13x + 7x - 4x = -40
combine like terms o0n the left
16x = -40
divide both sides by 16
x = -5/2 or -2.5
N% x 1.60 = 6 (I turned it from English to math)
Can't move n% back two places to make it a decimal so I will move the number I am multiplying by n% back two places instead.
Here is a sample to show you why it works. .34 x 57 = 34 x .57
So
.016n = 6 (.016 is 1.60 decimal moved back two places)
Now divide both sides by .016
<u>.016</u>n = <u>6
</u><u />.016 .016 n = 375%
Why is the percent over 100% you might ask?
What % of 1.60 is 1.60 (Answer - all of it or 100%)
So What % of 1.60 is 6 - the number 6 being much bigger than 1.60, it is not surprising that the percent is more than 100.
What % of 1.60 is 1.60 - 100%
What % of 1.60 is 3.20 - 200% (notice that 3.20 is twice 1.60)
What % of 1.6 is 4.80 - 300% (notice that 4.80 is three times 1.60)
What % of 1.6 is 6.40 - 400% (notice that 6.40 is four times 1.60)
6 (the number in the problem) is just a bit less than 6.40 so 375% makes a lot a sense.
Hope you found this helpful.
Answer:
(B) 
Step-by-step explanation:
(A) The given expression is: 
=
The value of this expression is 8 which is greater than the base of the expression that is 2.
(B) The given expression is:
=
=
The value of this expression is 0.09 which is smaller than the base of the given expression that is 0.83.
(C) The given expression is: 
=
The value of this expression is 9 which is greater than the base of the given expression that is 3.
(D) The given expression is: 
=
The value of this expression is 256 which is greater than the base of the given expression that is 4.
Hence, Option B is correct.
Answer:
a) y = 0.74x + 18.99; b) 80; c) r = 0.92, r² = 0.85; r² tells us that 85% of the variance in the dependent variable, the final average, is predictable from the independent variable, the first test score.
Step-by-step explanation:
For part a,
We first plot the data using a graphing calculator. We then run a linear regression on the data.
In the form y = ax + b, we get an a value that rounds to 0.74 and a b value that rounds to 18.99. This gives us the equation
y = 0.74x + 18.99.
For part b,
To find the final average of a student who made an 83 on the first test, we substitute 83 in place of x in our regression equation:
y = 0.74(83) + 18.99
y = 61.42 + 18.99 = 80.41
Rounded to the nearest percent, this is 80.
For part c,
The value of r is 0.92. This tells us that the line is a 92% fit for the data.
The value of r² is 0.85. This is the coefficient of determination; it tells us how much of the dependent variable can be predicted from the independent variable.
