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Nitella [24]
3 years ago
7

A framing company is putting out a new product this summer. The width of the frame will be uniform all the way around. The desig

ned frame will be cut out of a piece of steel, and to keep the weight down, the final area of the frame alone should be 100 cm2. The inside of the frame has to be 10 cm by 8 cm. What should the width x of the metal be?
11.2 cm

7.4 cm

3.4 cm

2.2 cm
Mathematics
1 answer:
Lisa [10]3 years ago
8 0

Answer:

Correct option: Fourth one -> 2.2 cm

Step-by-step explanation:

The inside of the frame is 10 cm by 8 cm. To find the whole frame, we need to add two times the width of the metal to each dimension, so the final dimension is 10+2x cm by 8+2x cm.

The area of the frame itself is the area with the bigger dimensions (10+2x and 8+2x) minus the inside area (80 cm2)

If the final area is 100 cm2, we have that:

Area = (10+2x) * (8+2x) - 80

100 = 80 + 36x + 4x2 - 80

4x2 + 36x -100 = 0

x2 + 9x - 25 = 0

Using Bhaskara's formula to solve the quadratic function, we have:

Delta = 81 + 4*25 = 181

sqrt(Delta) = 13.45

x1 = (-9 + 13.45)/2 = 2.225 cm

x2 = (-9 - 13.45)/2 = -11.225 cm (not a valid measurement)

So the width x of the metal is 2.2 cm

Correct option: Fourth one

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Answer:

The sample size n = 4225

Step-by-step explanation:

We will use maximum error formula = \frac{z_{a} S.D}{\sqrt{n} }

but we will find sample size "n"

\sqrt{n}  = \frac{z_{a} S.D}{maximum error}

Squaring on both sides , we get

n  = (\frac{z_{a} S.D}{maximum error})^2

Given 99% confidence interval (z value) = 2.56

given maximum error = 0.02

n  = (\frac{z_{a} p(1-p)}{maximum error})^2

n≤ (\frac{2.56X\frac{1}{2} }{0.02}) ^{2}    ( here S.D = p(1-p) ≤ 1/2

on simplification , we get n = 4225

<u>Conclusion</u>:

The sample size of two samples is  n = 4225

<u>verification</u>:-

We will use maximum error formula = \frac{z_{a} S.D}{\sqrt{n} } = \frac{2.56 1/2}{\ \sqrt{4225} }  = 0.0196

substitute all values and simplify we get maximum error is 0.02

4 0
3 years ago
Bill will randomly pick one marker a bag and one crayon from another bag.There are three red markers, 2 green markers , and 1 bl
Tanzania [10]

Answer:

i believe it is 2/6

Step-by-step explanation:

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3 years ago
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Can you help me? <br> y= x + 7
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Answer:

your slope is 1/1 and your y-intercept is 7. you have to plot this on a graph.

Step-by-step explanation:

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5 5/8 - 5 1/8 simplify .
uranmaximum [27]

Answer: 5 : 3 1/8 = 8 : 5

Step-by-step explanation:

Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

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4 0
3 years ago
The length of a postage stamp is
AleksAgata [21]
<h3>Answer: Choice B</h3><h3>2W+2( W+4 1/4) = 124 1/2</h3>

=========================================

Explanation:

L = length

W = width

"The length is 4 1/4 longer than the width" (paraphrase) so

L = W + 4 1/4

This means,

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P = 2L+2W

2L+2W = P

2W+2L = P

2W+2( L ) = P

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