Math Homework Questions & Answers Archive

Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent. (a) List the equally likely events for the gender of the 4 children, from oldest to youngest. (Let M represent a boy (male) and F represent a girl (female), Select all that apply?) FMMF MFMM FFMF MFFF FMFM FMMM MMMF FFFF FFMM MFFM FMFF MMMM MMFF MFMF MMFM FFFM (b) What is the probability that all 4 children are male? (Enter your answer as a fraction.) Notice that the complement of the event "all four children are male" is "at least one of the children is female," Use this information to compute the probability that at least one child is female: (Enter your answer as a fraction.)

79. (3^2)^-2 83. (-c)^3 87. 4^-2 + 8^-1

Re-write the quadratic function below in Standard Form y=-7(x-1)^2-1

Evaluate x^3 - y^2 + z for x=3, y=-10, and z=1

Por alquilar un salón de juntas, cierta universidad cobra una tarifa de reserva de 48 y un cargo adicional de 8.40 por hora. El club de matemáticas desea gastar una cantidad menor de 98.40 en alquilar el salón de juntas. ¿Para qué posibles números de horas podrían ellos alquilar el salón de juntas? utilizar t para el número de horas que el salón de juntas se alquila y resolver la desigualdad para t.

4 groups of square tenths is 3.6.

The following frequency distribution represents the scores on a math test. Find the class midpoint of scores for the interval 40-59. Scores Number of Students ------ 0-19 2 20-39 4 40-59 6 60-79 15 80-99 5 A. 49.5 B. 49.0 C. 50.5 D. 48.5

Find the derivative. [ fracdd xleft[2 xleft(x^7+1right)^6right] ]

Question number 8. A random sample of 1444 16-ounce cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 16 ounces and a standard deviation of 0.16 ounce. What is the probability that the mean contents of the 1444 sample cans is less than 15.992 ounces? 0.039 0.029 0.069 0.059 0.079 None of the above

Find the inverse of (x=e^y).

State the domain, intercepts, and asymptotes of the rational function f(x) = (2x-3)/(x-4). If the function does not have the requested characteristic, enter DNE. If there are multiple instances of a characteristic, separate them with commas. 1) Domain (in interval notation): 2) x-intercept(s) (as ordered pair(s)): 3) y-intercept (as ordered pair): 4) Equation(s) of vertical asymptote(s): 5) Equation of horizontal asymptote:

donde la función azul es f(x)=((-x^2/16)+x/4) * e^x Para determinar los siguientes volúmenes considere una partición equidistante del intervalo de integración de tamaño n=22 - La aproximación del volumen obtenido al rotar la región alrededor de la recta y=-2, usando la regla del trapecio, es (aproxime usando 4 cifras decimales): La aproximación del volumen obtenido al rotar la región alrededor de la recta x=-4, usando la regla de Simpson, es (aproxime 4 cifras decimales):

Use the data in the following table, which lists survey results from high school drivers at least 16 years of age. Assume that subjects are randomly selected from those included in the table. Drove When Drinking Alcohol? Yes No --------- Texted While Driving 692 3143 No Texting While Driving 189 4671 If one of the high school drivers is randomly selected, find the probability that the selected driver texted while driving and drove when drinking alcohol. The probability that one randomly selected high school driver texted while driving and drove when drinking alcohol is 0 . (Round to three decimal places as needed.)

What is the percent of increase from 30 to 42 ? Write your answer using a percent sign (%).

Find a positive angle less than 360° or 2π that is coterminal with the given angle. -84° 84° 96° 276° 456°

Consider the four data sets shown in the accompanying table. Complete parts (a) and (b) below. Click the icon to view the data table. (a) Compute the linear correlation coefficient for each data set. The linear correlation coefficient for the first data set is (Round to three decimal places as needed.) Data Table Full data set Data Set 1 Data Set 2 Data Set 3 Data Set 4 x y x y x y x y 8 9.04 8 10.14 8 8.46 17 7.58 10 7.95 10 9.14 10 7.77 17 6.76 5 8.58 5 9.74 5 13.74 17 8.71 9 9.81 9 9.77 9 8.11 17 9.84 7 9.33 7 10.26 7 8.81 17 9.47 4 10.96 4 9.10 4 9.84 17 8.04 12 8.24 12 7.13 12 7.08 17 6.25 14 5.26 14 4.10 14 6.39 17 6.56 6 11.84 6 10.13 6 9.15 17 8.91 11 5.82 11 8.26 11 7.42 17 7.89 13 6.68 13 5.47 13 6.73 6 13.50

The equation 5 x^2=28 x can be written in standard form by both sides.

Find the domain of the function. f(x)=-3x+2 The domain is (Type your answer in interval notation.)

Solve. When two is subtracted from half of a number the result is 28 . What is the original number?

Find the minimum and maximum P value for the following system. Minimize and Maximize P=30x+10y Subject to: 2x+2y ≥ 4 6x+4y ≤ 36 2x+y ≤ 10 x, y ≥ 0 The minimum value of P for this system is and occurs at The maximum value of P for this system is and occurs at

Evaluate the following limit: lim as x approaches -∞ of (6x^2 + 17x - 3) / (5x^2 + 14x - 3).

Each of the following is a confidence interval for μ= true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type: (117.6,118.4) (117.4,118.6) (a) What is the value of the sample mean resonance frequency? Hz (b) Both intervals were calculated from the same sample data. The confidence level for one of these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, and why? The first interval has the 90% confidence level because it is a narrower interval. The second interval has the 90% confidence level because it is a wider interval. The second interval has the 90% confidence level because it is a narrower interval. The first interval has the 90% confidence level because it is a wider interval.

After giving a test to a group of students, below is the summary of grades by gender. A B C Total --------------- Male 3 9 10 22 Female 20 15 12 47 Total 23 24 22 69 If a student was randomly chosen, find the probability that the student earned a C. Use a reduced fraction answer.

The average price of a ticket to a baseball game can be approximated by p(x)=0.03 x^2+0.59 x+5.49, where x is the number of years after 1991 and p(x) is in dollars. a) Find p(3). b) Find p(13). c) Find p(13)-p(3). d) Find (p(13)-p(3))/(13-3), and interpret this result. a) p(3)= (Simplify your answer.)

Construct a table of solutions and then graph the equation. y=9x-3

1. Are these shapes similar? If yes, identify the scale factor. If not, explain how you know. Assume that all shapes are symmetrical. 2. Add to the set of triangles by providing their new dimensions.

Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ^2=q/p^2. A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. Let x be the number of times you play the lottery before winning the first time. (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs 1 to play and winners are paid 900. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is (Type an integer or a decimal.)

-3/2 ÷ (9/10) =

Differentiate. y=ln(5x^2-3x+4) y'=

Counting and Probability Probabilities of an event and its complement 1 2 3 4 5 6 7 8 9 10 ------------------------------------ X P(X)=1/5 not X P(not X)=4/5 (b) Subtract. 1-P(x)=4/5 (c) Select the answer that makes the sentence true. 1-P(X) is the same as (Choose one) P(not X) 1-P(not X) None of the above

QUESTION 5 If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. 7x = 7 - 7y -4x + 3y = 45

The model below is used to represent a given situation, in which (t) is the independent variable. What type of model is it? [ F=C(1.08)^t ] Linear Exponential Quadratic None of these

Divide. (x-3)/(4x-4) ÷ (x+1)/(x^2+x-2)

Give the domain and range. Then, use the graph to find (a) f(-3), (b) f(0), (c) f(1), and (d) any values of x such that f(x)=3. (b) f(0)= (Type an integer or a decimal.) (c) f(1)= (Type an integer or a decimal.) (d) What are the values of x for which f(x)=3? (Use a comma to separate answers as needed.)

Simplify the expression by combining like terms. [ (-5 x^4+x^3-7 x-6)-(-7 x^3+5 x^2-11) ] (a) 2 x^4+x^3-5 x^2-7 x+5 (b) -5 x^4+7 x^3+6 x^2-7 x-17 (c) -5 x^4+8 x^3+5 x^2-7 x-17 (d) -5 x^4+8 x^3-5 x^2-7 x+5

A professor wants to create a test that has 12 true-false questions, 8 multiple-choice questions, and 4 essay questions. She wants the test to be worth 200 points, with each multiple-choice question worth twice as many points as a true-false question and with each essay question equal to three times the number of points of a true-false question. a. Write a system of equations to represent this problem, with x, y, and z equal to the number of points for a true-false, multiple-choice, and essay question, respectively. Select all the equations that are needed for the system that represents this problem. A. 12x+8y+4z=0 B. 12x+8y+4z=200 C. x=2y D. z=3x E. z=2x F. x+y+z=0 G. x=2z H. x+y+z=200 I. y=2x J. y=3z

As part of your work for an environmental group, you want to see if the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day. You take a simple random sample of 23 adults in your community and find that they average 4.6 pounds with a standard deviation of 1.1 pounds. Suppose you know the amount of waste generated per day follows a normal distribution. Test at 0.01 significance. Round answers to 4 decimal places. a. H0: Select an answer ✓ b. H1= Select an answer v ? ∨ c. Test Statistic: d. P-value: e. Select the Decision Rule: Select an answer f. There Select an answer ✓ enough evidence to conclude

Determine how many weeks Amanda can purchase lunches before her account is depleted: SCHOOL LUNCH Amanda has 210 in her school lunch account. She spends 35 each week on school lunches. The equation y=210-35x represents the total amount in Amanda's school lunch account y for x weeks of purchasing lunches.

For each value of x, determine whether it is a solution to 36 > 25 + x. x Is it a solution? Yes No --------- 9 6 14 11

7/8 x inverse notation negative

Remember that perimeter means distance around. Write the perimeter of the rectangle to the right as a simplified polynomial. Then factor the polynomial. Write the perimeter of the rectangle as a simplified polynomial. The simplified polynomial for the perimeter is (Do not factor.)

About 11% of the population of a large country is nervous around strangers. If two people are randomly selected, what is the probability both are nervous around strangers? What is the probability at least one is nervous around strangers? Assume the events are independent. (a) The probability that both will be nervous around strangers is .0121 (Round to four decimal places as needed.) (b) The probability that at least one person is nervous around strangers is (Round to four decimal places as needed.)

Question 2 - of 23 Step 1 of 1 Graph the line by locating any two ordered pairs that satisfy the equation. Round to the nearest thousandth, if necessary. y = (4/3)x - 4

Below is the graph of y=x. Translate it to make it the graph of y=x-4.

In the following, let (Ti) be an elementary matrix that performs the given row operation. Find (leftTiright). (A stackrel9 R5 rightarrow R5longrightarrow T1 A) (leftT1right=) (square) (8 R5+R3 rightarrow R3) (A quad ldots quad T2 A) (leftT2right=) (square)

The graph of f(x)=x^3-5x-2 is shown below. Estimate the solution(s) to the equation f(x)=4.

A rectangle has a length of 16 units and a width of 4 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x.

What is the domain of the transformation y=f(x-7)+6? -13 ≤ x ≤ -3 -4 ≤ x ≤ 6 3 ≤ x ≤ 13 1 ≤ x ≤ 11 7 ≤ x ≤ 17

A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.6 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 5616 MB. How many downloads of the standard version were there? Number of standard version downloads:

Convert 2,300 mg to grams: (use appropriate unit abbreviation)

Use the graph of y=f(x) to answer the following.

Graphs and Functions Composition of a function with itself Suppose that the functions h and f are defined as follows. h(x) = 7 / (2x), x ≠ 0 f(x) = 6x - 9 Find the compositions h ∘ h and f ∘ f. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (h ∘ h)(x) = (f ∘ f)(x) =

The polynomial (P(x)) of degree 4 has - a root of multiplicity 2 at (x=1) - a root of multiplicity 1 at (x=0) and at (x=-4) - It goes through the point ((5,576)) Find a formula for (P(x)).

Find the determinant of matrix A=[3 -2; 5 3]

Solve the equation. b(4b+5)(5b+4)=0

Write an equation of the line passing through (-3,1) and (4,2). Give the answer in standard form.

Question 11 Solve for (x). [ -9 x+37=-5(x-9) ] Simplify your answer as much as possible. [ x= ]

x^4 * x^4

Rewrite the expression so that the terms have a common binomial factor. a(x-2)+b(2-x)

Which of the following shapes are quadrilaterals? Choose 2 answers: A B C D

L is the midpoint of KM. If KL=5x and LM=x+4, what is KL?

Consider the following matrices. A = [ [3, -1, -1], [1, -3, 3] ] x = [ [x1], [x2], [x3] ] 0 = [ [0], [0] ] Solve the matrix equation Ax=0. (If there is no solution, enter No Solution. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.) (x1, x2, x3) = ( )

Calculate the derivative of h(x) = 2 sin x + 3 cos x.

Evaluate f(g(1)) and g(f(2)), if possible. If not type NA. f(x) = x / (2 - x), g(x) = 4 - x^2 f(g(1)) = g(f(2)) =

There are 1760 yards in a mile. Therefore, what does 1 cubic mile represent? Choose the correct answer below. A. 1760^3 yards ^3 B. 1760 yards ^3 C. 1760 square yards D. 1760^3 yards

A sidewalk alongside a garden at the conservatory is to be 12 3/4' long. Rectangular stone tiles that are each 1 8 1/4' long are used to form the sidewalk. How many tiles are used?

Below are three mathematical expressions. Are these expressions equivalent? Jus (hint: write them all as a single base) Expression 3 ∛625^12 × √5^176

Find the exact value of each of the remaining trigonometric functions of θ. sin θ = 12/13, θ in Quadrant I sec θ =

Solve the equation for (x). [ left(frac19right)^x=81 ]

To determine the number of distinct ways two or more experiments can be performed, the principle can be used.

Convert 0.16 to a fraction. 0.16 = (Type a whole number or a simplified fraction.)

Finding the percentage increase or decrease: Basic The price of an item yesterday was 140. Today, the price rose to 343. Find the percentage increase. %

Find an approximate irrational solution to (3^x=5).

Find the distance between the points (5,10) and (8,6). Write your answer as a whole number or a fully simplified radical expression. units

Rewrite the following without an exponent. 2^-3

Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.) 10,29,43,41,6,12,42,33 mean median mode(s)

Is the function (f(x)=3 x^3+3) a one-to-one function? Does it have an inverse? Is the function one-to-one? No Yes Does it have an inverse? No Yes

Use the prime factorization to group the factors and write as a product of two factors. -6 k^10=(-1 cdot 3 cdot k cdot k cdot k cdot k cdot k cdot k cdot k) cdot(2 cdot k cdot k cdot k) -6 k^10=-3 k^7(square) (Type your answer using exponential notation.)

Identify the graph of the following function. y = √(x-4)

Use properties of logarithms to find the exact value of the expression. Do not use a calculator. log6 48 - log6 8 log6 48 - log6 8 = (Type an integer or a simplified fraction.)

Function Evaluation Given the function (f(x)=23(0.71)^x), evaluate each of the following. Round answers to the nearest hundredth as needed. (f(-3)=) (f(-2)=) (f(-1)=) (f(0)=) (f(1)=) (f(2)=) (f(3)=)

6/8 = /80

In Exercises 19-26, find the discriminant of the quadratic equation and describe the number and type of solutions of the equation. 21. 4 n^2 - 4 n - 24 = 0 23. 4 x^2 = 5 x - 10

Question Given that matrix A is defined by [[4, 7, 3], [-1, 0, 0], [2, -3, -1]], find the inverse of A if it exists.

Shown below is the output from a linear model predicting armspan (in cm) from height (in inches) and summary statistics. Assume that the association between armspan and height is linear. Use the output and summary statistics to complete parts a through d. LinReg y=a+bx a=27.336548588 b=2.085486727 Height, x: 63.59, 3.58 Armspan, y: 159.95, 7.70 a. Report the regression equation, using the words "Height" and "Armspan," not x and y. A. Predicted Armspan = 2.09 + 27.34 Height B. Predicted Height = 27.34 + 2.09 Armspan C. Predicted Armspan = 27.34 + 2.09 Height D. Predicted Height = 2.09 + 27.34 Armspan

(4a^5bc^-4)^-3

(b) Subtract. 1-P(x) = 3/8 (c) Select the answer that makes the sentence true.

Graphs and Functions Graphing a function of the form f(x)=a x^2+c Graph the function. h(x)=3 x^2-4

Is the displayed graph the graph of a polynomial function?

Fill in the table using this function rule. f(x) = √x + 2 Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -9 0 9 16

Sean las siguientes hipótesis: H0: mu=400 H1: mu neq 400 En el caso de una muestra aleatoria de 12 observaciones seleccionada de una población normal, la media muestral fue de 407, y la desviación estándar de la muestra, de 6. Utilice el nivel de significancia 0.01 : a) Formule la regla de decisión. b) Calcule el valor del estadistico de prueba. c) ¿Cuál es su decisión respecto de la hipótesis nula?

Form 4 Homework Assignment #2 STATISTICS 1. The table below shows the grades of the top five students of form 4 F at a secondary school. Help the teacher work out the following information for her records. A. The mean mark for each student is corrected to one decimal place. B. The Median of the Averages. C. Which subject(s) could you find a grade representing a mode for the subject? If there is a mode, what is it? Students AG/SC ENGA MATH IT SS Hist INT/Sci RE Average --- --- --- --- --- --- --- --- --- --- AA 84 86 87 66 88 44 68 100 BZ 68 69 40 69 85 50 57 92 CC 73 71 36 72 92 42 83 99 DJ 77 86 74 78 69 92 80 100 ET 81 79 66 56 88 89 59 100 2. The table below shows the goals scored by a school's football team over a season of 20 games. Goals Scored Frequency --- --- 0 3 1 3 2 6 3 4 4 3 5 1 20 Use the table to find: A. The mean Goals scored by a school's football team B. The Median Goals scored by the team. C. The modal Goals scored by the team. 3. The table below shows the times taken by 144 runners at their local 5K park Run. A. Draw a histogram for the frequency distribution. (Use an appropriate scale of your own on the Vertical axis.) (Use a scale of 2 cm to represent 6 minutes on the horizontal axis) B. Use your chart drawn in part A to estimate the mode. (Appropriate markings must be shown on the chart to receive all marks.) Time (Mins) Frequency (F) --- --- 15-20 6 20-25 43 25-30 56 30-35 20 35-40 7 40-45 3 45-50 9 144 C. Add two new columns to the table and label them Midpoints and F X (i) Fill in the columns with the appropriate information. (ii) Hence or otherwise, find the mean minutes taken for the race.

Use the graphs, if necessary, of the functions to the right. Find all values of x such that f(x)=-5.

For the linear function y=f(x)=-5x+8: a. Find d f/d x at x=-5. b. Find a formula for x=f^(-1)(y).

Solve the inequality. 3(x-1)/2 ≤ x-3

A random sample of vehicle mileage expectancies has a sample mean of x̄=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles. Round your answer to the nearest whole number (percent).

We have a deck of 10 cards numbered from 1 to 10. Some are grey and some are white. The cards numbered 1,2,3,5,6,8, and 9 are grey. The cards numbered 4,7, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P (not X) be the probability of not X. (a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event Outcomes Probability - 1 2 3 4 5 6 7 8 9 10 - X P(X)= - not X P(not X)= (b) Subtract. 1-P(not X)=

Consider the ordered pairs of the form (C,F), then the two most common methods of measuring temperature, Celsius and Fahrenheit, can be related as follows: When C=10, F=50, and when C=110, F=230. Complete parts a through h. a. Write two ordered pairs relating these two temperature scales.

Consider the quadratic function (y=3 x^2+30 x+65) Rewrite the function in vertex format.

Simplify the following expression. (5x+2)^2

Suppose the graph of y=x^(5/2) is shifted to the right 3 units. What is the equation that gives the new graph?

Se construirá una caja sin tapa cortando pequeños cuadrados de las esquinas de una lámina de hojalata de 12 por 12 cm y doblando hacia arriba los lados. ¿Qué tan grandes deben ser los cuadrados que se van a cortar para hacer que la caja tenga la máxima capacidad posible? ¿Cuáles son las dimensiones y el volumen de dicha caja?

Simplify and reduce to a fraction 10x/(5x+3)-(0x-6)/(5x+3)=(10x+)/(5x+3)

Solve the exponential equation. Express irrational solutions in exact form. 3^x = 6 What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Simplify your answer. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) B. There is no solution.

What is the value of d?

Ho: μautomatic = μmanual Ha: μautomatic > μmanual Ho: μautomatic = μmanual Ha: μautomatic < μmanual Ho: μautomatic = μmanual Ha: μautomatic ≠ μmanual The test statistic is: -3.30 The p-value is: (please round to four decimal places)

What is the value of j?

Write the number in decimal notation without the use of e 2.6 × 10^0 2.6 × 10^0=

Find ∫∫ R 6x dA, where R is a region enclosed by the ellipse x^2/9 + y^2/36 = 1. (Give an exact answer. Use symbolic notation and fractions where needed.)

Divide the following and then check by multiplying. 7048 ÷ 14 Select the correct choice below and, if necessary, fill in the answer box to complete A. The quotient does not have a remainder. The quotient is B. The quotient has a remainder not equal to 0. The quotient is R . C. The quotient is undefined.

Find the derivative of the function. y=(7x^2+2)/(x^2+3)

Define the Poisson probability function for a given mean: Consider a Poisson distribution with a mean of two occurrences per time period. (a) Write the appropriate Poisson probability function. p(x)=

Polynomial and Rational Functions Word problem involving optimizing area by using a quadratic function Linda has 440 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing. As shown below, one of the sides has length x (in meters). (a) Find a function that gives the area A(x) of the field (in square meters) in terms of x. A(x) = (b) What side length x gives the maximum area that the field can have? Side length x: meters (c) What is the maximum area that the field can have? Maximum area: square meters

Does the 90% confidence interval you constructed contradict the claim from the study? Choose the best answer from the choices below. No, the confidence interval does not contradict the claim. The proportion 0.3 from the study is inside the 90% confidence interval. No, the confidence interval does not contradict the claim. The proportion 0.3 from the study is outside the 90% confidence interval. Yes, the confidence interval contradicts the claim. The proportion 0.3 from the study is inside the 90% confidence interval. Yes, the confidence interval contradicts the claim. The proportion 0.3 from the study is outside the 90% confidence interval.

If b is the y-intercept of the graph y=f(x) where b>0 and it is always decreasing, what is the y-intercept and the increase/decrease of the graph of y=-f(-x) after the appropriate transformations?

At a particular college, 85% of the undergraduates are female. If 3485 women attend the college, how many total undergraduates attend the college? The total number of undergraduates is

[Question 7 of 10, Step 1 of 1 A certain insecticide kills 70% of all insects in a laboratory experiment. A sample of 71 insects is exposed to the insecticide that is randomly chosen. What is the probability that exactly 47 insects will survive? Round your answer to four decimal places. Answer How to enter your answer (opens in new window) Tables Keyboard Shortcuts]

Mort bought his house in 2004 for 339,000. It was recently appraised at 281,000. What is the approximate percent of decrease in value? The approximate percent of decrease in value is % (Round to the nearest percent as needed.)

In 2020, there were 13,800 students at college A, with a projected enrollment increase of 500 students per year. In the same year, there were 20,800 students at college B, with a projected enrollment decline of 1250 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time?

The following is the breakdown of male patients with high blood pressure, high cholesterol, and diabetes at a medical center by age. Each condition is independent and no patient on the table has multiple conditions. - 25-29, 30-39, 40-49, 50-59, 60+ - High Blood Pressure: 0.01, 0.04, 0.05, 0.08, 0.22 - High Cholesterol: 0.02, 0.05, 0.08, 0.09, 0.10 - Diabetes: 0.01, 0.05, 0.05, 0.08, 0.07 What is the probability a patient does not have diabetes?

A random sample of 100 freshman showed 8 had satisfied the university mathematics requirement and a second random sample of 50 sophomores showed that 12 had satisfied the university mathematics requirement. Enter answers below rounded to three decimal places. (a) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is (b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is

If 85% of the girls in a class wanted to have a prom and 71% of the boys wanted a prom, is it possible that only 58% of the students in the class wanted a prom? Explain your answer. Choose the correct answer below. A. No, it is not possible. Since more than 58% of boys and more than 58% of girls wanted a prom, more than 58% of all students must have wanted to have a prom. B. Yes, it is possible. If the number of boys in the class was equal to the number of girls, then it would be possible that only 58% of the students wanted to have a prom. C. Yes, it is possible. If there were enough more boys than girls in the class, then it would be possible that only 58% of the students wanted to have a prom. D. No, it is not possible. Since a lesser percentage of boys than girls wanted to have a prom, less than 58% of all students must have wanted to have a prom. E. Yes, it is possible. If there were enough more girls than boys in the class, then it would be possible that only 58% of the students wanted to have a prom.

Question 13 13. Let h(x)=(x-2)(x+1)^2/(x+1)(x-2)^2, Which of the following statements about the graph of h is correct? (A) The graph of h has one hole and one vertical asymptote. (B) The graph of h has two holes and no vertical asymptotes. (C) The graph of h has no holes and two vertical asymptotes. (D) The graph of h has one hole and two vertical asymptotes.

Resuelva la desigualdad: x-4>4(x-1) x>4 x<0 x<1 x<4

Evaluate the line integral, where C is the given curve. ∫C xy^4 ds, C is the right half of the circle x^2+y^2=9 oriented counterclockwise

40% of 142 is what?

Solve the equation by the quadratic formula. Give only real number solutions. (x-3)(x+9)=-16

Find f(a), f(a+h), and the difference quotient (f(a+h)-f(a))/h, where h ≠ 0. f(x)=4/(x+2) f(a)= f(a+h)= (f(a+h)-f(a))/h=

Measurement Area of a piecewise rectangular figure Find the area of the figure. (Sides meet at right angles.) cm

Find the square root. If the square root [ sqrtfrac64169 ] sqrtfrac64169= square (Simplify your answer.)

calcular el número total de bolsas de snack en la camioneta antes de la entrega: 72 bolsas de snack que representa el 24% del total de todas de snack que había en la camioneta hasta antes de hacer la entrega.

Let f(x)=(x+7)^2 Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain. f^(-1)(x)=

Use the graph to determine (a) intervals on which the function is increasing, if any. (b) intervals on which the function is decreasing, if any. (c) intervals on which the function is constant, if any.

Question 10 Which of the following is a one-to-one function? (A) f(x)=(1,4),(2,5),(3,4),(2,7) (B) f(x)=(-1,-1),(-2,-8),(2,-8),(1,1) (C) f(x)=(1,4),(2,5),(3,6),(4,7) (D) f(x)=(-1,1),(-2,4),(2,4),(1,1)

A=[9 2 6; -4 -5 -6] (A^T)^T=

CHALLeNGE ACTIVITY 5.9.1: Function errors: Copying one function to create another. Using the celsius tokelvin function as a guide, create a new function, changing the name to kelvintocelsius, and modifying the function accordingly. Sample output with input: 283.15 10.0 C is 283.15 K 283.15 K is 10.0 C

What is the sum of 2 of the interior angles of a regular hexagon?

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, ŷ = b0 + b1 x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0 0.5 1 2 4.5 5 6 Overall Grades 100 96 88 73 71 68 67 Table Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is a.) 14.2857 b.) 7.0001 c.) 7.6923 d) 32.8719

The equation D=1/2 n(n-3) gives the number of diagonals D for a polygon with n sides. Use this equation to find the number of sides n for a polygon that has 77 diagonals. The polygon has sides.

Find all solutions of the equation in the interval [0,2π sqrt(1-sin x)=cos x

How many feet of fencing should be purchased to enclose a rectangular garden that is 18 ft long and 14 ft wide? The wood framing for an art canvas costs 4.86 per foot. How much would the wood framing cost for a rectangular picture that measures 3 ft by 7 ft ?

You are given two tables below. The data from the frequency distribution table was used to calculate the values in the probability distribution table. Find the missing values of x and y in the table: Frequency Distribution Table Number of fish caught 0 1 2 3 4 Frequency 88 72 30 8 2 Probability Distribution Table Number of fish caught 0 1 2 3 4 Probability 0.44 x 0.15 y 0.01 x= y=

One of the factors of 3p^5 - 12p^3 is - p^4 - p+2 - p^2+4 - 4 Question 4(Multiple Choice Worth 1 points) (02.01 MC) Factor completely 50a^2b^5 - 35a^4b^3 + 5a^3b^4. - 5a^2b^3(10b^2 - 7a^2 + ab) - 10b^2 - 7a^2 + ab - a^2b^3(50b^2 - 35a^2 + 5ab) - 5(10a^2b^5 - 7a^4b^3 + a^3b^4)

Ryan is building a matchstick sequence as shown below. How many matchsticks will he use for the nth figure if the pattern of adding two new squares horizontally and two vertically continues? The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)

Solve: 3/4 y-6=2+1/4 y y=16 y=4 y=-8 y=8

2x^2 + 3x - 27 = 0

A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Outcomes Probability ------------------------------ Event A: Two or more odd numbers Event B: Exactly one odd number ? Event C: An even number on the first roll

According to a recent reporting on a standardized test, the average math score for students in a particular state was 555. Assume the scores are Normally distributed with a standard deviation of 100. Answer parts (a) through (c) below including an appropriately labeled and shaded Normal curve for each part. a. What percentage of the math test takers from this state scored 600 or more?

Solve the equation √(x+3)+4=5 for the variable. Show each step of your solution process.

Use synthetic division to find the result when x^4-10x^2-13x-50 is divided by x+5. Write your answer in the form q(x)+r(x)/d(x), where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Question 10 For the equation, identify the amplitude, period, and phase shift and sketch (at least) one complete cycle of the graph. y = 1/2 sin(3x + π/2) Amplitude: Period: Phase Shift: Clear All Draw: M

5/6 5/6 5/6

Jamal wants to know why 0.3 and 0.30 are equal. How do you respond? Choose the correct answer below. A. The values 0.3 and 0.30 are equal because adding a trailing 0 does not change the value of the number. B. The values 0.3 and 0.30 are not equal because they have a different number of digits. C. The values 0.3 and 0.30 are equal because they have the same digit in the tenths place. It doesn't matter what digit is in the hundredths place. D. The values 0.3 and 0.30 are equal because adding a trailing 0 changes the value of a number.

Solve x^2-9x=0

A worker costs 60 a day, and the firm has fixed costs of 120. Use this information to fill in the column for total cost Fill in the column for marginal cost in the previous table. (Hint: MC = (Delta TC)/(Delta Q).) Fill in the column for average total cost in the previous table. (Hint: ATC = TC/Q.) Which of the following statements are true about the patterns found in this table? Check all that apply. - Average total cost is not U-shaped. - Marginal product rises at first, then declines. - When marginal product is rising, marginal cost is also rising. - When marginal cost is less than average total cost, average total cost is falling.

Find (y') and (y''). [ y=ln (sec (9 x)+tan (9 x)) y'=square y''=square ]

Solve. 2(4y+5)=34

A dog kennel uses 85 lb of dog food per day. How many pounds are used in a year? The kennel uses lb of dog food in a year.

M^2 * a^12 / 1 * 1 / M^3 a^2

The circle graph below shows us how an average consumer spends money. Use this information to answer the question. Suppose your family spent 53000 on the items in the graph below. How much might we expect was spent on food? Choose the correct choice below. 5300 9275 7950 10600

Let f(x) = sqrt(2x - 1) and g(x) = 1/x. Find (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x). Give the domain of each. (f+g)(x) = (f-g)(x) = (fg)(x) = (f/g)(x) = The domain of f+g is The domain of f-g is The domain of fg is

A vending machine dispenses coffee into a sixteen-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.03 ounce. You can allow the cup to overfill 2% of the time. What amount should you set as the mean amount of coffee to be dispensed? ounces (Round to two decimal places as needed.)

For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. h(x)=4 x^3-48 x

The data in the graph show the wind speed y (in mph) for a recent hurricane versus the barometric pressure x (in millibars, mb). Wind Speed vs. Barometric Pressure Part: 0 / 4 Part 1 of 4 (a) Use the points (950,130) and (1000,70) to write a linear model for these data. y =

What is the probability that the letter "e" is selected? Each individual letter of the word "Machigan" placed on a piece of paper and placed in a hat. If one letter is selected at random from the hat, find the probability that the letter "a" is selected.

Problem. 23: Use a double integral to find the volume of the solid shown in the figure. ? cubic units Problem. 24: Find the volume of the solid bounded above by the surface z=f(x, y) and below by the plane region R. f(x, y)=3y/(1+x^2) ; R is the region bounded by y=0, y=sqrt(x), x=16 ? cubic units Problem. 25: The price of land in a rectangular region R of a city is approximated by the function p(x, y)=150-13(x-1/2)^2-13(y-1)^2, 0 ≤ x ≤ 1, 0 ≤ y ≤ 2 where p(x, y) is the price of land in dollars per square foot and x and y are measured in miles. What is the average price of land per square foot in R? (Round your answer to the nearest dollar.) 1575

Which is the equation for the line containing points (8,-5) and (8,3) ? y=8 y=-13/5 x+119/5 y=-13/5 x+89/5 x=8

The table below shows the frequency distribution of the rainfall on 52 consecutive Fridays in a certain city. Use the frequency distribution to construct a histogram. Do the data appear to have a distribution that is approximately normal? Class Frequency 0-0.19 24 0.20-0.39 11 0.40-0.59 3 0.60-0.79 3 0.80-0.99 8 1.00-1.19 1 1.20-1.39 2 Choose the correct histogram below. A. B. C.

The equation of the parabola y=3x^2-6x+7 in vertex form is a.) y=3(x-1)^2+4 b.) y=3(x+1)^2+4 c.) y=3(x+1)^2-4 d.) y=3(x-1)^2-4

When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a five-number bet is betting that the marble will land in a slot numbered 2, 3, 4, 5, or 6. The probability of winning with the given five-number bet is (Type an integer or a simplified fraction.)

Find the average value of the function on the given interval. f(x) = sqrt(x+3) ; [6,13]

Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. 8+7=22-5 and 50+5=3 * 3 The simple statement 9+7=22-5 is false. The simple statement 50+5=3 * 3 is

USING TOOLS The table shows the numbers y of students absent from school x days after a flu outbreak. Write a function that models the data. Use the model to approximate the number of students absent 10 days after the outbreak. Time (days), x: 2, 4, 5, 6, 8, 9, 11 Number of students, y: 11, 17, 19, 19, 17, 14, 7

Write the domain and range of the function using interval notation.

Parallel Lines Lines A and B are parallel. Find the measure of angle a. m angle a=[?]

Given that 27% of college students have repeated a course to improve their grade, in a sample of size n=24, use the Binomial Probability formula to find (a) the probability that exactly 8 students have repeated a course. (b) the probability that fewer than 2 students have repeated a course Round answers to the nearest thousandth (3 decimal places). (a) The probability that exactly 8 students have repeated a course is: (b) The probability that fewer than 2 students have repeated a course is

Use synthetic division to perform the division. x^5-1 / x-1 x^5-1 / x-1 =

A population P is initially 3950 and four hours later reaches the given number. Find the four-hour growth or decay factor. (Round your answers to three decimal places.) (a) 5900 (b) 9100 (c) 1725 (d) 1450

If f(x)=√(x-1) and g(x)=1/(x^2+1) then g[f(x)]= a) 1/x b) 1/√(x-1+1) c) 1/(x-1) d) -1/√(x^2+1)

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