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deff fn [24]
3 years ago
13

A 170-inch board is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.

The shorter piece is ___ inches long. PLS HELP ILL GIVE BRAINLIST!!!!​
Mathematics
1 answer:
matrenka [14]3 years ago
4 0

Answer:

34 in

Step-by-step explanation:

Short piece= x

Longer piece= 4x

The shorter piece and longer piece = 170 in, so 5x= 170

To find "x", divide both sides by 5

5x/5= x

170/5=34

x=34

Hope this helps! :)

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Use the sample data and confidence level given below to complete parts a through d.
Sholpan [36]

Answer:

Step-by-step explanation:

Given that a research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1096 and x=542 who said yes.

i.e. sample size = n=1096\\

who said yes =x=542\\

Sample proportion = p=\frac{542}{1096} =0.4945

Std error of proportion = \sqrt{\frac{p(1-p)}{n} } \\=\sqrt{\frac{0.4945(1-0.4945)}{1096} } \\=0.0151

Margin of error 95% = 1.96 (se)\\=0.0296

Hence confidence interval for proportions

=(0.4945-0.0296, 0.4945+0.0296)\\= (0.4649,0.5241)

a) Point estimate =0.4945

B) Margin of error = 0.0296

C) Conf interval = (0.4649,0.5241

D) We are 95% confident that for large random samples representing the population, the proportion of yes will lie between these two values.

4 0
3 years ago
What two positive real numbers whose product is 21 have the smallest possible​ sum?
GalinKa [24]

Answer:

x=\sqrt{21}

y=\sqrt{21}

Step-by-step explanation:

Let x  and y are the two positive real numbers

product of two numbers is 21

x y=21

y=\frac{21}{x}

The sum of the two numbers is f(x) =x+y

Replace y with 21/x

f(x) =x+\frac{21}{x}

we need to find smallest possible sum , so we take derivative using power rule

f'(x)= 1-\frac{21}{x^2}

when sum is minimum then the derivative is equal to 0

0= 1-\frac{21}{x^2}

0=\frac{x^2-21}{x^2}

multiply both sides by x^2

x^2-21=0

x^2=21

Take square root on both sides

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y=\frac{21}{x}

y=\frac{21}{\sqrt{21}}

y=\sqrt{21}

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4 years ago
A student took a system of equations, multiplied the first equation by and the second equation by , then added the results toget
Ierofanga [76]

Answer:

option A

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Step-by-step explanation:

In option A, if the student multiply the first equation by 3 and the second equation by -2, then the equations become

-6x+12y = 12 and

6x-12y =-12

If she adds both equations, she will get 0 = 0

This means that the system has infinite number of solutions.

Hence, the student could have started with equations -2x + 4y = 4 and -3x + 6y = 6.

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Answer:

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