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LenKa [72]
3 years ago
15

There are 80 students in a school. Every student is taking either algebra or pre-calculus, and some students are taking both. Th

ere are 60 students in the algebra class. If 15 students are taking both algebra and pre-calculus, what is the probability that a randomly selected student is taking pre-calculus but not algebra?
Mathematics
1 answer:
Finger [1]3 years ago
3 0

Answer:

1/4

Step-by-step explanation:

Total students = 80

Students taking both classes =  15

Students taking algebra class = 60

Students taking only algebra class = 60 - 15 = 45

Students taking only pre-calculus class = 80- (45+15) = 80 - 60 = 20

P( students taking pre-calculus but not algebra) = 20/80 = 1/4

                         

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A prism is 6 × 1 × 6 units.<br><br> Volume = ______ units3
hodyreva [135]
The answer is 36

Explanation:6x1=6
6x6=36
7 0
3 years ago
How many joules of gravitational potential energy are stored in an object that has a mass of 8.5 kilograms and is held 2 meters
adoni [48]

Answer:

I believe the answer is 166.6 Joules or (if rounding to the nearest whole number) 167 Joules.

Step-by-step explanation:

Here is the formula to find the gravitational potential energy of an object:

U = m * g * h (potential energy equals mass times gravitational acceleration * the height)

The mass is 8.5 kilograms, the height is 2 meters, and Earth's gravitational acceleration is always, no matter the other values or earthly situations, 9.8 m/s.

Now we solve:

8.5 * 9.8 * 2 = 166.6 which is rounded to 167 Joules.

8 0
3 years ago
A shipping company needs to determine the number of Styrofoam packing peanuts that fit per square foot in a box that measures 20
Mumz [18]
1) We have 1300 packing peanuts, and 20 ft^2. Therefore, to find out how many packing peanuts there are per square foot, we divide the number of peanuts (1300) by the number of square feet (20 ft^2). This gives us 1300 / 20 = 65 packing peanuts per square foot.
2) We do not know the current volume of the box which fits the 1300 packing peanuts (all we know is its area). But it is reasonable to expect that if we increase the volume by 25%, the number of packing peanuts will also increase by 25%. This means we can fit 1300*(1.25) = 1625 peanuts in the larger box.
3) This will depend on how the box is larger. If its height remains the same, and its floor area increases to accommodate the greater volume, then the number of packing peanuts per square foot remains the same.
However, if the height of the box is different, then the number of packing peanuts per square foot will change, since the floor area will not increase by the same 25% any more.
3 0
4 years ago
D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
MA_775_DIABLO [31]
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

r^2-16k=0\implies r=\pm4\sqrt k

which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
b(1-16k)=30\implies b=\dfrac{30}{1-16k}

and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
8 0
3 years ago
Which expression is equivalent to (x y) z?
stepan [7]

Answer:

x(yz)

Step-by-step explanation:

(xy)z = x(yz) by the associative property of multiplication.

Answer: x(yz)

5 0
3 years ago
Read 2 more answers
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