We can answer this question by solving each equation for one variable, and then substituting.
3x + y = 11 Given
y = -3x + 11 Subtract 3x from both sides
This equation is now solved for y. Now, let's do the other equation. Make sure to solve it for the same variable.
-2x + y = 1 Given
y = 2x + 1 Add 2x to both sides
Now, let's set both equations equal to each other, since they both equal y.
2x + 1 = -3x + 11 Set both equations equal to each other
1 = -5x + 11 Subtract 2x from both sides
-10 = -5x Subtract 11 from both sides
2 = x Divide both sides by -5
Now, let's substitute x in for one of the equations we found earlier, so that we can find y.
y = 2x + 1 Given
y = (2)(2) + 1 Substitute the x-value, 2
y = 4 + 1 Multiply
y = 5 Add
So, x = 2 and y = 5.
Hope this helps!
Answer:
10 : 3
Step-by-step explanation:
Convert one of the measurements so that it is in the same form as the other. (Easiest to convert m to cms so we are not working with decimals)
2.5 m = 2.5 x 100 = 250 cm (since there are 100 cm in a meter)
Therefore, as a ratio:
250 : 75
We can divide both by 5:
50 : 15
We can further divide by 5:
10 : 3
(no further simplifying)
So 2.5 m to 75cm as a ratio is 10 : 3
42.41 cubic meters
The volume of a cylinder is bh where b is the area of the base and h is the height of the cylinder. And since the area of a circle is pi r^2, we have this equation for the volume of a cylinder
V = pi*r^2*h
Now substitute, the known values for r and h, then calculate the result:
V = pi*r^2*h
V = 3.14159*3^2*1.5
V = 3.14159*9*1.5
V = 42.411465
V = 42.41
So the volume of the coal pile is 42.41 cubic meters.
X = The cost of each book of stamps
There for your expression would be:
3x + 4.50
3x is 3 book of stamps times x cost of each book.
Your 4.50 is your one time fee to mail the package.
Hope this helps! (:
Answer:
Option D) At least 3600
Step-by-step explanation:
We are given the following in the question:
The distribution of scores of individual students on the American College Testing is a bell shaped distribution that is a normal distribution.
Population standard deviation =
![\sigma = 6.0](https://tex.z-dn.net/?f=%5Csigma%20%3D%206.0)
We want that the standard deviation of the sample should not be more than 0.1 that is the standard error should not be more than 0.1
Formula for standard error:
![S.E = \dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=S.E%20%3D%20%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![S.E\leq 0.1\\\\\dfrac{\sigma}{\sqrt{n}}\leq 0.1\\\\\dfrac{6}{\sqrt{n}}\leq 0.1\\\\\sqrt{n}\geq \dfrac{6}{0.1}\\\\\sqrt{n}\geq 60\\n\geq 3600](https://tex.z-dn.net/?f=S.E%5Cleq%200.1%5C%5C%5C%5C%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5Cleq%200.1%5C%5C%5C%5C%5Cdfrac%7B6%7D%7B%5Csqrt%7Bn%7D%7D%5Cleq%200.1%5C%5C%5C%5C%5Csqrt%7Bn%7D%5Cgeq%20%5Cdfrac%7B6%7D%7B0.1%7D%5C%5C%5C%5C%5Csqrt%7Bn%7D%5Cgeq%2060%5C%5Cn%5Cgeq%203600)
Thus, the sample size must be atleast 3600 so that the sample standard deviation is not more than 0.1.
Thus, the correct answer is
Option D) At least 3600