MATHEMATICS COLLEGE

Find the area.
4 cm
6 cm
6 cm
Find the area. 4 cm 6 cm 6 cm - 1

Answers

Answer 1
Answer:

Answer:

30 cm²

Step-by-step explanation:

6*(4+6)/2=30 cm²

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According to a medical journal, the average daily U.S. diet contains 6,000 mg of sodium. How many grams is this?

Answers

OK so for every gram it is 1,000 mg so the answer to your question will be for 6,000 mg it will be 6 grams.

A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

The question is incomplete! the complete question along with answer and step by step explanation is provided below.

Question:

A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.

Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2 : Construct the 95% confidence interval. Round your answer to two decimal places.

Given Information:  

Sample mean repair cost  = $57.89

Sample standard deviation = σ = $23.69

Sample size = 8

Confidence level = 95%

Required Information:  

step 1: critical value = ?

step 2: 95% confidence interval = ?

Answer:

step 1: critical value = 2.365

step 2: 95% confidence interval = ($38.08, $77.70)

Step-by-step explanation:

Since the sample size is less than 30 and the standard deviation of the population is also unknown therefore, we can use the t-distribution to find the required confidence interval.

The confidence interval is given by

CI = \bar{x} \pm MoE\n\n

Where \bar{x} is the mean repair cost and MoE is the margin of error that is given by

$ MoE = t_(\alpha/2)((s)/(√(n) ) ) $ \n\n

Where n is the sample size, s is the sample standard deviation, and t_(\alpha/2)  is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom (DoF) = n - 1 = 8 - 1 = 7

From the t-table at α = 0.025 and DoF = 7

t-score = 2.365

Therefore, the critical value that should be used in constructing the confidence interval is 2.365

MoE = 2.365\cdot (23.69)/(√(8) ) \n\nMoE = 2.365\cdot 8.3756\n\nMoE = 19.808 \n\n

So the required 95% confidence interval is

CI = \bar{x} \pm MoE\n\nCI = 57.89 \pm 19.808\n\nCI = 57.89 - 19.808 \: and \: 57.89 + 19.808\n\nCI = \$38.08 \: and \:\:\$77.70\n

Therefore, we are 95% confident that the mean repair cost for the refrigerators is within the range of ($38.08, $77.70)

What is the solution of |x − 1| + 2 = 4? Enter your answers from least to greatest in the boxes.

Answers

Answer:

x=3 or -3

Step-by-step explanation:

hope it helps

What is the inequality solution for y+2<4

Answers

Answer:

y<2

Step-by-step explanation:

Subtract 2 on both sides

Answer:

y<2

Step-by-step explanation:

a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???

Answers

Answer:

89

Step-by-step explanation:

a sum of 1000 invested at an jntrest rate 12% per year. Find the amounts in the account after 3 years if intrest is compounded annualy, semiannually, quarerterly, monthly, and daily.

Answers

Given Information:

Annual interest rate = r = 12%

Principal amount = P = $1000

Number of years = t = 3  

Required Information

Accumulated amount = A = ?

Answer:

Annual compounding = A = $1404.93

Semi-annuall compounding = A = $1418.52

Quarterly compounding = A = $1425.76

Monthly compounding = A = $1432.30

Daily compounding = A = $1433.14

Step-by-step explanation:

The accumulated amounts in terms of compound interest is given by  

A = P(1 + i)^N

Where  P is the initial amount invested and A is the accumulated amount.

For annual compounding:

i = 0.12

N = 3

A = 1000(1 + 0.12)^3 \n\nA = \$ 1404.93

For semiannually compounding:

i = 0.12/2 = 0.06

N = 2*3 = 6

A = 1000(1 + 0.06)^6 \n\nA = \$ 1418.52

For quarerterly compounding:

i = 0.12/4 = 0.03

N = 4*3 = 12

A = 1000(1 + 0.03)^12 \n\nA = \$ 1425.76

For monthly compounding:

i = 0.12/30 = 0.004

N = 30*3 = 90

A = 1000(1 + 0.004)^90 \n\nA = \$ 1432.30

For daily compounding:

i = 0.12/365 = 0.0003287

N = 365*3 = 1095

A = 1000(1 + 0.0003287)^1095 \n\nA = \$ 1433.14
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