X + y = 75<br> 10x + y = 48<br> Can someone help me?

Find the length of YX

koban [17]

Answer:

YX = 22

Step-by-step explanation:

Similar triangles. So,

$\frac{VW}{XW}=\frac{VZ}{YX}\\\\\frac{45}{30}=\frac{3x-9}{x+8}\\$

Cross multiplication

45*(x+8) = 30 * (3x - 9)

45x + 360 = 90x - 270

360 = 90x - 270 - 45x

360 = 45x - 270

360 + 270 = 45x

45x = 630

x = 630/45

x = 14

YX = x +8 = 14 + 8 = 22

8 0

3 years ago

SAT scores (out of 2400) are distributed normally with a mean of 1500 and a standard deviation of 300. Suppose a school council

alekssr [168]

Answer:

10.78% probability this student's score will be at least 2200

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

$\mu = 1500, \sigma = 300$

We pick a recognized student. What is the probability this student's score will be at least 2200

Event A: Recognized(scored at least 1900).

Event B: At least 1900.

Probability of scoring at least 1900.

1 subtracted by the pvalue of Z when X = 1900. So

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

$Z = \frac{1900 - 1500}{300}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082.

1 - 0.9082 = 0.0918.

So P(A) = 0.0918

Intersection:

The intersection between at least 1900 and at least 2200 is at least 2200.

Probability:

1 subtracted by the pvalue of Z when X = 2200. So

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

$Z = \frac{2200 - 1500}{300}$

$Z = 2.33$

$Z = 2.33$ has a pvalue of 0.9901.

So $P(A \cap B) = 1 - 0.9901 = 0.0099$

Then

$P(B|A) = \frac{0.0099}{0.0918} = 0.1078$

10.78% probability this student's score will be at least 2200

4 0

3 years ago

Quick algebra 1 assignment for some points and brainliest!

Juli2301 [7.4K]

1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a $\frac{1}{2}$ chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is $(\frac{1}{2})^{100}$ , which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.

The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.

Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.

2. I select the 100-prisoner experiment.

3. A curved graph like -x^2 would fit perfectly.

4. A quadratic function would fit my experiment the best. The best graph to use would be $y = -x^2$ . An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.

4 0

1 year ago

According to data from the American Medical Association, 10% of us are left handed. If three people are randomly selected, find

satela [25.4K]

Answer:

For each person, there are only two possible outcomes. Either they are left handed, or they are not. The probability of a person being left-handed is independent from other people. So we use the binomial probability distribution to solve this question.

0.1% probability that they are all left-handed.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are left handed, or they are not. The probability of a person being left-handed is independent from other people. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$