A tennis ball is dropped from a certain height. Its height in feet is given by h(t)=−16t^2 +14 where t represents the time in seconds after launch. What is the ball’s initial height?

The absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

To find the absolute maximum and minimum values of the function f(x) = 1 - 5x² on the interval [-3, 2], we first find the critical points of f(x) and then evaluate f(x) at the critical points and endpoints of the interval.

The derivative of f(x) is:

f'(x) = -10x

Setting f'(x) = 0, we get:

-10x = 0

which has only one critical point at x = 0.

Now, we evaluate f(x) at the critical point and endpoints of the interval:

f(-3) = 1 - 5(-3)² = -44

f(0) = 1 - 5(0)² = 1

f(2) = 1 - 5(2)² = -49

Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

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The best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

The sampling distribution of the mean of a sample is approximately normal if the sample size is sufficiently large, regardless of the distribution of the population from which the sample is drawn.

According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean, which is $3.2$ million. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, which is [tex]$2/\sqrt{40} \approx 0.3162$[/tex] million.

Therefore, the best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

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Answer:

c = 12

Step-by-step explanation:

[tex] {5}^{2} + {c}^{2} = {13}^{2} [/tex]

[tex]25 + {c}^{2} = 169[/tex]

[tex] {c}^{2} = 144[/tex]

[tex]c = 12[/tex]

Answer:

y = -6/7x - 3/7 or 7y = -6x - 3

Step-by-step explanation:

I'm guessing you mean line c: y = -6/7x - 1

Parallel lines have same slope => line d will have slope = -6/7

y = mx + b

-9 = -6/7(10) + b

-9 = -60/7 + b

b = 60/7 - 9 = 60/7 - 63/7 = -3/7

y = -6/7x - 3/7

or 7y = -6x - 3

The true statements about the rectangular prism are Prism B has a greater volume than Prism C, Prism B has the greatest volume, and Prism A has the least volume.

To understand, the differences between the prisms and therefore to verify the statements about them, let's calculate the volume of each by using the formula length x width x height.

Prism A: 2 x 2 x  3= 12 cubic units

Prism B: 2 x 3 x 4 = 24 cubic units

Prism C: 3 x 2 x 3 = 18cubic units

Based on this, the statements A, D, and E are correct.

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14 revolutions per second can be expressed as 28π radians per second.

A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.

1 revolution per second is expressed as 2π radians per second.

To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.

14 revolutions per second = 14 * 2π

= 28π radians per second

Thus, the answer to the given question comes out to be 28 π radians per second

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The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.

To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.

According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years.  Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.

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The next minimal monthly payment will be $110.54.

To calculate the next minimal monthly price, we want to follow these steps:

First, we want to calculate the interest charged at the current monthly statement stability.

To do that, we multiply the statement stability by using the monthly interest price. The monthly interest fee is the annual percentage rate (APR) divided by way of 12. consequently:

Interest charged = $3,651.21 x (21.ninety nine%/12) = $sixty seven.25

next, we upload the interest charged to the statement balance to get the new balance:

New stability = $three,651.21 + $sixty seven.25 = $three,718.46

We then subtract any payments made throughout the month. In this situation, the price was $210.00, so:

New balance after price = $three,718.46 - $210.00 = $3,508.forty six

Ultimately, we calculate the minimal monthly charge. The minimum month-to-month payment is the greater of $25 or 3.15% of the new stability. therefore:

Minimum month-to-month fee = max($25, 3.15% x $3,508.46) = $110.54

So, the next minimal monthly payment will be $110.54.

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The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.

To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
  f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
  0 = -2*cos(π/2) + C1
  C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
  f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
  -3 = -4*sin(π/6) + C2
  -3 = -4*(1/2) + C2
  C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.

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a) The table is completed as follows:

b) The graph is given by the image presented at the end of the answer.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y=  x + 2.

Hence the numeric values of the function are given as follows:

Then the graph is constructed connecting two of these points and tracing a line through them.

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The statement that  describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.

The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.

Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.

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Answer:

Length: 22 inches × 3.5 = 77 inches

Width: 10 inches × 3.5 = 35 inches

The difference between the radii of the two circular tracks is 15ft

The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft

we find the diameter of each track.

The circumference of a circle can be found  using the formula

P = πd

d = P /π

track 1, we have

d1 = P1 / π

d1 = 220 / π

d1 = 70.03 ft.

track 2, we have

d2 = P2 / π

d2 = 126 / π

d2 = 40.11 ft.

radius of tract 1  = 35.01 ft

radius of track 2 = 20.05 ft

The difference between the two track radius is

∆r = r1 - r2

∆r = 110 / π - 63 / π

∆r = (110 - 63) / π

∆r = 47 / π

∆r = 14.96 ft.

∆r =  15 ft

In conclusion, difference between the radii of the two circular tracks is  15ft

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#complete question:

What is the difference between the radii of the two circular tracks? Answer the questions to find out.

1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?

The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.

A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.

Volume of cube = length × breadth × height

length = 5 unit

breadth = 5 unit

height = 5 unit

Volume = 5 × 5 × 5

= 125 unit³

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The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.

The null hypothesis (H₀) states,

That there is no significant difference between the population means of the experimental group and the control group.

The alternative hypothesis (H₁) states that there is a significant difference between the two means.

State the hypotheses as,

H₀: μ₁ - μ₂ = 0 (there is no difference in means)

H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)

where μ₁ is the population mean of the experimental group

And μ₂ is the population mean of the control group.

The test statistic,

Use the t-test formula,

t = (x - μ) / (s / sqrt(n))

where x is the sample mean = 102

μ is the hypothesized population mean = 100

s is the sample standard deviation =88

n is the sample size= 10

Plugging in the values, we get,

t = (102 - 100) / (88 / sqrt(10))

 = 0.45

Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of  88, a mean of 100, and with a sample size of 10.  

a. State the null and the alternative hypotheses.

b. Compute the test statistic for sample mean 102.

Answer:

[tex]h = \sqrt{ {21}^{2} - {19}^{2} } = \sqrt{441 - 361} = \sqrt{80} = 4 \sqrt{5} [/tex]

h = 4√5 feet = 8.9 feet

the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3. Thus, option B is correct.

To write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans, we need to find the common factor between the number of pairs of blue jeans each person donated.

Hallie donated 4 pairs of blue jeans, and Mattie donated 6 pairs of blue jeans.

The common factor between 4 and 6 is 2. We can divide both 4 and 6 by 2 to get:

Hallie donated 2 pairs of blue jeans.

Mattie donated 3 pairs of blue jeans.

Now we can write the ratio of Hallie's donation to Mattie's donation as:

2:3

Therefore, the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3.

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Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.

Given coordinates of points A, B and C

A(6, 10), B(2, -8), C(-4 , -7)

After reflection  (x, y) ---> (-x, y).

Thus,  Coordinates of image of points A', B' and C' are-

A'(-6, 10), B'(-2, -8), C'(4 , -7)

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Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]

The equipment's value after 8 years, given its original value was $75,000 and it depreciates by 12% each year, is approximately $27,506.62.

To find the value of the equipment after 8 years, we need to calculate its value at the end of each year, taking into account the 12% depreciation per year.

At the end of year 1, the equipment will be worth 88% of its original value

Value at end of year 1 = 0.88 x $75,000 = $66,000

At the end of year 2, the equipment will be worth 88% of its value at the end of year 1

Value at end of year 2 = 0.88 x $66,000 = $58,080

We can continue this process for each year

Value at end of year 3 = 0.88 x $58,080 = $51,206.40

Value at end of year 4 = 0.88 x $51,206.40 = $45,065.91

Value at end of year 5 = 0.88 x $45,065.91 = $39,654.02

Value at end of year 6 = 0.88 x $39,654.02 = $34,991.23

Value at end of year 7 = 0.88 x $34,991.23 = $31,191.80

Value at end of year 8 = 0.88 x $31,191.80 = $27,506.62

Therefore, the value of the equipment after 8 years is $27,506.62.

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Answer:

x = 30 , y = 54

Step-by-step explanation:

the figure is a trapezium

each lower base angle is supplementary to the upper base angle on the same side, then

4x + y + 6 = 180 ( subtract 6 from both sides )

4x + y = 174 ( subtract 4x from both sides )

y = 174 - 4x → (1)

and

2x + 12 + 2y = 180 → (2)

substitute y = 174 - 4x into (2)

2x + 12 + 2(174 - 4x) = 180

2x + 12 + 348 - 8x = 180

- 6x + 360 = 180 ( subtract 360 from both sides )

- 6x = - 180 ( divide both sides by - 6 )

x = 30

substitute x = 30 into (1)

y = 174 - 4(30) = 174 - 120 = 54

thus x = 30 and y = 54

To determine the number of liters needed for an order of Kefzol 1.125 g IV q6h, we first need to convert the grams to milligrams.
1.125 g = 1,125 mg

Next, we need to calculate the total volume of Kefzol needed for each dose.

225 mg is equal to 4 mL, so:

1,125 mg ÷ 225 mg/mL = 5 mL

Therefore, each dose of Kefzol requires 5 mL.

To determine the number of liters needed for the entire order, we need to know how many doses will be given per day.

Assuming a standard dosing schedule of q6h, this means the patient will receive 4 doses per day.

So, the total volume of Kefzol needed per day is:

4 doses/day x 5 mL/dose = 20 mL/day

To convert this to liters, we divide by 1000:

20 mL/day ÷ 1000 = 0.02 L/day

Therefore, for an order of Kefzol 1.125 g IV q6h, we will need approximately 0.02 liters per day.

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The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.

The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.

However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.

Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.

Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.

The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

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The area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

From the question, we have the following parameters that can be used in our computation:

Radii = 21 cm, 81 ft, 45/2 cm

The area of a circle is calculated as

Area = πr²

substitute the known values in the above equation, so, we have the following representation

Area = 3.14 * 21² = 1384.74

Area = 3.14 * 81² = 20601.54

Area = 3.14 * (45/2)² = 1589.625

Hence, the area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

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An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.

Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;

2.15p + 3.75w + 4.48 = 29.68

This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).

To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;

p + w + 1 = T

Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.

Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;

T = p + w + 1

Substitute this expression for T into first equation;

2.15p + 3.75w + 4.48 = 29.68

Simplify;

2.15p + 3.75w = 25.20

Therefore, the model of this situation is; 2.15p + 3.75w = 25.20

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The meaning of the intercept of the regression line is option B- When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced

We are given the equation of the experiment that tells a relationship.

y = 0.43x + 28.5

The linear regression line is an algebraic model to show the relationship between the two models by putting the value of one variable to get the value of the other.

A linear regression line can be represented as,

y = Ax + B

Here y is the dependent variable and x is the explanatory variable. A is the slope of the line and

B is the intercept here. In the given equation there are two variables given.

Variable x representsthe amount of nitrogen added, and the variable y represents the number of bushels of corn produced.

As putting the value of x, y increases with the value of number 0.43. Therefore, as we are increasing the value of the nitrogen by one unit, the number of bushels of corn produced is increasing by 0.43 units. Hence, for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

Therefore option B is the correct option.

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The complete question is "An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of

bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of

nitrogen.

y = 0.43x + 28.5

What is the meaning of the slope of the regression line?

O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels."

Answer:

9/7

explain:

(36-27) 7

9/7

Answer: 32000

Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.

Answer:

The present ages of A and B will be 48 and 18 years.

Step-by-step explanation:

Let the coefficient be x.

A's age = 8x

B's age = 3x

Six years hence,

Ages will be 8x+6 and 3x+6.

Now, As per the question,

(8x+6) /(3x+6) = 9/4

32x+24 = 27x+54

5x = 30

x = 6.