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3 years ago

The mean of a normally distributed dataset is 12, and the standard deviation is 2.

1 answer:

5 0

So lets do it like this:
z = (X-Mean)/SD
z1 = (8-12)/2 = - 2 
z2 = (16-12)/2 = + 2 
According to the Empirical Rule 68-95-99.7 
Mean more or less 2SD covers 95% of the values 
So the percentage of data points falling between 8 and 16 = 95%
I hope this can help

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What is the vertex of the absolute value function defined by ƒ(x) = |x + 2| + 4?

Marrrta [24]

Answer:

C. (-2,4)

Step-by-step explanation:

We have been given a function $f(x)=|x+2|+4$ and we are asked to find the vertex of our absolute value function.

The rules for the translation of a function are as follows:

$f|x-h|=\text{Graph shifted to right by h units}$

$f|x+h|=\text{ Graph shifted to left by h units}$

$f|x|+h=\text{ Graph shifted upward by h units}$

$f|x|-h=\text{ Graph shifted down by h units}$

Upon comparing our absolute function with above transformations we can see that our function is shifted to two units right of the origin(0,0) so x coordinate of our absolute function will be -2.

Our function is shifted upward from origin by 4 units, therefore, y-coordinate of our absolute value function will be 4.

$f(x)=|x--2|+4$

Therefore, the vertex of our absolute value function will be on point (-2,4) and option C is the correct choice.

4 0

2 years ago

Read 2 more answers

Convert phrases to numerical expressions and solve

almond37 [142]

Answer:

10000 - 1000 + 1000 = 10000

Step-by-step explanation:

10 to the forth power = 10000 - 1000 = 9000 + 1000 = 10000

3 0

2 years ago

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There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - W

jenyasd209 [6]

Answer:

Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old.

Step-by-step explanation:

Let $k$ be Kirk's age.

Let $b$ be Brian's age.

Let $m$ be Matt's age.

Let $m_{1}$ be the boss/manager's age.

From the information given, we can set up 4 equations:

$k+b+m+m_{1}=106$

$k=2(m_{1}-10)$

$b=2m_{1}-12$

$m=\frac{1}{2}m_{1}+6$

Rewrite the first equation, substituting $k$ , $b$ , and $m$ in terms of $m_{1}$ to get:

$2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106$

Open up the parentheses using the distributive property (which is $a(b-c)=ab-ac$ ) and combine like terms to get:

$5.5m_{1}-26=106$

Add 26 to both sides to reach:

$5.5m_{1}=132$

Thus, $m_{1}=24$ . Substitute $24$ for $m_{1}$ in the second, third, and fourth original equations to find that $k=28$ , $b=36$ , and $m=18$ . Therefore, Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old. To check, you can add up all of the ages to get 106.