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2 years ago

Need help on all plz

Mathematics

1 answer:

olga55 [171]2 years ago

7 0

3.
a. 380 ÷ 38 = 10
b. 190 ÷ 38 = 5
c. 570 ÷ 38 = 15
d. use 10 times 38 = 380, 190 is half of 380 so half of 10 is 5, 570 is 380 + 190 so 10 + 5

4.
a. 670 ÷ 67 = 10
b. 603 ÷ 67 = 9
c. 737 ÷ 67 = 11
d. use 10 times 67 = 670, 603 is 670 - 67 so 10 - 1 = 9, 737 is 670 + 67 so 10 + 1 = 11

Challenge:
1062 - 279 = 783
$\frac{1}{3} (783)=261$
783 - 261 = 522
522 ÷ 15 = 34 remainder 12
So she put 34 books in each box

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A rectangle is 3 1/3 ft long and 2 1/3 feet wide. What is the distance around the rectangle?

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3 1/3= 10/3
2 1/3= 7/3
7/3 + 10/3= 17/3
17/3 (2)+ 34/3
34/3= 11 1/3
final answer = 11 1/3

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

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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:

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

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

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

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___________________________
another way to solve the equation...

150 177
_____=_____
100% x

Cross Multiply
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divide both sides by 150
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This means that:

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