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Nitella [24]
3 years ago
14

the students in Mr. hardings gym class went on a class ski trip. Each student paid $25 and the school paid a total of $300. Alto

gether, the trip cost at most $550. How many students went on the trip? Can you right this as an inequality?
Mathematics
2 answers:
vlada-n [284]3 years ago
6 0
There are 22 students
Anton [14]3 years ago
5 0
300/25= 12 students on trip
550-300=250
25x+250 is less than or equal to $550
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Sofias gym membership is $275 per year in addition to an annual locker fee of $95. What is the monthly fee?
Stels [109]
275+95= 370
370/12= $30.88
5 0
3 years ago
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Find the indefinite integral using the substitution provided.
Nady [450]

Answer:  7\text{Ln}\left(e^{2x}+10\right)+C

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation u = e^{2x}+10

Apply the derivative and multiply both sides by 7 like so

u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\

Integrating leads to

\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of \frac{14e^{2x}}{e^{2x}+10}

4 0
2 years ago
Zoey made 6 1/2 cups of trail mix for a camping trip. She wants to divide the trail mix into 3/4 cup of servings. Twelve people
AlekseyPX

Answer:

No

Step-by-step explanation:

Given that:

Total number of cups of trail mix available for camping trip = 6\frac{1}{2}

Amount of one serving contains = \frac{3}{4} cups

Number of people at the trip = 12

To find:

Whether each person will be able to get the servings?

Solution:

Here, we can find the total number of servings by dividing the total number of cups of trail mix with the amount of one serving.

First of all, let us convert the mixed fraction into fractional number.

6\dfrac{1}{2} = \dfrac{6\times 2+1}{2} = \dfrac{13}{2}

Therefore, total number of servings available as per the given quantities:

\dfrac{\frac{13}2}{\frac{3}4}\\\Rightarrow \dfrac{13\times 4}{2\times 3} \\\Rightarrow \dfrac{26}{3}\\\Rightarrow \approx 8

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Therefore, there is not enough servings.

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Alik [6]

Step-by-step explanation:

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3 years ago
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