The width of the walkway is 3.27 feet.
We have,
Let's assume that the width of the walkway is y feet.
Dimensions of the pool and the walkway can be represented as follows:
Length = 2(x+y) + 13
Width = 2(x+y) + 10
The area of the pool and the walkway.
Area = Length x Width
Area = (2(x+y) + 13) x (2(x+y) + 10)
We know that the total area of the pool and the walkway is 304 square feet.
So,
(2(x+y) + 13) x (2(x+y) + 10) = 304
Expanding the left-hand side and simplifying, we get:
4x² + 28x + 39y + 65 = 304
Rearranging and simplifying, we get:
4x² + 28x + 39y - 239 = 0
We can use the quadratic formula to find the solution:
y = (-b ± √(b² - 4ac)) / 2a
where a = 4, b = 39, and c = -239.
Substituting these values, we get:
y = (-39 ± √(39² - 44(-239))) / 8
Simplifying, we get:
y ≈ 3.27 or y ≈ -18.27 (rejected)
Therefore,
The width of the walkway is 3.27 feet.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
What can you deduce about the height of a binary tree if you know that it has the following properties? (a) 26 leave nodes (b) 44 leave nodes(c) 64 leave nodes
The height of a binary tree depends on the number of nodes and the distribution of those nodes throughout the tree. However, knowing the number of leaf nodes in a binary tree can provide a lower bound on its height.
For a binary tree with 26 leaf nodes, the minimum height is 5, meaning the tree has at least 5 levels. For a binary tree with 44 leaf nodes, the minimum height is 6, and for a binary tree with 64 leaf nodes, the minimum height is 7.
This lower bound on height can be determined by recognizing that each level of a binary tree can contain at most twice as many nodes as the previous level. If a binary tree has L levels and K leaf nodes, then the number of nodes in the last level is at least K, and the number of nodes in the previous level is at least K/2. By repeating this reasoning, we can derive the minimum number of levels needed to accommodate a given number of leaf nodes.
Therefore, if a binary tree has a fixed number of leaf nodes, the minimum height is determined by the number of leaf nodes and the shape of the tree. However, it's important to note that this lower bound is not necessarily tight, as a binary tree with the same number of leaf nodes can have different heights depending on its structure.
Learn more about Height:
brainly.com/question/29131380
#SPJ11
Use the parabola tool to graph the quadratic function f(x)=−1/2x2+7
Answer:
use desmos cant add pcitures
Step-by-step explanation:
Which graph is that of the inequality shown below
Answer:
The correct graph is graph B.
The mean amount spent by each customer on non-medical mask at Chopper Drug Mart is 28 dollars with a standard deviation of 8 dollars. The population distribution for the amount spent on non-medical mask is positively skewed. For a sample of 36 customers, what is the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars?
the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.
We can use the central limit theorem to approximate the sampling distribution of the sample mean. The mean of the sampling distribution of the sample mean is equal to the population mean, which is 28 dollars, and the standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population divided by the square root of the sample size, which is 8/sqrt(36) = 4/3 dollars.
Now we need to find the probability that the sample mean is greater than 22 dollars but less than 25 dollars. Let X be the sample mean amount spent on non-medical mask. Then we need to find P(22 < X < 25).
We can standardize X as follows:
Z = (X - μ) / (σ / sqrt(n))
where μ = 28, σ = 8, and n = 36.
Substituting the values, we get:
Z = (X - 28) / (8/√36)
Z = (X - 28) / (4/3)
So we need to find P((22 - 28)/(4/3) < Z < (25 - 28)/(4/3)), which simplifies to P(-4.5 < Z < -1.5).
Using a standard normal table or calculator, we find:
P(Z < -1.5) ≈ 0.0668
P(Z < -4.5) ≈ 0.00003
Therefore, P(-4.5 < Z < -1.5) ≈ 0.0668 - 0.00003 ≈ 0.0668.
So the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.
To learn more about probability visit:
https://brainly.com/question/15124899
#SPJ11
In each of the following settings, say which inference procedure from Chapter 8, 9, 10, or 11 you would use. Be specific. For example, you might say "two-sample zz test for the difference between two proportions." You do not need to carry out any procedures.34. separate random samples of 75 college students and 75 high school students were asked how much time, on average, they spend watching television each week. we want to estimate the difference in the average amount of tv watched by high school and college students.
In this scenario, the appropriate inference procedure would be the two-sample t-test for the difference between means.
Based on the given information, you would use a "two-sample t-test for the difference between two means" to estimate the difference in the average amount of TV watched by high school and college students. This procedure is suitable because you have separate random samples from two distinct groups and you're comparing their means.
To learn more about t-test, click here:
brainly.com/question/15870238
#SPJ11
In an effort to cut costs and improve profits, many U.S. companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. a. What is the probability that 336 or more companies outsourced some part of their manufacturing process in the past two to three years? b. What is the probability that 286 or more companies outsourced some part of their manufacturing process in the past two to three years? c. What is the probability that 49% or less of these companies outsourced some part of their manufacturing process in the past two to three years?
The probability that 49% or less of these companies outsourced some part of their manufacturing process in the past two to three years is approximately 0.0094.
a) To solve this problem, we need to use the binomial distribution formula:
P(X ≥ 336) = 1 - P(X < 336)
where X is the number of companies that outsourced some part of their manufacturing process.
We know that n = 555, p = 0.54, and q = 1 - p = 0.46.
Using the binomial distribution formula, we get:
P(X < 336) = Σ (nCx) * p^x * q^(n-x) from x = 0 to 335
However, computing this sum directly can be very time-consuming. Instead, we can use the normal approximation to the binomial distribution since n is large and p is not too close to 0 or 1.
Using the normal approximation, we can calculate the mean and standard deviation of the binomial distribution:
μ = np = 555 * 0.54 = 299.7
σ = sqrt(npq) = sqrt(555 * 0.54 * 0.46) ≈ 11.85
Then, we can transform the binomial distribution to a standard normal distribution:
Z = (X - μ) / σ
P(X < 336) ≈ P(Z < (336 - μ) / σ) = P(Z < (336 - 299.7) / 11.85) ≈ P(Z < 3.05)
Using a standard normal distribution table or a calculator, we find that P(Z < 3.05) ≈ 0.9983.
Therefore, P(X ≥ 336) = 1 - P(X < 336) ≈ 1 - 0.9983 = 0.0017.
b) We can use the same approach as in part (a):
P(X ≥ 286) = 1 - P(X < 286)
μ = np = 555 * 0.54 = 299.7
σ = sqrt(npq) = sqrt(555 * 0.54 * 0.46) ≈ 11.85
Z = (X - μ) / σ
P(X < 286) ≈ P(Z < (286 - μ) / σ) = P(Z < (286 - 299.7) / 11.85) ≈ P(Z < -1.15)
Using a standard normal distribution table or a calculator, we find that P(Z < -1.15) ≈ 0.1251.
Therefore, P(X ≥ 286) = 1 - P(X < 286) ≈ 1 - 0.1251 = 0.8749.
c) We want to find P(X ≤ 0.49n) = P(X ≤ 0.49 * 555) = P(X ≤ 271.95).
We can again use the normal approximation to the binomial distribution:
μ = np = 299.7
σ = sqrt(npq) ≈ 11.85
Z = (X - μ) / σ
P(X ≤ 271.95) ≈ P(Z < (271.95 - 299.7) / 11.85) ≈ P(Z < -2.34)
Using a standard normal distribution table or a calculator, we find that P(Z < -2.34) ≈ 0.0094.
Therefore, the probability that 49% or less of these companies outsourced some part of their manufacturing process in the past two to three years is approximately 0.0094.
To learn more about manufacturing visit:
https://brainly.com/question/21892860
#SPJ11
Find the exact area of a circle having the given circumference.
4pi√3
A =
4pi√3
2pi√3
12pi
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=4\pi \sqrt{3} \end{cases}\implies 4\pi \sqrt{3}=2\pi r\implies \cfrac{4\pi \sqrt{3}}{2\pi }=r\implies 2\sqrt{3}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2\sqrt{3} \end{cases}\implies A=\pi (2\sqrt{3})^2 \\\\\\ A=\pi ( ~~ 2^2\sqrt{3^2} ~~ )\implies A=\pi ( ~~ 2^2(3) ~~ )\implies A=\implies A=12\pi[/tex]
The sum of two numbers is 16 the smaller number is 9 less than the larger number
If on addition of two numbers we get 16 as the sum and their difference comes out to be 9 thus the numbers are 12.5 and 3.5
Let one of the numbers be x
the second number be y
According to the question,
Sum = 16
x + y = 16 ----- (i)
Difference = 9
x - y = 9 ------ (ii)
Add the equations (i) and (ii)
x + y + x - y = 16 + 9
2x = 25
x = 25/2 = 12.5
Put the calculated value of x in equation (i)
12.5 + y = 16
y = 16 - 12.5
y = 3.5
Thus, the numbers in the question are 12.5 and 3.5
Learn more about Equations:
https://brainly.com/question/28871326
#SPJ4
Hector helps out at an animal shelter. One of his jobs is to track the weights of the puppies. He recorded the number of ounces gained or lost by five puppies and tried to place them on a number line. . Which error did Hector make? A. He placed Puppy 3 at –3. 4 instead of at –0. 75. B. He placed Puppy 5 to the left of 0 instead of to the right. C. He placed Puppy 1 between 7 and 8 instead of between 15 and 16. D. He placed Puppy 2 between 3 and 3. 5 instead of between 3. 5 and 4
Based on the given information, it seems that Hector made error A. He placed Puppy 3 at -3.4 instead of at -0.75.
To determine which error Hector made, we need to compare his placements with the correct placements of the puppies on the number line based on the recorded weight changes.
According to the number line-
Puppy 3 is placed at -3.4. However, if we look at the data given in the chart, Puppy 3 gained 0.75 ounces, not lost that amount. Therefore, the correct placement for Puppy 3 should be to the right of 0 at -0.75.So, Hector's error was placing Puppy 3 at -3.4 instead of at -0.75.To know more about probability, here
https://brainly.com/question/13604758
#SPJ4
A group of 25 students spent 1,625 minutes studying for an upcoming test. What prediction can you make about the time it will take 130 students to study for the test?
It will take them 3,250 minutes.
It will take them 4,875 minutes.
It will take them 6,435 minutes.
It will take them 8,450 minutes.
Answer:
8,450 minutes
Step-by-step explanation:
7. Determine the total amount of commission: sales: $5,000.00, commission: 3 percent on sales up to $2,000.00, 5 percent on sales from $2,000.00 to $4,000.00, 7 percent on sales over $4,000.00
The total amount of commission is 660 dollars.
Given that,
3 percent on sales up to $2,000.00
Commission = 3% of 2000
= 3/100 × 2000
= $60
5 percent on sales from $2,000.00 to $4,000.00
Commission = 5% of 4000
= 5/100 × 5000
= $250
7 percent on sales over $4,000.00
Commission = 7% of 4000
= 7/100 × 5000
= $350
Total commission=60+250+350
= $660
Therefore, the total amount of commission is 660 dollars.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ1
What is the difference in cubic inches between the volume of the large prism and volume of the smaller prism?
The difference between the large prism and the small prism is 276 inches cube.
How to find the volume of a prism?The prisms above are rectangular base prisms. Therefore, the difference between the volume of the large prism and volume of the smaller prism can be calculated as follows:
Volume of the larger prisms = lwh
where
l = lengthw = widthh = heightTherefore,
Volume of the larger prisms = 6 × 4 × 15
Volume of the larger prisms = 360 inches³
volume of the smaller prism = 7 × 4 × 3
Volume of the larger prisms = 28 × 3
Volume of the larger prisms = 84 inches³
Therefore,
difference of the volume = 360 - 84
difference of the volume = 276 inches³
learn more on volume here: brainly.com/question/22907480
#SPJ1
1. What is the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up?
The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is [tex]\frac{3}{8}[/tex] or 0.375.
The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is as follows:
1. Each coin has 2 possible outcomes: heads (H) or tails (T).
2. Since there are 3 coins, there are [tex]2^3 = 8[/tex] total possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).
3. We're interested in the outcomes where 2 coins are heads up: HHT, HTH, THH.
4. There are 3 favorable outcomes out of 8 total outcomes.
So, the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is 3/8 or 0.375.
To know more about probability visit:
https://brainly.com/question/16988487
#SPJ11
Explain why the graph is misleading
For all three points say the reason and explain what specifically is going on in the graph
The graph is misleading because the y values are not labeled
Explaining why the graph is misleadingThe graph represents the given parameter where
The x-axis represent the yearThe y-axis represent the marriage rateExamining the y-axis of the graph, we can see that
The y-axis is not labeled
This means that
We cannot determine what the y values represent
This is because not labelling the y-axis do not show the correct representation of the graph
Read more about graphs at
https://brainly.com/question/24741444
#SPJ1
One apple cost 2x one banana cost x+1 what is the total cost of 2 apples and 5 bananas?
Nolan bought 2 apples and 10 bananas.
To solve this problem form the system of equations first, then solve them to find the values of the variables.
Nolan bought 2 apples and 10 bananas.
It's given that,
Nolan and his children bought fruits (Apples and bananas) worth $8.
Cost of each apple and bananas are $2 and $0.40 respectively.
Let the number of bananas he bought = y
And the number of apples = x
Therefore, cost of the apples =$2x
And the cost of bananas = $0.40y
Total cost of 'x' apples and 'y' bananas = $(2x + 0.40y)
Equation representing the total cost of fruits will be,
(2x + 0.40y) = 8
10(2x + 0.40y) = 10(8)
20x + 4y = 80
5x + y = 20 --------(1)
If he bought 5 times as many bananas as apples,
y = 5x ------(2)
Substitute the value of y from equation (2) to equation (1),
5x + 5x = 20
10x = 20
x = 2
Substitute the value of 'x' in equation (2)
y = 5(2)
y = 10
Therefore, Nolan bought 2 apples and 10 bananas.
Learn more variables,
https://brainly.com/question/17344045
#SPJ4
Full Question ;
Nolan and his children went into a grocery store and he bought $8 worth of apples
and bananas. Each apple costs $2 and each banana costs $0.40. He bought 5 times as
many bananas as apples. By following the steps below, determine the number of
apples, 2, and the number of bananas, y, that Nolan bought.
A cylindrical cooler has a diameter of 30 inches and a height of 24 inches. How many gallons of water can the cooler hold? (1 ft³ ≈ 7. 5 gal) Round your answer to the nearest tenth of a gallon
Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
In this case, the diameter of the cooler is 30 inches, which means the radius is 15 inches (since the radius is half the diameter). The height is 24 inches.
Using the formula for the volume of a cylinder, we have:
V = π[tex]r^2h[/tex]
= π([tex]15^2)(24[/tex])
= 5400π cubic inches
To convert cubic inches to gallons, we need to divide by the conversion factor 231 cubic inches per gallon. Therefore, the volume of the cooler in gallons is:
[tex]V_gal[/tex]= (5400π cubic inches) / (231 cubic inches/gallon) ≈ 74.0 gallons
Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.
To know more about volume here
https://brainly.com/question/463363
#SPJ4
Sweet Glee is an ice cream shop chain that has locations all across the nation. Customers at Sweet Glee have the option of ordering 1, 2 or 3 Scoops of ice cream in their cone. The mean number of scoops ordered is y=2.86, with a standard deviation of o=0.23. Suppose that we will take a random sample of n-7 ice cream cone orders and record the number of scoops for each, Let x represent the sample mean of the number of scoops for the 7 ice cream cone orders. Consider the sampling distribution of the sample meanx Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find (the mean of the sampling distribution of the sample mean). х (b) Find the standard deviation of the sampling distribution of the sample mean). o ?
(a) The mean of the sampling distribution of the sample mean is equal to the population mean, which is y=2.86. So, х = 2.86.
(b) The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. So, o = 0.23 / sqrt(7) = 0.087.
To learn more about Standard Deviation : https://brainly.com/question/31697586
#SPJ11
Let T be an unbiased estimator of parameter 0. We have that: (a multiple choice question -- please mark all that apply). a. E (T-0)2 = 0 b. E,(T-0) = 0 c. E(T - ET)2 = 0 d. The MSE of T is the same as the variance of T
If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.
(a) E(T-0)^2=Var(T) + [E(T)-0]^2, which is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (a) is false in general.
(b) If E(T-0)=0, then T is an unbiased estimator of 0. This statement is true.
(c) E(T-ET)^2=Var(T) is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (c) is false in general.
(d) The Mean Squared Error (MSE) of T is defined as MSE(T) = E[(T-0)^2]. If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.
To learn more about decomposed visit:
https://brainly.com/question/28896356
#SPJ11
Determine the standard deviation of the random variable, B(400,0.9). O A. 10 B. 360 • CV40 D.2 E. 6
The standard deviation of the random variable B(400, 0.9) is 6 (option E).
To determine the standard deviation of the random variable B(400, 0.9), we need to use the formula for the standard deviation of a binomial distribution:
Standard deviation (σ) = √(n * p * (1 - p))
Here, n is the number of trials (400) and p is the probability of success (0.9). Now, let's calculate the standard deviation step by step:
1. Calculate the probability of failure (1 - p): 1 - 0.9 = 0.1
2. Multiply n, p, and the probability of failure: 400 * 0.9 * 0.1 = 36
3. Calculate the square root of the result: √36 = 6
So, the standard deviation of the random variable B(400, 0.9) is 6 (option E).
Learn more about standard deviation: https://brainly.com/question/23907081
#SPJ11
Choose the correct description of the following quadratic formula hen compared to the parent function (x^2)
Answer:
is the answer C is correct bro
Answer: B
Step-by-step explanation:
B. The negative in front indicates direction. It's a quadratic opening down. and the 6 is the stretch
Instead of over 1 down 1 it goes over 1 down 6 from the vertex. so it's skinnier
The student council wants to raise 370$ and has raised 120$ so far. The students are selling t-shirts for 25$ each to raise more money. Write an equation and solve for t, the number of shirts they need to sell to reach their goal. Explain how you can find the value of the variable
The equation stating requirement for goal is 250 = 25t and value of variable or shirts is 10.
The amount remaining to be raised = 370 - 120
Remaining amount = $250
The number of t-shirts need to be sold to meet the goal will be given by the formula -
Amount required = number of shirts × cost of each shirt
Keep the values in formula to find the expression and value of variable
250 = 25t
Solving the equation for the value of t
t = 250/25
Divide the values
t = 10
Hence, the expression is 250 = 25t and value of variable is 10.
Learn more about expression -
https://brainly.com/question/723406
#SPJ4
In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $36.6 and standard deviation of $14.7. Estimate how much a typical parent would spend on their child's birthday gift (use a 98% confidence level). Give your answers to 3 decimal places Express your answer in the format of £ + E. E____+ S___
The format of £ + E.E___+S___. Therefore, the answer is £36.6 + E. E14.284 + S0.
To lea
To estimate the mean amount a typical parent would spend on their child's birthday gift, we can use a confidence interval with the given information. Since the sample size is relatively small (n=13) and the population standard deviation is unknown, we can use a t-distribution with n-1 degrees of freedom.
The formula for a confidence interval for the population mean is:
x ± t*(s/√n)*
where x is the sample mean, s is the sample standard deviation, n is the sample size, and t* is the critical t-value from the t-distribution for a given level of confidence and degrees of freedom.
For a 98% confidence level and 12 degrees of freedom (n-1), the critical t-value is 2.681.
Plugging in the given values, we get:
36.6 ± 2.681*(14.7/√13) ≈ 36.6 ± 14.284
So the 98% confidence interval for the mean amount a typical parent would spend on their child's birthday gift is £22.316 to £50.884, or in the format of £ + E.E___+S___. Therefore, the answer is £36.6 + E. E14.284 + S0.
To learn more about confidence visit:
https://brainly.com/question/22989641
#SPJ11
Find the length of the diagonal AC in the rectangle below.
Answer: 26
Step-by-step explanation:
So what its basically asking is for you to find the hypotenuse because you can see that the rectangle splits in half with the green line.
So to find the hypotenuse you would use these steps:
1. formula for hypotenuse
[tex]\sqrt{a^2+b^2}[/tex]
2. plug in numbers
[tex]\sqrt{10^2+24^2}=26[/tex]
Neeed helppppp?!!!!!!!!
a. The first step we take to solve the radical equation is adding x to both sides.
b. The next step is to square both sides.
c. Solving the equation for x yields x = 0 or x = 16
d. Checking the solution, shows that it is correct.
What is a radical equation?A radical equation is an equation that contains a root.
Given the radical equation [tex]4x^{\frac{1}{2} } - x = 0[/tex]. To sove this, we proceed as follows.
a. The first step we take to solve the equation is adding x to both sides.
So, we have that
[tex]4x^{\frac{1}{2} } - x = 0[/tex]
[tex]4x^{\frac{1}{2} } - x + x= 0 + x\\4x^{\frac{1}{2} } - 0= x\\4x^{\frac{1}{2} } = x[/tex]
b. The next step is to square both sides. So, we have that
[tex]4x^{\frac{1}{2} } = x\\(4x^{\frac{1}{2} } )^{2} = x^{2} \\16x = x^{2}[/tex]
c. The next step is to subtract 16x from both sides. So, we have that
16x = x²
16x - 16x = x² - 16x
0 = x² - 16x
x² - 16x = 0
Factorizing to solve for x, we have that
x² - 16x = 0
x(x - 16) = 0
x =0 or x - 16 = 0
x = 0 or x = 16
Solving the equation for x yields x = 0 or x = 16
d. Next, we check the solution.
So, when x = 0
[tex]4x^{\frac{1}{2} } - x = 0\\4(0)^{\frac{1}{2} } - 0 = 0\\4(0) - 0 = 0\\0 - 0 = 0\\0 = 0[/tex]
When x = 16
[tex]4x^{\frac{1}{2} } - x = 0\\4(16)^{\frac{1}{2} } - 16 = 0\\4(4) - 16 = 0\\16 - 16 = 0\\0 = 0[/tex]
Checking the solution, we see that it is correct.
Learn more about radical equation here:
https://brainly.com/question/28006794
#SPJ1
Find the value of c on the interval (a, b) such that f'(c) = f(b) − f(a)/b- a
f(x) = 2x^3 - 3x^² - 12x - 4 on interval [5,9]
average rate of change =
The value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.
First, we can find the average rate of change of f(x) on the interval [a,b] using the formula:
average rate of change = [f(b) - f(a)] / (b - a)
Substituting the given values of a = 5 and b = 9 into the formula, we get:
average rate of change = [f(9) - f(5)] / (9 - 5)
Next, we need to find f(9) and f(5) to calculate the average rate of change. To do this, we first need to find the derivative of f(x) using the power rule:
f'(x) = 6x² - 6x - 12
Now, we can use the Mean Value Theorem to find a value c in the interval (5,9) such that f'(c) equals the average rate of change. According to the Mean Value Theorem, there exists a value c in the interval (5,9) such that:
f'(c) = [f(9) - f(5)] / (9 - 5)
Substituting the derivative of f(x) and the values of f(9) and f(5) into the equation, we get:
6c² - 6c - 12 = [2(9)³ - 3(9)² - 12(9) - 4 - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)
Simplifying the right-hand side of the equation, we get:
6c² - 6c - 12 = (658 - 204) / 4
6c² - 6c - 12 = 114
6c² - 6c - 126 = 0
Dividing both sides by 6, we get:
c² - c - 21 = 0
Using the quadratic formula, we can solve for c:
c = [1 ± sqrt(1 + 4(21))] / 2
c = [1 ± 5] / 2
The two possible values of c are:
c = 3 or c = -4
However, since the interval is (5,9), c must be between 5 and 9. Therefore, the value of c that satisfies the Mean Value Theorem is c = 3.
Finally, substituting f(5) and f(9) into the formula for the average rate of change, we get:
average rate of change = [f(9) - f(5)] / (9 - 5)
= [(2(9)³ - 3(9)² - 12(9) - 4) - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)
= [434 - (-104)] / 4
= 139
Therefore, the value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.
Learn more about the average rate of change at
https://brainly.com/question/28744270
#SPJ4
Please give an explanation!
Find a polynomial function of degree 7 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 3 as a zero multiplicity 1
Finally, we can use the fact that 3 is a zero of multiplicity 1 to determine: f(0) = 0 = -81ac.
A polynomial function of degree 7 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 3 as a zero of multiplicity 1 can be written as:
f(x) = [tex]a(x + 3)^3 * b(x)^3 * c(x - 3)[/tex]
where a, b, and c are constants to be determined.
Since -3 is a zero of multiplicity 3, we know that (x + 3) appears in the function three times as a factor, so we can write:
f(x) =[tex]a(x + 3)^3 * g(x)[/tex]
Here g(x) is some function of degree 4 (since we have accounted for 3 of the 7 total factors). Similarly, since 0 is a zero of multiplicity 3, we know that [tex]x^3[/tex] appears in the function three times as a factor, so we can write:
g(x) = [tex]b(x)^3 * h(x)[/tex]
Here h(x) is some function of degree 1 (since we have accounted for 3 of the remaining 4 factors). Finally, we know that 3 is a zero of multiplicity 1, so we can write:
h(x) = c(x - 3)
Putting it all together, we have:
[tex]f(x) = a(x + 3)^3 * g(x)\\= a(x + 3)^3 * b(x)^3 * h(x)\\= a(x + 3)^3 * b(x)^3 * c(x - 3)[/tex]
Substituting h(x) into g(x), we get:
[tex]g(x) = b(x)^3 * h(x)\\= b(x)^3 * c(x - 3)[/tex]
Substituting g(x) into f(x), we get:
[tex]f(x) = a(x + 3)^3 * g(x)\\= a(x + 3)^3 * b(x)^3 * h(x)\\= a(x + 3)^3 * b(x)^3 * c(x - 3)\\= a(x + 3)^3 * b(x)^3 * c(x - 3)\\[/tex]
Expanding the terms, we get:
[tex]f(x) = a(x^3 + 9x^2 + 27x + 27) * b(x^3)^3 * c(x - 3)\\= a(x^3 + 9x^2 + 27x + 27) * b(x^6) * c(x - 3)\\\\= a(x^3 + 9x^2 + 27x + 27) * b(x^6) * c(x) - 3c(x^5)[/tex]
Now, we can use the fact that -3 is a zero of multiplicity 3 to determine the value of a:
[tex]f(-3) = a(-3 + 3)^3 * b(0)^3 * c(-3) = 0[/tex]
= 0
Since [tex](-3 + 3)^3 = 0,[/tex] we can simplify this equation to:
f(-3) = 0 = [tex]b(0)^3 * c(-3)[/tex]
Since 0 is a zero of multiplicity 3, we can also determine the value of b:
f(0) = [tex]a(0 + 3)^3 * b(0)^3 * c(0 - 3) = 0[/tex]
= 27a * 0 * (-3c)
Simplifying, we get:
f(0) = 0 = -81ac
Learn more about polynomial function visit: brainly.com/question/1600696
#SPJ4
4. The number of picks from Toledo and Nevada were compared and the results are as follows:
Test and Cl For Two Proportions: Picked Toledo, Picked Nevada
Variable X n Sample p
Picked Toledo 18 64 0.281250
Picked Nevada 8 64 0.125000
Difference = p (Picked Toledo) -p (Picked Nevada)
Estimate for Difference: 0.15625
95% lower bound for difference: 0.0414921
Test for difference = 0 ( vs > 0 ) : z = 2.24 P-value = 0.013
Fill in the blanks based on the Minitab output shown above:
1. a. H0: ___________________
b. Ha: ___________________
c. α= ____________________
d. Compute the pooled proportion:
2. Value of the Test Statistic: _________________
3. What decision can you make?
4. What conclusion can you make?
1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
c. α= 0.05
d. Pooled proportion = 0.203125
2. The value of the Test Statistic is 2.24.
3. We can reject the null hypothesis.
4. The proportion of people who picked Toledo is greater than those who picked Nevada.
Based on the Minitab output provided, here is the information you're looking for:
1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
c. α= 0.05 (typically used in hypothesis tests, not given in the output)
d. Compute the pooled proportion:
Pooled proportion = (X1 + X2) / (n1 + n2) = (18 + 8) / (64 + 64) = 26 / 128 = 0.203125
2. Value of the Test Statistic: z = 2.24
3. To answer "What decision can you make?"
Since the P-value (0.013) is less than the significance level (α=0.05), you can reject the null hypothesis.
4. To answer "What conclusion can you make?"
Based on the test results, there is significant evidence to conclude that the proportion of people who picked Toledo is greater than the proportion who picked Nevada.
Learn more about the null hypothesis:
https://brainly.com/question/25263462
#SPJ11
log(x + 2) - log 3 = log (5x + 1)
What is the equation of a circle with center (-3,-5) and radius 4?
A. (x-3)2 + (y- 5)² = 16
B. (x+3)2 + (y+ 5)² = 16
C. (x-3)2 + (v-5)2 = 4
O D. (x+3)2 + (y + 5)² = 4
SUB
The equation of the circle with center (-3, -5) and radius 4 is (x + 3)² + (y + 5)² = 16.
What is the equation of a circle with center (-3,-5) and radius 4?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given that the center of the circle is (-3, -5) and the radius is 4.
Hence, we can substitute these values into the formula to get the equation of the circle:
Plug in h = -3, k = -5 and r = 4
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - (-5))² = 4²
Simplifying and expanding the equation, we get:
(x + 3)² + (y + 5)² = 16
Therefore, the equation of the circle is (x + 3)² + (y + 5)² = 16.
Option B) (x + 3)² + (y + 5)² = 16 is the correct answer.
Learn more about equation of circle here: brainly.com/question/29288238
#SPJ1