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8 months ago

Solve. (Enter your answer using interval notation.) |3x + 15| > 21

Mathematics

1 answer:

Katarina [22]8 months ago

4 0

Answer:

(-∞, -12), (2, ∞)

(-∞, -12) U (2, ∞)

Step-by-step explanation:

|3x + 15| > 21, |3x + 15| < -21

3x + 15 > 21, 3x + 15 < - 21

-15 -15 -15 -15

------------------ -------------------

3x > 6 3x < - 36

÷3 ÷3 ÷3 ÷3

------------ ------------------

x > 2 x < -12

(-∞, -12), (2, ∞)

(-∞, -12) U (2, ∞)

I hope this helps!

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If two of these shapes are randomly chosen, one after the other without replacement, what is the probability that the first will

aleksandrvk [35]

Answer:

$P(T\ n\ S) = \frac{1}{14}$

Step-by-step explanation:

*Missing Part of the Question*

4 stars

5 triangles

3 circles

3 squares

Required

Determine the probability of triangle being first then square being second

$Total = 4 + 5 + 3 + 3$

$Total = 15$

Represent the triangle with T and square with S

So, we're solving for P(T n S)

$P(T\ n\ S) = P(T) * P(S)$

Solving for P(T)

$P(T) = \frac{n(T)}{Total}$

$P(T) = \frac{5}{15}$

Solving for P(S)

The question implies a probability without replacement;

Hence Total has now been reduced by 1

Total = 14

$P(S) = \frac{n(S)}{Total}$

$P(S) = \frac{3}{14}$

Recall that

$P(T\ n\ S) = P(T) * P(S)$

$P(T\ n\ S) = \frac{5}{15} * \frac{3}{14}$

$P(T\ n\ S) = \frac{15}{15 * 14}$

$P(T\ n\ S) = \frac{1}{14}$

Hence, the required probability is

$P(T\ n\ S) = \frac{1}{14}$

3 0

2 years ago

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 2.575\sqrt{\frac{0.25*0.75}{n}}$

$0.1\sqrt{n} = 2.575{0.25*0.75}$

$\sqrt{n} = \frac{2.575{0.25*0.75}}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575{0.25*0.75}}{0.1})^{2}$

$n = 124.32$

Rounding up

The minimum sample size needed is 125.

5 0

3 years ago

You want to walk from home to a clothing store that is 3/4 miles away. You stop for a rest after 1/2 miles. How much farther do

dmitriy555 [2]

Answer:

1/4 miles.

Step-by-step explanation:

If I want to walk from my house to a clothing store 3/4 of a mile away, this implies that the location is 0.75 miles from my home.

Now, if after walking 1/2 mile I decide to stop, I will have traveled 0.5 miles in total. In this way, when I get back on my way, I will have to travel 0.25 miles to reach my destination (0.75 - 0.50).

Therefore, since 1 divided by 4 equals 0.25, I have to walk 1/4 mile to reach my destination.

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3 years ago

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Ymorist [56]

Answer:

1. True

2. False

3. False

4. True

5. False

Step-by-step explanation:

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2 years ago

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Hayden will attend a craft show the cost of admission ticket is eight dollars the cost of a raffle ticket for a handmade quilt a

ruslelena [56]

Answer: 7 tickets

Step-by-step explanation:

First you need to remove the cost of entrance from the $45 that Hayden has:

= 45 - 8

= $37

The $37 is the amount that is left for Hayden to be able to buy tickets for the raffle.

The tickets cost $5 each so the highest number of tickets that can be bought with $37 is:

= 37 / 5

= 7 tickets

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3 years ago