Which values for x, y, and z satisfy the equation 7xy/z=28

Most college-bound students take either the SAT(Scholastic Assessment Test) or the ACT (which originally stood for American coll

Jlenok [28]

Answer:

Luis would need to have a SAT score of 574.

Step-by-step explanation:

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.

Nicole's z-score:

ACT scores have a mean of about 21 with a standard deviation of about 5, which means that $\mu = 21, \sigma = 5$

Nicole gets a score of 24, which means that $X = 24$ . Her z-score is:

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

$Z = \frac{24 - 21}{5}$

$Z = 0.6$

What score would Luis have to have on the SAT to have the same standardized score(z-score) as Nicole's standardized score on the ACT?

Luis would have to get a score with a z-score of 0.6, that is, X when Z = 0.6.

SAT scores have a mean of about 508 with a standard deviation of about 110, which means that $\mu = 508, \sigma = 110$ .

The score is:

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

$0.6 = \frac{X - 508}{110}$

$X - 508 = 0.6*110$

$X = 574$

Luis would need to have a SAT score of 574.

8 0

3 years ago

There are 50 tickets in a raffle bag, and 10 of the tickets belong to Gary. A ticket is chosen at random, and the ticket owner's

IgorC [24]

1/25 or .04% would be the correct answer

4 0

3 years ago

Solve using the quadratic formula: <img src="https://tex.z-dn.net/?f=%20%7B3x%7D%5E%7B2%7D%20%20%2B%202%20%3D%206" id="TexFo

satela [25.4K]

Answer:

x = 2/3, -2/3

Step-by-step explanation:

Solve the equation for x by finding a , b , and c of the quadratic then apply the quadratic formula.

7 0

3 years ago

0.34 into a percent

vivado [14]

34% is the correct answer

3 0

4 years ago

Read 2 more answers

Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.

azamat

Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.

Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(a - b) • (a - c) = 0

or

(a - b) • (b - c) = 0

or

(a - c) • (b - c) = 0

We have

a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)

a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)

b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)

Case 1: If (a - b) • (a - c) = 0, then

(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0 ==> x = -6

which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (a - b) • (b - c) = 0, then

(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0 ==> x = -2

which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (a - c) • (b - c) = 0, then

(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0

but the solutions to x here are non-real, so we throw out this case.

So there are two possible values of x that make a right triangle, x = -6 and x = -2.

3 0

3 years ago