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Mumz [18]
3 years ago
14

Jack is a car salesman who works strictly on commission. For every car he sells, he earns a 2% commission. Cars sell for $35,000

each. How many cars does jack need to sell in order to reach his target income of $5,000 for the end of the month?
Mathematics
1 answer:
Nadya [2.5K]3 years ago
4 0
First we need to find 2% of 35,000

2% equals 0.02 so we'll multiply 35,000 by 0.02

35,000 × 0.02 = 700

for every car he sells jack gets $700

now we need to divide that into 5,000

5,000 ÷ 700 = 7.14

now since you cannot sell 0.14 of a car you need to round up

he needs to sell 8 cars to meet his target income
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An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m
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Answer:

a) y=-6.254 x +75.064  

b) r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y)     Interest Rate (X)

       22                               9.2

       20                               7.6

       10                                10.4

       45                                5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

m=\frac{S_{xy}}{S_{xx}}  

Where:  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}  

With these we can find the sums:  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225  

And the slope would be:  

m=\frac{-91.225}{14.5875}=-6.254  

Nowe we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125  

\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25  

And we can find the intercept using this:  

b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064  

So the line would be given by:  

y=-6.254 x +75.064  

Part b

For this case we need to calculate the correlation coefficient given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937  

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

6 0
3 years ago
there are 6 buses transporting students to a baseball game with 32 students on each bus.each row at the baseball stadium seats 8
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Answer:

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Step-by-step explanation:

4 0
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Answer:

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L = 6 cm

W = 5 cm

H = 20 cm

Surface area = 2(6*5 + 6*20 + 5*20)

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L = 12 cm

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Area = 12*6

= 72 cm²

✅Surface area of the composite figure = 500 + 288 - 2(72)

= 644 cm²

7 0
2 years ago
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