Brainlist if you answered it correctly and give a well done explanation

John received $9,000 in student loans. Part of the money he was able to borrow at 7% simple interest, but on the rest of the mon

lidiya [134]

He borrowed "a" at 7% and "b" at 8.25%

now, whatever "a" and "b" are, we know, his student loan was 9000, thus
a+b = 9000

now, he owes 7% or 7/100 for "a", what's 7% of a? well, 7/100 * a or 0.07a

he owes 8.25% of "b", how much is 8.25% of b? well, 8.25/100 * b or 0.0825b

now, we know, at the end of the year, he owed for both loans, 706.25 in interest
thus we know that 0.07a + 0.0825b = 706.25

thus $\bf \begin{cases}
a+b=9000\implies \boxed{b}=9000-a\\
0.07a+0.0825b=706.25\\
----------\\
0.07a+0.0825\left(\boxed{9000-a} \right)=706.25
\end{cases}$

solve for "a", to see how much he borrowed at 7%

what about "b"? well, b = 9000-a

6 0

3 years ago

The LCM of 12ab² and 3ab³

lions [1.4K]

Answer:3ab^2 or 12ab^3

i think this is it

Step-by-step explanation:

8 0

3 years ago

A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

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

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

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:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

3 years ago

What is the equation of the line in slope-intercept form?

Anna35 [415]

<span>To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y -intercept--this should be of the form (0, b) . ... Therefore, the equation for this line is y = - x + 2 .</span>

5 0

3 years ago

Read 2 more answers

Is 58 a prime or composite number

Nata [24]

58 is a composite number because it has more than 3 factors.
Composite numbers are numbers that has 3 or more factors.
Prime numbers are numbers that only has 2 factors.

3 0

3 years ago