Answer:
B. 1/3 multiplied by k=7
Step-by-step explanation:
7 ÷ ⅓ = k
Multiply both sides by ⅓
7 ÷ ⅓ × ⅓ = k × ⅓
7 = k × ⅓
Answer:
a) ![z = \frac{40-35.33}{1.794}= 2.60](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B40-35.33%7D%7B1.794%7D%3D%202.60)
b) ![z = \frac{40-35.33}{1.794}= 2.60](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B40-35.33%7D%7B1.794%7D%3D%202.60)
c) ![z = \frac{30-35.33}{1.794}= -2.97](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B30-35.33%7D%7B1.794%7D%3D%20-2.97)
Step-by-step explanation:
For this case we know that the mean for the random variable of interest is
and the variance
so then the deviation would be ![\sigma = \sqrt{3.22}= 1.794](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B3.22%7D%3D%201.794)
The z score is given by thsi formula:
![z = \frac{X -\mu}{\sigma}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%7D)
Part a
We want this probability:
![P(X>40)](https://tex.z-dn.net/?f=%20P%28X%3E40%29)
And if we find the z score we got:
![z = \frac{40-35.33}{1.794}= 2.60](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B40-35.33%7D%7B1.794%7D%3D%202.60)
And we can find this probability: ![P(Z>2.60)](https://tex.z-dn.net/?f=%20P%28Z%3E2.60%29)
Part b
We want this probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C40%29)
And if we find the z score we got:
![z = \frac{40-35.33}{1.794}= 2.60](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B40-35.33%7D%7B1.794%7D%3D%202.60)
And we can find this probability: ![P(Z](https://tex.z-dn.net/?f=%20P%28Z%3C2.60%29)
Part c
We want this probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C30%29)
And if we find the z score we got:
![z = \frac{30-35.33}{1.794}= -2.97](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B30-35.33%7D%7B1.794%7D%3D%20-2.97)
And we can find this probability: ![P(Z](https://tex.z-dn.net/?f=%20P%28Z%3C-2.97%29)
Answer:
![=20x^4-36x^3+47x^2-13x+66](https://tex.z-dn.net/?f=%3D20x%5E4-36x%5E3%2B47x%5E2-13x%2B66)
Step-by-step explanation:
![\left(10x^2+7x+11\right)\left(2x^2-5x+6\right)\\=10x^2\cdot \:2x^2+10x^2\left(-5x\right)+10x^2\cdot \:6+7x\cdot \:2x^2+7x\left(-5x\right)+7x\cdot \:6+11\cdot \:2x^2+11\left(-5x\right)+11\cdot \:6\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a\\=10\cdot \:2x^2x^2-10\cdot \:5x^2x+10\cdot \:6x^2+7\cdot \:2x^2x-7\cdot \:5xx+7\cdot \:6x+11\cdot \:2x^2-11\cdot \:5x+11\cdot \:6\\=20x^4-50x^3+60x^2+14x^3-35x^2+42x+22x^2-55x+66\\=20x^4-50x^3+14x^3+60x^2-35x^2+22x^2+42x-55x+66\\](https://tex.z-dn.net/?f=%5Cleft%2810x%5E2%2B7x%2B11%5Cright%29%5Cleft%282x%5E2-5x%2B6%5Cright%29%5C%5C%3D10x%5E2%5Ccdot%20%5C%3A2x%5E2%2B10x%5E2%5Cleft%28-5x%5Cright%29%2B10x%5E2%5Ccdot%20%5C%3A6%2B7x%5Ccdot%20%5C%3A2x%5E2%2B7x%5Cleft%28-5x%5Cright%29%2B7x%5Ccdot%20%5C%3A6%2B11%5Ccdot%20%5C%3A2x%5E2%2B11%5Cleft%28-5x%5Cright%29%2B11%5Ccdot%20%5C%3A6%5C%5C%5Cmathrm%7BApply%5C%3Aminus-plus%5C%3Arules%7D%5C%5C%2B%5Cleft%28-a%5Cright%29%3D-a%5C%5C%3D10%5Ccdot%20%5C%3A2x%5E2x%5E2-10%5Ccdot%20%5C%3A5x%5E2x%2B10%5Ccdot%20%5C%3A6x%5E2%2B7%5Ccdot%20%5C%3A2x%5E2x-7%5Ccdot%20%5C%3A5xx%2B7%5Ccdot%20%5C%3A6x%2B11%5Ccdot%20%5C%3A2x%5E2-11%5Ccdot%20%5C%3A5x%2B11%5Ccdot%20%5C%3A6%5C%5C%3D20x%5E4-50x%5E3%2B60x%5E2%2B14x%5E3-35x%5E2%2B42x%2B22x%5E2-55x%2B66%5C%5C%3D20x%5E4-50x%5E3%2B14x%5E3%2B60x%5E2-35x%5E2%2B22x%5E2%2B42x-55x%2B66%5C%5C)
![\mathrm{Add\:similar\:elements:}\:60x^2-35x^2+22x^2=47x^2\\=20x^4-50x^3+14x^3+47x^2+42x-55x+66\\\mathrm{Add\:similar\:elements:}\:-50x^3+14x^3=-36x^3\\=20x^4-36x^3+47x^2+42x-55x+66\\\mathrm{Add\:similar\:elements:}\:42x-55x=-13x\\=20x^4-36x^3+47x^2-13x+66](https://tex.z-dn.net/?f=%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A60x%5E2-35x%5E2%2B22x%5E2%3D47x%5E2%5C%5C%3D20x%5E4-50x%5E3%2B14x%5E3%2B47x%5E2%2B42x-55x%2B66%5C%5C%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A-50x%5E3%2B14x%5E3%3D-36x%5E3%5C%5C%3D20x%5E4-36x%5E3%2B47x%5E2%2B42x-55x%2B66%5C%5C%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A42x-55x%3D-13x%5C%5C%3D20x%5E4-36x%5E3%2B47x%5E2-13x%2B66)
1. (x + 5, y - 6) 3/4
2. c
3. b and c
4. b and c
5. c
Answer:
Ratio of their perimeters is 6:7
Step-by-step explanation:
Ratio of Area of Hexagon = 36: 49
We need to find ratio of their perimeters
The formula used to find Area of Hexagon is: ![Area\: of\: Hexagon=\frac{3\sqrt{3} }{2}a^2](https://tex.z-dn.net/?f=Area%5C%3A%20of%5C%3A%20Hexagon%3D%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7Da%5E2)
So, we can write:
![Area\: of\: Hexagon\: 1: Area\: of\: Hexagon\: 2=36:49\\\frac{3\sqrt{3} }{2}a_1^2:\frac{3\sqrt{3} }{2}a_2^2=36:49\\\frac{\frac{3\sqrt{3} }{2}a_1^2}{\frac{3\sqrt{3} }{2}a_2^2} =\frac{36}{49} \\\frac{a_1^2}{a_2^2}= \frac{36}{49}\\Taking\:square\:root\\\sqrt\frac{a_1^2}{a_2^2}}=\sqrt{\frac{36}{49}}\\\frac{a_1}{a_2}=\frac{6}{7}](https://tex.z-dn.net/?f=Area%5C%3A%20of%5C%3A%20Hexagon%5C%3A%201%3A%20Area%5C%3A%20of%5C%3A%20Hexagon%5C%3A%202%3D36%3A49%5C%5C%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7Da_1%5E2%3A%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7Da_2%5E2%3D36%3A49%5C%5C%5Cfrac%7B%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7Da_1%5E2%7D%7B%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7Da_2%5E2%7D%20%3D%5Cfrac%7B36%7D%7B49%7D%20%5C%5C%5Cfrac%7Ba_1%5E2%7D%7Ba_2%5E2%7D%3D%20%5Cfrac%7B36%7D%7B49%7D%5C%5CTaking%5C%3Asquare%5C%3Aroot%5C%5C%5Csqrt%5Cfrac%7Ba_1%5E2%7D%7Ba_2%5E2%7D%7D%3D%5Csqrt%7B%5Cfrac%7B36%7D%7B49%7D%7D%5C%5C%5Cfrac%7Ba_1%7D%7Ba_2%7D%3D%5Cfrac%7B6%7D%7B7%7D)
So, we get a₁=6 and a₂=7
Now, finding ratio of perimeters:
The formula used is:
![Perimeter\:of\:hexagon=6a](https://tex.z-dn.net/?f=Perimeter%5C%3Aof%5C%3Ahexagon%3D6a)
Ratio will be:
![Perimeter\:of\:hexagon\:1:Perimeter\:of\:hexagon\:2\\6a_1:6a_2\\Put\;a_1=6,a_2=7\\6(6):6(7)\\=\frac{6(6)}{6(7)}\\=\frac{6}{7}](https://tex.z-dn.net/?f=Perimeter%5C%3Aof%5C%3Ahexagon%5C%3A1%3APerimeter%5C%3Aof%5C%3Ahexagon%5C%3A2%5C%5C6a_1%3A6a_2%5C%5CPut%5C%3Ba_1%3D6%2Ca_2%3D7%5C%5C6%286%29%3A6%287%29%5C%5C%3D%5Cfrac%7B6%286%29%7D%7B6%287%29%7D%5C%5C%3D%5Cfrac%7B6%7D%7B7%7D)
So, Ratio of their perimeters is 6:7