Find two numbers whose sum is 44 and whose difference is 20 (PLEASE HELP I HAVE 5 MINUTES)

A filling machine fills bottles of nail polish with amounts that are normallydistributed with mean 18 mL and standard deviation

natulia [17]

Answer:

a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish

b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 18 mL and standard deviation 0.6 mL.

This means that $\mu = 18, \sigma = 0.6$

a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?

This is the p-value of Z when X = 17.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17.5 - 18}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a p-value of 0.2033

0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish.

b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?

Twelve bottles, so now $n = 12, s = \frac{0.6}{\sqrt{12}}$

The probability is:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{17.5 - 18}{\frac{0.6}{\sqrt{12}}}$

$Z = -2.89$

$Z = -2.89$ has a p-value of 0.0019

0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL

4 0

2 years ago

PLEASEEE HELP I WILL GIVE YOU BRAINIEST!!!!!

nydimaria [60]

It’s B because the equations is something greater than -1

7 0

2 years ago

. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Marianna [84]

You need a system of 3 equations to solve for the 3 unknowns in our parabola, standard form of $y=ax^2+bx+c$ . Since the second point there has an x of 0, we'll start there to make it easy. In this point, x = 0 and y = -4. $-4=a(0)^2+b(0)+c$ . That gives us our first value...c = -4. Let's do the first equation now the same way, but this time we have a c value to sub in: $-20=a(-2)^2+b(-2)+c$ and $-20=4a-2b-4$ which simplifies to $-16=4a-2b$ . We'll use that in a bit. Let's do the third point now the same way. $-20=a(4)^2+b(4)+c$ and $-20=16a+4b-4$ which simplifies to $-16=16a+4b$ . Now we have a new system of equations. We need to solve for a and b. Let's multiply the 2nd equation by -4 to get rid of the a terms. Doing that we have $64=-16a+8b$ and we will add that to $-16=16a+4b$ . The a terms cancel each other out leaving us with 48=12b and b = 4. Now we'll sub that b into one of the equations in terms of a and b and solve for a. -16 = 16a + 4(4) and -16=16a+16. Subtracting 16 from both sides and we have -32=16a and a = -2. Here's what we have for our values now: a = -2 b = 4, c = -4. So the quadratic in standard form is $y=-2x^2+4x-4$ . And you're done!

5 0

3 years ago

4. At the end of the school year, Rachel and Amber threw their Algebra terbooks off the top of a 12-story

defon

I'm going to decode the gibberish in the question and guess the equations are

Rachel:

$h=-16t^2+36t+160$

Amber:

$h=-16t^2+50t+160$

These equations tell us a few things not explicitly mentioned in the problem. Namely h is in feet, t is in seconds (because of the 16) and the building is 160 feet tall. h=0 corresponds to ground level. I made the constants of the equations the same because they're both on the twelfth floor. The difference between 36t and 50t reflect different vertical components of the velocity of the throw. The positive signs mean they each threw their book upwards. Air resistance is ignored.

So we need to solve two quadratic equations and compare the t values.

$0=-16t^2+36t+160$