MATHEMATICS COLLEGE

A new homeowner is mulching a flower bed in his back yard. The flower bed is 9 feet long and 3.5 feet wide. How many square feet will be needed to cover it in mulch?

Answers

Answer 1

Answer:

Answer:

31.5ft²

Step-by-step explanation:

Formula for area:

Area = Length * Width

Calculate area by substituting in known values

Area = 9 * 3.5

Area = 31.5ft²

31.5ft²

Hope this helps :)

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A local BBQ restaurants offers 2 side dishes with a lunch plate. There are 7 side dishes. How many choices of side dishes does a customer have

Answers

Step-by-step explanation:

This is a question that bothers combination. Combination has to do with selection.

When selecting r objects out of a pool of n objects, the number of ways this can be done is:

nCr = n!/(n-r)!r!

If a local BBQ restaurants offers 2 side dishes with a lunch plate, and there are 7 side dishes, the number of choices that the customer have is expressed as:

7C2 = 7!/(7-2)!2!

7C2 = 7!/(5)!2!

7C2 = 7*6*5!/5! * 2

7C2 = 7*6/2

7C2 = 42/2

7C2 = 21 choices

Hence the customer has 21 choices of side dishes to make

The skip interval in systematic random sampling is computed by dividing the number of potential sampling units on the list by the desired sample size .O True
O False

Answers

Answer:

True

Step-by-step explanation:

The skip interval in systematic random sampling is computed by dividing the number of potential sampling units on the list by the desired sample size .

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval (the sampling interval).

Sampling interval is calculated by dividing the population size by the desired sample size

When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know whether his IL or FL electric bill is relatively more or less expensive, when compared to the distribution of electric bills for each state. In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20. In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00. Compute the z-scores for Stephan's IL and FL electric bills. Round to three decimal places if necessary.

Answers

Using it's formula, it is found that the z-scores are:

For Illinois, of Z = -0.625.

For Florida, of Z = -0.75.

Due to the lower z-score, the bill is relatively lower in Florida.

Z-score:

In a distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It measures how many standard deviations the measure is from the mean.

The higher z-score means that the measure X is relatively higher.

In Illinois:

Bill of $83, mean of $85, standard deviation of $3.2, hence $X = 83, \mu = 85, \sigma = 3.2$

Then:

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

$Z = (83 - 85)/(3.2)$

$Z = -0.625$

In Florida:

Bill of $102, mean of $105, standard deviation of $4, hence $X = 102, \mu = 105, \sigma = 4$

Then:

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

$Z = (102 - 105)/(4)$

$Z = -0.75$

Due to the lower z-score, the bill is relatively lower in Florida.

To learn more about z-scores, you can take a look at brainly.com/question/21620274

Answer: The z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

Step-by-step explanation:

Given: Average monthly electric bill in Illinois = $83

Average monthly electric bill in Florida = $102

Formula of z : $z=(X-mean)/(standard\ deviaton)$

In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20.

$z=(83-85)/(3.20)= -0.625$

In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.

$z=(105-102)/(4)=(3)/(4)=0.75$

Hence, the z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

A random survey of teachers found that 224 of 395 elementary school teachers, and 126 of 266 high school teachers, were very satisfied with their work. Find a 95% confidence interval for the difference (elementary minus high school) in proportions of teachers who are very satisfied with their work.

Answers

Answer: 95% confidence interval would be (0.013,0.167).

Step-by-step explanation:

Since we have given that

survey of teachers found that 224 of 395 elementary school teachers,

So, n₁ = 395

x₁ = 224

So, $p_1=(224)/(395)=0.567$

n₂ = 266

x₂ = 126

So, $p_2=(x_2)/(n_2)=(126)/(266)=0.473$

At 95% confidence level, z = 1.96

So, interval would be

$(p_1-p_2)\pm z\sqrt{((p_1(1-p_1))/(n_1)+(p_2(1-p_2))/(n_2)}}\n\n=(0.567-0.473)\pm 1.96\sqrt{(0.567* 0.433)/(395)+(0.527* 0.473)/(266)}}\n\n=0.09\pm 1.96* 0.0394\n\n=0.09\pm 0.077\n\n=(0.09-0.077,0.09+0.077)\n\n=(0.013,0.167)$