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love history [14]
3 years ago
5

Evaluate the following expression (-3)^2

Mathematics
1 answer:
Cloud [144]3 years ago
8 0

Answer:

9

Step-by-step explanation:

negative times a negative is a positive. Negative three squared is 9.

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Solve the problem. Use the Central Limit Theorem.The annual precipitation amounts in a certain mountain range are normally distr
bazaltina [42]

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use 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:

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.

Central Limit Theorem

The Central Limit Theorem establishes 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 109.0 inches, and a standard deviation of 12 inches.

This means that \mu = 109, \sigma = 12

Sample of 25.

This means that n = 25, s = \frac{12}{\sqrt{25}} = 2.4

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

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

By the Central Limit Theorem

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

Z = \frac{112 - 109}{2.4}

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

7 0
3 years ago
There are 24 students on the math team. If the probability of a new student being drawn at random is 1/3, then how many of the s
andreev551 [17]

Answer:

24

Step-by-step explanation:

24/3 =8

8=1/3

6 0
3 years ago
Read 2 more answers
Write the following as a ratio: 304 calories burned in 56 minutes
IgorC [24]

Answer:

The required ratio is 38 : 7

Step-by-step explanation:

Given,

304 calories burned in 56 minutes,

That is, the number of calories burnt in 56 minutes = 304

So, the ratio of the calories burnt and time in minutes  = \frac{304}{56}

∵ HCF(304, 56) = 8,

Thus, the ratio of price of photos and number of photos = \frac{304\div 8}{56\div 8}

= \frac{38}{7}

6 0
3 years ago
Since Beth was born the population of her towns has increased at a rate of 850 people per year. On beths 9th birthday the total
Lana71 [14]

Answer:

313,600

Step-by-step explanation:

Let t represent number of years after Beth's 9th birthday.

We have been given that since Beth was born the population of her towns has increased at a rate of 850 people per year. So number of people increased in t years would be 850t.

We are also told that on Beth's 9th birthday the total population was nearly 307,650. This means that t-intercept is 307,650.

The population of town t years after Beth's birthday would be P(t)=850t+307,650.

To find population on Beth's 16th birthday, we will substitute t=7 in our equation as Beth's 16th birthday would be 7 years after 9th birthday.

P(t)=850(7)+307,650

P(7)=5950+307,650

P(7)=313,600

Therefore, the population on Beth's 16th birthday would be 313,600.

3 0
3 years ago
What is the value of x?
Ad libitum [116K]

Answer:

x = 15

Step-by-step explanation:

We are told that a right angle is divided into two parts

A right angle = 90°

Part A = 30°

Part B = 4x

Hence:

30° + 4x = 90°

Collect like terms

4x = 90° - 30°

4x = 60°

4x = 60/4

x = 15

Therefore, the value of x = 15

5 0
2 years ago
Read 2 more answers
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