60 % of 80 ASAP pls bruuh

Answer:

Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

  = x(1080 - 138x + 4x²)

  = 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.

12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

Final answer:

The size of the square that should be cut away from each corner to obtain the maximum volume for a box made from a cardboard measuring 45 by 24 inches is 3 inches.

Explanation:

To find the size of the square that should be cut from each corner to obtain the maximum volume, we should first make an equation for the volume of the box. If x is the length of the side of the square, then the dimensions of the box are (45-2x) by (24-2x) by x, thus the volume of the box V is (45-2x)(24-2x)x.

By using calculus, we can find the derivative of this function, set it to zero and solve, this will give the critical points where the maximum and minimum volumes will be.

The derivative is found to be -4x^2 + 138x - 1080. Setting this to zero and solving, we find that x = 3 and x = 90 are the critical points for the maximum and minimum volumes. Since we cannot cut corners more than 24 inches (this would make the width negative), x = 3 inches is the only feasible solution.

So, 3 inches should be cut away from each corner to obtain the maximum volume.

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Answer:

  19.9 days

Step-by-step explanation:

The amount remaining after d days is ...

  a = (1/2)^(d/7)

We want to find d when a = 0.14

  log(a) = (d/7)log(1/2)

  d = 7·log(0.14)/log(1/2) ≈ 19.855 ≈ 19.9

The farmers need to wait about 19.9 days for it to be safe.

Answer:

• a = -25: -555
• a = 1: 69
• a = 10: -30

Step-by-step explanation:

Put the value where "a" is in the expression and do the arithmetic.

1. For a = -25: 70 - (-25)² = 70 - 625 = -555
2. For a = 1: 70 - (1)² = 70 - 1 = 69
3. For a = 10: 70 - (10)² = 70 - 100 = -30

_____

If you're unsure of your own arithmetic skills, you can always use a calculator.

The equation of the circle with the given center and radius is x²-2x+y²+10y-74=0.

What is a circle equation?

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

Given that, the center of a circle is (1, -5) and the radius is 10 units.

Now, equation of a circle is

(x-1)²+(y+5)²=10²

x²+1-2x+y²+25+10y=100

x²-2x+y²+10y+26=100

x²-2x+y²+10y-74=0

Therefore, the equation of the circle with the given center and radius is x²-2x+y²+10y-74=0.

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Final answer:

To find the number of part-time employees in California, set up a proportion and solve for x.

Explanation:

To find the number of part-time employees statewide, we can set up a proportion using the given information. We know that there are 25 full-time employees for every 4 part-time employees. So, we can write the proportion as:

25 full-time employees / 4 part-time employees = 250,000 full-time employees / x part-time employees

Cross-multiplying, we get:

25x = 4 * 250,000

Simplifying, we have:

25x = 1,000,000

Dividing both sides by 25, we find:

x = 40,000

Therefore, there are 40,000 part-time employees statewide in California.

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Answer:

G: Inverse multiplication

Step-by-step explanation:

Statement is 2•1/2=1

Now, what this means is that when we multiply a number by it's inverse form, the result will be 1.

This means that this statement denotes an inverse multiplication.

Thus, the last option is the correct answer