The path of a football kicked by a field goal kicker can be modeled by the equation y = -0.04x2 + 1.56x, where x is the
horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the
football?
15.21 yd
19.5 yd
38.94 yd
45.63 yd

Answer:

\(y=-\frac{1}{9}(x-2)^2-3\)

Step-by-step explanation:

When a quadratic equation is in the form \(y=a(x-h)^2+k\) (vertex form):

Therefore, if the vertex of the function is at (2,-3), h needs to be 2 for \((x-h)^2\)  to equal 0 and k needs to be -3. The only equation that displays this is G:

\(y=-\frac{1}{9}(x-2)^2-3\)

I hope this helps!

The probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

The power of a hypothesis test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the power of the test is given as 0.8, and the null hypothesis is that the true value of the parameter is 10, while the alternative hypothesis is that the true value is 8.

We are given the sample size, n = 25, and the standard deviation, σ = 4. To calculate the probability of a Type I error, we need to determine the significance level of the test, denoted by α.

The significance level is the probability of rejecting the null hypothesis when it is actually true. It is usually set before conducting the test, and commonly set at 0.05 or 0.01.

To calculate α, we can use the following formula:

α = 1 - power = 1 - 0.8 = 0.2

So, the probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

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By using combination, it can be obtained that

Number of simple random samples of size 3 that can be selected from a population of size 7 = 35

What is combination?

Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.

Here, concept of combination is used

Number of simple random samples of size 3 that can be selected from a population of size 7 = \({7 \choose 3}\) = 35

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The true statement about the polynomial function is (d) 0 relative minimum

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

f(x) = x³ + 2x² - 1

Differentiate and set the function o 0

So, we have

3x² + 4x = 0

Factor the expression

So, we have

x(3x + 4) = 0

Next, we have

x = 0 or x = -4/3

So, we have

f(0) = (0)³ + 2(0)² - 1 = -1

f(-4/3) = (-4/3)³ + 2(-4/3)² - 1 = 0.2

This means that it has a relative minimum at x = 0

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Answer:

40

Step-by-step explanation:

The denominators are 4, 5, and 8.

Write the prime factorizations:

4 = 2²

5 = 5

8 = 2³

To find the least common denominator, multiply the prime numbers with the highest exponents.

2³ × 5 = 40

Answer:

LCD=40

EXPLANATION= To find the least common denominator first convert all integers and mixed numbers (mixed fractions) into fractions. Then find the lowest common multiple (LCM) of the denominators.

The given statement is incomplete as the matrix A is not provided. We cannot determine the values of a and b without knowing the dimensions of the matrix A.

The dimensions of A will determine the number of inputs and outputs of the linear transformation T. Once we know the dimensions, we can determine the values of a and b as follows:

Let m and n be the dimensions of A, then a = n (number of inputs) and b = m (number of outputs). So, the linear transformation T: Ra --> Rb is defined as T(x) = Ax, where x is a vector of length n and A is a matrix of dimensions m x n.

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Answer:

y=6

Step-by-step explanation:

By Similar triangles

\(\frac{y}{4} =\frac{9}{y}\)

\(y^2=36\)

\(y=6\)

Answer: 2

Step-by-step explanation:

To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.

Adding 5 to both sides of the inequality, we get:

x ≥ 2

This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.

The resulting graph looks like this:

     ------•-------------------------------->

           2

The shaded region on the right of 2 represents all the values of x that make the inequality true.

Answer:

= −1 ± 17 √8

Step-by-step explanation:

i think, im sorry if this doesn't help...

a. f'(x) = 40x³

To find the derivative of f(x) = 10x⁴, we apply the power rule.

The power rule states that if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹. Applying this rule, we get f'(x) = 4 * 10x³ = 40x³.

b. : f'(x) = 20 + 90x²

To find the derivative of f(x) = 20x + 30x³, we differentiate each term separately. The derivative of 20x is 20, and the derivative of 30x³ is 90x² (applying the power rule). Adding these derivatives, we get f'(x) = 20 + 90x².

r: f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5)

To find the derivative of f(x) = (10 + 2x²)(5x - x²), we apply the product rule. The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). Differentiating each term, we get f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5).

d.: f'(x) = 40x

To find the derivative of f(x) = 20x / (x²), we use the quotient rule. The quotient rule states that if f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x)²). In this case, g(x) = 20x and h(x) = x². After differentiating and simplifying, we obtain f'(x) = 40x.

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Answer:

Research that verifies the number of people who preferred the pillow.

Sorry, if I'm wrong.

When f(x) = x⁴ is reflected about the x-axis and translated 3 units to left we get y = -(x - 3)⁴.

Therefore, g(x) = -(x - 3)⁴.

When a function, f(x) is reflected about the x-axis, we get y = -f(x). Therefore here when f(x) = x⁴ is reflected about the x-axis we get y = -x⁴.

When a function, f(x) is translated by a units to the left we get y = f(x-a).

Thus here we obtain y = -(x - 3)⁴

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Answer:

Step-by-step explanation:

In decimal form it’s 3.5 but if you want a fraction it’s 7/2 hope this helped you sorry if it isn’t what you where looking for

Answer:

it could be 3.5 because 1/2 is half of one whole so yea haha.

Answer:

What is the equation to solve for x?

Step-by-step explanation:

Answer:

2/10 or 0.2

i dont know which tenths you wanted so i did both

Answer:

attached the drawing

Step-by-step explanation:

hope it works

Answer:

(5, 3)

Step-by-step explanation:

\(x = 17 - 4y \\ y = x - 2\)

Substitute x into y:

\(y = (17 - 4y) - 2 \\ y = 15 - 4y \\ y + 4y = 15 \\ 5y = 15 \\ y = 3\)

Substitute y into x:

\(y = x - 2 \\ 3 = x - 2 \\ 3 + 2 = x \\ x = 5\)

Therefore your answer is (5, 3).

Answer:

x= -2

Step-by-step explanation:

since we know what y equals we fill it into the second equation

3(x+4)= -2x+2

3x+12=-2x+2

   -12.      -12

3x=-2x-10

+2x +2x

5x=-10

/5. /5

x= -2

hopes this helps please mark brainliest

we have that

the equation that represents this situation is

87.00=55.50+0.35x

where

x is the number of local calls made above 50

solve for x

0.35x=87-55.50

0.35x=31.50

x=90

therefore

the total of local calls is equal to

90+50=140

The correct responses for the arithmetic and exponential sequence and function are;

1. First part; 32 pennies

Second part; Approximately 50 days

2. 24.6 gallons

3,738.5 minutes

3. $67.2

Approximately 24 months

4. 1106.14 gallons

66.56 minutes

The difference is 1 is an arithmetic sequence while 3 is an exponential function

An arithmetic sequence is a group of numbers in which the difference between subsequent terms is a constant

1. The given parameters are;

The initial amount Savannah placed in the piggy bank = 5 pennies

The amount given to Savannah each day = 3 pennies

Required;

First part;

The amount Savannah will have after 10 days

Solution;

The mathematical model for the situation is an arithmetic sequence or progression

The equation for an arithmetic progression is;

\(a_n = a_1 + (n - 1) \times d\)

Where;

\(a_n\) = The amount after n days

\(a_1 \) = The first amount Savannah placed in the piggy bank = 5 pennies

n = The number of days

d = The common difference between the amount present in consecutive days = 3 pennies

The amount after 10 days is therefore;

\(a_{10} = 5 + (10 - 1) \times 3=32\)

The money after 10 days is 32 pennies

Second part;

The number of days it would take for there to be $1.50 in the piggy bank.

Solution;

100 pennies = $1.00

Therefore;

$1.50 = 150 pennies

Which gives;

150 = 5 + (n - 1) × 3

(n - 1) × 3 = 150 - 5 = 145

(n - 1) × 3 = 145

n - 1 = 145 ÷ 3

n = 145 ÷ 3 + 1 ≈ 49.3 ≈ 50

It will take approximately 50 days for the amount in the piggy bank to be $1.50

2. The volume of the pool = 1,500 gallons

The initial amount of water in the pool = 5 gallons

The rate at which water enters the pool = 2 gallons in 5 minutes

Required;

First part

The volume of water in the pool after 50 minutes

Solution;

2 gallons in 5 minutes = (2/5) gallons/minute = 0.4 gallons/minute

Therefore;

\(a_{50} = 5 + (50 - 1) \times 0.4 =24.6\)

After 50 minutes, 24.6 gallons will be in the pool

Second part;

The time it will take to fill the pool is given by the equation;

\(1500 = 5 + (n - 1) \times 0.4\)

number

Which gives;

n = 3738.5

It will take 3,738.5 minutes to fill the pool

3. The formula for finding the amount in the account is the compound interest formula;

\(\displaystyle{A = P\cdot (1 + r)^n }\)

Where;

A = The amount in the account after n months

P = The initial amount in the account = $50.0

r = The interest rate = 3.0%

n = The number of periods (months)

After 10 months, we have;

\(\displaystyle{A = 50 \times (1 + 0.03)^{10} \approx 67.2 }\)

The amount in the account after 10 months is therefore, approximately $67.2

Second part;

Double the initial amount is 2×$50 = $100

Which gives;

\(100 = \displaystyle{50 \times (1 + 0.03)^{n} \approx 67.2 } \)

Which gives;

n ≈ 23.45

Therefore it will take approximately 23.45 months or approximately 24 months for the amount to double

4. Using the exponential function formula, we have;

Number of 5 minutes in 50 minutes = 10

\( \displaystyle{1500 \times (1 - 0.03)^{10} \approx 1106.14} \)

The water remaining after 50 minutes is approximately 1106.14 gallons

The time it takes for there to be less than 1,000 gallons in the pool is given as follows;

\( \displaystyle{ 1000= 1500 \times (1 - 0.03)^{n}} \)

Which gives;

n = 13.3

Therefore;

The water in the pool will be less than 1000 gallons after 13.3, 5 minute periods or 13.3 × 5 minutes≈ 66.56 minutes

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The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

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Answer:

B

Step-by-step explanation:

Answer: 4

         ______

           _\ _~-\___

   =  = ==(____AA____D

               \_____\___________________,-~~~~~~~`-.._

               /     o O o o o o O O o o o o o o O o  |\_

               `~-.__        ___..----..                  )

                     `---~~\___________/------------`````

                     =  ===(_________D

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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The probability that exactly 6 patients is 2.0669, and the probability that at least 2 patients is 0.0017.

In large restaurants, an average of 3 out of every 5 customers ask for water with their meal. A random sample of 10 customers was selected. We need to estimate the probability that exactly 6 patients and at least 2 patients. The given situation is a binomial distribution since the experiment has only two outcomes, success or failure.

Here, Success is defined as requesting water with a meal, and failure as not requesting water with a meal. The probability of success is p = 3/5 = 0.6 and the probability of failure is q = 1 - p = 1 - 0.6 = 0.4. Let X be the number of patients requesting water with a meal out of 10 patients selected.

P(X = 6) = 10C6 (0.6) (0.4)⁴

= 210 × 0.31104 × 0.0256

= 2.0669P(X ≥ 2)

= P(X = 2) + P(X = 3) + .... + P(X = 10)P(X ≥ 2)

= 10C2 (0.6)² (0.4)⁸ + 10C3 (0.6)³ (0.4)⁷ + ..... + 10C10 (0.6)¹⁰ (0.4)⁰ P(X ≥ 2)

= 0.0022 + 0.0185 + 0.0881 + 0.2353 + 0.3454 + 0.2508 + 0.0986 + 0.0180 + 0.0016P(X ≥ 2)

= 1 - P(X < 2)P(X < 2) = P(X = 0) + P(X = 1)P(X < 2)

= 10C0 (0.6)⁰ (0.4)¹⁰ + 10C1 (0.6)¹ (0.4)⁹ P(X < 2)

= 0.0001 + 0.0016P(X < 2)

= 0.0017

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Answer:

$0.25 per ounce

Step-by-step explanation:

3.75 divided by 15 is 0.25

Answer:

0.25 per ounce

Step-by-step explanation:

3.75 divided by 15 is 0.25

area is a square measure the if we multiply by a factor we need to multiply by the square of the factor

then the area of the dilated rectangle is

9 square units

Remember that if f and g are inverses of one another, then

f(g(x)) = g(f(x)) = x

1/2. Take a = 0 and b = 1 (or any non-zero number) so that

f(x) = x + 0/1   ⇒   f(x) = x

If g is to be an inverse of f, we need

g(f(x)) = g(x) = x

so that c = 1 and d = 0.

3. With f(x) = x + a/b and g(x) = cx - d, we have

g(f(x)) = g(x + a/b) = c (x + a/b) - d = cx + ac/b - d

and of course, with a,b,c,d as before, we get g(f(x)) = x.

4. This would be a very uninteresting graph for the example I've cooked up here, just containing the line y = x...

Answer:

x + 37 ≥ 65

Step-by-step explanation:

Given:

Money Micah wants = $65

Money Micah had = $37

Find:

Money Micah need

Computation:

Money Micah need(x)

x + 37 ≥ 65

So,

Money Micah need = 65 - 37

Money Micah need = $28