MATHEMATICS COLLEGE

1 point 7. Jayven buys a wooden board that is 7 feet long. The cost of the board is $0.50 per foot, including tax. What is the total cost, in dollars, of Jayven's board. *​

Answers

Answer 1
Answer: Answer
$3.5

Explanation
$.50 x 7 = $3.5

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The owner of a fabric store has determined that the profits P of the store are approximately given by P(x) = -x^2 + 70x+67, where x is the yards of fabric sold daily. Find the maximum profit to the nearest dollar. a) $617 b) $792 c) $1017 d) $1292 e) none

Answers

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given that

Profit function of the store is given by

P(x)=-x^2+70x+67

We need to find the maximum profit.

For this, we first derivate the above function:

P'(x)=-2x+70

Now, put P(x) = 0, we get that

-2x+70=0\n\n-2x=-70\n\nx=35

Now, we will check that its maximality by finding the second derivative:

P''(x)=-2<0

it gives maximum profit at x = 35 yards.

And the maximum profit would be

P(35)=-(35)^2+70* 35+67=\$1292

Hence, Option 'd' is correct.

Please help me 80% of what number is 16 What is the part?
What is the total?
What is the percent?
What is the answer?​

Answers

Answer:

80 percent of 16 is 12.8 I'm sorry but that's all I know

What is the value of x? 2.5x = 35 x = 14 x = 16

Answers

The value of X is 14. It is 14 because two point 2.5×14 = 35!

HELPPP PLESSEEE I NEEDIT RN TYY

Answers

Answer:

1. 12

2. 0

3. 10

4. 6

Step-by-step explanation:

More on the Leaning Tower of Pisa. Refer to the previous exercise. (a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987, calculate a predicted value for the lean in 1918. (Note that you must use the coded value 18 for year.)

Answers

Answer:

2.9106

Step-by-step explanation:

According to the information of the problem

Year 75   76   77   78    79    80    81      82 83 84 85 86 87

Lean 642 644 656  667   673  688 696  698 713 717 725 742 757

If you use a linear regressor calculator you find that approximately

y = 9.318 x - 61.123

so you just find x = 18  and then the predicted value would be 106mm

therefore the predicted value for the lean in 1918 was 2.9106

Sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/x^3 .a. Find (exactly) the number a such that the line x = a divides R into two parts of equal area.
b. Then find (to 3 decimal places) the number b such that the line y = b divides R into two parts of equal area.

Answers

For part (a), you're looking to find a such that

\displaystyle\int_1^a(\mathrm dx)/(x^3)=\int_a^2(\mathrm dx)/(x^3)

You have

\displaystyle\int_1^a(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=1)^(x=a)=-\frac12\left(\frac1{a^2}-1\right)

and

\displaystyle\int_a^2(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=a)^(x=2)=-\frac12\left(\frac14-\frac1{a^2}\right)

Setting these equal, you get

\displaystyle-\frac12\left(\frac1{a^2}-1\right)=-\frac12\left(\frac14-\frac1{a^2}\right)\implies a=2√(\frac25)

For part (b), you have

y=\frac1{x^3}\implies x=\frac1{\sqrt[3]y}

and you want to find b such that

\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(\sqrt[3]y)=\int_b^1(\mathrm dy)/(\sqrt[3]y)

You have

\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(y^(1/3))=\frac18+\frac32y^(2/3)\bigg|_(y=1/8)^(y=b)=-frac14+\frac32b^(2/3)

and

\displaystyle\int_b^1(\mathrm dy)/(y^(1/3))=\frac32y^(2/3)\bigg|_(y=b)^(y=1)=\frac32-\frac32b^(2/3)

Setting them equal gives

-\frac14+\frac32b^(2/3)=\frac32-\frac32b^(2/3)\implies b=\frac7{24}√(\frac73)\approx0.446
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