Assume that a constant rate of change exists for the model formed. The table lists data regarding the average salaries of
several professional athletes in the years 1991 and 2001.
a) Use the two data points to find a linear function that fits the data. Let x = the number of years after 1990 and S(x) = the
average salary.
b) Use the function of part (a) to estimate the average salary in 2005. Predict the average salary in 2010.

Answer: Tim sent 25 text messages

Step-by-step explanation:

y=mx+c is being used

Since it increases by 0.15 each time so m=0.15 and the starting charge is 23.79 so c=23.79. We also know that his phone bill is 27.54 so y=27.54

Now this can be used to solve x

27.54 = 0.15x + 23.79

3.75 = 0.15x

25=x

Answer: 23456789ol.09876

Step-by-step explanation:

Answer:

Hi, I don't mean to scam you out of points. But every method I use the answer is indeed 19. So im not sure what you mean by it isn't 19. is that the whole question?

Answer:

The growth rate is 1.07%

Step-by-step explanation:

y=ab(to the power of x)

b is the growth/decay rate

b is 1.07% here

Answer:

7%

Step-by-step explanation:

The population of ants in the colony can be represented by the function f(t) = 1400(1.07)

Function = 1400( 1 + 7%)

= 1400(1 + 0.07)

= 1400(1.07)

Growth rate = 7%

Answer:

(- 4, 29 ) and ( [tex]\frac{1}{2}[/tex], - [tex]\frac{5}{2}[/tex] )

Step-by-step explanation:

7x + y = 1 ( subtract 7x from both sides )

y = 1 - 7x → (1)

2x² - y = 3 → (2)

substitute y = 1 - 7x into (2)

2x² - (1 - 7x) = 3

2x² - 1 + 7x = 3

2x² + 7x - 1 = 3 ( subtract 3 from both sides )

2x² + 7x - 4 = 0 ← in standard form

(x + 4)(2x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

substitute these values into (1) for corresponding values of y

x = - 4 : y = 1 - 7(- 4) = 1 + 28 = 29 ⇒ (- 4, 29 )

x = [tex]\frac{1}{2}[/tex] : y = 1 - 7([tex]\frac{1}{2}[/tex] ) = 1 - [tex]\frac{7}{2}[/tex] = - [tex]\frac{5}{2}[/tex] ⇒ ([tex]\frac{1}{2}[/tex], - [tex]\frac{5}{2}[/tex] )

The function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Given, a function y = 7|x + 1| - 5

Now, we have to write the given function as a piecewise function

|x + 1| = (x + 1) for x > -1 and

|x + 1| = - (x + 1) for x < -1

So, the given function can be written as a piecewise function

               7(x + 1) - 5                for x > -1

y   =

              -7(x + 1) - 5                for x < -1

On simplifying, we get

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Hence, the given function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

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Answer:  The correct answer is on Day 39 they both have the same amount (38) of naxvips

Step-by-step explanation:

First, determine the rate of change for each using the formula (end-start/days):

Min-jun:

start=36

end=41

days (constant)=15

Rate=41-36/15=5/15 = 1/3 (increment/day)

Tran:

start=56

end=11

days (constant)=15

Rate=11-56/15=-45/15 = -3 (decrement/day)

Build the table using the rate of change for every 3 days:

DAY    MJ    ROC    TRAN    ROC

33       36       0         56          0       <---Start date

36       37      +1          47          -9

39       38      +1          38          -9     <-----SAME!

42       39      +1          29          -9

45       40      +1          20          -9

48       41       +1           11           -9

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Answer:

[tex]\frac{8}{6} = \frac{20}{15}[/tex]

Step-by-step explanation:

It appears that a is the missing value that needs to be solved. The equal sign means that the two values are equal to each other and the other not equal sign means that they don't equal each other.

Whenever dealing with two fractions that equal each other, you can use the fraction cross-product property, where you would multiply the numerator with the denominator and vice versa.

[tex]\frac{8}{a} = \frac{20}{15} \\\\8 \times 15 = 20 \times a\\\\120 = 20a\\\\a = 6[/tex]

So, the fraction would be

[tex]\frac{8}{6} = \frac{20}{15}[/tex]

Answer:

42

Step-by-step explanation:

[tex]\frac{eraser}{cost}[/tex] = [tex]\frac{eraser}{cost}[/tex]  Fill in what you know and solve for the unknown

[tex]\frac{6}{7}[/tex] = [tex]\frac{x}{49}[/tex]   7 x 7 is 49.  Multiply 6 by 7 to find the unknown.  42

The perimeter if ΔSTU is 64 units

What is perimeter ?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Perimeter of ΔPQR is 48 units

and PQ = 18 units

ΔPQR≅ ΔSTU ;

ST = 24 units

Then the[tex]\frac{Perimeter of PQR}{Perimeter of STU} = \frac{PQ}{ST}[/tex] formula is

Since ΔPQR ≅ ΔSTU

Putting the values the equation becomes

40 / Perimeter of ΔSTU = 18 / 24

40 / Perimeter of ΔSTU = 3 / 4

Perimeter of ΔSTU = 48 * 4/3

                               = 16 *4

                              = 64 units

The Perimeter of the ΔSTU is 64 units

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In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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Answer: 8.3

Step-by-step explanation:

50/6= 8.3

Answer:

b=1519.87? (If not correct please clarify what sides the 1600 and 500 ft are on. In my answer the 1600 ft was the hypotenuse since it was the longest of the two and it said to find the base of the triangle. This means the 500 ft is the side adjacent to 90 degrees and 1600 ft is the hypotenuse. Sorry if it's not clear!)

Step-by-step explanation:

[tex]500^{2} +b^2=1600^2\\250000+b^2=2560000\\b^2=2560000-250000\\b^2=2310000\\\sqrt{b^2}=\sqrt{2310000}\\ b=1519.87[/tex]

Answer:

side 2 ([tex]b^{2}[/tex]) = 1519.87

OR

hypotenuse ([tex]c^{2}[/tex])= 1676.31

Explanation:

If 1600 ft = hypotenuse and 500 ft = side

[tex]1600^{2}[/tex] = [tex]500^{2}[/tex] + [tex]b^{2}[/tex]

2560000 = 250000 + [tex]b^{2}[/tex]

2560000 - 250000 = [tex]b^{2}[/tex]

2310000 = [tex]b^{2}[/tex]

[tex]\sqrt{2310000}[/tex] = [tex]\sqrt{b^{2} }[/tex]

[tex]b[/tex] = 1519.87

side 2 = 1519.87

OR

If 1600 ft = side 1 and 500 ft = side 2

[tex]1600^{2}[/tex] + [tex]500^{2}[/tex] = [tex]c^{2}[/tex]

2560000 + 250000 = [tex]c^{2}[/tex]

2810000 = [tex]c^{2}[/tex]

[tex]\sqrt{2810000}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]c[/tex] = 1676.31

hypotenuse = 1676.31

The value of y so that WX ⊥ YZ is y = 4 .

In the question ,

it is given that

the line WX is perpendicular to line YZ

and the end points of WX is W(2,-3) and X(-4,9)

and the end points of YZ is Y(5,y) and Z(-1,1) .

let the slope of line WX = m₁

and slope of line YZ = m₂ .

we know that when two lines are perpendicular , then

m₁ * m₂ = -1

m₁ = (9-(-3))/(-4-2)

and m₂ = (1-y)/(-1-5)

Substituting the values of m₁ and m₂ in the equation m₁ * m₂ = -1  ,

we get

(9-(-3))/(-4-2) * (1-y)/(-1-5) = -1

(9+3)/(-6) * (1-y)/(-6) = -1

12/(-6) * (1-y)/(-6) = -1

-2* (1-y) = 6

-2 + 2y = 6

2y = 6+2

2y = 8

y = 4

Therefore , the value of y is = 4 .

The given question is incomplete , the compete question  is

Given W(2, -3) X(-4, 9) Y(5, y) and Z(-1, 1) . find the value of y so that WX ⊥ YZ ?

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The 99% confidence interval for the population proportion of printers that are used in small businesses is 0.150<p<0.674.

Do we use the sample size or do we use X two to get to 35? We visited 30 places. We are trying to locate the B hats that X gave us. Over 35, we are tested. Our margin of error is 7.751 over two, which is the same as the confidence interval. This gives us seven points. 258 were present. Since our alpha is 1 – 0.9 and they will want us, we wish to find that critical that is set out for two. We get 6 now they have provided us with a minimal sample size, apologize. Is it finished? If you will, visualizeus tying our p hats without the p hat on one. Yes, indeed. We get 1.645 over.

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The true statements about the slope are:

The graph that completes the question is added as an attachment'

From the question, we have

Slope of the trend line = 15

This can be represented as

Slope = 15

As a general rule

These mean that (a) and (e) are true options

Also, we have:

Slope = 15

Multiply by 1000

Value(1000) = 15 * 1000

Evaluate

Value(1000) = 15000

This means that sales increase $15,000 as ads increase by $1,000.

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Answer:

I need your statements please

Step-by-step explanation:

The equation for the line of best fit where x represents the month and y represents the time is: y = −2.14x + 45.

In order to determine a linear equation of the line of best fit (trend line) that models the data points contained in the table, we would have to use a scatter plot.

In this scenario, the number of months would be plotted on the x-axis of the scatter plot while the time (minutes) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of months and time in the table, a linear equation of the line of best fit is given by:

y = -2.14x + 45

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Answer:

The equation for the line of best fit where x represents the month and y represents the time is: y = −2.14x + 45.

Step-by-step explanation:

Answer:

9/40 of the book was left to read

Step-by-step explanation:

Required to find the fraction of remainder of the book:

first we need to find the (LCM) lowest common multiple so both fractions can have common denominator in order to complete addition or subtraction.

[tex] \frac{3}{8 } + \frac{2}{5} [/tex]

Look at the denominators, we see there is 8 and 5 so that means we have to list the multiples of both numbers until a common is found.

multiples of:

8 = 8, 16, 24, 32, 40

5 = 5, 10, 15, 20, 25, 30, 35, 40

from this we can distinguish that the LCM is 40.

Next we need to multiply each numerator of the fraction by the number of times it took for the denominator to reach the LCM.

It took 8 five multiples to reach the LCM so therefore its new numerator will be 3×5 = 15

[tex] \frac{5}{8} to \: give \frac{15}{40} [/tex]

It took 5 eight multiples to reach the LCM so therefore its new numerator will be 2×8 = 16

[tex] \frac{2}{5} to \: give \: \frac{16}{40} [/tex]

finally we can add but values together and subract from the whole to find the remainder.

[tex] \frac{15}{40} + \frac{16}{40} = \frac{31}{40} [/tex]

in total she read 31/40 of the book.

[tex] \frac{40}{40} - \frac{31}{40} = \frac{9}{40} [/tex]

and the remainder which she did not read was 9/40

The value of the given inequality mode function |2x + 4| ≥ 5 will be x  ≥ 1/2 and x ≤ -4.5.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given mode function,

|2x + 4| ≥ 5

For 2x + 4 > 0 or x > -2

2x + 4  ≥ 5

2x  ≥ 1

x  ≥ 1/2

For 2x + 4 < 0 or x < -2

-(2x + 4) ≥ 5

2x + 4 ≤ -5

2x ≤ -9

x ≤ -9/2

x ≤ -4.5

Hence "The value of the given inequality mode function |2x + 4| ≥ 5 will be x  ≥ 1/2 and x ≤ -4.5".

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The story problem that would use this equation: y = 5x + 3 is the cost of a chair is 3 more than 5 times the cost of the table and the cost of the table is x.

The equation is given in the question:

y = 5x+3

To satisfy this equation, we would construct a story problem:

Robbin goes to buy a chair the last week.  Now, the cost of the table is x but the seller says that the cost of the chair he wants to buy is 3 more than 5 times the cost of the table.

Hence, the story problem that would use this equation: y = 5x + 3 is the cost of a chair is 3 more than 5 times the cost of the table and the cost of the table is x.

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The probability that the sample mean is greater than 105 is 0.0384.

A simple random sample is a subset of persons chosen at random from a bigger collection. It is the process of randomly selecting a sample.

A simple random sample is a population subset chosen at random. Each member of the population has a precisely equal probability of being selected in this sampling approach, reducing the likelihood of selection bias.

Random sampling ensures that the results received from your sample are close to what would have been achieved if the full population had been measured.

The population mean is  μ =100.

The population standard deviation is σ= 20.

n=50 is the sample size

Let [tex]\bar{x}[/tex] be the mean of the sample

The chance that the sample mean is greater than 105 is then given by :

P( [tex]\bar{x}[/tex]>105)=1-P( [tex]\bar{x}[/tex]≤105)

=1-P(( [tex]\bar{x}[/tex]-μ)/(σ/√n) ≤ (105-100)/(20/√50))

=1-P(z≤1.77)

=1-0.96164

=0.03836≈0.0384

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The complete question is:

"According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than 105? (Round answer to 4 decimal places.)"

Answer:

x=5

Step-by-step explanation:

Because we know the sum of the interior angles should be 180, we can use this to create an equation to solve for x.

60+(7x+3)+(180-20x)=180

Simplify to find that x = 5

If you're confused about where the 180-20x comes from:

The line it lays on is straight, meaning the angle it creates is 180 degrees.

Thus, 180 - known angle = unknown angle.

Answer:

the answer is c, x=5

Step-by-step explanation:

now, if we look at the pic, there is already one angle given.

and we know that sum interior angles of a triangle must be 180;

so the sum of the other two angles is: angle 2 +angle 3=180-60.

now, let's pick any number and put it into x.

first, if we put 15 into x: 7(15)+5=120,

so 180-(120+60)=0. and for there is another angle, it is invalid.

if we put 6: 7(6)+5=47,

180-(60+47)=73.

let's look at the third angle.

for x=6, the angle UBI is 120°. and we also know that the sum of angles on a horizontal line is always 180°, so 180-120=60, and for the third angle is NOT 73°, this one is also invalid.

if x=5: 7(5)+5=40, 180-(60+40)=80.

the angle UBI= 100°, 180-100=80°;

for 80°+60°+40° equals 180°, the answer c is correct.

The value of a and b based on the given table when the number of pairs of tiles is 2 is given by 30 cm and 40 cm respectively.

When,

number of pairs of tiles is 1

Width of each tile = 20 cm

Length of each tile = 30 cm

number of pairs of tiles is 3

Width of each tile = 40 cm

Length of each tile = 50 cm

number of pairs of tiles is 2

Width of each tile, a = 20 cm + width of each tile

= 20 cm + 10 cm

= 30 cm

a = 30 cm

Length of each tile, b = 30 cm + width of each tile

= 30 cm.+ 10 cm

= 40 cm

b = 40 cm

In conclusion, the value of a and b from the above diagram is 30 cm and 40 cm respectively.

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Is it 102,8100? If not, tell me. I'll fix it!

Leaping deer company purchased a tractor at a cost of $440,000. The tractor has an estimated residual value of $40,000 and an estimated life of 8 years, or 12,000 hours of operation. The tractor was purchased on January 1, 2015 and was used 2,400 hours in 2015 and 2,200 hours in 2016.

To find out which method of depreciation will produce maximum depreciation, Depreciation expense for 2018 shall be calculated using all methods.

1) Double-declining balance method: Under this method, depreciation is charged to an accelerated rate to the asset by applying double depreciation instead of a regular depreciation rate. This rate is applied to the value of the depreciable assets.

Depreciable Value of Tractor = Gross Value - Salvage Value = $240,000 - $40,000 = $200,000

The regular rate of depreciation = 100% / Life of Tractor = 100% / 8 Years = 12.5%

Double-declining rate of depreciation = Regular rate X 2 = 12.5 % X 2 = 25%

Depreciation expense for 2018 = Depreciable value of tractor X Dobule-decling rate

= $200,000 X 25%

= $50,000

Depreciation expense as per double-declining method = $50,000

2) Straight-line method: Under this method, the value of the depreciable asset is spread over the useful life of the asset evenly.

Depreciation for 2018 = Useful life of Tractor / Useful life

= $200,000 / 8 Years

= $25,000

Depreciation expense as per straight line method = $25,000

3) Units of production method: Under this method, the depreciable value of assets is depreciated with the level of usage with respect to the overall capacity of assets with respect to usage. Hence, more usage shall lead to higher depreciation.

Total hours available during the life of asset = 12,000

Depreciation to be charged for each hour of usage = Depreciable value / Total hours

= $200,000 / 12,000 Hours

= $16.67 per hour

Depreciation for 2018 = Total hours of usage in 2018 X Depreciation per hour

= 3,800 Hours X $16.67

= $63,346

Depreciation under units of production method = $63,346.

Hence, Highest amount of depreciation is produced under units of production method as tractor has been used for more than one-third of its usage hour capacity. As the other two methods do not take into account the level of usage, their depreciation is just based on time. Hence, Depreciation under the unit production method is highest.

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The balance of jane at the end of the month is $9,348.24

Why not explain interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as an annual percentage of the loan amount. The interest rate on the loan is this proportion.

At the beginning of the December balance was $8,421.89

She deposited totally $3,721.33
So the balance now is $12,143.22

Now she wrote checks of totaling amount $2,794.43

So now her balance is $9,348.79

Now she paid maintenance fee of $14

So now her balance is $ 9,334.79

Now she  earned $13.45 in interest on the account

So now her balance is $9,348.24

Hence, The balance of jane at the end of the month is $9,348.24

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Answer:

y = -4x^2 - 40x - 103

Step-by-step explanation:

to get the standard form, you have to formulate the equation as

y = ax^2 + bx + c

we have to expand the (x+5)^2

y = -4((x+5)^2) - 3 = -4(x^2 + 10x + 25) - 3 = -4x^2 - 40x - 100 - 3 = -4x^2 - 40x - 103

The 90% confidence interval for the true difference between the proportions of rural and city voters who favor gun control is of:

(0.11, 0.346).

For each sample, the proportion and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences is given by:

The bounds of the confidence interval are given by the rule defined as follows:

p ± zs

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Then the bounds of the interval are obtained as follows:

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