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Mila [183]
3 years ago
11

A teacher has a 2-gallon (32-cup) container of juice. She gives each student One-half cup of juice. Which equation represents th

e amount of juice that remains, y, after x students are served?
Mathematics
1 answer:
Talja [164]3 years ago
4 0

Answer:

Step-by-step explanation:

You would need to figure out how many students, so for example let's say 24 students, if she gives each student half a cup (a pint) and there is 32 cups 32 x 2 = 64, Then you would want to divide 64 by 2, that would give you 32 pints. So each student gets 32 pints of juice. Could be different if the number of students weren't 24. You're welcome!

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you currently have 24 credit hours and a 2.8 gpa you need a 3.0 gpa to get into the college. if you are taking a 16 credit hours
Juliette [100K]

Answer:

\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

\bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0

And we can solve for \sum_{i=1}^n w_f *X_f and solving we got:

3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f

And from the previous result we got:

3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f

And solving we got:

\sum_{i=1}^n w_f *X_f =120 -67.2= 52.8

And then we can find the mean with this formula:

\bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0

Step-by-step explanation:

For this case we know that the currently mean is 2.8 and is given by:

\bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8

Where w_i represent the number of credits and X_i the grade for each subject. From this case we can find the following sum:

\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

\bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0

And we can solve for \sum_{i=1}^n w_f *X_f and solving we got:

3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f

And from the previous result we got:

3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f

And solving we got:

\sum_{i=1}^n w_f *X_f =120 -67.2= 52.8

And then we can find the mean with this formula:

\bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0

6 0
2 years ago
What is the surface area of the triangular pyramid that can be formed from this net? A net of a triangular pyramid. The area of
Sedaia [141]

Answer:

The answer is 150

Step-by-step explanation:

5 0
3 years ago
A book has 8 chapters of equal length. Mary has read 4 chapters. What fraction of the book does Mary have left to read
11111nata11111 [884]

Answer:  1/2 I am almost sure thesis the right answer

7 0
2 years ago
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Consider the function f(x)= 2/5x-4
Gre4nikov [31]

Answer: a) \frac{5}{2}x+10=f^{-1}(x)=g(x)

Step-by-step explanation:

Since we have given that

f(x)=\frac{2}{5}x-4

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

y=\frac{2}{5}x-4

Switching x to y , we get

x=\frac{2}{5}y-4

5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)

b) . Use composition to show that f(x) and g(x) are inverses of each other.

\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x

Similarly,

\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.


5 0
3 years ago
Which two points are on the graph of y=x-4
Ann [662]

The answer is C because since the answer is 4 and if u look at c it would equal to 4.

8 0
3 years ago
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