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2 years ago

Linda liked 80% of the movies she saw last year. If she liked 60 movies, how many did she see?

Mathematics

1 answer:

Mama L [17]2 years ago

4 0

Answer:

The correct answer Is that saw 75 movies last year.

Step-by-step explanation:

To solve this problem, we can write an equation. Let N equal the number of movies that he saw last year and we have:

N x (0.8) = 60

If we divide both sides by 0.8, we will get 75 for N.

Hope this helps you!!

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A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

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6 0

3 years ago

HELP ASAP ALL THREE PLEASE 1. if a cyclic alkene has 12 carbon atoms, how many hydrogen atoms does it have 2.if a cyclic alkene

Marina CMI [18]

Answer:

1. 24

2. 6

3. No

Step-by-step explanation:

The formula for cyclic alkene is $C^{n} H^{2n}$ , so if it has 12 carbon atoms, it will have double the amount of hydrogen atoms, therefore, 24 hydrogen atoms.

The same works in reverse. If we have 12 hydrogen atoms in this, then there will be half the amount of carbon atoms, therefore 6.

Since the relationship between Carbon and Hydrogen here is double and half, odd numbers can't be divided by 2 and end up with a whole number, so an odd number of hydrogen atoms is not possible.

Hope this helped!

5 0

3 years ago

Find the surface area of a cylinder with a base radius of 2 yd and a height of 3 yd.

kherson [118]

Answer:

20 π

Step-by-step explanation:

The surface area of a cylinder is made up of 2 circles and its side.

To find the circles' areas, use the area formula for a circle: A = π $r^2$ .

Since our radius is 2 yd, we can substitute r = 2 into this formula.

A = π $2^2$ = 4π

Now remember, this is only the area of once circle. Multiply 4π by 2 to get the area of both circles: 8π.

Now we need to find the surface area of the side.

If we flatten it out, we can see that the side is actually a curled up rectangle.

The length is the circumference of the circle and the width is the height of the cylinder.

To find the circumference, use the circumference formula for a circle: C = 2πr.

Substitute r = 2 into the formula.

C = 2π2 = 4π

Now that we know that the length is 4π, we can multiply the length by the width to find the area of the cylinder's side.

l = 4π

w = 3

A = lw = 4π * 3 = 12π

Finally, we can add the areas of the circles and the side to get the total surface area.

8π + 12π = 20π

And that is your answer!

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3 0

3 years ago

Line 1 passes through the points (-4, -6) and (12,2). line 2 passes through the points (-6,-2) and (-2,0). Do the lines intersec

kifflom [539]

The lines dont intersect

7 0

3 years ago

The manager of a warehouse would like to know how many errors are made when a product’s serial number is read by a bar-code read

stira [4]

The mean of the answer is 20.5 because you add all of the number together and divide by 6 because there's 6 numbers.
I'm sorry, but I don't know how to do the standard deviation...
Hope this helped!

4 0

3 years ago