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3 years ago

40% of college students scored more than 70% on a math test. 120 students scored below that.

1 answer:

4 0

So if 40% of college students scored above 70%, then 60% of college students scored below 70%.

Our equation would be: 0.60x=120
x=120/0.60
x=12000/60
So x equal 200 students took the math test

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A grandfather clock’s pendulum has a period of 4.5 seconds. What is its frequency? Round to the nearest hundredth.

Brilliant_brown [7]

Answer: 0.22hz

Step-by-step explanation:

Hi to answer this question we have to analyze the information given:

<em>Period (T) = 4.5 Seconds </em>

So, to calculate the frequency of the pendulum we have to apply the formula;

Frequency (f)= 1 / period

Replacing with the value given:

f = 1/ 4.5 sec = 0.22 hz

Feel free to ask for more if needed or if you did not understand something.

7 0

3 years ago

Heron wants to buy a video game. The price is regularly priced at 55 dollars. The store has a discount of 20% off and a sales ta

nadezda [96]

The amount paid by Heron for the video game is $46.64.

Step-by-step explanation:

Here, the marked price of the video game = $55

The discount percentage on the video game = 20%

Calculating 20% of the $55, we get:

$\frac{20}{100} \times 55 = 11$

So, the discount offered on the video game = $11

Selling Price = Marked Price - Discount

=$55 - $11 = $44

Now, the tax percentage on the video game = 6%

Calculating 6% of the $44, we get:

$\frac{6}{100} \times 44 =2.64$

So, the tax on the video game = $2.64

New Selling Price = Selling Price + Tax

=$44 + $2.64 = $46.64

So, the amount paid by Heron for the video game is $46.64.

4 0

3 years ago

Need help with AP CAL

anzhelika [568]

Answer: Choice C

$\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)$

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Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve $y = e^{-x}$

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is $e^{-x}$ where 0 < x < 1

Let's compute the area of each general cross section.

$\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\$

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

$\displaystyle \int_{0}^{1}e^{-2x}dx\\\\$

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

If x = 0, then u = -2x = -2(0) = 0
If x = 1, then u = -2x = -2(1) = -2

This means,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\$

I used the rule that $\displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx$ which says swapping the limits of integration will have us swap the sign out front.

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Furthermore,

$\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$