Answer:
4.1 centimeters
Step-by-step explanation:
The volume of a cube can be found using the following formula.
![V=s^3](https://tex.z-dn.net/?f=V%3Ds%5E3)
We know that the volume of the cube is 69 cm^3, therefore we can substitute 69 cm^3 in for V (volume).
![69 cm^3=s^3](https://tex.z-dn.net/?f=69%20cm%5E3%3Ds%5E3)
We want to find out what<em> s</em> (side length) is. Therefore, we must get<em> s </em>by itself.
s is being cubed. The inverse of a cube is the cube root. Take the cubed root of both sides.
![\sqrt[3]{69 cm^3} =\sqrt[3]{s^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B69%20cm%5E3%7D%20%3D%5Csqrt%5B3%5D%7Bs%5E3%7D)
![\sqrt[3]{69 cm^3}=s](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B69%20cm%5E3%7D%3Ds)
![4.10156593 cm=s](https://tex.z-dn.net/?f=4.10156593%20cm%3Ds)
The question tell us to round to the nearest tenth. The 0 in the hundredth place indicates we should leave the 1 in the tenth place.
![4.1 cm=s](https://tex.z-dn.net/?f=4.1%20cm%3Ds)
The side length of the cube is 4.1 centimeters.
Assuming that these are seperate equations:
<h3>Problem 1: x^2-5x-6</h3><h3>Problem 2: x^2+3x-40</h3><h3>Problem 3: x^2-7x-30</h3>
Problem 1:
1) Use the sum-product pattern.
x² - 5x - 6
x² + x - 6x - 6
2) Common factor from the two pairs.
x² + x - 6x - 6
x (x + 1) - 6 (x + 1)
3) Rewrite in factored form.
x (x + 1) - 6 (x + 1)
(x - 6) (x + 1) ----> Answer
Problem 2:
1) Use the sum-product pattern.
x² + 3x - 40
x² + 8x - 5x - 40
2) Common factor from the two pairs.
x² + 8x - 5x - 40
x (x + 8) - 5 (x + 8)
3) Rewrite in factored form.
x (x + 8) - 5 (x + 8)
(x - 5) (x + 8) ----> Answer
Problem 3:
1) Use the sum-product pattern.
x² - 7x - 30
x² + 3x - 10x - 30
2) Common factor from the two pairs.
x² + 3x - 10x - 30
x (x + 3) - 10 (x + 3)
3) Rewrite in factored form.
x (x + 3) - 10 (x + 3)
(x - 10) (x + 3) ----> Answer
Cheers,
ROR
Answer:
240 girls
Step-by-step explanation:
Let number of girls be x.
160:x = 2:3
Multiply right side by 80--> 160:x = 160:240
x=240.
So there are 240 girls.
Answer:
59 cm^3
Step-by-step explanation:
You can split the shape into two rectangular prisms.
3*3*1=9
10*5*1=50
9+50=59
Answer:
The probability of selling more than 2 properties in one week=0.9453
Step-by-step explanation:
We are given that
n=10
p=50%=0.50
q=1-p=1-0.50=0.50
We have to find the probability of selling more than 2 properties in one week.
Binomial probability distribution formula
![P(X=x)=nC_xp^{x}q^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3DnC_xp%5E%7Bx%7Dq%5E%7Bn-x%7D)
Using the formula
![P(x\geq 2)=10C_0(0.50)^{10}+10C_1(0.50)^{10}+10C_2(0.50)^{2}](https://tex.z-dn.net/?f=P%28x%5Cgeq%202%29%3D10C_0%280.50%29%5E%7B10%7D%2B10C_1%280.50%29%5E%7B10%7D%2B10C_2%280.50%29%5E%7B2%7D)
![P(x\leq 2)=\frac{10!}{0!10!}(0.50)^{10}+\frac{10\times 9!}{9!}(0.50)^{10}+\frac{10\times 9\times 8!}{2\times 1\times 8!}(0.50)^{10}](https://tex.z-dn.net/?f=P%28x%5Cleq%202%29%3D%5Cfrac%7B10%21%7D%7B0%2110%21%7D%280.50%29%5E%7B10%7D%2B%5Cfrac%7B10%5Ctimes%209%21%7D%7B9%21%7D%280.50%29%5E%7B10%7D%2B%5Cfrac%7B10%5Ctimes%209%5Ctimes%208%21%7D%7B2%5Ctimes%201%5Ctimes%208%21%7D%280.50%29%5E%7B10%7D)
Using the formula
![nC_r=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=nC_r%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
![P(x\leq 2)=(0.50)^{10}+10(0.50)^{10}+45(0.50)^{10}](https://tex.z-dn.net/?f=P%28x%5Cleq%202%29%3D%280.50%29%5E%7B10%7D%2B10%280.50%29%5E%7B10%7D%2B45%280.50%29%5E%7B10%7D)
![P(x\leq 2)=(0.50)^{10}(1+10+45)](https://tex.z-dn.net/?f=P%28x%5Cleq%202%29%3D%280.50%29%5E%7B10%7D%281%2B10%2B45%29)
![P(x\leq 2)=56(0.50)^{10}](https://tex.z-dn.net/?f=P%28x%5Cleq%202%29%3D56%280.50%29%5E%7B10%7D)
Now,
![P(x>2)=1-P(x\leq 2)](https://tex.z-dn.net/?f=P%28x%3E2%29%3D1-P%28x%5Cleq%202%29)
![P(x>2)=1-56(0.50)^{10}](https://tex.z-dn.net/?f=P%28x%3E2%29%3D1-56%280.50%29%5E%7B10%7D)
![P(x>2)=0.9453](https://tex.z-dn.net/?f=P%28x%3E2%29%3D0.9453)
Hence, the probability of selling more than 2 properties in one week=0.9453