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alina1380 [7]
3 years ago
13

Henry is buying school supplies for the start of the school year. For every 3 pencils he buys 2 pens. If Henry buys 21 pencils,

how many total pencils and pens did Henry purchase?
Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
3 0

Remark

The total number of items bought is represented by 2 + 3 = 5. So for pencils to pencils + pens his ratio of pencils to total is  3/5

Equation

3/5 = 21 / x   Cross multiply

3x = 5 * 21

3x = 105

x = 105/3

x = 35

Conclusion

The total number of pens and pencils that he bought was 35 <<< Answer.

Note

He bought 35 - 21 = 14 pens. That should be 2/5 of the total.

Check

2/5 * 35 = 70/5 = 14 So it checks.


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10.
Kay [80]

Answer:

\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}

4.535 \leq \sigma^2 \leq 7.602

Now we just take square root on both sides of the interval and we got:

2.2 \leq \sigma \leq 2.8

And the best option would be:

A.  2.2 < σ < 2.8

Step-by-step explanation:

Information provided

\bar X=32.1 represent the sample mean

\mu population mean  

s=2.4 represent the sample standard deviation

n=83 represent the sample size  

Confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

The degrees of freedom are given by:

df=n-1=83-1=82

The Confidence is given by 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, the critical values for this case are:

\chi^2_{\alpha/2}=62.132

\chi^2_{1- \alpha/2}=104.139

And replacing into the formula for the interval we got:

\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}

4.535 \leq \sigma^2 \leq 7.602

Now we just take square root on both sides of the interval and we got:

2.2 \leq \sigma \leq 2.8

And the best option would be:

A.  2.2 < σ < 2.8

3 0
3 years ago
HELPPPPPPPPPPPPPPPPP
marin [14]

Answer:

x=6

Step-by-step explanation:

24÷4=6

so 6×4=24 because of distributive proterty meaning that x=6 :))

4 0
2 years ago
Wassily Leontief (1906-1999) was a Russian-born, American economist who, aside from developing highly sophisticated economic the
yKpoI14uk [10]

Answer:

The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed.  There is no leftover.

When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.

Step-by-step explanation:

a) Data and Calculations:

                        Food   Clothes  Housing  Energy  High Quality 100

                                                                                Proof  Moonshine

Farmer             0.25      0.15       0.25        0.18            0.20                    

Tailor                0.15      0.28       0.18         0.17            0.05

Carpenter        0.22      0.19       0.22        0.22           0.10

Coal Miner       0.20      0.15       0.20        0.28           0.15

Slacker Bob     0.18      0.23        0.15        0.15            0.50

Total                 1.00      1.00        1.00         1.00            1.00

6 0
3 years ago
£72 shared in the ratio of 2:7
Goryan [66]
To do that we have to add 2+7=9
Next step is to divide 72 by 9
72:9=8 - its how many pounds its in"1"
Finally we can multiply 
2*8=16
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8 0
3 years ago
Does anyone have any idea how to do this?
Mashutka [201]

Answer: D and A, B and E, C and F

Step-by-step explanation:

8 0
2 years ago
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