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ale4655
7 days ago
14

A 100-gallon barrel, initially half-full of oil, develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at t

ime t. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. The mathematical model is:___________.
(a) =kA, A(0) = 0
(b) A = ktA, A(O) = 50
(c) A tA, A(0) = 100
(d) A = két +A), A
(e) = 50 None of the above.
Mathematics
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Explain two ways you could solve 20 = 5(-3 + x)
Leona [12618]

Answer:

The solution to your inquiry can be found below

Step-by-step explanation:

First method

                      20 = 5(-3 + x)                   expanding this equation

                     20 = -15 + 5x                    combine like terms

                     5x = 20 + 15

                     5x = 35                            dividing by 5

                     5x/5 = 35/5

                     x = 7

Second method

                     20/5 = 5/5 (-3 + x)          divide both sides by 5

                     4  = -3 + x                        adding 3 to both sides

                     4 + 3 = -3 + 3 + x            simplifying

                     7 = x

                     

3 0
3 months ago
A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week
tester [12383]

Answer:

a.[144;158]$

b. The parameter being estimated is the average weekly food expenses of American families.

Step-by-step explanation:

Hello!

The variable studied here represents "Weekly food expenses incurred by an American family"($)

From a sample of n=1014 American families, the sample mean is x[bar]=$151

It is indicated that for the 95% confidence interval, the margin of error is ±$7

a.

The estimated confidence interval for the population mean is formed as "estimator ± margin of error." In a Standard Normal distribution, the confidence interval formula is:

[x[bar]±Z_{\alpha/2}*(δ/√n)]

For the provided sample, we have:

[151±7]

The lower limit equates to 144$

The upper limit amounts to 158$

b.

The parameter being contemplated is the average weekly food expenses of American families.

The confidence level for this interval reflects the likelihood that if 100 such intervals were constructed, approximately 95 would encompass the true value of the population mean we aim to estimate.

Wishing you a wonderful day!

3 0
1 month ago
(1 point) Suppose F⃗ (x,y)=−yi⃗ +xj⃗ F→(x,y)=−yi→+xj→ and CC is the line segment from point P=(4,0)P=(4,0) to Q=(0,5)Q=(0,5). (a
Leona [12618]
I genuinely don’t grasp this response; it seems quite challenging.
4 0
1 month ago
In year 3 it is expected that the total value of clothing sales will reach 32 million if the total value of ASCO sells Remains t
tester [12383]

Answer:

The sales figure for the third year is [\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%].

Step-by-step explanation:

Since sales data for the second year is unavailable, we denote it as x million.

Year 3's total sales amount to 32 million.

Calculate the sales account for year 3 as follows:

\text{Percentage of sales for year 3}=\frac{\text{Total Sales in year 3}-\text{Total Sales in year 2}}{\text{Total Sales in year 2}}\times 100\%

                                                =\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%

3 0
3 months ago
After a 5% pay raise , Hermione is earning $21,000 per year. What was she earning before the pay raise?
zzz [12365]

Answer:

\$20,000

Explanation step-by-step:

Let

x represent Hermione's salary prior to the raise

Given:

100\%+5\%=105\%=105/100=1.05

Therefore, the equation that expresses this relationship is

1.05x=21,000

To find x, divide both sides by 1.05:

x=21,000/1.05

x=\$20,000

7 0
3 months ago
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