A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded: Advertising Costs ($) 40 Sales ($) 385 20 400 25 395 20 365 475 30 50 440 40 490 20 420 50 560 525 40 25 480 50 510 a) Plot a scatter diagram, you may use Excel. (5 marks) b) Find the equation of the regression line to predict weekly sales from advertising expenditures. (6 marks) c) Estimate the weekly sales when advertising costs are $35. (2 marks) d) Plot the residuals versus advertising costs. Comment. (5 marks) e) Using the t-test, test the hypothesis that 6 against the alternative that B< 6. Use a 0.025 level of significance. (10 marks) f) Construct a 95% confidence interval for the average weekly sales when $45 is spent on advertising. (5 marks) g) Construct a 95% prediction interval for the average weekly sales when $45 is spent on advertising (5 marks) h) What is the percentage of variations in weekly sales explained by the advertising costs? (2 marks)

Based on the given parameters, the car would be $497.9 expensive in 9 years

The given parameters about the compound interest are

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R)^t - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this case, we introduce the variable n

So, we have

A = P(1 + R/n)^nt

Where n is the number of times in a year

i.e. n = 12

Substitute the known values in the above equation

A = 325 * (1 + 4.75%/12)^(12 * 9)

Evaluate the percentages and the quotients

A = 325 * (1 + 0.0039583)^(108)

Evaluate the sum

A = 325 * (1 .0039583)^(108)

Evaluate the exponent

A = 325 * 1.532

Evaluate the product

A = 497.9

Hence, the value of the investment after 9 years is $497.9

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In a random sample of 125 people, 42 of them owned two vehicles. The sample proportion of people who own two vehicles is 0.336

The percentage of people in a sample that exhibit a particular attribute or trait is expressed by the sample proportion (p).

Divide the total number of individuals (or things) in the sample by the number of individuals (or items) who share the characteristic of interest to obtain the sample proportion.

p = x/n, where x stands for the sample's success rate and n for sample size, gives the sample proportion p.

According to the question,

Sample size = 125

Number of people owned two vehicles = 42

Sample Proportion (p) = x/n

=> p = 42 / 125

=> p = 0.336

Therefore , The sample proportion of people who own two vehicles is 0.336

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Dhara's Lifetime earnings when she retires at the age of 65 is;  $1,901,250

The first thing we will do here is to find the difference between Dhara's current age and the age he will be when he retires. Thus;

Difference in age = 65 - 26

Difference in age = 39 years old

Bi- weekly wage = 52 weeks/2

Bi- weekly wage = 26 paychecks per annum

Thus;

Lifetime earnings = $1875.00 × 26 paychecks per annum × 39

Lifetime earnings = $1,901,250

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The area and the circumference of the circular plate is 452.16 in² and  75.36 in

What is area and circumference of circular plate?

Area of circular plate , A = πr²

=3.14 * 12 * 12

= 452.16 in²

Circumference of the circular plate, C = π * 2r

= 3.14 * 2 * 12                
= 75.36 in

Hence, the area and the circumference of the circular plate is 452.16 in² and  75.36 inches.

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The information that we need to come up with her demand curve for milk is D how much milk she buys at each price point

A demand curve is a graph that shows the relationship between a commodity's price and the amount that is desired at that price. Demand curves can be applied to the price-quantity relationship for either a specific consumer or for every consumer in a given market.

Individual demand curves and market demand curves are the two types of demand curves. It shows a graphic depiction of the demand schedule. It should be noted that based on the information, the quantity is needed. The correct option is D.

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The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)

From the question, we have the table of values as the parameters that can be used in our computation:

From the table, we have

Table 1

(x, y) = (0, -3) and (4, 13)

A linear equation is represented as

y = mx + c

Where

Slope = m

c = y when x = 0

This means that

c = -3

So, we have

y = mx - 3

The point (4, 13) implies that

13 = m * 4 - 3

So, we have

4m = 16

m = 4

So, the equation is

y = 4x - 3

Table 2

(x, y) = (0, 4) and (4, 6)

A linear equation is represented as

y = mx + c

This means that

c = 4

So, we have

y = mx + 4

The point (4, 6) implies that

6 = m * 4 + 4

So, we have

4m = -2

m = -1/3

So, the equation is

y = -1/3x + 4

Substitute y = -1/3x + 4 in y = 4x - 3

-1/3x + 4 = 4x - 3

So, we have

-x + 12 = 12x - 9

Evaluate the like terms

13x = 21

Divide

x = 21/13

y = -1/3x + 4 implies that

y = -1/3 x 21/13 + 4

So, we have

y = -7/13 + 4

Evaluate

y = 45/13

So, the solution is (21/13, 45/13)

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Answer:

510

Step-by-step explanation:

1200-860x3 /2 = 510

Kayan will have enough money in the bank to get the phone.

It is important to note that percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since Aunt Georgia has $1000 and bought a gadget for $300, the remaining amount will be:

= $1000 - $300

= $700

Therefore, since also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99, she will have money left. This will be:

= $700 - $649.99

= $50.01

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Complete question

Aunt Georgia has $1000 and bought a gadget for $300 She also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?

Therefore the solution to the given question is option d)128.78 for this particular equation.

Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

Here,

=> v/9.4 = 13.7

=> v = 13.7*9.4

=> v= 128.78

Therefore the solution to the given question is option d)128.78 for this particular equation

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Answer:

  none of the above

  (1 -4n +3n^2)(-1)^n

Step-by-step explanation:

You have the recursive relation {a[0]=1, a[1]=0, a[2]=5, a[n]=-3a[n-1] -3a[n-2] -a[n-3]} and you want to know the explicit relation.

The given initial value a[0] = 1 rules out choice A.

The value a[1] = 0 rules out choices B and C.

We observe that changing the sign of the constant in the first choice will make it match the sequence:

  (1 -4n +3n^2)(-1)^n . . . . . . the solution for the recursive equation

Answer: To determine how much 5 inches of wire would cost at the same rate as 12 inches of wire, we can first determine the rate at which the wire is being sold by dividing the cost of the wire by the length of the wire:

36 cents / 12 inches = 3 cents/inch

We can then use this rate to determine the cost of 5 inches of wire by multiplying the rate by the length of the wire:

3 cents/inch * 5 inches = 15 cents

Therefore, 5 inches of wire would cost 15 cents at the same rate as 12 inches of wire.

The number of employees with petrol cars is 423

In exponential decay, a quantity initially drops gradually before decreasing quickly. Finding the exponential drop of a fast reduction over time is made easier by the exponential decay formula.

The exponentially decreasing formula is used to calculate the radioactivity decay, population decay, and half-life.

The formula for Exponential Decay is given by

Here we have

In 2010, a total of 2187 of the employees at Zoe's company owned a petrol car.

In 2013, there were 1029 employees with petrol cars.  

The number of cars decreases exponentially,  

As we know the formula for Exponential Decay, A = P (1 - r)^t

From the given data,  a = 2187 and t = 3

The number of cars decreased = 2187 (1 - r)³

=> 2187 (1 - r)³ = 1029  

=> (1 - r)³ = 1029/2187

=> (1 - r)³ = 343/729  

=> (1 - r)³ = 7³/ 9³

=> 1 - r = 7/9

=> r = 1 - 7/9

=> r = 2/9

=> r = 0.2222

The Number of cars in 2017 i.e after 4 years from 2013

=> (1029)(1 - 0.2222)⁴

=> 423.0721516 ≅ 423          

Therefore,

The number of employees with petrol cars is 423

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Answer: 21

Step-by-step explanation: 12 in 4 minutes means every minute 3 marshmallows are roasted, 4x3=12, so add three more minutes and you get 21. 7x3=21

Answer: 21 marshmallows

Step-by-step explanation:

4 minutes x 1.75 = 7 minutes

multiply marshmallows by 1.75 as well.

12 marshmallows x 1.75 = 21 marshmallows

The probability of flipping a coin 50 times and getting tails 22 times or fewer is given as follows:

A. 24%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are given as follows:

n = 50, p = 0.5.

Hence the mean and the standard deviation are obtained as follows:

Using continuity correction, the probability of 22 or fewer tails is the p-value of Z when X = 22.5, hence:

Z = (22.5 - 25)/3.54

Z = -0.71

Z = -0.71 has a p-value of 0.2709.

Which is closest to 24%.

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By using the concept of discount, it can be calculated that

The bike should be marked at $440

What is discount?

Sometimes during sale, the items are sold at a reduced price from the original price of the item. The difference between the reduced price and the original price of the item is called discount.

Price paid by John for a new mountain bike = $280

Markup price = [tex]\frac{10}{100} \times 280[/tex] = $28

Price after markup = $(280 + 28) - $308

Let the marked price be $x

Rate of discount = 30%

Discount = [tex]\frac{30}{100}\times x[/tex]

Price after discount = [tex]x - \frac{30}{100}\times x[/tex]

                                 = [tex]\frac{100x - 30x}{100}[/tex]

                                 = [tex]\frac{70}{100}x[/tex]

By the problem,

[tex]\frac{70}{100}x = 308\\x = \frac{308 \times 100}{70}\\[/tex]

x = $440

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Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

According to the given information

A.

Monthly payment for 20 year mortgage [tex]& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \[/tex]\

Monthly payment for 25 year mortgage [tex]& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\[/tex]

B

Total cost of interest for 20 year mortgage [tex]& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\[/tex]

Total cost of interest for 25 year mortgage [tex]$=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &[/tex]

C.

Difference in interest paid [tex]& $=\mathrm{B} 7-\mathrm{B} 6$ &[/tex] = Total interest for 25 year loan-total interest for 20 years

A.

Monthly payment for 20 year mortgage [tex]& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\[/tex]

Monthly payment for 25 year mortgage [tex]& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\[/tex]

B.

Total cost of interest for 20 year mortgage = [tex]& $\$ 197,343.88$ & $=$[/tex]  total monthly payments-loan taken

Total cost of interest for 25 year mortgage = [tex]& $\$ 280,084.40$ & $[/tex] = total monthly payments-loan taken

C.

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

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The compound interest is 61.342 years.

What is compound interest?

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

To find the time period the interest must be compounded quarterly.

Calculated twelve times a year is interest that is compounded monthly. Interest is calculated on a quarterly compound basis, four times a year.

Given that;

               A = 1700                         P = 500

                 r = 2%                          n = 4

                   = 2/100

                 r = 0.02 /year

 Using the formula  A=P(1+r/n)ⁿt  find the time period (t)

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )

t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )

t = 61.342 years

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Answer:

I think that's 11,8

Step-by-step explanation:

Hope its right

The required proportional relationship is given as y = 4x and shown in the graph.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
According to the question,
The proportional relationship gives the number of liters of water the facet supplies, y, after x minutes,
y = kx - - - - - (1)
Put x = 3 so y = 4
12 = k[3]
k = 4

From equation 1,
y = 4x

Thus, the required proportional relationship is given as y = 4x and shown in the graph.

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Answer: 57 dollars, hope this helps!

The absolute maximum is 1.29, which occurs at x= 9

What is absolute extrema?

An absolute extremum  of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.

Main body:

Given =

f(x) = [tex](x^{2} -64)^{1/11[/tex]

f' (x) = derivative of function f(x)

f'(x) = 1/11[tex](x^{2} -64)^{-10/11[/tex] . 2x

     = [tex]2 \frac{x}{11}[/tex][tex](x^{2} -64)^{-10/11[/tex]

putting f'(x) = 0

2x/11 [tex](x^{2} -64)^{-10/11[/tex] = 0

         [tex](x^{2} -64)^{-10/11[/tex] = 0

                     [tex]x^{2} -64[/tex] = 0

 x² = 64

x = ±8

We are given interval [-8,9].

Hence, calculating f(x) at -8, 8, 9.

f(-8) =  0

f(8) = 0

f(9) = [tex]17^{1/11}[/tex]

      = 1.29

Hence, absolute maximum value is 1.29 at x=9.

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Answer:

x=18

36/2=18

all good.

The value of AB is 6 units.

What are Similar Rectangles ?

Similar rectangles states that the corresponding sides are in proportion.Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.

As per the statement:

Rectangle ABCD is similar to rectangle WXYZ.

WX = 8 feet, AD = 12 feet and WZ = 16 feet.

Since. Rectangle ABCD and rectangle WXYZ are similar

then;

their corresponding sides are in proportion:

[tex]\frac{AB}{WX} =\frac{BC}{XY} = \frac{CD}{YZ} =\frac{AD}{ZW}[/tex]

To find the value of AB:

[tex]\frac{AB}{WX} =\frac{AD}{ZW}[/tex]

Substitute the given values we have;

[tex]\frac{AB}{8} =\frac{12}{16}[/tex]

Multiply both sides by 8 we have;

[tex]AB = \frac{12}{16} * 8 = 6[/tex]

Therefore, the value of AB is 6 units.

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So the RHS of the given equation is incorrect.

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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Answer:

Step-by-step explanation:

First find the hourly rate Carmen makes. You can find it by dividing the amount she made by the number of hours she worked

209 / 11 = 19

Now multiply that rate by the amount of hours you want to figure out.

19 * 8 = 152

Answer: $152

Step-by-step explanation:

Divide 209 by 11 to find how much money she gets for 1 hour of work ($19) then multiply that value by 8.

The required length of each panel would be 1 feet.

Given that,
A mural is 7  feet long and is divided into 7 equal-length panels. How many feet long is each panel to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
The required length of each panel = total length of the panel / 7
                                                     = 7 / 7 = 1 feet

Thus, the required length of each panel would be 1 feet.

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The margin of error for 16 eggs with sample means 2 ounce and standard deviation as 42 ounces is   18.407   .

In the question ,

it is given that ,

the number of eggs = 16

the sample means weight is = 2 ounce .

the standard deviation is = 42 ounces .

we have to find the margin of error .

degree of freedom is 16 - 1 = 15 .

and the t score for the 90% confidence interval is

t₁₅,₀.₀₅ = 1.753

So , the margin of error is =  t₁₅,₀.₀₅×(standard deviation/√n)

Substituting the values ,

we get ,

= 1.753×(42/√16)

On simplifying further ,

we get ,

= 18.407

Therefore , the margin of error is = 18.407 .

The given question is incomplete , the complete question is

A sample of 16 eggs yields a sample mean weight of 2.00 ounces and a sample standard deviation = 42.0 ounces, find the margin of error in estimating a confidence interval estimate at the 90% level of confidence. Round your answer to three decimal places. You may assume that egg weights are normally distributed .

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