Answer:
![\text{Smaller square's 15 inches, Bigger square's 18 inches}](https://tex.z-dn.net/?f=%5Ctext%7BSmaller%20square%27s%2015%20inches%2C%20Bigger%20square%27s%2018%20inches%7D)
Step-by-step explanation:
GIVEN: The length of each side of a square is
inches more than the length of each side of a small square. The sum of the areas of the square is
inches.
TO FIND: the lengths of the sides of the two squares.
SOLUTION:
let the length of side of small square be ![\text{x}](https://tex.z-dn.net/?f=%5Ctext%7Bx%7D)
Area of small square ![=(\text{side})^2=\text{x}^2](https://tex.z-dn.net/?f=%3D%28%5Ctext%7Bside%7D%29%5E2%3D%5Ctext%7Bx%7D%5E2)
As length of each side of bigger square is
more than the smaller square
length of side of bigger square ![=\text{x}+3\text{ inches}](https://tex.z-dn.net/?f=%3D%5Ctext%7Bx%7D%2B3%5Ctext%7B%20inches%7D)
Area of bigger square ![=(\text{x+3})^2](https://tex.z-dn.net/?f=%3D%28%5Ctext%7Bx%2B3%7D%29%5E2)
Also
Sum of areas of both square ![=549\text{ inch}^2](https://tex.z-dn.net/?f=%3D549%5Ctext%7B%20inch%7D%5E2)
![(\text{x})^2+(\text{x+3})^2=549](https://tex.z-dn.net/?f=%28%5Ctext%7Bx%7D%29%5E2%2B%28%5Ctext%7Bx%2B3%7D%29%5E2%3D549)
![2\text{x}^2+6\text{x}+9=549](https://tex.z-dn.net/?f=2%5Ctext%7Bx%7D%5E2%2B6%5Ctext%7Bx%7D%2B9%3D549)
![\text{x}^2+3\text{x}-270=0](https://tex.z-dn.net/?f=%5Ctext%7Bx%7D%5E2%2B3%5Ctext%7Bx%7D-270%3D0)
![\text{x}=15,-18](https://tex.z-dn.net/?f=%5Ctext%7Bx%7D%3D15%2C-18)
as the length of side can never be negative
![\text{x}=15](https://tex.z-dn.net/?f=%5Ctext%7Bx%7D%3D15)
length of side of smaller square ![=15\text{ inches}](https://tex.z-dn.net/?f=%3D15%5Ctext%7B%20inches%7D)
length of side of bigger square ![=\text{x}+3\text{ inches}](https://tex.z-dn.net/?f=%3D%5Ctext%7Bx%7D%2B3%5Ctext%7B%20inches%7D)
![=18\text{ inches}](https://tex.z-dn.net/?f=%3D18%5Ctext%7B%20inches%7D)
Hence the length of smaller and bigger square are
and
respectively.
Answer:
![3\sqrt{3}](https://tex.z-dn.net/?f=3%5Csqrt%7B3%7D)
Step-by-step explanation:
This triangle is a 30°-60°-90° triangle, so you should always remember the rule shown in the picture. Because y is across from the 60° angle, it will be
. 3 is x because it is across from the 30° angle, so y will be
.
Answer:
16 times
Step-by-step explanation:
Membership cost:
C = 135 + 2x
Non-members:
C = 11x
____
135 + 2x = 11x
135 = 9x
x = 15
The cost would be the same after renting 15 times, so after 16 times the cost would be cheaper for a member.
Answer:
The value of the test statistic is -3.14.
Step-by-step explanation:
Test statistic:
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which X is the sample mean,
is the expected value,
is the standard deviation and n is the size of the sample.
A company advertises that its cans of caviar each contain 100 g of their product.
This means that ![\mu = 100](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100)
They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. Sample of 8 cans.
This means that ![X = 99, \sigma = 0.9, n = 8](https://tex.z-dn.net/?f=X%20%3D%2099%2C%20%5Csigma%20%3D%200.9%2C%20n%20%3D%208)
So the test statistic will be given by:
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B99%20-%20100%7D%7B%5Cfrac%7B0.9%7D%7B%5Csqrt%7B8%7D%7D%7D)
![t = -3.14](https://tex.z-dn.net/?f=t%20%3D%20-3.14)
The value of the test statistic is -3.14.