5x-3y=12 what is the x-intercept

Stells [14]

The answer for this is A.

7 0

3 years ago

(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice

vesna_86 [32]

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

Binomial probability distribution

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

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that $\mu = 100, \sigma = 15$

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

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

$Z = \frac{107.5 - 100}{15}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

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

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549$

$P(X \geq 1) = 1 - P(X = 0) = 0.0451$

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

8 0

3 years ago

Abby's school is 6 blocks west of her house. Her mother works at a store that is 4 blocks east of her school. Use a number line

faltersainse [42]

Answer:

Step-by-step explanation:

Let us give a proper illustration in the number line

let H be Abby's house

and S be the school

let W be her mother's work.

kindly find attached a rough sketch of the number line for your reference

Question: What value represents the difference in position between Abby's house and her mother's store?

basically, the distance between two points on a number line is the difference between the points.

So the value that represents the position between Abby's house and her mother's store is the distance between the two points.

= 4-(-6)

=4+6

=10

7 0

3 years ago

The phone company B-Mobile has a monthly cellular plan where a customer pays a flat fee for unlimited voice calls and then a cer

Oxana [17]

Step-by-step explanation:

That's the rifgt answer for sure!!

Plz Mark brainliest...

6 0

3 years ago

MAY DAY MAY DAY, HELP

Pavlova-9 [17]

Have you heard the expressions "shooting fish in a barrel" or
"taking candy from a baby" ?

I've decided to take your points and try not to feel guilty about it.

A). That's it ! That's the equation, for ANY basketball on Earth.
You wrote it right there in your question.

In that equation that you wrote, the ' r ' is the initial velocity.
You said that Adam tossed it straight up, and it was going 10 meters per second
 when it left his hand.
So ' r ' in the equation is +10.
The equation is:
 d = 10t - 5t²  .
It tells you how high the ball is above its tossing height after any number of seconds.
The ' t ' in the equation is the number of seconds. Any letter could have been used,
but ' t ' was cleverly selected because it stands for 'time'.

B). You want to know where it is after 0.5 second ? All you have to do is put '0.5'
into the equation wherever there's a ' t '. Do you really need somebody to do that
for you ?

Well, OK. You're being so overly generous with your points . . .

 Distance = 10 t - 5 t²

 Distance = 10 (0.5) - 5 (0.5)²

 Distance = 5 - 5(0.25)

 Distance = 5 - 1.25

 Distance = 3.75 meters 

positive 3.75 means above Adam's hand.

A thinking exercise:
-- He tossed the ball upwards at 10 meters per second.
-- Why is it not 5 meters above his hands after 0.5 second?

7 0

3 years ago