Q1. ) Cathy has a prepaid cell phone. Last month she deposited $55. 00 into her cell phone


account and was able to talk for 700 minutes before running out of credit. What is the


charge per minute on Cathy's cell phone; Round to the nearest cent and assume no other


fees apply.

The reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

Let's solve the system of equations based on the given information:

Let b be the number of black buttons in one sack and w be the number of white buttons in one sack.

From the first equation, we know that the number of black buttons in one sack is 9 more than the number of white buttons:

b = w + 9

From the second equation, we know that the total number of buttons in one sack is 372 divided by the number of sacks (12):

b + w = 372/12

b + w = 31

We can substitute the value of b from the first equation into the second equation:

(w + 9) + w = 31

2w + 9 = 31

2w = 31 - 9

2w = 22

w = 22/2

w = 11

Substituting the value of w back into the first equation, we can find the value of b:

b = 11 + 9

b = 20

Therefore, the reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

for such more question on number

https://brainly.com/question/859564

#SPJ11

98 square feet of glass were used to build the aquarium.

Given that the public library has an aquarium in the shape of a rectangular prism, which has a base of 6 feet by 2.5 feet and a height of 4 feet. We are to find out how many square feet of glass were used to build the aquarium.

The surface area of a prism is given as;S.A of the rectangular prism = 2(lw + lh + wh)Where l = 6 feet, w = 2.5 feet, and h = 4 feetSubstituting the given values;S.A of the rectangular prism = 2(6 × 2.5 + 6 × 4 + 2.5 × 4)S.A of the rectangular prism = 2(15 + 24 + 10)S.A of the rectangular prism = 2(49)S.A of the rectangular prism = 98

In order to construct the aquarium, 98 square feet of glass were utilised.

To know more about aquarium refer here:

https://brainly.com/question/27245440#

#SPJ11

Given: Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is times the base length of the box (x).

Find the approximate height and the length of the box.

Let's assume the length of the base of the square is x.

The area of the base of the square is x^2.

If the height of the prism is y,

The volume of the prism is given by the product of the area of the base and the height.

Therefore, the volume of the prism is x^2 y.

The volume of the box is given to be 150 cubic inches.

Hence,x^2 y = 150.

Also, the height of the box (y) is times the base length of the box (x).i.e y = 3x.

Hence,x^2 (3x) = 1503x³ = 150x³ = 50x = 50³√1/3 = 3.684.

The length of the box is x = 3.684 inches (approx).

The height of the box is y = 3x = 3(3.684) = 11.052 inches (approx).

The height of the box is 11.052 inches and the length of the box is 3.684 inches.

#SPJ11

Learn more about Prism and square https://brainly.com/question/28490327

The number of false positives is 70, and the number of true positives is 249. Thus:PVP = 249 / (249 + 70)PVP = 0.78. There is a 78% chance that she actually has breast cancer.

The predictive value positive (PVP) is an essential parameter for understanding the accuracy of a medical test. It represents the proportion of people with a positive test result who actually have the condition.

PVP is influenced by the prevalence of the condition and the test's sensitivity and specificity.

In this case, we are given the prevalence of breast cancer in a certain population of women, the sensitivity of a mammogram, and the specificity of a mammogram.

Using this information, we can calculate the PVP for the mammogram in this population.

The prevalence of breast cancer in the population is 0.30. This means that out of 1000 women, 300 have breast cancer.
The sensitivity of the mammogram is 0.83, which means that out of the 300 women with breast cancer, 249 will test positive. The specificity of the mammogram is 0.90, which means that out of the 700 women without breast cancer, 630 will test negative.

Therefore, the number of false positives is 70, and the number of true positives is 249. We can now calculate the PVP:PVP = TP / (TP + FP)where TP is true positives and FP is false positives.

PVP = 249 / (249 + 70)PVP = 0.78Therefore, the PVP for this mammogram in this population is 0.78. This means that if a woman in this population tests positive for breast cancer, there is a 78% chance that she actually has breast cancer.

The predictive value positive is a critical parameter for evaluating the accuracy of a medical test. It indicates the likelihood that people with a positive test result actually have the condition. In this case, the PVP for a mammogram in a population with a prevalence of breast cancer of 0.30, a sensitivity of 0.83, and a specificity of 0.90 is 0.78. This means that if a woman in this population tests positive for breast cancer, there is a 78% chance that she actually has breast cancer.

To know more about predictive value  visit:

brainly.com/question/30719923

#SPJ11

the first student did better in terms of their performance relative to their respective class averages and standard deviations.

To determine which student did better on their respective tests, we need to compare their scores relative to their class averages and standard deviations.

Let's calculate the z-scores for each student, which will allow us to compare their scores in terms of standard deviations from their class averages.

For the first student:

Z-score = (Student's Score - Class Average) / Standard Deviation

Z-score = (80 - 85) / 5

Z-score = -1

For the second student:

Z-score = (Student's Score - Class Average) / Standard Deviation

Z-score = (65 - 50) / 10

Z-score = 1.5

The z-score represents the number of standard deviations a score is above or below the mean. A positive z-score indicates a score above the mean, while a negative z-score indicates a score below the mean.

Based on the z-scores, we can conclude that the first student performed better relative to their class average compared to the second student. The first student's score of 80 was 1 standard deviation below the class average, while the second student's score of 65 was 1.5 standard deviations above the class average.

Therefore, the first student did better in terms of their performance relative to their respective class averages and standard deviations.

Learn more about Z-score here

https://brainly.com/question/31971058

#SPJ4

The fraction will increase by 140% .

Given,

Numerator is increased by 20% .

Denominator is decreased by 50% .

Then,

Lets call one number x and the other one y

first you have the fraction x/y

When you increase the numerator by 20% you get 1.2

when you increase the denominator by 50% you get 0.5

Then you get the fraction 1.2x/0.5y

Since fractions are basically division you divide 1.2 by 0.5 which is 2.4

2.4 as a percent is 240%

you subtract that from 100 and you get 140% .

Know more about fractions,

https://brainly.com/question/10354322

#SPJ4

True: Rn has exactly one subspace of dimension m for each of m = 0, 1, 2, ..., n. This is because the dimension of a subspace can range from 0 (the zero subspace) to n (the entire space Rn), and there is exactly one subspace for each possible dimension within this range.

True: The set {0} forms a basis for the zero subspace since it satisfies the conditions for a basis. It is linearly independent and spans the zero vector.

False: If m > n, then U = {u1, u2, ..., um} in Rn cannot form a basis for Rn by removing m - n vectors. To form a basis for Rn, the number of vectors in the basis must be equal to the dimension of Rn, which is n.

True: The nullity of a matrix A is equal to the dimension of the subspace spanned by the columns of A. This is known as the Rank-Nullity Theorem, which states that the nullity of a matrix plus the rank of the matrix equals the number of columns in the matrix.

True: If {u1, u2, u3} is a basis for R3, then span{u1, u2} is a plane since it is a two-dimensional subspace within R3. It is spanned by u1 and u2, which are linearly independent vectors.

Learn more about dimension

brainly.com/question/31106945

#SPJ11

In this scenario, where the bank only recognizes and deals with whole numbers, the extra 50 cents cannot be directly represented. The bank only considers the integer portion of the amount and ignores the fractional part.

When Mary puts all her money, $6.50, into a bank, but the bank only understands numbers as integers, the extra 50 cents are lost or forfeited as they cannot be converted to integers. Therefore, Mary will only be credited with 6 dollars in the bank.

However, there are a couple of ways Mary could prevent losing the extra 50 cents. She could either round up to the nearest dollar and deposit $7, or she could exchange the coins for bills at a currency exchange, bank or other establishment.

To learn more about integers: https://brainly.com/question/929808

#SPJ11

To make iced tea using 8 cups of water, Marie will need an appropriate amount of drink mix.

The amount of drink mix needed depends on the desired strength or concentration of the iced tea. Generally, for a standard iced tea recipe, a ratio of 1 teaspoon of drink mix per 8 ounces (1 cup) of water is used.

In this case, since Marie is using 8 cups of water, she will need 8 teaspoons of drink mix.

This assumes that Marie wants to maintain a standard strength for her iced tea. However, individual preferences may vary, and adjustments can be made based on personal taste preferences for a stronger or weaker tea.

To learn more about iced tea click here: brainly.com/question/28531302

#SPJ11

The sum of the ten's digit and the hundredth digit in the number 1,764,823 is 9.

To find the sum of the ten's digit and the hundredth digit in the number 1,764,823, we first need to understand the place values of the digits in the number. In 1,764,823, the ten's digit is 2, and the hundredth digit is 4.

To calculate their sum, we simply add the two digits together: 2 + 4 = 6. Therefore, the sum of the ten's digit and the hundredth digit in the number 1,764,823 is 6.

To learn more about sum click here: brainly.com/question/29034036

#SPJ11

The 95% confidence interval for the mean score of actuarial students in the special study program is from 4.328 to 7.672.

We have,

To calculate the 95% confidence interval for the mean score of actuarial students in the special study program, we need to use the sample mean, sample standard deviation, and sample size.

Given that the sample mean is 6.0, the standard deviation of the sample is 2.0, and the sample size is 8, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean ± (Critical Value x Standard Error)

First, we need to find the critical value corresponding to a 95% confidence level.

For a sample size of 8, the t-distribution is typically used.

The critical value for a 95% confidence level with 7 degrees of freedom (n - 1) is approximately 2.365.

Next, we calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

Standard Error = Sample Standard Deviation / √Sample Size

Standard Error = 2.0 / √8

Standard Error ≈ 0.707

Now, we can calculate the confidence interval:

Confidence Interval = 6.0 ± (2.365 x 0.707)

Confidence Interval ≈ 6.0 ± 1.672

Confidence Interval ≈ (4.328, 7.672)

Therefore,

The 95% confidence interval for the mean score of actuarial students in the special study program is from 4.328 to 7.672.

Learn more about confidence intervals here:

https://brainly.com/question/32546207

#SPJ4

We would need to fill the 6.75 L bucket approximately 4,720 times in order to empty the pool of volume 31,860 liters.

To calculate the number of times a 6.75 L bucket has to be filled in order to empty the pool, we first need to find the volume of water in the pool. We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

In this case, the length is 20.0 ft, the width is 12.5 ft, and the height (or depth) is 4.50 ft. Substituting these values into the formula, we get:

Volume = 20.0 ft x 12.5 ft x 4.50 ft

Volume = 1125 cubic feet

However, we need to convert this volume into liters in order to compare it with the volume of the bucket. To do this, we can use the conversion factor that 1 cubic foot is equal to 28.32 liters. Therefore:

Volume = 1125 cubic feet x 28.32 L/cubic foot

Volume = 31,860 liters

Now we can divide this volume by the volume of one bucket:

Number of buckets = Volume ÷ Bucket volume

Number of buckets = 31,860 L ÷ 6.75 L

Number of buckets = <<31860/6.75=4720>>4,720

To know more about  volume refer here:

https://brainly.com/question/24086520#

#SPJ11

The Probability that both cards are spades and one of them is ace of the spade is 0.0026.

Total number of cards = 52

Number of ace cards = 4

Number of ace of spade = 1

a). Probability that both cards are spades and one of them is ace of spade is:

p=(1׳C₁)/⁵²C₂

= 0.0026

Here, ³C₁ is the number of ways of selecting one ace from the rest 3 aces (club, diamond, heart) and ⁵²C₂ is the number of ways of selecting 2cards from 52 cards and 1 is the sole way of selecting an ace of spade.

Therefore, the Probability that both cards are spades and one of them is ace of the spade is 0.0026.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ4

This equation states that Kree's total earnings (E) are equal to the product of his hourly wage (w) and the number of hours he worked (h).

The correct relationship between Kree's total earnings in a week (E), the number of hours he worked during the week (h), and his hourly wage (w) can be represented by the equation:

C. E = wh

This equation states that Kree's total earnings (E) are equal to the product of his hourly wage (w) and the number of hours he worked (h).

To know more about equation visit:

brainly.com/question/29538993

#SPJ11

Given the matrix T₁(x) and the values of x, we can compute the resulting matrix T₁(x) by substituting the given values into the matrix expression.

The matrix T₁(x) is

T₁(x) = | 15x - 6 |

To compute T₁(x), we substitute the given values of x into the matrix expression.

For x = 3:

T₁(3) = | 15 * 3 - 6 | = | 45 - 6 | = | 39 | = 15 -6

Therefore, when x = 3, the resulting matrix is 15 -6.

For x = 5:

T₁(5) = | 15 * 5 - 6 | = | 75 - 6 | = | 69 | = 3 -1

| 20 - 0 | | 20 | 4 -0

Therefore, when x = 5, the resulting matrix is 3 -1 4 -0.

In summary, when substituting x = 3 into the matrix expression, the resulting matrix is 15 -6. When substituting x = 5, the resulting matrix is 3 -1 4 -0.

Learn more about matrix here:

brainly.com/question/28180105

#SPJ11

To show that 5n² - 4n - 4 is even when n is even, we can use the definition of even numbers.

An even number can be expressed as 2k, where k is an integer. Let's substitute 2k for n in the given expression: 5(2k)² - 4(2k) - 4. Simplifying, we have: 20k² - 8k - 4. Notice that both terms 20k² and -8k are divisible by 2, resulting in an even number. Additionally, the constant term -4 is also even.

Therefore, the expression 5n² - 4n - 4 is composed entirely of even terms when n is even, which implies that it is itself an even number. Hence, we have shown that 5n² - 4n - 4 is even if n is even.

To learn more about even numbers click here: brainly.com/question/2289438

#SPJ11

the correct statements are:1. The y-intercept of the function will decrease by [tex]$50.2.[/tex] The domain of the function will not change.3. The range of the function will change.

Given, function

[tex]$f(x)= 3,000-299x+350$[/tex]

where x is the number of tablets they buy.If a teacher finds the tablets on sale for $249 each, the cost of the tablets will change from $299 to $249, which means that the tablets will cost $50 less per unit.Therefore, the function will change as follows:

[tex]$f(x)= 3,000-299x+350$[/tex]

[tex]$f(x)= 3,350-299x$[/tex]

We can see that the y-intercept of the function will decrease by $50.The function will not have any effect on the intercept of the function.Domain is the set of all possible input values of x for which the function is defined. In the given function, we can say that the domain is 0 to 10 as the school has $3,000 to spend on technology and the tablets cost $249 each, which means they can buy 12 tablets at the most. Therefore, the domain of the function will not change.The range is the set of all possible output values of the function. The minimum value of the function is $3,350, which is equal to the price of a new projector and no tablets. The maximum value of the function is $2,978, which is the price of all the 12 tablets and no projector. Therefore, the range of the function will change by $50. Hence, the correct statements are:1. The y-intercept of the function will decrease by $50.2. The domain of the function will not change.3. The range of the function will change.

To know more about function visit;

brainly.com/question/30721594

#SPJ11

To efficiently parallelize the heapify operation and create a minheap, we can use the parallel heapify algorithm. This algorithm utilizes the power of parallel processing to improve the performance of the heapify operation.

The parallel-heapify algorithm can be implemented as follows:

1. Divide the input array of values into equal-sized chunks, assigning each chunk to a separate processor or thread.

2. Each processor/thread performs the heapify operation independently on its assigned chunk of the array. This involves comparing each element with its parent and swapping if necessary to maintain the minheap property.

3. After completing the local heapify operation, the processors/threads synchronize and exchange boundary elements with their adjacent processors/threads to ensure that the entire array is correctly sorted.

4. Repeat steps 2 and 3 until the minheap property is satisfied throughout the entire array.

By distributing the heapify operation across multiple processors/threads, the parallel-heapify algorithm can significantly reduce the execution time compared to a sequential implementation. This allows for faster sorting of large arrays and improves the efficiency of heap-related operations.

Learn more about parallel algorithm here: brainly.com/question/30189645

#SPJ11

The value of the account after 10 years is $539.69 (to the nearest cent). The correct answer is $539.69.

The formula for V Pert is V = [tex]Pe^{rt},[/tex] where V is the value of the investment account in t years, P is the principal initially invested, e is the base of the natural logarithm, and r is the rate of interest.

A person places $277 in an investment account earning an annual rate of 6.7%, compounded continuously.

Using the formula, we can determine the amount of money, to the nearest cent, in the account after 10 years.

Using the formula, we get; V =[tex]Pe^{rt}V = 277e^{0.067*10}V = 277e^{0.67}V = 277*1.9517V = 539.69[/tex]

Therefore, the value of the account after 10 years is $539.69 (to the nearest cent).

An investment account refers to a type of financial account that is specifically designed for holding and managing investments. It is a platform or vehicle that allows individuals, businesses, or organizations to invest their money in various financial instruments, such as stocks, bonds, mutual funds, exchange-traded funds (ETFs), and more.

know more about investment account

https://brainly.com/question/28935213

#SPJ11

The confidence interval in "The 95% confidence interval for the mean, based on the given information, is (9.85, 11.32)" indicates that we are 95% confident that the true population mean falls within this range.

Interpreting the confidence interval, it means that if we were to take multiple samples from the same population and calculate the confidence intervals, approximately 95% of those intervals would contain the true population mean.

In this specific case, it suggests that we are 95% confident that the true mean lies between 9.85 and 11.32.

The confidence interval refers to the precision of our estimate, not the likelihood of the true mean falling within the specific interval calculated from a single sample.

To know more about confidence interval refer here:

https://brainly.com/question/13067956#

#SPJ11

The boat is approaching the dock is 3 feet per second at the instant the boat is 2 feet from the dock.

Given that a pulley is on the edge of a dock, 10 feet above the water level.

A rope is being used to pull in a boat. The rope is attached to the boat at water level. The rope is being pulled in at the rate of 3 feet per second.

We need to find the rate at which the boat is approaching the dock at the instant the boat is 2 feet from the dock.

Let the distance between the boat and the dock be y and the length of the rope be x.

Therefore, y + 10 = x

Now, we have to find the rate at which the boat is approaching the dock at the instant the boat is 2 feet from the dock. We need to differentiate the above equation with respect to time.

We have the rate of change of the distance between the boat and the dock with respect to time.

Therefore, we get d(x) / d(t) = d(y + 10) / d(t)

Or, [tex]dx/dt = dy/dt[/tex] ---------(1)

Now differentiate y + 10 = x with respect to time to get the value of dy/dt

We get [tex]dy/dt + 0 = dx/dt[/tex]

Or, [tex]dy/dt = dx/dt[/tex]------------- (2)

Substitute equation (2) in equation (1), we get

[tex]dx/dt = dy/dt = 3[/tex] feet per second.

This means that the rate at which the boat is approaching the dock is 3 feet per second at the instant the boat is 2 feet from the dock.

Learn more about Dock and pulley :https://brainly.com/question/32890961

#SPJ11

I recycled 24 cans and 6 bottles for cans earning is $0. 05 and for bottles earning is $0. 15 by using equation.

Let's assume the number of cans recycled as 'x' and the number of bottles as 'y'.

Given that the total number of cans and bottles recycled is 30, we can write the equation: x + y = 30.

Also, the total amount earned from recycling cans and bottles is $1.80, which can be expressed as: 0.05x + 0.15y = 1.80.

To solve these equations simultaneously, we can use the substitution method. First, we solve the first equation for 'x' in terms of 'y': x = 30 - y.

Substituting this value of 'x' into the second equation, we get: 0.05(30 - y) + 0.15y = 1.80.

Simplifying the equation, we have: 1.50 - 0.05y + 0.15y = 1.80.

Combining like terms, we get: 0.10y = 0.30.

Dividing both sides by 0.10, we find: y = 3.

Substituting this value of 'y' back into the first equation, we can calculate: x + 3 = 30.

Solving for 'x', we find: x = 27.

Therefore, I recycled a total of 24 cans (x) and 6 bottles (y) to earn $1.80.

To know more about Equation, visit

https://brainly.com/question/29174899

#SPJ11

The y-coordinate for the point located 3/5 the distance from L to M is 6.

A line segment is a part of a line that extends between two endpoints. The length of a line segment can be calculated by determining the difference between the coordinates of the endpoints of the line segment, both horizontally (the x-coordinates) and vertically (the y-coordinates).

Using these information, we will find the coordinates of a point which is 3/5 of the distance from L to M.

The distance between L(0,1) and M(2,8) is calculated as follows:

d(L, M) = √[(8 - 1)² + (2 - 0)²] = √65.

To determine the x-coordinate of the point 3/5 of the way from L to M, we can use the formula:

x = x₁ + (3/5)(x₂ - x₁) = 0 + (3/5)(2 - 0) = 1.2

To determine the y-coordinate of the point, we can use the formula:

y = y₁ + (3/5)(y₂ - y₁) = 1 + (3/5)(8 - 1) = 6

Therefore, the y-coordinate of the point 3/5 of the way from L to M is 6.

Learn more about line segment from the given link

https://brainly.com/question/280216

#SPJ11

The p-value Group of answer choices can be any negative value must be a number between zero and one by null hypothesis.

The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. It is a measure of the strength of evidence against the null hypothesis.

The p-value is always between zero and one because it is a probability value. A p-value of zero indicates that the observed result is extremely unlikely to occur under the null hypothesis, while a p-value of one suggests that the observed result is very likely to occur even if the null hypothesis is true. Values between zero and one represent varying degrees of evidence against the null hypothesis.

Learn more about  null hypothesis

brainly.com/question/30484892

#SPJ4

Approximately 156 of the test results should be statistically significant if the null hypothesis is correct.

A significance level is a probability threshold, which is used to determine whether a given hypothesis can be rejected.

The significance level can be expressed as a percentage, such as 0.05 or 5 percent.

When performing significance tests, if the p-value is less than the significance level, the null hypothesis can be rejected.

The number of test results that would be expected to be statistically significant is calculated using the following formula:

Expected Number of Statistically

Significant Results = Significance Level × Total Number of Tests

PerformedUsing the values provided, the expected number of statistically significant results can be calculated as follows:

Significance Level = 3% = 0.03

Total Number of Tests Performed = 5200

Expected Number of Statistically

Significant Results = 0.03 × 5200

= 156

Hence, if the null hypothesis is true, we would expect approximately 156 of the test results to be statistically significant.

This answer is supported by the fact that the significance level is very low at just 3 percent.

learn more about  null hypothesis from given link

https://brainly.com/question/28042334

#SPJ11

To find Piper's total balance in one year, she should multiply her current balance by a factor of 1.06. This factor represents the 6% annual interest rate applied to the initial investment without any additional deposits or withdrawals.

When calculating simple interest, the total balance after one year can be found by multiplying the current balance by the sum of 1 and the interest rate expressed as a decimal. In this case, the interest rate is 6%, which is equivalent to 0.06 as a decimal.

To find the total balance, Piper would multiply her current balance by 1 + 0.06, which simplifies to 1.06. This factor of 1.06 accounts for the initial investment and the 6% interest earned over the course of one year. It assumes that no additional funds are added or removed from the investment during that time.

Learn more about interest here : brainly.com/question/30393144

#SPJ11

Point estimate = (Lower limit + Upper limit)/2 = (671.06 + 786.16)/2 = 728.61This means that the average of Agent 015's 112 rockets was 728.61.

The average of Agent 015's 112 rockets is 728.61, given the confidence interval (671.06, 786.16) and the fact that we assume normality we can conclude that the point estimate of the sample mean is equal to the true population mean. This is due to the Central Limit Theorem (CLT). Here, we are given the confidence interval (671.06, 786.16). The midpoint of this interval gives us the point estimate of the sample mean.

Since we don't know the standard deviation of the population, we use the sample standard deviation as an estimate. Also, the critical value is found in the z-tables and is dependent on the level of confidence (1 - α) and the degrees of freedom (df) which in this case is 111.

To know more about average visit :-

https://brainly.com/question/8501033

#SPJ11

The correct option is: 4) 0.1286; fail to reject the null hypothesis.

Given h1: p(=/)4/5 and the test statistic is z = 1.521.

Also, we need to use a 0.05 significance level.

The formula to calculate the p-value is:

P-value = P(Z > 1.521) + P(Z < -1.521)

P-value = P(Z > 1.521) + P(Z > 1.521) [because Z-distribution is symmetrical]

P-value = 2 * P(Z > 1.521)

To find the p-value, we can use a standard normal table or calculator.Using standard normal distribution table, we get:

P(Z > 1.521) = 0.0636

Therefore, the p-value is 2 * 0.0636 = 0.1272.

Since the p-value (0.1272) is greater than the level of significance (0.05), We are unable to rule out the alternative.

learn more about null hypothesis from given link

https://brainly.com/question/4436370

#SPJ11

a) There are 34,459 possible committees. b) There are 1,001 committees consisting of all juniors. c) There are 4,845 committees consisting of no juniors. d) There are 29,614 committees consisting of at least one junior by using combinations.

a) The number of committees possible can be calculated using the combination formula:

Number of committees = C(n, r) = n! / (r! * (n - r)!)

In this case, there are 34 students in total (14 juniors + 20 seniors) and we need to select 4 members for the committee.

Number of committees = C(34, 4) = 34! / (4! * (34 - 4)!)

= 34! / (4! * 30!)

= (34 * 33 * 32 * 31) / (4 * 3 * 2 * 1)

= 34,459

Therefore, there are 34,459 possible committees.

b) To find the number of committees consisting of all juniors, we need to select 4 juniors from the 14 juniors available:

Number of committees consisting of all juniors = C(14, 4) = 14! / (4! * (14 - 4)!)

= 14! / (4! * 10!)

= (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1)

= 1,001

There are 1,001 committees consisting of all juniors.

c) To find the number of committees consisting of no juniors, we need to select 4 seniors from the 20 seniors available:

Number of committees consisting of no juniors = C(20, 4) = 20! / (4! * (20 - 4)!)

= 20! / (4! * 16!)

= (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)

= 4,845

There are 4,845 committees consisting of no juniors.

d) To find the number of committees consisting of at least one junior, we subtract the number of committees consisting of no juniors from the total number of committees:

Number of committees consisting of at least one junior = Total number of committees - Number of committees consisting of no juniors

= 34,459 - 4,845

= 29,614

There are 29,614 committees consisting of at least one junior.

learn more about combination here

brainly.com/question/9304221

#SPJ4

The required polynomial function is `f(x)=4x⁴-24x³+54x²-48x`.

A polynomial function f(x) of degree 3 with real coefficients that satisfies the following conditions with the given information is as follows:

Given information:

Zero of 0 and zero of 3 having multiplicity​ 2; ​f(​4)=16

Let the zeros of the polynomial be x=0, x=3 since they have a multiplicity of 2, they will appear twice in the equation.

Thus, the polynomial will have the following factors:

`(x−0)²(x−3)²`

We also know that `f(4)=16`

Substituting x=4 in the equation gives:

`f(4) = (4−0)²(4−3)²a=16`

Solving for a, we get:

`16=(4−0)²(4−3)²a=16`a=4

Hence, the required polynomial is:

`f(x)=(x−0)²(x−3)²(4)`

which expands to

`f(x)=4x⁴-24x³+54x²-48x`

Therefore, the required polynomial function is `f(x)=4x⁴-24x³+54x²-48x`.

learn more about polynomial function here:

https://brainly.com/question/11298461

#SPJ11