MATHEMATICS COLLEGE

Find the time needed for
a $500 to gain an interest of $150 at 7.5% rate.

Answers

Answer 1

Answer:

Answer:

4 years

Step-by-step explanation:

This is a problem in simple interest: i = prt, where:

p is the principal (intial amount), i is the interest, r is the annual interest rate and t is the time in years.

Solving i = prt for t, we get t = ------

$150

which comes out to t = --------------------- = 4 years

($500)(0.075)

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According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 57% of the college graduates who cannot find a job are female and that 18% of the college graduates who can find a job are female. Given a male college graduate, find the probability he can find a full time job in his chosen profession? (See exercise 58 on page 220 of your textbook for a similar problem.)

What is the answer too 6+3=x-8?

Answers

Answer:

x = 17

Step-by-step explanation:

Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group?

Answers

Answer: 1.48

Step-by-step explanation:

From binomial distribution, the formula to find the standard deviation is given by :-

$\sigma=√(np(1-p))$ , where n is the sample size and p is the proportion of success.

Given : The percent of chance that a candle is defective. If the company selected 50 candles off the line : 4.6%

i.e. The proportion of success : p=0.046

Sample size : n=50

Then, Standard deviation = $\sigma=√(50(0.046)(1-0.046))$

$\sigma=1.48128322748\approx1.48$

Hence, the standard deviation of the number of defective candles in the group=1.48

2.02 Graded Assignment: Graphing Exponential Equationssum consumer mathwill give brainliest1. We mentioned how the price of movie tickets has increased over time with inflation in Unit 6. Let’s let the equation y = 0.50(1.06)x represent the price of movie tickets for the years after 1950.Using this equation, find the price for 2022, 2023 and 2024

Answers

Answer:

2022: 33.19

2023: 35.18

2024: 37.29

Explanation:

The given equation to find the ticket price is

$y=0.5(1.06)^x$

Where x is the number of years after 1950.

So, to find the price for 2022, 2023 and 2024, we need to replace x by 72, 73 and 74 respectively because

2022 - 1950 = 72

2023 - 1950 = 73

2024 - 1950 = 74

Then, the price for each year is

$\begin{gathered} 2022\colon y=0.5(1.06)^(72) \n y=0.5(66.37) \n y=33.19 \n 2023\colon y=0.5(1.06)^(73) \n y=0.5(70.36) \n y=35.18 \n 2024\colon y=0.5(1.06)^(74) \n y=0.5(74.58) \n y=37.29 \end{gathered}$

Y/9 + 5 = 0 ???????????

Answers

Answer:

$y=-45$

Step-by-step explanation:

$(y)/(9)+5=0$

$(y)/(9)=-5$

$y=-45$

Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

Answers

Answer:

1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean

2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

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 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 $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?

The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.

Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.

2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

We have that:

$\mu = 168000, \sigma = 40000, n = 100, s = (40000)/(√(100)) = 4000$

This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (164000 - 168000)/(4000)$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Final answer:

1. We have a higher probability of obtaining a sample estimate within $10,000 of the population mean when the standard deviation is smaller. In this case, the standard deviation for female graduates is smaller, so the probability is higher. 2. The probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean can be calculated using the z-score formula and the z-table.

Explanation:

1. In the case where the standard deviation is smaller, we have a higher probability of obtaining a sample estimate within $10,000 of the population mean. This is because a smaller standard deviation indicates less variability in the data, making it more likely for the sample mean to be closer to the population mean. In this case, the standard deviation for female graduates is smaller, so the probability is higher.

2. To calculate the probability, we need to calculate the z-score and then use the z-table. The z-score formula is z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values, we find the z-score and use the z-table to find the probability.

Learn more about Probability here:

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If a shoe company has $1 million in fixed costs, its average shoe sells for $50 a pair, and variable costs are $30 per unit, how many units does the company need to sell to break even? (Show work)