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Answer:

7.25 each or 7.00 if rounded

Step-by-step explanation:

Answer:

(a) The table

\(\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}\)

(b) See attachment for graph

(c) He swapped the values of the x and y coordinates for one another

Step-by-step explanation:

Given

See attachment for complete question

Solving (a): Complete the table

\(f(x) = -x^2 + 8x\)

\(x = 0\):   \(f(0) = -0^2 + 8*0 = 0 + 0 = 0\)

\(x = 1\):   \(f(1) = -1^2 + 8*1 = -1 + 9 = 7\)

\(x = 2\):   \(f(2) = -2^2 + 8 *2 = -4 + 16 = 12\)

\(x = 3\):   \(f(3) = -3^2 + 8 *3 = -9 + 24 = 15\)

\(x = 4\):  \(f(4) = -4^2 + 8 *4 = -16 + 32 = 16\)

\(x = 5\):  \(f(5) = -5^2 + 8 *5 = -25 + 40 = 15\)

\(x = 6\):  \(f(6) = -6^2 + 8 *6 = -36 + 48 = 12\)

\(x= 7\):  \(f(7) = -7^2 + 8 *7 = -49 + 56 = 7\)

\(x = 8\):  \(f(8) = -8^2 + 8 *8 = -64 + 64 = 0\)

So, the complete table is:

\(\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}\)

Solving (b): Plot the graph

See attachment 2 for graph

Solving (c): Why he was marked as incorrect

By comparing the new attached graph (in b) and the graph of the original question, one will notice that the values of the x and y coordinates are switched.

This is why he was marked as incorrect.

Answer:

Step-by-step explanation:

im not sure

Answer:

  (e)  0.75

Step-by-step explanation:

The correlation coefficient is not affected by translation or scaling of scores. Converting them from "raw scores" to z-scores does not affect their correlation.

The correlation coefficient of the z-scores is 0.75.

Answer: The equation a+b+c=240 degrees is not true for any triangle, since the sum of the angles of a triangle is always 180 degrees. However, it could be true for a quadrilateral, which has four angles. One way to explain why a+b+c=240 degrees is to use the fact that opposite angles of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) are supplementary, meaning they add up to 180 degrees. If we label the opposite angle of c as d, then we have c+d=180 degrees. Subtracting c from both sides, we get d=180-c. Then, adding a+b to both sides, we get a+b+d=240-c+c, which simplifies to a+b+c=240 degrees. Another way to explain why a+b+c=240 degrees is to use the fact that an exterior angle of a triangle is equal to the sum of the opposite interior angles. If we extend one side of the triangle and label the exterior angle as e, then we have e=a+b. Then, adding c to both sides, we get e+c=a+b+c. Since e+c is an exterior angle of another triangle formed by extending the side, it is equal to 180 degrees. Therefore, we have 180=a+b+c, which implies that a+b+c=240 degrees.

Answer:

y= -1 , 1, 4

plug in the values and solve :)

If f(1) = 1 that means c is -2 because when you substitute x = 1 and when c = -2, you'll get f(1) = -2(1)+3 = -2+3 = 1

So the constant c is -2 and that means the value of f(-4) is

f(-4)=-2(-4)+3=8+3=11

Thus, the value of f(-4) is 11.

About why does "c" have to be -2, here's the proof.

 Given y = f(x), therefore.

y=cx+3

Since when x = 1 and y = 1, then Substitute x = 1 and y = 1, thus 1 = c+3

1 - 3 = c and therefore, -2 = c #

So this is the proof that c = -2

Answer:

0.97

Step-by-step explanation:

\(\frac{1}{2^2}\) - 0.54 + 1.26

= \(\frac{1}{4}\) - 0.54 + 1.26

= 0.25 - 0.54 + 1.26 ← evaluate from left to right

= - 0.29 + 1.26

= 0.97

Answer: Domain: x<-2 Range: y>1

Step-by-step explanation:

I don't know for sure but I am taking the test and that was the outcome of the answer.

The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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Answer:

16% drop

Step-by-step explanation:

4/25 drop

Multiply by 4/4

16/100

16% drop

Answer:

16%

Step-by-step explanation:

SInce 4 students left the class, and there are 25 students, let's make it a fraction.

4/25.

As it is asking for a percentage though we could simply convert our fraction to a percentage.

Simply divide the numerator (4) by the denominator (25).

This gives us 0.16.

Which is 16%.

Answer:

C

Step-by-step explanation:

I read it.

Answer:

Step-by-step explanation:

To increase Readers' interest.

Explanation: The similarity in this excerpt is that, The sun's disappearance after sunset is similar to the way an object disappears near a black hole.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

5 miles ===> $1.75 x1 = 5 y1 = 1.75

9 miles ===> $2.75 x2 = 9 y2 = 2.75

point slope form of the line​ = ?

Step 02:

Slope formula

Point-slope form of the line

(y - y1) = m (x - x1)

(y - 1.75) = 0.25 (x - 5)

y - 1.75 = 0.25x - 1.25

y = 0.25x - 1.25 + 1.75

y = 0.25x + 0.5

The answer is:

The point slope form of the line is y = 0.25x + 0.5

Answer:

19

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

is the answer 7ft?

Step-by-step explanation:

i am not completely sure

Set up a ratio of the height over the distance to the mirror/

X/5 = 28/7

Cross multiply:

7x = 140

7? = 140

Divide both sides by 7

? = 140/7

? = 20

The answer is 20 feet

The points that are 4 units apart are B and D

Which points are 4 units apart? On a coordinate plane, point A is at (-2, 4), point B is at (3, -6), point C is at (-1, 0), point D is at (3, -2).

B and C

C and D

A and C

B and D

To do this, we simply calculate the distance using the following equation

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\)

Using the given points, we have:

\(BC = \sqrt{(3+ 1)^2 + (-6 -0)^2} = 7.2\)

\(CD = \sqrt{(-1 - 3)^2 + (0 +2)^2} = 4.5\)

\(AC = \sqrt{(-2 + 1)^2 + (4 -0)^2} = 4.1\)

\(BD = \sqrt{(3 - 3)^2 + (-6 +2)^2} = 4\)

Hence, the points that are 4 units apart are B and D

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Answer:

9 : 25

Step-by-step explanation:

Given the ratio of the sides of 2 similar equilateral triangles = a : b , then

the ratio of their areas = a² : b²

Given ratio of sides = 3 : 5 , then

ratio of areas = 3² : 5² = 9 : 25

A manager wants to test whether two normally distributed and independent populations have equal variances. the appropriate test statistic for this test is a "F-statistics."

An F statistic is a value obtained after performing an ANOVA test or even a regression analysis to determine whether the means of two populations differ significantly.

Some key features regarding the F-statistics are-

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Answer:

x=4

Step-by-step explanation:

2x+3x+1=21

(2x+3x)+(1)=21

5x+1=21

5x+1=21

Step 2: Subtract 1 from both sides.

5x+1−1=21−1

5x=20

Step 3: Divide both sides by 5.

Answer:

x=4

Step-by-step explanation:

2x+3x+1=21

Simplify both sides of the equation.

2x+3x+1=21

(2x+3x)+(1)=21(Combine Like Terms)

5x+1=21

5x+1=21

Subtract 1 from both sides.

5x+1−1=21−1

5x=20

Divide both sides by 5.

5x /5 = 20 /5

x=4

Answer:

Step-by-step explanation:

Find either c or d first. Those are easy and everything will fall into place after those 2 are found.

c: angle c is supplementary with 115. That means that they add up to equal 180; therefore, 115° + c° = 180° so c = 65°.

d: angle d is supplementary with 70. Therefore, 70° + d° = 180° so d = 110°.

a and c are same side interior, so they are also supplementary. That means that a = 115°.

b and d are also same side interior, so they are also supplementary. That means that b = 70°.

Answer:

$4

Step-by-step explanation:

x-.25x=3.      (since it’s 25% off)

.75x=3

x=3/.75

x=4

For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

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The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?

To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Answer:

3

Step-by-step explanation:

if m is the number of months

Beckett: 90 + 25m

Lakota Hills 45 + 40m

so 90 + 25m = 45 + 40m

40m - 25 = 90 - 45

15m = 45

m = 45/15 = 3

Answer:

x^3 + 10x^2 + 21x - 12

Step-by-step explanation:

(x + 4)(x^2 + 6x - 3)

you can separate to make it easier for u

x(x^2 + 6x - 3) + 4(x^2 + 6x - 3), this is optional u don't have to do this part

x^3 + 6x^2 - 3x + 4x^2 + 24x - 12

add like terms together

x^3 + 10x^2 + 21x - 12

Answer:

91

Step-by-step explanation:

91

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

Answer:

3 3/4 cm ^3

Step-by-step explanation:

The length is 2.5 the width is 1 and the height is 1.5  so 2.5x1x1.5

Hope it helps!