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Arte-miy333 [17]

3 years ago

14

jonathan bought a new computer for $2,016, using the electronics store's finance plan. he will pay $112 a month for 18 months. w

hich equation can jonathan use to find out how much money he still owes after each month of the plan?

1 answer:

vekshin13 years ago

6 0

Y - the money he still owes,
x - the number of months ( from x = 0 to x = 18 ):
y = 2,016 - 112 x

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(-2/3)^7*(3/5)^6*(5/6)^5*(1/3)^-7 simplify of law of indices

Wewaii [24]

Answer:

$\boxed {-\frac{12}{5}}$

Step-by-step explanation:

Solve the following expression:

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $-\frac{2}{3}$ to the power of $7$ :

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{3}{5}$ to the power of $6$ :

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{2187}$ and $\frac{729}{15625}$ :

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{5}{6}$ to the power of $5$ :

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{46875}$ and $\frac{3125}{7776}$ :

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{1}{3}$ to the power of $-7$ :

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times 2181$

-Multiply both the $-\frac{4}{3645}$ and $2187$ :

$-\frac{4}{3645} \times 2181$

$\boxed {-\frac{12}{5}}$

Therefore, the final answer is $-\frac{12}{5}$ .

3 0

3 years ago

Five observations taken for two variables follow.

I am Lyosha [343]

Answer:

a) Figure attached

b) If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

c) $Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}$

We can find the numerator like this:

$\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106$

And then:

$Cov(X,Y) = \frac{106}{5-1}=26.5$

d) $r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693$

Step-by-step explanation:

Part a

For this part we use excel in order to create the scatterplot and we got the result on the figure attached.

Part b

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

Part c

The sample covariance is defined as:

$Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}$

We can find the numerator like this:

$\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106$

And then:

$Cov(X,Y) = \frac{106}{5-1}=26.5$

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

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

For our case we have this:

n=5 $\sum x = 80, \sum y = 50, \sum xy = 906, \sum x^2 =1552, \sum y^2 =586$

$r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693$

So then the correlation coefficient would be r =0.693

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3 years ago

List the first 5 multiples of, find all the factors of 7

Aleksandr [31]

What # do you need the first five multiples for? and the only factors for 7 are one and seven because it is a prime number!

8 0

3 years ago

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there are 3 boys for every 2 girls in the class. there are 90 students total. how many total girls? how many total boys?

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Answer: There is 36 girls and 54 boys.

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