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3 years ago

Estimate the sum 1 3/7 + 3 5/9 + 1/2 show your work

Mathematics

2 answers:

yarga [219]3 years ago

5 0

691/126
Answer as fractions form

stiv31 [10]3 years ago

3 0

Answer:

5.48

Step-by-step explanation:

First, we convert all the fractions into improper fractions. 1 3/7 is 10/7, 3 5/9 is 32/9, and 1/2 stays the same. then we find a common denominator, which would be the LCM of 7, 9 and 2, which is 126. Finally, we rewrite the fractions with the common denominator of 56, and we get 180/126, 448/9 and 63/126. adding these together we get 691/126, which is approximately 5.48412698, which we can round to 5.48

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3 years ago

The area of a sector of a circle with a central angle of radians is . Find the radius of the circle. Do not round any intermedia

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Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the complete question in the diagram attached.

Area of a sector = θ/360 * πr² where;

r is the radius

θ is the angle substended by the sector

Given parameters

Area of the sector = 9ft²

central angle θ = 1.5 radians

Since 1 radians = 57.2958°

1.5 radians = (1.5 * 57.2958)

1.5 rad = 85.9437°

Substituting the given values into the formula;

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3 years ago

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Given that in 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008.

Part a) :

Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of (to 4 decimals).

Population proportion = 0.75
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$Standard\ error=\sqrt{\frac{p(1-p)}{n}} \\ \\ =\sqrt{\frac{(0.75)(0.25)}{450}} = 0.0204$

Therefore, the sampling distribution has a proportion of 0.75 and a standard error of 0.0204.

Part b) :

Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion (to 4 decimals)?

The probability that the sample proportion will be within 0.04 of the population proportion is given by:

$P(p\ \textless \ 0.75\pm0.04)=2P\left(z\ \textless \ \frac{0.04}{0.0204} \right)-1 \\ \\ 2P(z\ \textless \ 1.961)-1=2(0.97505)-1=1.9501-1 \\ \\ =\bold{0.9501}$

Therefore, the probability that the sample proportion will be within .04 of the population proportion is 0.9501.

Part C:

Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of (to 4 decimals).

Population proportion = 0.75
sample size. n = 200
$Standard\ error=\sqrt{\frac{p(1-p)}{n}} \\ \\ =\sqrt{\frac{(0.75)(0.25)}{200}} = 0.0306$

Therefore, the sampling distribution has a proportion of 0.75 and a standard error of 0.0306.

Part D):

Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion (to 4 decimals)?


The probability that the sample proportion will be within 0.04 of the population proportion is given by:

$P(p\
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\right)-1 \\ \\ 2P(z\ \textless \ 1.306)-1=2(0.90429)-1=1.80858-1 \\ \\
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Therefore, the probability that the sample proportion will be within .04 of the population proportion is 0.8086.

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3 years ago