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vladimir2022 [97]
3 years ago
9

Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did she have?

Mathematics
2 answers:
Nonamiya [84]3 years ago
8 0
0.05n + 0.25q = 1.60
q = 3n

0.05n + 0.25(3n) = 160
0.05n + 0.75n = 1.60...multiply by 100 to get rid of the decimals
5n + 75n = 160...answer D

horrorfan [7]3 years ago
4 0
To answer the question, let the number of nickels Peggy has be n. By this, the Peggy has 3n quarters. The total amount of all his nickels and quarter is equal to $1.60. The equation that best describe the situation is, 
                            25(3n) + 5(n) = 160
Simplification leads to,
                             75n + 5n = 160
Thus, the answer is letter D. 
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The time a randomly selected individual waits for an elevator in an office building has a uniform distribution with a mean of 0.
Amiraneli [1.4K]

Answer:

The mean of the sampling distribution of means for SRS of size 50 is \mu = 0.5 and the standard deviation is s = 0.0409

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size, of at least 30, can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 0.5, \sigma = 0.289

What are the mean and standard deviation of the sampling distribution of means for SRS of size 50?

By the Central Limit Theorem

\mu = 0.5, s = \frac{0.289}{\sqrt{50}} = 0.0409

The mean of the sampling distribution of means for SRS of size 50 is \mu = 0.5 and the standard deviation is s = 0.0409

Does it matter that the underlying population distribution is not normal?

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

What is the probability a sample of 50 people will wait longer than 45 seconds for an elevator?

We have to use 45 seconds as minutes, since the mean and the standard deviation are in minutes.

Each minute has 60 seconds.

So 45 seconds is 45/60 = 0.75 min.

This probability is 1 subtracted by the pvalue of Z when X = 0.75. So

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

By the Central Limit Theorem

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

Z = \frac{0.75 - 0.5}{0.0409}

Z = 6.11

Z = 6.11 has a pvalue of 1

1-1 = 0

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

8 0
3 years ago
PLEASE HELP!!!!!!!!!!
agasfer [191]

Answer:

a = 30

b = 15

c = 3

d = 30

e = 10

f = 20

Step-by-step explanation:

60 deg and a + 30 are alt int <S and congruent

a + 30 = 60

a = 30

a + 30 and a + 2b are corresponding angles and congruent

a + 2b = a + 30

2b = 30

b = 15

a + 2b and 5b - 5c are vertical angles and congruent

5b - 5c = a + 2b

5(15) - 5c = 30 + 2(15)

75 - 5c = 30 + 30

75 - 5c = 60

-5c = -15

c = 3

a + 2b and 10c + d are corresponding angles and congruent

10c + d = a + 2b

10(3) + d = 30 + 2(15)

d + 30 = 60

d = 30

5b - 5c and 2d + 6e are supplementary and add to 180

5b - 5c + 2d + 6e = 180

5(15) - 5(3) + 2(30) + 6e = 180

75 - 15 + 60 + 6e = 180

6e + 120 = 180

6e = 60

e = 10

2d + 6e and 4f + 4e are alt int angles and congruent.

4f + 4e = 2d + 6e

4f + 4(10) + 2(30) + 6(10)

4f + 40 = 60 + 60

4f + 40 = 120

4f = 80

f = 20

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