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3 years ago

Twice the sum of a number and negative three is ten. Find the number. Round your answer to the nearest integer, if necessary.

Mathematics

2 answers:

andreev551 [17]3 years ago

6 0

Answer:

x=8

Step-by-step explanation:

2(x-3)=10

2x-6=10

2x=16

x=8

Lina20 [59]3 years ago

3 0

Answer:

x=8

Step-by-step explanation:

The equation is:

2(x + -3) =10

x=8

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True of false? the slope of thia equation is zero <br>y=x+5<br>

Ugo [173]

Answer:

false

Step-by-step explanation:

no solution

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3 years ago

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Which of the following numbers would have 10^3 in its scientific notation?

Monica [59]

Answer:

D. 9,700

Step-by-step explanation:

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3 years ago

The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean

Marysya12 [62]

Answer:

a) 15.87% of the scores are expected to be greater than 600.

b) 2.28% of the scores are expected to be greater than 700.

c) 30.85% of the scores are expected to be less than 450.

d) 53.28% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

$\mu = 500, \sigma = 100$

a. Greater than 600

This is 1 subtracted by the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% of the scores are expected to be greater than 600.

b. Greater than 700

This is 1 subtracted by the pvalue of Z when X = 700. So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of the scores are expected to be greater than 700.

c. Less than 450

Pvalue of Z when X = 450. So

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

30.85% of the scores are expected to be less than 450.

d. Between 450 and 600

pvalue of Z when X = 600 subtracted by the pvalue of Z when X = 450. So

X = 600

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 450

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

0.8413 - 0.3085 = 0.5328

53.28% of the scores are expected to be between 450 and 600.

6 0

3 years ago

What are the solutions to the nonlinear equations below y=4x x^2 + y^2=17

wolverine [178]

Answer:

x = 1 and x = -1

Step-by-step explanation:

Next time, please separate the equations with a comma or semicolon. Thanks.

We can substitute 4x for y in the quadratic equation x^2 + y^2=17:

x² + (4x)²=17.

Then x² + 16x² = 17, or

17x² = 17, or x² = 1. There are two solutions: x = 1 and x = -1.

8 0

4 years ago

Given that z is a standard normal random variable, find z for each situation. The area between 0 and z is .4750. Answer The area

algol13

Answer:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

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

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.8686,0,1)"

And we got z =1.120

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.67,0,1)"

And we got z =0.440

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".

Solution to the problem

We want this probability:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

For the next part we want to calculate:

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

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

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.8686,0,1)"

And we got z =1.120

For the next part we want to calculate:

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.67,0,1)"

And we got z =0.440

6 0

3 years ago