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Rama09 [41]
3 years ago
7

IMPOSSIBLE PLEASE HELP! ALSO MAKE SURE TO WRITE A LET STATEMENT

Mathematics
1 answer:
madam [21]3 years ago
4 0
Q1 :
x + (x+25) = 131
2x + 25 = 131
2x = 131-25
2x = 106
x = 53
53+25 = 78
Therefore, 53+78=131

Q2 :
x + (x+14) = 58
2x + 14 = 58
2x = 58-14
2x = 44
x = 22
22+14 = 36
Therefore, 22+36=58

Q3 :
let ‘b’ be basketball
b + (3+b) = 27
2b + 3 = 27
2b = 27-3
2b = 24
b = 12
12 + 3 = 15
Therefore, 12 + 15 = 27
12 basketballs and 15 footballs were sold on Saturday

Q4 :
let ‘s’ be soup
s + 2s = 738
3s = 738
s = 246
246 x 2 = 492
Therefore, the hamburger has 492 calories while the soup as 246 calories

hope it helps somehow!

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3 years ago
The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 1
yarga [219]

Answer:

  A.  26 ft

Step-by-step explanation:

You might recognize that this triangle is a 5-12-13 triangle scaled up by a factor of 2. If so, you know immediately, that the hypotenuse is 2×13 = 26 feet in length.

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If you're not so lucky, you can write equations involving the lengths of the legs of the triangle. Let those be x and y, with x being the shorter leg. Then the Pythagorean relation tells you ...

  x² + y² = (x+16)²

and the area relation tells you ...

  120 = (1/2)xy

Using the second equation to write an expression for y, we have ...

  y = 240/x

Substituting this into the first equation gives ...

  x² + (240/x)² = (x+16)²

  (240/x)² = 32x +256 . . . . subtract x²

  1800 = x²(x +8) . . . . . . . . .multiply by x²/32

This is a cubic with one real root. It can be solved several ways. I like "graphing" as it is quick and easy. Trial and error also works. The factors of 1800 include 10²·18, so it is clear that x=10 is the solution.

The hypotenuse length is x+16, so is 26 feet.

___

The attachment shows the graphical solution of the original two equations. This tells you the legs of the triangle are 10 and 24, so the hypotenuse will be 10+16 = 26. The 10-24-26 triangle is recognizable as a scaled version of the 5-12-13 triangle often used in math problems.

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3 years ago
An automobile manufacturer would like to know what proportion of its customers are not satisfied by the service provided by the
zheka24 [161]

Answer:

The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Past studies suggest this proportion will be about 0.15

This means that p = 0.15

Find the sample size needed if the margin of error of the confidence interval is to be about 0.04

This is n when M = 0.04. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.04 = 1.96\sqrt{\frac{0.15*0.85}{n}}

0.04\sqrt{n} = 1.96\sqrt{0.15*0.85}

\sqrt{n} = \frac{1.96\sqrt{0.15*0.85}}{0.04}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.15*0.85}}{0.04})^{2}

n = 17.5

Rounding up

The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

8 0
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