Use the first derivative test to locate the relative extrema of the function in the given domain, and determine the intervals of increase and decrease.f(t)=5t3+5t with domain (-2, 2)Find the coordinates of the critical points and endpoints for the following function on the given interval.

[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]

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-

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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).

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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.

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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.

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.

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The difference between the large prism and the small prism is 276 inches cube.

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

Therefore,

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

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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.

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Answer:

The correct graph is graph B.

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

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.

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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.

The ordered pair (1, -4) is the solution of equation 5x + 2y = -3.

We can check which of the ordered pairs is a solution of equation 5x + 2y = -3 by substituting the values of x and y in the equation and checking if it is true.

a. (2, -4)

Substituting x = 2 and y = -4 in 5x + 2y = -3, we get:

5(2) + 2(-4) = 10 - 8 = 2

So, (2, -4) is not a solution to the equation.

Similarly

b. (-4, 2)

5(-4) + 2(2) = -20 + 4 = -16

So, (-4, 2) is not a solution to the equation.

c. (1, -4)

5(1) + 2(-4) = 5 - 8 = -3

So, (1, -4) is a solution to the equation.

d. (-4, 1)

5(-4) + 2(1) = -20 + 2 = -18

So, (-4, 1) is not a solution to the equation.

Therefore, the ordered pair (1, -4) is the solution of equation 5x + 2y = -3.

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The equation of the circle with center (-3, -5) and radius 4 is (x + 3)² + (y + 5)² = 16.

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.

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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.

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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.

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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

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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.

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The graph is misleading because the y values are not labeled

The graph represents the given parameter where

Examining 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

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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.

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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.

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(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.

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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.

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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.

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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]

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.

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Answer:

use desmos cant add pcitures

Step-by-step explanation:

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

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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.

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Answer:

8,450 minutes

Step-by-step explanation: