will need to determine the mean and standard deviation for the p-hat model. Round your SD to four decimal places.) Question: P(25 or fewer women got "Divorced" last year) = Round your answer to four decimal places.

parxmaths.uk Maths 4.572 XP Roo Holcombe Mer 4A 4B 4C 4D Summary Bookwork code: 4D Calculator not allowed Round 7982 to 2 significant figures. Watch video

Solve the equation for P. N = (9/7)P + 26 P = □ (Simplify your answer.)

Find the exact value of csc[2 tan^(-1)(-3/4)].

If P(E)=0.71, find the odds in favor of E What are the odds in favor of E?

Mrs. Page is taking a group of students to see an exhibit. The cost of the bus rental is 250 and the cost per ticket to see the exhibit is 15. Create an equation with two variables that models this situation, and find the total cost for the event if 40 students teachers plan to attend. C=250-15 x ; 600 C=250+15 x ; 265 C=250 x+15: 10,015 C=250+15 x ; 850

In 2000, 52% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.8% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000. P(x)=

(a) Which measures of central tendency do not exist for this data set? Choose all that apply. Mean Median Mode All of these measures exist (b) Suppose that the measurement 182 (the largest measurement in the data set) were replaced by 245 . Which measures of central tendency would be affected by the change? Choose all that apply. Mean Median Mode None of these measures (c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply. Mean Median Mode None of these measures (d) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set? Choose only one. Mean is greater Median is greater Cannot be determined

Decide which of the ordered pairs are solutions for the equation (y=3 x-2). (0,-2) solution not a solution

Homework (Ch 15) Suppose Fire Dragon charges 2.75 per bottle. Your classmate Taio says that because Fire Dragon is a monopoly with market power, it should charge the higher price of 3.00 per bottle in order to increase its profit. Complete the following table to determine whether Taio is correct. Price (Dollars per bottle) Quantity Demanded (Cans) Total Revenue (Dollars) Total Cost (Dollars) Profit (Dollars) 2.75 1,500 4,125.00 - 3.00 1,000 3,000.00 - Given the earlier information, Taio is correct in his assertion that Fire Dragon should charge 3.00 per bottle. Suppose that a technological innovation decreases Fire Dragon's costs so that it now faces the marginal cost (MC) and average total cost (ATC) given on the following graph. Specifically, the technological innovation causes a decrease in average fixed costs, thereby lowering the ATC curve and moving the MC curve.

If P(A)=0.72, P(B)=0.11, and A and B are independent, find P(A B). A. 0.72 B. 0.83 C. 0.11 D. 0.0792

Evaluate the following limit. Enter an exact answer. lim (x -> -8) (x^2 - 64) / (x + 8) = Number T

Given the function below: f(x)=1.5(x-6)(x-4) What is the vertex for the graph of f(x) ? Enter your answer using coordinate pair notation. What is the stretch/compression factor for the graph of f(x) when compared to the graph of y=x^2 ? Stretch/Compression Factor:

Find the equation of the line tangent to the graph of f(x) = (ln x)^2 at x = 8.

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x^4+3x^3+6x^2-7x-7; f(4) f(4)=

Solve the equation with rational exponents. Check all proposed solutions. 4 x^(7/5)-28=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. The solution set is ∅.

Perform the indicated operation and express the result as a simplified complex number. If (y=x^3-2), evaluate (y) given (x=1).

y=ln(ln(4x)) dy/dx=

Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions [ (3 x^5+9 x^3-4)/(x^4) ]

Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. The series is ∑ from n=1 to ∞ of n/(n+5). A. The test is inconclusive. B. The series diverges.

A = 9,8,0,2,7 A = Ex: 50 P(A) = EX: 5

Solve the inequality for (u). [10 > fracu4] Simplify your answer as much as possible.

Solve the inequality, and graph the solution set. (4x+5)/(x-2) ≤ 0

Simplify and convert to radical notation. If r^(5 / 20) = sqrt[-](r^n) then m = and n =

Let F(x)=tan(x-3) for x<3, cos(x-3) for 3 ≤ x. Then lim x→3- F(x)=

Divide using synthetic division. (3x^2+7x-5) ÷ (x+4)

Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. (-5x-5)/(-5)

Sea (an=operatornamesen(n) / n) La sucesión (leftanright) converge a 1

Comparisons of Inequality: más/menos Ejercicio 1 Haz comparaciones según las indicaciones. Usa más/menos que. MODElos: El sofá cuesta 550. El sofá-cama cuesta 800. (cuesto) → El sofá cuesta menos que el sofá-cama. La casa de mi prima tiene dos balcones. Mi casa tiene un balcón. (tiene) → La casa de mi prima tiene más balcones que mi casa. 1. La mesa pesa veinticinco kilos. El sillón pesa cuarenta y ocho. (pesa) La mesa pesa menos que el sillón. 2. En mi casa viven ocho personas. En la casa de los vecinos viven cinco. (viven) En mi casa viven más personas que en la casa de los vecinos. 3. La casa de los Chen tiene cuatro dormitorios. La casa de los vecinos tiene dos. (tiene) La casa de los Chen tiene más dormitorios que la casa de los vecinos. 4. En el patio de mis abuelos hay tres árboles. En nuestro patio hay cinco. (hay) En el patio de mis abuelos hay menos árboles que en nuestro patio. 5. Eloy tiene dos perros. Omar tiene un perro. (tiene) Eloy tiene más perros que Omar.

Select your answer (13 out of 14) At a rehearsal dinner the night before a wedding, the bride and groom need to assign 10 people to two tables of five people. How many different seating arrangements are there?

- Approximately 68 percent of the data are within one standard deviation ( σ ) of the mean ( μ ). - Approximately 95 percent of the data are within two standard deviations ( σ ) of the mean ( μ ). - Approximately 99.7 percent of the data are within three standard deviations (σ) of the mean (μ). 2. The mean of people 65 and older in populations across all U.S. counties is 18% and the interval and the percentage of data each comprises, based on the normal approximation of those values. In other words, label the intervals with the percentages of the curve they represent. Each interval will have a value.

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 99% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 250 220 175 168 160 158 153 153 153 148 What is the confidence interval estimate of the population mean μ ? million < μ < million (Round to one decimal place as needed.)

Which of the following ratios are equivalent? Select all correct options

Exercice I: 1. Simplifier l'écriture des rationnels suivants, puis indiquer lesquels sont des décimaux: A=(2^3 * 3^2 * 5^3)/((-2)^2 *(-3) * 5^4) B=((-7)^-2 * 3 * 11^-3)/(7^-3 * 3^2 * 11^(4-2)) C=(2^3 * 10^-4-3^2 * 10^-3)/((-41) * 10^-3) 2. Simplifier chacune des écritures suivantes: D=4 a b^3 *(-2 a^5 b^-1) E=-2 *(-3 x^3)^3 F=(a^4 * a^-10 * a^2)/(a^5 * a^-8) 3. Ecrire l'expression suivante sous la forme d'une fraction irréductible : G=(0,04 * 2^-2 *(10^-3)^3 * 10^2)/(3 * 10^-8 * 10^-2) 4. Donner l'écriture scientifique de l'expression suivante : H=(2^2 * 10^-10 * 2^7 * 10^-6)/(-32 * 10^-10) 5. Ecrire I sous la forme a^n b^m c^p où m, n et p sont des entiers relatifs : I=((a b^2)^2(a b^-1)^3(a^2 b)^-2)/(a^2 c^-5(a^-1 b c^2)^3) Exercice II : 1. Développer, réduire et ordonner: A=4 x^2-(2 x+5)(x+4) C=-3(a^2+2)-(a-3)(2 a+7) E=(2 x-1)^2+(1/2 x+1)^2-x^2+1 B=(2 x^3+3)^2-(5+x)(5-x) D=(12 x+3)(2 x-7)-(x+1)^2 F=-2^2(x+1)^2+(-2)^2 *(-2)(x-2)(x+2)

Solve for (v). [ v^2+8 v+16=0 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution." [ v= ]

What does (1/(cos x+1))-(1/(cos x-1)) equal? A. 2/(-sin^2 x) B. 2 csc^2 x C. 1 D. -sin^2 x

Use the point-slope formula to find an equation of the line passing through the point (4,-6) and having slope 3. Write your answer in slope-intercept form.

Consider the following functions. f=(-4,-1),(-3,-1),(-2,-3),(3,0) and g=(5,3),(4,-1),(-2,-4),(-4,-5) Step 1 of 4: Find (f+g)(-2).

Finding the perimeter or area of a rectangle given one of these values The length of a rectangle is 3 in longer than its width. If the perimeter of the rectangle is 26 in, find its area.

В треугольнике PQR на стороне PQ выбрана точка K, а на стороне QR - точка Lн Отрезки PL и KR пересекаются в точке T. Чему равня площадь треугольника PQR, если SPKT=11, SPIR=12, SRTL=13?

Newhard Company applies overhead cost to jobs on the basis of 113% of direct labor cost. Job 313 includes 1,800 units and its job cost sheet contains 37,248 in direct materials and 10,400 in direct labor. Required: a. What is the total manufacturing cost applied to Job 313? b. What is this job's unit product cost?

One study claimed that 87% of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 143 college students and finds that 117 of them identify themselves as procrastinators. Does this evidence support the professor's claim that fewer than 87% of college students are procrastinators? Use a 0.01 level of significance. Compute the value of the test statistic. Round your answer to two decimal places.

Use the Square Root Property to solve the quadratic equation 3z^2 + 11 = 14 use a comma to separate solutions z=

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 61 and 67 miles per hour. (Assume the data set has a normal distribution.) Approximately % of vehicles travel between 61 miles per hour and 67 miles per hour.

Debra must choose a number between 49 and 95 that is a multiple of 2,3 , and 9 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Find the antiderivative: [ int frac8 x^6+6 x^3+8x^5 d x= ] [ +C ]

Evaluate the limit as n approaches infinity of (sqrt(16n^2 + 7n) - 4n). Enter your answer as a reduced fraction.

Construct a data set that has the given statistics. N=6 μ=6 σ=2 A. The most common value in the population data set. B. The range of the population data set. C. The mean of the population data set. D. The difference between all the values in the population data set. This means the population mean of the 6 values in the data set s. What does the value σ mean? A. The range of the population data set. B. The number of values that equal the population mean. C. The spread of the data from the population mean. D. The most common value in the population data.

One card is drawn from an ordinary deck of 52 cards. Find the probabilities of drawing the following cards. a. A 5 or 9 b. A red card or an 8 c. A 9 or a black 8 d. A diamond or a black card e. A face card or a heart

(18/12 t-7) 2

Based on a poll, 63% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result The probability that at least one of them is careful about personal information is (Round to three decimal places as needed.).

Find the space inside a parallelogram with a base of 17 and a height of 14.

10/(1/4)

Solve. Verify your result by checking that it satisfies or approximately satisfies the original equation. 3^(4x+7)=15 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Round to four decimal places as needed.) B. There is no real-number solution.

Given that g(x)=x^5, find (g ∘ g)(x). (g ∘ g)(x)= (Simplify your answer.)

Begin by graphing f(x)=2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x)=2^x-2 Which transformation is needed to graph the function g(x)=2^x-2 ? Choose the correct answer below. A. The graph of f(x)=2^x should be shifted 2 units downward. B. The graph of f(x)=2^x should be shifted 2 units upward. C. The graph of f(x)=2^x should be shifted 2 units to the right. D. The graph of f(x)=2^x should be shifted 2 units to the left. Graph g(x)=2^x-2 and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. The equation of the asymptote for g(x)=2^x-2 is . (Type an equation.) The domain of g(x)=2^x-2 is . (Type your answer in interval notation.) The range of g(x)=2^x-2 is .

Weight Away, a company that sells weight-loss plans, often advertises the effectiveness of its plans by highlighting the stories of a few clients who have lost extraordinary amounts of weight. The following histogram gives information about more "typical" clients, summarizing the weight loss (in pounds) over the past month for a sample of 50 clients. Based on the histogram, find the proportion of weight loss values in the sample that are less than 40 pounds. Write your answer as a decimal, and do not round your answer.

Sixty students were given a history exam. Their scores are shown below, sorted from smallest to largest. 9 32 33 34 35 37 38 38 39 39 40 40 42 43 43 47 53 65 67 69 71 72 72 73 73 73 74 75 75 75 76 76 77 77 77 77 77 78 78 78 79 79 81 81 81 81 81 82 83 83 84 85 85 85 85 86 88 91 93 94 1) Compute the 5-number summary for this data: 9 43 75 81 94 2) Create a histogram of the data. You can create it using software on your computer, using online software, or you can draw it by hand and scan it or take a picture of it. If you can't figure out how to include your histogram in the entry area below, you are welcome to email it to me instead. 3) Finally, write a couple sentences describing what conclusions you can draw about performance on the exam from the 5-number summary and the histogram.

Seven of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected DVR is defective? The probability is

The "net up" counter (using technology to count fish passing upstream) at Roe River42 showed that there were 5801 fish in 2006, but that number dropped by 1911 fish in 2013. Compute the percentage change from 2006 to 2013: %.

Use properties of logarithms to condense the logarithmic expression below. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 4 ln x + 3 ln y - 2 ln z 4 ln x + 3 ln y - 2 ln z =

Solve (2 x^2+16 x-1>-2 x^2+12 x+47). Enter the solution in interval notation.

Factor. 81 a^2-25 81 a^2-25= (Factor completely.)

Find the derivative of the function g(x) = e^x / (5-5x)

(5x^4 - 2x^2 + 2x + 9) / (x^3 - x + 6)

Suppose 52% of the population has a college degree. If a random sample of size 563 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5%?

If the Central location used 120 notepads, use the graph to determine how mary notepads the Midtown location used. Use the barchart and table to determine how many notepads per department the Midtown location used.

The function h is defined below. h(x) = (x-8)/(x^2-5x-36) Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas.

Decide whether the given number is a solution of the equation. Is 1/3 a solution of (x+10)/(9-x)=31/26 ? Choose the correct answer below. Yes No

The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e) 60 25 41 47 44 9 (a) Compute the population mean, μ μ= (Type an integer or a decimal)

Which of the following measures the length of time it takes to acquire, sell, and replace inventory? O. inventory turnover O. retail method of inventory costing Oc. gross profit method of inventory costing Od. days' sales in inventory

Finding a difference quotient for a linear or quadratic function Find the difference quotient (f(x+h)-f(x))/h, where h ≠ 0, for the function below. f(x)=-8x+4 Simplify your answer as much as possible. (f(x+h)-f(x))/h= П.

Factor completely. 10x^3 - 81x^2 - 81x

Find the equation of the horizontal line that contains the point (8,-7). Express the equation using either the general form or the slope-intercept form of the equation of a line. The equation of the line is . (Type an equation.)

If f(-4)=16 and f(4)=16, then f cannot have an inverse because it is not a one-to-one function.

If log81 x = 1/2, find the value of x without a calculator. x =

In this assignment you will practice building and interpreting confidence intervals. Confidence intervals are used to give a range of plausible values for the population mean or proportion under consideration. If you have ever read the results of a poll, you might recall that a percentage is given followed by the statement, "...plus or minus..." some value. For example, the presidential approval rating is 49% plus or minus 1.73%. The 49% is the sample proportion with the 1.73% noting the margin of error. Understanding how confidence intervals are built and interpreted will help you become a better consumer of information. Confidence intervals are used in a variety of applications besides analyzing polling data. For instance, manufacturing clothing (sizes are based on an average plus or minus an acceptable error), volume of food items (the 12 oz cereal box holds on average 12 oz plus or minus a margin of error), lifetimes of items (a lightbulb will last on average 400 hours plus or minus an acceptable error), etc. Task Based on USDA suggestion, a U.S. adult should be spending anywhere from 165 to 345 per month on food, depending on age and gender. A random sample of 120 adults in Washington State is polled regarding the amount of money they spend each month on food. The sample has an average of 273.61 with a standard deviation of 61.59. Based on this information, complete the following questions. a) (5pts)Show that the requirements to build a confidence interval are met. b) (5 pts) State the critical value for a 90% confidence interval c) (5pts)Compute the 90% confidence interval. State values to two decimal places. d) (5pts) Interpret the 90% confidence interval using complete sentences.

Iris weighed 5 large watermelons from her garden. Here are the weights in pounds. 17, 11, 12, 24, 22 What is the mean weight of the watermelons? a. 11 pounds b. 24 pounds c. 21 pounds d. 19 pounds

Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation. 6x-4=3x-70

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count th number not resulting in a defect. Assume the births are independent. What is the probability that exactly two births do not result in defects? 0.0003 0.1328 0.0008 0.0082

Find the difference between the highest and lowest temperatures.

Find the requested approximation for the definite integral using the indicated value of n. Give all answers to three decimal places, when necessary. Find Ln, Rn, and their average ∫ from 3 to 6 (x^2 - 2) dx: n=3

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. f(x)=6-4/x Determine whether f(x) is a polynomial or not. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is not a polynomial because the variable x is raised to the power, which is not a nonnegative integer. (Type an integer or a fraction.) B. It is a polynomial of degree . (Type an integer or a fraction.)

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of (barX1-barX2) is approximately normal only if both sample sizes are sufficiently large-that is, when Multiple Choice - (n1+n2=30) - (n1+n2 geq 30) - (n1=30) and (n2=30) - (n1 geq 30) and (n2 geq 30)

Use the properties of logarithms to evaluate the expression without the use of a calculator. [ log a a, a>1 log a a= ]

Find the 10th term of the arithmetic sequence 2, 6, 18, 54, ... a. 4,374 b. 13,122 c. 39,366 d. 118,098

Find the domain of the function. (Enter your answer using interval notation.) f(x) = sqrt(x) + sqrt(5-x)

Day 3 Unit 3 Determining Equations from Graphs 1) (Exemplar) Consider the following graph. a. Determine the following information for the graphed function. (i) Midline (ii) Period (iii) Angular speed (iv) Amplitude

Consider the function f(x)=(1/6)^x a. Graph the function. b. Equation of the asymptote: c. Domain in interval notation: d. Range in interval notation:

Identify the type of sequence Match the sequence to the type of property it presents Matching · 3 points a. ak=2,3,3,4,5,6,7,7 Choose an answer b. bk=6,5,3,2,1,0,-2,-3 Choose an answer c. ck=7,4,8,3,2,5,4,2 Choose an answer d. dk=7,5,5,4,3,2,2,1 Choose an answer e. ek=-6,-4,-2,0,1,2,3,5 Choose an answer

f(x)=(x^2+1)e^(4x)

Graph the logarithmic function. g(x) = 2 + log base (1 / 3) of x Plot two points on the graph of the function, and also draw the asymptote.

Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition. Part 1 (a) The mean of the numbers is substantially less than the median. 51,52,53,54,

Exponential and Logarithmic Functions Graphing a logarithmic function: Basic Graph the logarithmic function. g(x)=log(1 / 2) x Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Find the length of CD. Round to the nearest tenth. (Use distance formula). a. 3.6 b. 4.5 c. 5.4 d. 2.8

If pointer 1 is spun and then pointer 2 is spun, determine the probability of landing on yellow on both spins. Pointer 2 The probability is (Type an integer or a simplified fraction.)

Use the laws of exponents to simplify. (2^(11/10))^(2/7) (2^(11/10))^(2/7) = □ (Simplify your answer. Type exponential notation with rational exponents.)

Crane Company has accounts receivable of 98,600 at March 31, 2025. Credit terms are 2/10, n / 30. At March 31, 2025, there is a 2,200 credit balance in Allowance for Doubtful Accounts prior to adjustment. The company uses the percentage-of-receivables basis for estimating uncollectible accounts. The company's estimates of bad debts are as shown below. Age of Accounts Balance, March 31 2025 Balance, March 31 2024 Estimated Percentage Uncollectible ------------ Current 68,400 69,990 2% 1-30 days past due 13,700 7,880 5% 31-90 days past due 9,700 2,400 28% Over 90 days past due 6,800 1,100 49% 98,600 81,370 · Determine the total estimated uncollectibles at March 31, 2025. Total estimated uncollectibles

The TTC has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,950 bus miles and a sample standard deviation of 175 bus miles. Complete parts (a) and (b) below. a. Is there evidence that the population mean bus miles is more than 3,900 bus miles? (Use a 0.05 level of significance.) State the null and alternative hypotheses. H0: μ = T H1: μ ≠ T (Type integers) Find the test statistic for this hypothesis test. The test statistic t= (Round to two decimal places as needed.) The critical value for the test statistic is(are) . (Round to two decimal places as needed) Is there sufficient evidence to reject the null hypothesis using α=0.05 ? A. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is less than 3,900 bus miles. B. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3,900 bus miles. C. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean bus miles is less than 3,900 bus miles. D. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3,900 bus miles. b. The p-value is . (Round to 3 decimal places as needed.) What does this p-value mean given the results of part (a)? A. The p-value is the probability of getting a sample mean of 3,950 bus miles or greater if the actual mean is 3,900 bus miles. B. The p-value is the probability that the actual mean is 3,950 bus miles or less. C. The p-value is the probability that the actual mean is 3,900 bus miles or greater given the sample mean is 3,950 bus miles.

Simplify the algebraic expression by combining the like (or similar) terms. 1/3 + 4a + 1/4

المعادلة 3 x=-3 log10 هو تساوي

Find the x - and y-intercepts for the function. f(x) = (x+6)/(x^2+4) Enter your answers as points, (a, b). The x-intercept is The y-intercept is

Find the derivative of f(t) = e^(t+3)

Escribir 1/5 como un porcentaje.

Honors Algebra Il: Section 3 IXL: Solve a System of Equation: IXL - Solve a system of equ ixl.com/math/level-m/solve-a-system-of-equations-in-three-variables-using-substitutic My IXL Learning Level M > E. 12 Solve system of equations in three variables using substitution X 8 H Solve the system of equations by substitution. -x + 3y + 2z = -4 x - y + 3z = -10 x = -6 Submit Work it Not feeling ready yet Solve a system of equations using any method Type here to search

The exponential model A = 634.0(1.16)t describes the population, A, of a county in millions, t years after 2003. Use this model to determine the population of the county in 2003.

Multiply using the rule for the product of the sum and difference of two terms. (6x+7)(6x-7)

Check my work Problem 12-7 (Algo) The following table lists all costs of quality incurred by Sam's Surf Shop last year. Annual inspection costs 235,000 Annual cost of scrap materials 426,000 Annual rework cost 174,679 Annual cost of quality training 596,000 Annual warranty cost 1,826,000 Annual testing cost 648,000 What was Sam's appraisal cost for quality last year? Appraisal cost

Finding the Area of a Triangle Use the diagram of the triangle in Figure A to answer the questions. (Each small square has a side length of 1 mm and an area of 1 mm^2.); Note: Use a side of the triangle that has a whole number length as the base. Figure A What is the length of the base of the triangle? mm What is the height of the triangle? mm What is the area of the triangle? mm^2 Round your result to two decimal places as needed.

Multiply the value of c by the number below the line. Write line, and write the result below the line. -9 6 13 4 -54 6 -41

Graph the function. F(x) = 3-x, if x ≤ 2 1+2x, if x > 2

During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 15% per month. State whether this increase was linear or exponential. If your food bill was 120 in one month during this period, what was it three months later? Was the growth in inflation linear or exponential? - linear - exponential What was the monthly food bill after three months? (Round to the nearest dollar as needed.)

Bids were placed in a silent auction for a sword reputed to have been used at the Battle of Hastings, worth a reported 20,000. The respective bids (in thousands of dollars) placed by the 7 bidders were as follows. 25,23,16,24,13,15,12 (a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. (b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.

Solve. x-2 y=10 y=x. Enter your answer as an ordered pair in the form (x, y). Remember to include the parentheses and the comma.

Determine algebraically whether the function is even, odd, or neither. √[3]7 x^2+6 even odd neither

The following frequency histogram represents the IQ scores of a random sample of seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. Use the histogram to answers parts (a) through (g). 10s of 7th Grade Students (a) How many students were sampled? 200 students (b) Determine the class width. The class width is .

Write the calculator answer in the correct mathematical form of scientific notation. Indicate if the answer is large or small. 8.3100045 E-13 Note that scientific notation consists of two factors connected with the symbol × for multiplication. Determine the first factor and the second factor in scientific notation. Choose the correct answer below. A. The first factor is a number n, with 1 ≤n<10, and the second factor is e raised to a power. B. The first factor is a number n, with 0 ≤n<10, and the second factor is e raised to a power. C. The first factor is a number n, with 0 ≤n<10, and the second factor is 10 raised to a power. D. The first factor is a number n, with 1 ≤n<10, and the second factor is 10 raised to a power.

Evaluate the following expression. (-13.67-6.33) ÷(-5) (-13.67-6.33) ÷(-5)= (Type an integer

Exponential Regression The table below shows the value, V, of an investment (in dollars) after n years. n 0 3 7 12 14 19 V 2900 3481.57 4656.77 6727.3 7477.75 9963.53 Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicated variables. Based on your regression model, what is the percent increase per year? Use the rounded regression model from part 1 to find V when n=20. Round your answer to two decimal places. Interpret your answer by completing the following sentence. Be sure to use units in your answer. The value of the investment after 20 years

For the following equation, find the intercepts. Then use the intercepts to graph the equation. 6x + 24y = 6 Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Click to enlarge graph

Exponents Evaluating an expression with a negative exponent: Positive fraction b Rewrite the following without an exponent. (5/7)^-2

Simplify the following expression completely. [ frac10 x-70x^2+3 x-70 ]

Rewrite the expression with only positive exponents. Assume the variables do not equal zero.

For each ordered pair (x, y), determine whether it is a solution to the inequality y<0. (x, y) Is it a solution? Yes No --------- (8,42) (2,13) (-7,-37) (-9,-39)

Completely factor the polynomial, if possible. 12-12 x+3 x^2

Translate the following phrase into an algebraic expression using the variable w. Do not simplify. the perimeter of a rectangle if the width is w centimeters and the length is 2 cm more than twice the width.

Find the Z-score such that the area under the standard normal curve to the left is 0.52. Click the icon to view a table of areas under the normal curve. The Z-score such that the area under the curve to the left is 0.52. (Round to two decimal places as needed.)

An open-top box is constructed by starting with a square section of material 594 mm by 594 mm, removing a small square of material from each corner, and folding up each edge. See the diagram below. Determine the dimensions of such a box such that the volume is maximal. Determine the maximum volume of such a box. Volume = mm^3

Find a positive number x such that the sum of its reciprocal and 6,912 times its square is as small as possible. x=

Patricia Richardson invested 4000 four times a year in an annuity due at Southern Trust Company for a period of 2 years at an interest rate of 12% compounded quarterly. Using the ordinary annuity table, calculate the total value of the annuity due at the end of the 2-year period.

Consider the function f(x)=29(x-15)^2+7/9 Step 2 of 2: Find an equation for the axis of symmetry of the parabola defined by the given function. Write the exact answer. Do not round.

A baby that weighs 6 lb at birth may increase his weight by 12% per month. Use the function f(t)=K(1+r)^t, where K is the initial value, r is the decimal value of the percentage of increase (r=0.12) and t is the time in months. How much would the baby weigh in one month? Two months? Six months? Nine months? One year? Round your answers to the nearest tenth of a pound. Age Weight (lbs) one month two months six months nine months one year

Use the properties of logarithms to expand the following expression. log sqrt(y z^3 / x^5) Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 32 tires surveyed, the mean lifespan was 46,700 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test. (Round your answers to two decimal places.)

b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value of the objective function z=5x+3y is at , ). (Type integers or decimals.) B. The maximum does not exist.

Given (f(x)=-3 x^2-18 x-22), write the function in vertex form. Write your answer in function notation by starting your answer with (f(x)=)

To quantify the intensity of sound, the decibel scale was developed. The formula for loudness L on the decibel scale is L=10 log (1/L0), where 10 is the intensity of sound just below the threshold of hearing, which is approximately 10^-16 watt per square centimeter. Find the decibel reading for a sound with intensity 32,000 times 10. The decibel reading is approximately . (Round to the nearest whole number as needed.)

The domain of the piecewise function is (-∞, ∞). a. Graph the function. b. Use your graph to determine the function's range. f(x)= 1/4 x^2 if x<3 5x-10 if x ≥ 3 a. Choose the correct graph below. xA. B. C b. What is the range of the entire piecewise function? Select the correct choice below and, if necessary, fill in the answer box(es) to complete A. The range does not have any isolated values. It can be described by (Type your answer in interval notation.) B. The range has at least one isolated value. It can be described as the union of the interval(s) and the set . (Use a comma to

A population has mean ψ=25 and standard deviation π=5, Round the answers to two decimal places as needed. (a) Find the z-score for a population value of 8. The z-score for a population value of 8 is -3.4. (b) Find the x-score for a population value of 17. The x-score for a population value of 17 is .

If f(x)=5 e^x, find f(3) rounded to the nearest tenth.

At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Choose the function that models the average number of symptoms, y, after x weeks.

If f(x)=x, then f'(5)= 5 25/2 1 None of these 1/5

Solve: 10b + 3 = 4 Write your answer as an integer, proper fraction, or mixed number in simplest form. b =

The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual. A. 3647 g B. 1200 g C. 2000 g D. 2353 g

If the second exam scores in our class were normally distributed and the average exam score was 78, what would be the median?

Solve the following inequality. [ frac-121-x>x-2 ] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

Identify the quadrant for the angle θ satisfying the following conditions. cos(θ)<0 and csc(θ)<0 A. Quadrant IV B. Quadrant II C. Quadrant I D. Quadrant III

Simplify. 5x - 3(-3y + 5x) + 3y

Solve this equation and enter your answer in the box. Make sure your answer is fully reduced. If the answer turns out to be a false equation or identity, click on the appropriate button. [ (x+10)/2=7(x-1) ]

f(x) = 3x + 9

Sketch the graph of the rational function. f(x) = 2x / (x^2 - 3x - 4)

In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. If a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (g) below. E. The probability of success is the same for each trial of the experiment. F. The trials are independent. G. The probability of success is different for each trial of the experiment. H. There are two mutually exclusive outcomes, success or failure. (b) Using the binomial distribution, determine the values of n and p. n=20 (Type an integer or a decimal. Do not round.) p=0.45 (Type an integer or a decimal. Do not round.) (c) Using the binomial distribution, find and interpret the probability that exactly 12 of those surveyed feel the state of morals is poor. The probability that exactly 12 of those surveyed feel the state of morals is poor is 0.0727. (Round to four decimal places as needed.) Interpret the results. In 100 trials of this experiment, we expect about to result in exactly 12 adults who feel the state of morals is

Complete the table of values for the graph with equation [y=2 x+10] x -2 -1 0 1 2 3 y 6 12

Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros -1,0,3, 1/3; coefficient of x^3 is 7 f(x)=

Use the dot plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry? Choose the correct actual data entries below. A. 122,123,124,125,126,127,128,222,223,224,226,323,324,424,524 B. 22,22,23,23,23,24,24,24,24,24,25,26 ; 26,27,28 C. 22,23,24,25,26,27,28 D. 2.2 .2 .2 .2 .3,2.3,2.3,2.4,2.4,2.4 .2 .4,2.4,2.5,2.6,2.6,2.7 .2 .8 The maximum data entry is The minimum data entry is

Converting between Fahrenheit and Kelvin Temperature Scales Complete the table. Rowkelvin FahrenheitCelsius ------------------------------- 1 0.0 K -273.0°C 2 82.8°F 3 8.7°C Complete the first row. Express your answer in degrees Fahrenheit to four significant figures. Row 1: °F

Graph the following function. y=(x+2)^2

Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.3 0.1 0.2 0.1 0.3 Step 3 of 5: Find the standard deviation, Round your answer to one decimal place.

On the blueprint of a house, 36 millimeters represents 8 meters. The actual length of the living room is 6 meters. What is its length on the blueprint?

The right side of a tower has a shape that can be approximated by the graph of the function defined by f(x)=-301 ln(x/207). Answer parts (a) through (c). (a) Explain why the shape of the left side of the tower has the formula given by f(-x). A. The left side is a reflection of the right side with respect to the axis of the tower. The graph of f(-x) is the reflection of f(x) with respect to the x-axis B. The left side is a reflection of the right side with respect to the axis of the tower. The graph of f(-x) is the reflection of f(x) with respect to the y-axis.

Find the volume of the figure: The volume of the figure is

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=73 and σ=14; n=16

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. w+3 x+4 y-z=7 3 x-4 y+z=5 w-6 x+y=3 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is ( , , , ). (Simplify your answers.) B. There are infinitely many solutions. The solution set is ( , , , z), where z is any real number. C. There is no solution. The solution set is ∅.

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at most 44 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim contains a statement of equality, it represents the null hypothesis. (a) How should you interpret a decision that rejects the null hypothesis? There is evidence to the claim that the mean incubation period for the eggs of a species of bird is at most 44 days.

Katrina wants to estimate the proportion of adults who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adults and constructs a 95% confidence interval. Matthew also wants to estimate the proportion of adults who read at least 10 books last year. He obtains a simple random sample of 400 adults and constructs a 99% confidence interval. Assuming both Katrina and Matthew obtained the same point estimate, whose estimate will have the smaller margin of error? Justify your answer. Whose estimate will have the smaller margin of error and why? A. Matthew's estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence. B. Matthew's estimate will have the smaller margin of error because the sample size is larger and the level of confidence is higher. C. Katrina's estimate will have the smaller margin of error because the lower level of confidence more than compensates for the smaller sample size. D. Katrina's estimate will have the smaller margin of error because the sample size is smaller and the level of confidence is lower.

Simplify the following radical expression. √[7]64 x^3

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