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Strike441 [17]
3 years ago
8

The average spending at Neco's salad bar is $9.03 with a standard deviation of $3.26. The distribution follows t-distribution. T

he management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
Mathematics
1 answer:
arlik [135]3 years ago
8 0

Answer:

The difference between these cut-offs is of $1.9.

Step-by-step explanation:

In this question, we have to find the 90% confidence interval, using the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.684

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.684\frac{3.26}{\sqrt{41}} = 0.95

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.03 - 0.95 = $8.08.

The upper end of the interval is the sample mean added to M. So it is 9.03 + 0.95 = $9.98.

What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers

$9.98 - $8.08 = $1.9

The difference between these cut-offs is of $1.9.

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Answer:

<u>Approximately 16 tablets of medicine</u>

Step-by-step explanation:

Based on the information above , we can use a <u>Rule of Three</u> to first figure out how many mg the cat would need to ingest per day.

\frac{5mg}{1kg} = \frac{x}{4.5kg}

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Now we see that the cat needs to take a daily dose of 22.5mg. Since the Tablets come at a strength of 10 mg per tablet then,

22.5 / 10 = 2.25

The cat would need to take 2.25 tablets per day. Since she needs to take the dose for the next 7 days then,

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5 0
3 years ago
shayla is financing a house for $126,750. She has to pay $450 plus 1.15% for a brokerage fee. How much are the mortgage brokerag
ANEK [815]
Answer: $1,907.63

Explanation:

It is stated in the problem that the brokerage fee is $450 plus 1.15% (meaning 1.15% of $126,750). Hence the brokerage fee is computed as follows
  
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Since there is no half cents today, we round-off the brokerage fee to the nearest cent. Hence the brokerage fee is $1,907.63.

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A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. whic
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The inequality that represents the possible ways nina can eat 12 or more grams of protein is 2x + 3y ≥ 12

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

Let x be the number of cheese squares that she eats and y is the number of turkey slices that she eats. If nina can eat 12 or more grams of protein, hence:

2x + 3y ≥ 12

The inequality that represents the possible ways nina can eat 12 or more grams of protein is 2x + 3y ≥ 12

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6 0
2 years ago
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Step-by-step explanation:

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A young couple purchases their first new home in 2011 for​ $95,000. They sell it to move into a bigger home in 2018 for​ $105,00
mart [117]

Given:

The value of home in 2011 is $95,000.

The value of home in 2018 is $105,000.

To find:

The exponential model for the value of the home.

Solution:

The general exponential model is

y=ab^x       ...(i)

where, a is initial value and b is growth factor.

Let 2011 is initial year and x be the number of years after 2011.

So, initial value of home is 95,000, i.e., a=95,000.

Put a=95000 in (i).

y=95000b^x       ...(ii)

The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.

105000=95000b^7

\dfrac{105000}{95000}=b^7

\dfrac{21}{19}=b^7

Taking 7th root on both sides, we get

\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b

Put b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}} in (ii).

y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x

y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}

Therefore, the required exponential model for the value of home is y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}, where x is the number of years after 2011.

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