NEED HELP QUICK!!! WILL GIVE LIKE

Which of the following correctly uses absolute value to show the distance between –80 and 15?

scoray [572]

It should be |-80+15|=65 units because absolute value makes it positive.

4 0

3 years ago

SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

$P(Z>1.25)=1-P(Z$

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.25)=1-P(Z$

Part b

We are interested on this probability

$P(400$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(400$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.8$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

8 0

3 years ago

How does the graph of f(x)=3|x+2|+4 relate to its parent function

Mariana [72]

If parent functin is f(x)=|x|
it is moved to the left 2 units
vertically streched by a factor of 3
and moved up by 4 units in that order

because
to move a function to left c units, add c to every x
to vertically strech function by factor of c, multiply whole function by c
to move funciotn up c units, add c to whole function

so it is 2 to the left, verteically streched by a factor of 3 then moved up 4 units

5 0

4 years ago

Read 2 more answers

Please help solve this, I’ve tried my best. My answers are a height of 6.7 using 30-60-90 as a last resort, and the glass volume

Neko [114]

Answer:

A) To ensure the correct and exact straight height

B) 15 inches

C) 24.87 in $^{3}$

Step-by-step explanation:

Hello! Lets start!

First, it asks us to explain why the two bases must be parallel. In order to measure the correct and exact height, we must be sure that the bases are parallel, or else there would be a range of heights; in order to ensure that you are measuring a straight distance, they must be parallel!

Second, it asks us to identify the height of cone. To do this, we must make a slope! We can see that, for every time we go down 5 inches, we lose 1 inch of our base! Our slope in this situation would be -5. So, lets continue to see how long before the cone reaches its tip, in which the base would be equal to 0. At 5 inches, our base is 2 inches. At 10 inches, our base is 1 inch. At 15 inches, we do not have a base, as it equals 0! So therefore, our cone height is 15 inches.

Third, it asks us to identify the volume of the cup, which is also called a <em>circular truncated cone. </em>To do so, we can use the formula:

₁ $V = \frac{1}{3} \pi (r_{1}^2 + r_{1}r_{2} + r_2^2)h$

Lets plug in our information!

$V = \frac{1}{3} \pi (1.5^{2} + (1.5)(1) + 1^{2}) (5)\\V = 24.87$

Hope this helps! Remember, math is fun!

3 0

3 years ago

Zack has two strings of equal length. One string is red the other is yellow. After cutting 2.5 meters of the red string and 3.8

ddd [48]

Answer:

6.4 m

Step-by-step explanation:

We have 2 expressions here. The first one is the fact that r = y. That's one of 2 equations. The second one involves whats' left after cutting off certain lengths of each color string. We cut 2.5 m from red, we cut 3.8 m from yellow. We know that what's left of red is 1.5 times the length of what's left of yellow. What's left of red is r - 2.5; what's left of yellow is y - 3.8. We know that r = 1.5y, so filling that in with our corresponding expressions gives us

r - 2.5 = 1.5(y - 3.8)

Distribute to get

r - 25 = 1.5y - 3.2

Now from the first expression, r = y, so fill in y for r to get an equation in one variable:

y - 2.5 = 1.5y - 3.2

Combine like terms:

-.5y = -3.2 and divide to get

y = 6.4

Check it to make sure it works. What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:

What's left of red: 6.4 - 2.5 = 3.9

What's left of yellow: 6.4 - 3.8 = 2.6

1.5 x 2.6 = 3.9, just like it should!

4 0

3 years ago