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3 years ago

6

Rickey has been commissioned to paint a mutual that is allowed to have an area 60 square meters to make the rectangulr shape of

the mural pleasing the eye Rickey wants the length to be 15 meters longer than twice its width ehat length should Rickey use for the mural

1 answer:

Svet_ta [14]3 years ago

5 0

Answer:

Length of the mural should be 20.78 m

Step-by-step explanation:

Let the length of the mural be L and the width W

Area = L × W = 60 m²

Ticket wants the L = 15 + 2W

Substitute for L in the Area eqn

(15 + 2W) × W = 60

15W + 2W² = 60

2W² + 15W - 60 = 0

Solving the quadratic equation

W = 2.89 m or - 10.39 m

Obviously, the width cannot be negative,

So, W = 2.89 m

L = 15 + 2W = 15 + 2(2.89) = 20.78 m

Check - L × W = 20.78 × 2.89 = 60 m²

Hope this Helps!!!

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Step-by-step explanation:

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3 years ago

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A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const

Ludmilka [50]

Answer:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation

s=0.68 represent the sample standard deviation

$\bar x =98.90$ represent the sample mean

n=98 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=98-1=97$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,97)" "=CHISQ.INV(0.95,97)". so for this case the critical values are:

$\chi^2_{\alpha/2}=120.990$

$\chi^2_{1- \alpha/2}=75.282$

And replacing into the formula for the interval we got:

$\frac{(97)(0.68)^2}{120.990} \leq \sigma \leq \frac{(97)(0.68)^2}{75.282}$

$0.371 \leq \sigma^2 \leq 0.596$

Now we just take square root on both sides of the interval and we got:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

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4 years ago

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I am Lyosha [343]

Answer:

Solving the equation $(2.4 \times 103) \times (3 \times 10n) = 7.2 \times 109$ we get $\mathbf{n=0.10582}$

Step-by-step explanation:

We need to find the value of n in the given equation

$(2.4 \times 103) \times (3 \times 10n) = 7.2 \times 109$

The equation can be simplified by using multiplication and division rules.

The first step is to solve brackets.

$(2.4 \times 103) \times (3 \times 10n) = 7.2 \times 109\\247.2 \times 30n=784.8$

Then, Divide both sides by 247.2

$30n=\frac{784.8}{247.2}\\30n=3.1746$

Now, divide both sides by 30

$n=\frac{3.1746}{30} \\n=0.10582$

We get the value of n: n=0.10582

So, solving the equation $(2.4 \times 103) \times (3 \times 10n) = 7.2 \times 109$ we get $\mathbf{n=0.10582}$

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3 years ago