A 5-ounce container of Greek yogurt contains 
135
calories. Find the unit rate of calories per ounce.

The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

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The percentage increase per year in the winner's check over the given period. If the winner's prize increases at the same rate, it will be $1,454,735,139.69 in 2040.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2007, we can use the following formula:

Percentage Increase = (Final Value - Initial Value) / Initial Value * 100

a. Calculating the percentage increase:

Initial Value = $140

Final Value = $1,171,000

Percentage Increase = (1,171,000 - 140) / 140 * 100 ≈ 835,714.29%

b. To estimate the winner's prize in 2040, we can assume the same annual percentage increase will continue. We need to calculate the number of years from 2007 to 2040 and apply the percentage increase to the 2007 prize.

Number of years = 2040 - 2007 = 33 years

Estimated prize in 2040 = 1,171,000 * (1 + (Percentage Increase / 100))^33

Estimated prize in 2040 = 1,171,000 * (1 + (835,714.29 / 100))^33 ≈ $1,454,735,139.69

Therefore, if the winner's prize increases at the same rate, it is estimated to be approximately $1,454,735,139.69 in 2040.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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The slope, y-intercept, and equation of each of the lines are:

a. m = 2, b = -1.

y = 2x - 1

b. m = -1; b = 2.

y = -x + 2

c. m = -2/3; b = 1

y = -2/3x + 1

d. m = 1/2; b = -2.

y = 1/2x - 2

The slope-intercept form is y = mx + b, where b equals the y-intercept and m is the slope.

a. Slope (m) = change in y/change in x = (3 -(-1))/(2 - 0) = 4/2 = 2

y-intercept (b) = -1.

The equation is: y = 2x - 1

b. Slope (m) = change in y/change in x = (2 -(-2))/(0 - 4) = 4/-4 = -1

y-intercept (b) = 2.

The equation is: y = -x + 2

c. Slope (m) = change in y/change in x = (3 -(-1))/(-3 - 3) = 4/-6 = -2/3

Substitute m = -2/3 and (x, y) = (3, -1) into y = mx + b to find the y-intercept (b):

-1 = -2/3(3) + b

-1 = -2 + b

-1 + 2 = b

1 = b

b = 1

The equation is: y = -2/3x + 1

d. Slope (m) = change in y/change in x = (0 -(-1))/(4 - 2) = 1/2 = 1/2

y-intercept (b) = -2.

The equation is: y = 1/2x - 2

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Answer:

10 hours

Step-by-step explanation:

Because if u divide the speed t= 4320miles/432mph=10h

The probability that x is between 134.4 and 140.1 is 0.3211.

Given that the mean is μ = 137.0 and the standard deviation is σ = 5.3.

The formula to find the probability is given as:  `z = (x-μ) / σ`

Where, `z` is the standard score, `x` is the raw score, `μ` is the population mean and `σ` is the standard deviation.

To find the probability that x is between 134.4 and 140.1, we have to find the z scores for these values.

Hence, calculating the z score of 134.4:  `z = (x - μ)/σ = (134.4 - 137)/5.3 = -0.45`

Similarly, calculating the z score of 140.1:  `z = (x - μ)/σ = (140.1 - 137)/5.3 = 0.64`

Now, we can find the probability using the z-score table.

The area between -0.45 and 0.64 is the required probability.

Using the standard normal distribution table, the probability is found to be 0.3211 (rounded to 4 decimal places).

Hence, the probability that x is between 134.4 and 140.1 is 0.3211.

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A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

Interquartile Range:

In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).

The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1

Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.

From the figure, we can find:

The interquartile range of the bus driver is: 20 -10 = 10

The interquartile range of the teacher is: 30 -15 = 15

Therefore,

the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.

Complete Question:

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.

(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.

(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.

(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.

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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

a. The replacement free cash flows is $255,000

b.  The Payback Period time required to recover the initial investment is 2.7778 years.

d. By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

a. To calculate the replacement free cash flows, we need to consider the cash flows associated with the new fleet of trucks. Here's the calculation:

Initial cash outflow: Purchase cost of new trucks + Shipping cost

= $350,000 + $50,000

= $400,000

Annual cash flows:

Operating cost savings:

Diesel fuel savings: $250,000 - $150,000 = $100,000

Maintenance cost savings: $35,000 - $10,000 = $25,000

Net operating working capital reduction: $20,000

Total operating cost savings per year: $100,000 + $25,000 + $20,000 = $145,000

Revenue increase:

Revenue growth rate: 10%

Year 1 revenue increase: $800,000 * 10% = $80,000

Year 2 revenue increase: $800,000 * 10% = $80,000

Year 3 revenue increase: $800,000 * 10% = $80,000

Year 4 revenue increase: $800,000 * 10% = $80,000

Year 5 revenue increase: $800,000 * 10% = $80,000

Salvage value: Market value of the new trucks at the end of 5 years = $30,000

Free cash flows:

Year 0: Initial cash outflow = -$400,000

Year 1: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 2: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 3: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 4: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 5: Cash flow = Operating cost savings + Revenue increase + Salvage value = $145,000 + $80,000 + $30,000 = $255,000

b. The Payback Period is the time required to recover the initial investment. To calculate it, we sum the cash flows until they equal or exceed the initial investment. Here's the calculation:

Payback Period = Number of years to recover initial investment

= 2 years (Year 1 cash flow + Year 2 cash flow)

+ (Remaining investment / Year 3 cash flow)

= 2 years + ($400,000 - $225,000) / $225,000

= 2 years + 0.7778 years

= 2.7778 years

c. To calculate the Net Present Value (NPV) and Profitability Index (PI), we need to discount the cash flows using the given discount rate of 15%. Here's the calculation:

Discount rate: 15%

Present value factor for each year:

Year 0: 1 / (1 + Discount rate)^0 = 1

Year 1: 1 / (1 + Discount rate)^1 = 0.8696

Year 2: 1 / (1 + Discount rate)^2 = 0.7561

Year 3: 1 / (1 + Discount rate)^3 = 0.6575

Year 4: 1 / (1 + Discount rate)^4 = 0.5718

Year 5: 1 / (1 + Discount rate)^5 = 0.4972

NPV calculation:

NPV = (Year 0 cash flow) + (Year 1 cash flow * Present value factor) + (Year 2 cash flow * Present value factor) + ...

= -$400,000 + ($225,000 * 0.8696) + ($225,000 * 0.7561) + ($225,000 * 0.6575) + ($225,000 * 0.5718) + ($255,000 * 0.4972)

Profitability Index calculation:

PI = NPV / Initial investment

= NPV / $400,000

d. To calculate the Internal Rate of Return (IRR), we find the discount rate that makes the NPV equal to zero. Here's the calculation:

IRR = Discount rate that makes NPV equal to zero

By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

e. Based on the information provided, we can determine if the fleet should be replaced by considering the Payback Period, NPV, Profitability Index, and IRR.

If the Payback Period is within the company's acceptable timeframe and the NPV is positive, or the Profitability Index is greater than 1, and the IRR exceeds the company's required rate of return, then replacing the fleet would be financially favorable. If any of these criteria are not met, it would indicate that the replacement may not be the best option.

Please note that the calculation of IRR requires further information, and the final decision should consider additional factors such as qualitative aspects, operational requirements, and strategic considerations.

Without the specific values for cash flows in each year, it is not possible to provide a definitive answer to whether the fleet should be replaced based on the given information.

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Answer:

solution given:

product of (4a-5b) and (3a+4b-2c) is:

the value of the product when A=2 b-3 and C= -2 :

(4a-5b)*(3a+4b-2c)

Answer:

Step-by-step explanation:

#1) Find the polynomial with roots at 2 and 6

#2) Find the polynomial with a double root at -3 and another root at 4

#3) Find the polynomial with roots 0, -3 and 5

Answer:

The coordinates of point C' are (4, -2)

here's why:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y). So if we use this information with the original coordinates, (-4, -2), the new coordinates will be (4, -2).

Answer:

m(A) = 23°

m(B) = 109°

m(C) = 48°

Step-by-step explanation:

Answer:

a^2+a-6

Step-by-step explanation:

i have attached your answer

Answer: 96

Step-by-step explanation:

A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121

Then, we have 9 digits, and all the digits need to be even.

the options are: 0, 2, 4, 6, 8.

Now, we can tink a 9 digit number as 9 empty slots, and in each slot, we can put a number.

But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.

So we can tink it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.

For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9 digit number).

for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)

for the third digit, we have 3 options

for the fourth digit, we have 2 options

for the fifth digit, we have only one option.

The total number of combinations is equal to the product of the number of options for each selection:

C = 4*4*3*2*1 = 96

Answer:

96

Step-by-step explanation:

The answer for the 95% confidence interval between the means of the two populations is 1.12 to 12.88.

Given:

Point estimate of the difference in means = 7

Margin of error = 5.88

To find:

95% confidence interval for the difference between the means of the two populations

Confidence Interval (C.I.) = Difference in mean +/- Margin of error.

C.I. = 7 – 5.88

C.I. = 1.12

C.I. = 7 + 5.88

C.I. = 12.88

Confidence intervals for a difference between means is a range of values that should most likely have the true value of the two populations within the range with a confidence value of 95%. Since 95% of the values come under two standard deviations of the mean, the margin of error simply has to be added or subtracted to get the answer.

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Answer:

s+0

Step-by-step explanation:

h.o mean of f= S =0

H.a mean of F=S >0

Answer:

(x - √7*√x) / (x - 7)

Step-by-step explanation:

I suppose your expression is √x / (√x + √7)

(√x * (√x - √7)) / ((√x + √7) * √x - √7)) = (√x * √x - √7 * √x) / (x - 7)

= (x - √7*√x) / (x - 7)

Answer:

Its A

Step-by-step explanation:

I just took the test on edge

Answer:

its A

Step-by-step explanation:

Answer:

the slope is M=-4

Step-by-step explanation:

Answer:

to find slope you need to

Step-by-step explanation:

first the slope formula

\(\frac{y2}{y1}\frac{x2}{x1}\)

then you replace them with the numbers

\(\frac{-10-6}{4-3}\)

solve equasion

\(-10-6=-16\\4-3=1\)

\(\frac{-16}{1}\)

slope=-16

Answer:

3 quarters and 19 nickles

Step-by-step explanation:

.

Answer:

Step-by-step explanation:

This Graph represents all the real numbers which are less than or equal to 8.(Please see the attached image.)

Graphing Inequalities -

While graphing inequalities, we have to keep the following things in mind.

If the endpoint is included(i.e., incase of ≤ or ≥ ) use a closed circle.

If the endpoint is not included (i.e., in case of < or >), use an open circle.

Use open circle at either ∞ or -∞ .  

Draw a line from the endpoint that extends to the right side if the variable     is greater than the number.

Draw a line from the endpoint that extends  to the left side if the variable is lesser than the number.

Writing Inequality in Interval Notation-

If the endpoint is included (i.e., in case of ≤ or ≥) use the closed brackets '[' or ']'.

If the endpoint is not included(i.e., in case of < or > ), use the open brackets '(' or ')'

Use always open bracket at either ∞ or - ∞

inequality form = q ≤ 8

interval notation = ( -∞, 8]

It means q = (-∞......................... -4,-3,-2,-1,0,1,2,3,4,5,6,7,8] (Please see the attached image).

Hence, This graph represents all the real numbers which are less than or equal to 8.

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Answer:

Step-by-step explanation:

area of two sides of ramp=2*1/2*11*1.5=16.5 ft²

Answer:

8.3 ft

Step-by-step explanation:

area of two sides of ramp=2*1/2*11.1*1.5= 8.3 ft

Answer:

7

Step-by-step explanation

The first thing you do is plug in zero for y the you solve it

The given equation when you plug 0 in for y is

0=-5x²+25x+70

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

x=-1

Step-by-step explanation:

-4x=y+8

-8-4x=y

7x-2y=1

7x-2(-8-4x)=1

7x+16+8x=1

15×+16=1

15x=-15

x=-1