The number of questions Tyler answers correctly is within 2 of the number of Benjamin's correct answers. Part A Write and solve an absolute value inequality to determine the number of questions Tyler answers correctly. Part B Based on your answer to Part A, what prizes will Tyler win? Explain.

Answer:

1). 10  2). 8/5  3). 8

Step-by-step explanation:

I. f(2) = 3(2) + 4

= 6 + 4

= 10

II. f(4) = 3(4) - 4/5

= 12 - 4/5

= 8/5

III). 3y - 6 = y + 10

2y - 6 = 10

2y = 16

y = 8

Answer:

62.83in

Step-by-step explanation:

C=2 π r = 2• π • 10= 62.83185in

The circumference of a circle with a radius of 10 inches is 62.8 inches

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by: C = 2πr,

Given that,

A circle having radius 10 inches.

The circumference = ?

Substituting the given value of the radius, we get:

C = 2π(10) = 20π

To find the circumference to the nearest tenth of an inch, we can substitute the value of π as 3.14 (an approximation of π accurate to two decimal places).

Therefore,

C = 20π ≈ 20(3.14) = 62.8 inches (rounded to one decimal place)

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Answer:

36.9 gallons were used in one month.

Step-by-step explanation:

In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other:

3 ÷ 5 = 0.6

Then, we can set up this equation to figure out how much gallons of gasoline was used:

0.6 x 61.5 = 36.9

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Answer: 36.9 gallons were used in one month.

Step-by-step explanation:

In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other: 3 ÷ 5 = 0.6

Then, we can set up this equation to figure out how much gallons of gasoline was used: 0.6 x 61.5 = 36.9

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Answer:

8x + 12

Step-by-step explanation:

The integral Pπ/4 tan4(0) sec²(0) de is equal to 0. The integral Pπ/4 tan4(0) sec²(0) de can be evaluated using the following steps:

1. Use the identity tan4(0) = (4tan²(0) - 1).

2. Substitute u = tan(0) and du = sec²(0) de.

3. Use integration in the following formula: ∫ uⁿ du = uⁿ+1 / (n+1).

4. Substitute back to get the final answer.

Here are the steps in more detail:

We can use the identity tan4(0) = (4tan²(0) - 1) to rewrite the integral as follows:

∫ Pπ/4 (4tan²(0) - 1) sec²(0) de

We can then substitute u = tan(0) and du = sec²(0) de. This gives us the following integral:

∫ Pπ/4 (4u² - 1) du

We can now integrate using the following formula: ∫ uⁿ du = uⁿ+1 / (n+1). This gives us the following:

Pπ/4 (4u³ / 3 - u) |0 to ∞

Finally, we can substitute back to get the final answer:

Pπ/4 (4∞³ / 3 - ∞) - (4(0)³ / 3 - 0) = 0

Therefore, the integral Pπ/4 tan4(0) sec²(0) de is equal to 0.

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The percentile rank / score in the setting of statistics denotes the percentage of the population that falls below it when the data is organized in ascending order.

For the given question.

The difference in the percentiles and raw scores is-

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Answer:

B

Step-by-step explanation:

Answer:

-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

Answer:-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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Tan(A) = sin(A) / cos(A) = (-√11/6) / (-5/6) = √11/5

We know that sec(A) = 4/3 in quadrant IV, so we can use the Pythagorean identity to find the value of cos(A):

sec^2(A) - 1 = tan^2(A)

cos^2(A)/sin^2(A) - 1 = sin^2(A)/cos^2(A)

cos^2(A) - sin^2(A) = 4^2

cos^2(A) - (1 - cos^2(A)) = 16/9

2cos^2(A) - 1 = 16/9

cos^2(A) = 25/36

cos(A) = -5/6

Since A is in quadrant IV, sin(A) = -√(1-cos^2(A)) = -√(1-(25/36)) = -√(11/36) = -√11/6.

Therefore, we have:

cot(A) = cos(A) / sin(A) = (-5/6) / (-√11/6) = 5/√11 * √6

To find tan(A), we can use the identity tan(A) = sin(A) / cos(A):

tan(A) = sin(A) / cos(A) = (-√11/6) / (-5/6) = √11/5

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Step-by-step explanation:

a.

\(f(2) = 0\)

b.

\(f(x) = 4 \\ f(5) = 4 \\ x = 5\)

c.

[—3,2] union [3.4, 4]

The decision to reject or not reject the null hypothesis depends on the specific research question and the level of confidence chosen by the researcher.

If the null hypothesis is not rejected at a 95% confidence level, it may or may not be rejected at a 99% confidence level. The decision to reject or not reject the null hypothesis depends on the level of significance chosen by the researcher. A higher level of significance, such as 99%, requires stronger evidence against the null hypothesis for it to be rejected compared to a lower level of significance, such as 95%.        

Therefore, the decision to reject or not reject the null hypothesis depends on the specific research question and the level of confidence chosen by the researcher.

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The measure of angle x is equal to: D. 96⁰​.

In Mathematics, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the vertical angle and its adjacent angle that are formed are supplementary angles, which makes the following angles congruent:

96° and ∠x.

∠x = 96°

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Answer:

m<ABC = 45

m<DBC = 34°

Step-by-step explanation:

Given:

m<ABD = 79°

m<ABC = (8x - 3)°

m<DBC = (5x + 4)°

Step 1: Generate an equation to find the value of x

m<ABC + m<DBC = m<ABD (angle addition postulate)

(8x - 3) + (5x + 4) = 79

Solve for x

8x - 3 + 5x + 4 = 79

13x + 1 = 79

Subtract 1 from both sides

13x + 1 - 1 = 79 - 1

13x = 78

Divide both sides by 13

x = 6

Step 2: find m<ABC and m<DBC by plugging the value of x into the expression of each angle

m<ABC = (8x - 3)°

m<ABC = 8(6) - 3 = 48 - 3 = 45°

m<DBC = (5x + 4)°

m<DBC = 5(6) + 4 = 30 + 4 = 34°

Step-by-step explanation:

!!

Answer:

32, and 48. This is the greatest factor of 16

To get the limit of the function (lim(√(1 + 7x) - √(1 - 4x))/x as x → 0), let's first try an elementary method. However, in this case, the elementary method does not seem to lead to a simple solution. Therefore, we will use l'Hospital's Rule, which can be applied when the limit is in the form of 0/0 or ∞/∞.

Step:1. First, differentiate the numerator and denominator with respect to x:
Numerator derivative: d(√(1 + 7x))/dx - d(√(1 - 4x))/dx = (7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2)
Denominator derivative: dx/dx = 1
Step:2. Now, apply l'Hospital's Rule by taking the limit of the derivatives:
lim((7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2))/1 as x → 0
Step:3. Plug in x = 0:
(7/2)(1)^(-1/2) - (-4/2)(1)^(-1/2) = (7/2) - (-4/2) = 11/2
Therefore, the limit of the function as x → 0 is 11/2.

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Answer: 6.5<6.55

Step-by-step explanation: Because you add the zero to the 6.50 but it’s still less than 6.55.

Answer:

−6.5<6.55

Step-by-step explanation:

I took the K12 test

Answer:

y = -3/4 x - 9

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

9x+ 12y = -108

Subtract 9x from each side

12y = -9x - 108

Divide by 12

12y/12 = -9x/12 -108/12

y = -9/12 x - 108/12

y = -3/4 x - 9

Answer:

y = (-3/4)x - 9

Step-by-step explanation:

Given equation,

→ 9x + 12y = -108

Now we have to,

→ convert into slope-intercept form.

Solving for the value of y,

→ 9x + 12y = -108

→ 12y = -9x - 108

→ y = (-9x - 108)/12

→ y = (-9/12)x - 9

→ y = (-3/4)x - 9

Hence, the form is y = (-3/4)x - 9.

21/14 and 12/8 are the ratios which are proportional.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The two ratios that form a proportion are the ones that have the same ratio of their corresponding terms. This can be expressed as:

a/b = c/d

where a, b, c, and d are the terms of the ratios.

Option A:

21/14

Divide numerator and denominator by 7

3/2

Option B:

21/7=3/1

Option C

12/27

4/9

Option D

12/8

Divide numerator and denominator by 4

3/2

Hence, 21/14 and 12/8 are the ratios which are proportional.

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Complete question

Which two ratios form a proportion? Responses

A) 21 and 14

B 21 and 7

C) 12 and 271

D 12 and 8

Answer:

Your estimated monthly payments are $22 and you will pay $26 in interest over the life of the loan.

Step-by-step explanation:

Answer:

A) two          (they are 7 and -7)

Step-by-step explanation:

Answer:

-3,4 4,4 this is your answer I hope it help you plz. like it and rate it

Answer:

Do you mean this?

..........

Answer:

Can u space them out so i know which ones are exponents

Step-by-step explanation:

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

False

Step-by-step explanation:

Check using Pythagorean theorem (proof for right triangles)

\(10^2+24^2=25^2\)

\(100+576=625\)

\(676\neq 625\)

False

Answer:

$177,107.70

Step-by-step explanation:

We Know

- A family wishes to accumulate $400,000 in a college fund at the

end of 15 years.

- 8% compounded quarterly

How much should the investment be?

We use the formula:

FV = PV(1 + r/n)^(n·t)

PV = present value (or initial investment)

r = annual interest rate

n = number of compounding periods per year

t = number of years

FV = $400,000

r = 8% = 0.08

n = 4 (quarterly compounding)

t = 15 years

$400,000 = PV(1 + 0.08/4)^(4·15)

$400,000 = PV(1.02)^60

PV = $400,000 / (1.02)^60

PV ≈ $177,107.70

So, the investment should be $177,107.70

Answer: h= V/2πr^2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

To analyze the function f(x) = 4 sin ((2-3)x) + 8, we can identify its key characteristics:

Amplitude (A): The amplitude of a sinusoidal function represents the maximum displacement from the midline. In this case, the amplitude is 4, indicating that the graph oscillates between 4 units above and below the midline.

Period (P): The period of a sinusoidal function represents the length of one complete cycle. To find the period, we use the formula P = 2π/|B|, where B is the coefficient of x in the argument of the sine function. In this case, B = 2-3, so the period is P = 2π/(2-3) = 2π.

Midline: The midline is the horizontal line that the sinusoidal function oscillates around. In this case, the midline is y = 8.

Phase Shift: The phase shift indicates any horizontal translation of the graph. In this case, there is no phase shift since the argument of the sine function is (2-3)x, which is equivalent to x.

Vertical Translation: The vertical translation represents a vertical shift of the graph. In this case, the graph is shifted 8 units upward.

Maximum and Minimum Values: The maximum value occurs when the sine function reaches its peak value of 1, multiplied by the amplitude and added to the vertical translation. So the maximum y-value is 4(1) + 8 = 12. The corresponding x-value can be found at any point where the sine function reaches its maximum value, which is at the start of each cycle. So the x-values corresponding to the maximum y-value are 0, 2π, 4π, 6π, etc.

Similarly, the minimum value occurs when the sine function reaches its minimum value of -1, multiplied by the amplitude and added to the vertical translation. So the minimum y-value is 4(-1) + 8 = 4. The corresponding x-values can be found at any point where the sine function reaches its minimum value, which is halfway between each pair of maximum values. So the x-values corresponding to the minimum y-value are π, 3π, 5π, 7π, etc.

To summarize:

Amplitude (A): 4

Period (P): 2π

Midline: y = 8

Phase Shift: None

Vertical Translation: 8 units upward

Maximum y-value: 12 (corresponding x-values: 0, 2π, 4π, 6π, etc.)

Minimum y-value: 4 (corresponding x-values: π, 3π, 5π, 7π, etc.)

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From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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