4. You remove the brackets
Remember:
-a × -b = positive ab / +ab
a × b = positive ab / +ab
-a × b = negative ab/ -ab
a × -b = negative ab / -ab
Where ab is the product of the two numbers & - or + are the signs.
a) 5(2x+3y) -4(3x-5y)
= 10x + 15y -12x + 20y
= 10x - 12x + 15y + 20y
= -2x + 35y
= 35y - 2x [I've been told that most people prefer the positive number in front rather than the negative number]
b) x- 2(x+ 3y) -(2x+3y) -4(x+y)b
= x - 2x - 6y - 2x - 3y - 4x - 4y
= x - 2x - 2x - 4x - 6y - 3y - 4y
= -7x - 13y
c) 3(a + 2b -2) -2(2a - 5b - 1)
= 3a + 6b - 6 -4a + 10b + 2
= 3a - 4a + 6b + 10b - 6 +2
= - a + 16b - 4
= 16b - a - 4
Answer:
A. 12.68 - 14.72 hours
B. Normal distribution.
Step-by-step explanation:
Part A
This question is using quantitative data. A 99% confidence interval means that you want to know the range where 99% of the population will be. To find this you have to convert the 99% CI into the z-score which is -2.58SD to + 2.58SD.
Note that the standard deviation(SD) is from the sample, not the population. We still need to find the standard deviation of the population. The formula is:
population SD = ![\frac{o}{\sqrt[]{n} }](https://tex.z-dn.net/?f=%5Cfrac%7Bo%7D%7B%5Csqrt%5B%5D%7Bn%7D%20%7D)
Where the o= sample SD = 7.4
n= number of sample = 463
The calculation will be:
population SD = ![\frac{o}{\sqrt[]{n} }](https://tex.z-dn.net/?f=%5Cfrac%7Bo%7D%7B%5Csqrt%5B%5D%7Bn%7D%20%7D)
population SD =
= 0.3951
The bottom limit will be:
Mean - SD * z-score= 13.7 - 0.3951*2.58 = 12.68 hours
The upper limit will be:
Mean + SD * z-score= 13.7 + 0.3951*2.58 =14.72 hours
The 99% CI range will be 12.68 - 14.72 hours
Part B
The table used to convert confidence interval into z-score depends on the distribution type of the data. Most data is classified as normal distributed, a data type that will concentrated at mean and spread equally from the mean. Normal distribution data will look like a bell which make it also called bell curve.
The question tells you that the data is normal distribution, but that doesn't mean every data is normally distributed. There are a lot of other data distribution type so we have to do some tests to know the normality of the data in real-life data.
Answer:
g(x) = x+1
Step-by-step explanation:
f(x) = ![\sqrt[3]{x+2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B2%7D)
h(x) =![\sqrt[3]{x+3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B3%7D)
h(x)= (fog)(x)= f(g(x))= ![\sqrt[3]{g(x)+2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bg%28x%29%2B2%7D)
so
=![\sqrt[3]{g(x)+2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bg%28x%29%2B2%7D)
cubing both sides ,we get
x+3 = g(x) +2
solving for g(x) ,we get
g(x) = x+1
Answer:
it should be 42 hope it helps
Step-by-step explanation:
Answer:8x+11
Step-by-step explanation:2 x+ 6x=8x +11
add 2x to 6x and add 11 to it .