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emmasim [6.3K]
2 years ago
10

Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes

the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy?
Mathematics
1 answer:
schepotkina [342]2 years ago
5 0

Let number of caps =x

charge of one cap =$6

charge of x caps =6x

shipping fee =$25

total budget =$1000

let us make an inequality equation here,

Since amount cannot be greater than 1000 , so

25+6x ≤1000

6x≤975

x≤162.5

rounding off ,

x≤163

So she can buy maximum 163 caps

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A large school district is considering moving up the start date for the school year by two weeks. In order to determine if famil
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Answer:

(a) Confirmation bias

(b) Likely less than actual proportion of families who support the proposal

(c) Random sample

(d) Nonresponse bias

Step-by-step explanation:

In confirmation bias, the researcher already has and intends to prove an assumption about the effect the of a treatment before carrying out the survey, such that the survey or research is tries to dictate to the participants in the survey about the desired outcome

In the question, the belief of the researcher is expressed to the participants in a form of brief at the start of the survey which is attempting to influence the responses to the survey, such that the actual result should be less than what was observed.

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The Polk Company reported that the average age of a car on U.S. roads in a recent year was 7.5 years. Suppose the distribution o
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Answer:

The standard deviation of car age is 2.17 years.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5

(a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age?

This means that 1 is 3 standard deviations below the mean and 14 is 3 standard deviations above the mean.

So

14 = 7.5 + 3\sigma

I want to find \sigma

3\sigma = 6.5

\sigma = \frac{6.5}{3}

\sigma = 2.17

The standard deviation of car age is 2.17 years.

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<span>(    7 x    -    11    )

<span>(   7   -   5x   )</span></span>
4 0
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The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la
cluponka [151]

Answer:

x = 31 hundred dolars   and      

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

P(x) is the profit

R(x) is the revenue

and C(x) is the costs

In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

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⇒ P'(x) = -8x²-7y²-141x+203y+14xy-1850

The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

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Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

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we get the solution

x = 31     and       y = 91/2 = 45.5

Finally, the company should produce  3100  units of the first system, and  4550 units of the second system.

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