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3 years ago

Eight times a number increased by 9 exceeds 7 times the number by 15. Find the number.

Mathematics

2 answers:

Pavel [41]3 years ago

8 0

Remark

Reading the problem is more than 1/2 the trouble you will have with this question.

Start phrase by phrase. Let the number = x

The first phrase is 8 times a number so that is 8x

increased by 9. So that is 8x + 9

exceeds 7 times the number 8x + 9 - 7x

by 15 (translate that to equals 15)

Equation

8x + 9 - 7x = 15 Combine like terms.

x + 9 = 15 Subtract 9

x = 15 - 9

x = 6

Alborosie3 years ago

5 0

Turn it into math terms bit by bit. let x be "a number"

8 times a number is 8×x

increased by 9 is +9

7 times a number is 7×x

exceeds is minus

by 15 is =15

now we put it together.

$8 \times x + 9 - 7 \times x = 15$
solve
$8x + 9 - 7x = 15 \\ x + 9 = 15 \\ x = 6$

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3 years ago

The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$