Answer:
Prime numbes
Step-by-step explanation:
Numbers whose only factors are 1 and itself are called prime numbers.
Such numbers have only two factors.
Examples are: 2, 3, 5, 7 ,9... etc.
Answer:
C. They are the same line.
Step-by-step explanation:
In order to compare the linear equations given, they need to be in the same form. The best form in order to evaluate slope and y-intercept is slope-intercept form, y = mx + b. Since the second equation is already in slope-intercept form, we need to use inverse operations to convert the first equation:
6x - 2y = 16 ---- 6x - 2y - 6x = 16 - 6x ---- -2y = -6x + 16
-2y/-2 = -6x/-2 + 16/-2
y = 3x - 8
Since both equations are in the form y = 3x - 8, then they are both the same line.
Answer:
960 ft²
Since you are doing volume, your multiplication sentence would look like
Length * Width * Height
Now, if you multiply 10 * 8 * 12, your answer will be 960 ft²
we have been asked to find the sum of the series
![\sum _{n=1}^5\left(\frac{1}{3}\right)^{n-1}](https://tex.z-dn.net/?f=%20%5Csum%20_%7Bn%3D1%7D%5E5%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D%20)
As we know that a geometric series has a constant ratio "r" and it is defined as
![r=\frac{a_{n+1}}{a_n}=\frac{\left(\frac{1}{3}\right)^{\left(n+1\right)-1}}{\left(\frac{1}{3}\right)^{n-1}}=\frac{1}{3}](https://tex.z-dn.net/?f=%20r%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B%5Cleft%28n%2B1%5Cright%29-1%7D%7D%7B%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D%7D%3D%5Cfrac%7B1%7D%7B3%7D%20)
The first term of the series is ![a_1=\left(\frac{1}{3}\right)^{1-1}=1](https://tex.z-dn.net/?f=%20a_1%3D%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B1-1%7D%3D1%20)
Geometric series sum formula is
![S_n=a_1\frac{1-r^n}{1-r}](https://tex.z-dn.net/?f=%20S_n%3Da_1%5Cfrac%7B1-r%5En%7D%7B1-r%7D%20)
Plugin the values we get
![S_5=1\cdot \frac{1-\left(\frac{1}{3}\right)^5}{1-\frac{1}{3}}](https://tex.z-dn.net/?f=%20S_5%3D1%5Ccdot%20%5Cfrac%7B1-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E5%7D%7B1-%5Cfrac%7B1%7D%7B3%7D%7D%20)
On simplification we get
![S_5=\frac{121}{81}](https://tex.z-dn.net/?f=%20S_5%3D%5Cfrac%7B121%7D%7B81%7D%20)
Hence the sum of the given series is
Answer:
D) 14.25
Step-by-step explanation:
It's basically saying when you use the ruler to measure something it will measure in 0.25. And will continue on to 0.50, 0.75, 1.00, 1.25, etc..