Answer:
3 + 4x
Step-by-step explanation:
Let "a number" be x.
Therefore "four times a number" is 4 multiplied by x which is 4x.
Now add 3 for "3 plus".
3 + 4x
Answer:
Step-by-step explanation:
11x+6 = 15x-26
Answer:
distributive property of multiplication over addition
Step-by-step explanation:
The distributive property of multiplication over addition:
a(b + c) = ab + ac
You have
-4(x + 4) = -4x - 16
which is an application of that property.
Answer: distributive property of multiplication over addition
Answer:
The right answer is:
(a) 0.01252
(b) 0.8882
(c) 0.9544
Step-by-step explanation:
Given:
Population proportion,
P = 0.17
Sample size,
n = 900
(a)
The standard error of proportion will be:
⇒ ![SE_p=\sqrt{\frac{P(1-P)}{n} }](https://tex.z-dn.net/?f=SE_p%3D%5Csqrt%7B%5Cfrac%7BP%281-P%29%7D%7Bn%7D%20%7D)
By putting the values, we get
![=\sqrt{\frac{0.17(1-0.17)}{900} }](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B0.17%281-0.17%29%7D%7B900%7D%20%7D)
![=\sqrt{0.000158}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B0.000158%7D)
![=0.01252](https://tex.z-dn.net/?f=%3D0.01252)
(b)
We know that,
![\hat{P}-P=\pm 0.02](https://tex.z-dn.net/?f=%5Chat%7BP%7D-P%3D%5Cpm%200.02)
Now,
⇒ ![z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Chat%7BP%7D-P%7D%7B%5Csqrt%7B%5Cfrac%7BP%281-P%29%7D%7Bn%7D%20%7D%20%7D)
By substituting the values, we get
![=\frac{\pm 0.02}{\sqrt{\frac{0.17(1-0.17)}{900} } }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpm%200.02%7D%7B%5Csqrt%7B%5Cfrac%7B0.17%281-0.17%29%7D%7B900%7D%20%7D%20%7D)
![=\frac{\pm 0.02}{0.01252}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpm%200.02%7D%7B0.01252%7D)
![=\pm 1.59](https://tex.z-dn.net/?f=%3D%5Cpm%201.59)
⇒ ![P(I\hat{P}-PI](https://tex.z-dn.net/?f=P%28I%5Chat%7BP%7D-PI%3C0%2C02%29%3DP%28-1.59%3Cz%3C1.59%29)
![=1-2P(z](https://tex.z-dn.net/?f=%3D1-2P%28z%3C-1.59%29)
![=1-2(0.0559)](https://tex.z-dn.net/?f=%3D1-2%280.0559%29)
![=0.8882](https://tex.z-dn.net/?f=%3D0.8882)
(c)
We know that,
![n = 1400](https://tex.z-dn.net/?f=n%20%3D%201400)
Now,
⇒ ![z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Chat%7BP%7D-P%7D%7B%5Csqrt%7B%5Cfrac%7BP%281-P%29%7D%7Bn%7D%20%7D%20%7D)
By substituting the values, we get
![=\frac{\pm 0.02}{\sqrt{\frac{0.17(1-0.17)}{1400} } }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpm%200.02%7D%7B%5Csqrt%7B%5Cfrac%7B0.17%281-0.17%29%7D%7B1400%7D%20%7D%20%7D)
![=\frac{\pm 0.02}{0.01}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpm%200.02%7D%7B0.01%7D)
![=\pm 2](https://tex.z-dn.net/?f=%3D%5Cpm%202)
⇒ ![P(I \hat P-PI](https://tex.z-dn.net/?f=P%28I%20%5Chat%20P-PI%3C0.02%29%3DP%28-2%3Cz%3C2%29)
![=1-2P(z](https://tex.z-dn.net/?f=%3D1-2P%28z%3C-2%29)
![=1-2(0.0228)](https://tex.z-dn.net/?f=%3D1-2%280.0228%29)
Answer:
M and N are points on sides AC and BC respectively of a `triangleABC`. State whether MN||BC` if CM = 4.2 cm, MA= 2.8 cm , NB = 3.6 cm, CN = 5.7 cm.