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3 years ago

10

The loan that Nate and Isaac got from their parents was at 2% interest for one year. How much will the boys pay in interest on t

heir loan of \$2,500 ? Show your work .

1 answer:

kirill [66]3 years ago

3 0

Answer: they will have to pay 50 dollars

Step-by-step explanation: you have to multiply 2,500 by 0.02 as it is the same as a percent then you should get 50

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Rosa can make 8 dozen cupcakes in 3 hours. How many dozen cupcakes can she make if she has 10 1/2 hours to bake the cupcakes

Scorpion4ik [409]

Answer: 28 dozen

Step-by-step explanation:

If 8 dozen cupcakes can be made in 3 hours:

8/3=2.6666...

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Select all ratios equivalent to 7:4

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If the coordinates of A are (1, 1) and the midpoint of AB is

yuradex [85]

Answer:

The coordinates of B are (-5, -1).

Step-by-step explanation:

You can make a linear relationship. Since AB is <em>1 unit down and 3 units to the left of</em> A, B must be <em>1 unit down and 3 units to the left of</em> AB.

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3 years ago

The profit function of a manufacturer, in dollars, when x units of a certain commodity are produced and sold is given by

Annette [7]

Answer:

Derivative: P’(x) = 200 - 2x

If P’(x) = 0 , x = 100

Therefore P’ is positive and P increases until x = 100

So the maximum units to maximize profits is 100 units

And for 100 units the profit in dollar is:

20000 - 10000 = 10000

10000 dollars

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3 years ago

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m

SVETLANKA909090 [29]

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