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IRISSAK [1]
3 years ago
15

A 60 inch board is to be cut into three peices so that the second peice is four times as long as the first peice and the third p

eice is 5 times as long as the first peice. If x represents the length of the first peice find the lengths of all three peices
Mathematics
1 answer:
Lostsunrise [7]3 years ago
6 0

Answer:

The first piece is 6 inches, the second piece is 24 inches, and the third piece is 30 inches

Step-by-step explanation:

Since the second piece is 4 times longer than the first one, it will be represented by 4x.

The third piece is 5 times as long as the first one, so it will be represented by 5x.

Create an equation adding up the 3 x values up to 60:

x + 4x + 5x = 60

Add like terms and solve for x:

10x = 60

x = 6

So, the first piece is 6 inches.

Then, plug in 6 for x to find the lengths of the second and third pieces.

4x

4(6)

= 24

The second piece is 24 inches

5x

5(6)

= 30

The third piece is 30 inches

So, the first piece is 6 inches, the second piece is 24 inches, and the third piece is 30 inches

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MA_775_DIABLO [31]

In order to find the scale they are using first you must divide 12 by 3.75.

But since we get to estimate, the 3.75 will be made into a 4 because it's the whole number closest to 3.75.

12/4=3

Take your 3 inch scale and multiply it by 3 (we are using 3 instead of 2.8 because it's a whole number) to get the real life fence size.

3x3=9

The fence is about 9 feet.

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
Navy PilotsThe US Navy requires that fighter pilots have heights between 62 inches and78 inches.(a) Find the percentage of women
Zigmanuir [339]

The first part of the question is missing and it says;

Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.

Answer:

A) Percentage of women meeting the height requirement = 72.24%

B) Percentage of men meeting the height requirement = 0.875%

C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches

Step-by-step explanation:

From the question,

For men;

Mean μ = 68.6 in

Standard deviation σ = 2.8 in

For women;

Mean μ = 63.7 in

Standard deviation σ = 2.9 in

Now let's calculate the standardized scores;

The formula is z = (x - μ)/σ

A) For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224

So, percentage of women meeting the height requirement is 72.24%.

B) For men;

Z = (62 - 68.6)/2.8 = -2.36

Z = (78 - 68.6)/2.8 = 3.36

Thus, the probability of only men will take the form of;

P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961

And P(Z > -2.36) = 0.99086

Thus;

P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875

So, percentage of women meeting the height requirement is 72.24%.

B)For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875

So, percentage of women meeting the height requirement is 0.875%

C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.

For women;

Let's find the z-value with a right-tail of 10%. From the second table i attached ;

invNorm(0.90) = 1.2816

Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches

For men;

We have seen that,

invNorm(0.90) = 1.2816

Thus ;

Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches

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