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3 years ago

What is the solution to the inequality? −6x+5>−1 a.x>1 B.x>−1 C.x<−1 D.x<1

2 answers:

3 0

$-6x+5 > -1\qquad\text{subtract 5 from both sides}\\\\-6x > -6\qquad\text{change the signs}\\\\6x < 6\qquad\text{divide both sides by 6}\\\\x < 1\to\boxed{D.}$

Viefleur [7K]3 years ago

3 0

Explanation:

Subtract by 5 both sides of an equation.

$-6x+5-5>-1-5$

Then, simplify.

$-6x>-6$

Change the sign to less than.

Multiply by the -1 both sides of an equation. it can also reverse inequality.

$(-6x)(-1)$

Simplify.

$6x$

Then you divide by 6 both sides of an equation.

6x/6<6/6

Finally, simplify dividing into the numbers.

$6/6=1$

$\boxed{D. x$

Hope this helps!

Thanks!

Have a great day!

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A piece of fabric measures 152.4 centimeters in length.

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The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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:

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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 estabilishes 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 of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

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

By the Central Limit Theorem

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

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

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

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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3 years ago

How can I write Five less than the quotient of a number and 3 is -7 in algabreaic expression

vladimir1956 [14]

Answer:

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3 years ago

Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog hou

Luda [366]

The complete question is
Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 2 feet, b = 1 foot, and c = 1.4 feet.
If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?

the picture in the attached figure

we know that

surface area of the figure=surface area of cube+surface area of triangular prism

surface area of cube=4*a²----> 4*2²-----> 16 ft²

surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]
surface area of triangular prism=5.6+2----> 7.6 ft²

surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²

the answer is
23.6 ft²

7 0

3 years ago

Read 2 more answers

What is the solution to the inequality? −6x+5>−1 ​ a.x>1 ​ ​ B.x>−1 ​ ​ C.x<−1 ​ ​ D.x<1 ​

What is the solution to the inequality? −6x+5>−1 a.x>1 B.x>−1 C.x<−1 D.x<1