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3 years ago

Use the greatest common factor and the distributive property to write and an equivalent expression: 20g+24h

Mathematics

1 answer:

n200080 [17]3 years ago

4 0

4(5g+6h)

You xan remove four from each number, but no letters since they dont have any of the same.

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What is the solution to this inequality: -4(3x-5)<2(3x+4)

Delicious77 [7]

Answer:

x > 2/3

Step-by-step explanation:

-4(3x - 5) < 2(3x + 4)

Divide both sides by 2.

-2(3x - 5) < 3x + 4

Distribute on the left side.

-6x + 10 < 3x + 4

Subtract 3x from both sides.

-9x + 10 < 4

Subtract 10 from both sides.

-9x < - 6

Divide both sides by -9. Remember that when you divide both sides of an inequality by a negative number, the inequality sign changes direction.

x > (-6)/(-9)

x > 6/9

x > 2/3

7 0

3 years ago

A sample of students from an introductory psychology class were polled regarding the number of hours they spent studying for the

Anni [7]

Answer:

$8.68,13.16$

Step-by-step explanation:

Hint- First we have to calculate the mean and standard deviation of the sample and then applying formula for confidence interval we can get the values.

Mean of the sample is,

$\mu=\dfrac{\sum _{i=1}^{24}a_i}{24}=\dfrac{262}{24}=10.92$

Standard deviation of the sample is,

$\sigma =\sqrt{\dfrac{\sum _{i=1}^{24}\left(x_i-10.92\right)^2}{24-1}}=5.6$

The confidence interval will be,

$=\mu \pm Z\dfrac{\sigma}{\sqrt{n}}$

Here,

Z for 95% confidence interval is 1.96, and n is sample size which is 24.

Putting the values,

$=10.92 \pm 1.96\cdot \dfrac{5.6}{\sqrt{24}}$

$=10.92 \pm 2.24$

$=8.68,13.16$

Confidence interval is used to express the degree of uncertainty associated with a sample.

95% confidence interval means that if we used the same sampling method to select different samples and calculate an interval, we would expect the true population parameter to fall within the interval for 95% of the time.

5 0

3 years ago

A 20 ft flag pole casts a shadow 32 ft long. What is the angle of elevation of the sun?

Nookie1986 [14]

Answer:

<em>The angle of elevation of the sun is 32°</em>

Step-by-step explanation:

<u>Right Triangles</u>

The flagpole and the ground form a right angle (90°). In triangles with right angles, the trigonometric ratios are satisfied.

Each acute angle has an adjacent leg and an opposite leg. The tangent ratio relates to both legs.

$\displaystyle \tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}$