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Rom4ik [11]
3 years ago
8

The ratio of students to faculty members in high school is 23:5. If there are 80 faculty members, how many students are there

Mathematics
1 answer:
Rzqust [24]3 years ago
7 0

Answer: 368

Step-by-step explanation: 80 divided by 5 is 16, so you would use 16 to find out how many students there are. To do that, you have to do 23 times 16, which is 368. Hope this helps!

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OlgaM077 [116]

Answer:140

Step-by-step explanation:

4 0
2 years ago
If fx = 2x^2 + 3 and g(x) = x^2 - 7 find (f - g) (x)
Semmy [17]

(f-g) (x) means to subtract g(x) from f(x)

F(x) = 2x^2 +3

g(x) = x^2

This becomes:

2x^2 + 3 - x^2 = x^2 +3

3 0
3 years ago
Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter
Vaselesa [24]

We have been given a function f(x)=2x^3+3x^2-336x. We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

f'(x)=2(3)x^{2}+3(2)x^1-336

f'(x)=6x^{2}+6x-336

6x^{2}+6x-336=0

x^{2}+x-56=0

x^{2}+8x-7x-56=0

(x+8)-7(x+8)=0

(x+8)(x-7)=0

x=-8,x=7

So x=-8,7 are critical points and these will divide our function in 3 intervals (-\infty,-8)U(-8,7)U(7,\infty).

Now we will find derivative over each interval as:

f'(x)=(x+8)(x-7)

f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16

Since f'(9)>0, therefore, function is increasing on interval (-\infty,-8).

f'(x)=(x+8)(x-7)

f'(1)=(1+8)(1-7)=(9)(-6)=-54

Since f'(1), therefore, function is decreasing on interval (-8,7).

Let us check for the derivative at x=8.

f'(x)=(x+8)(x-7)

f'(8)=(8+8)(8-7)=(16)(1)=16

Since f'(8)>0, therefore, function is increasing on interval (7,\infty).

(b) Since x=-8,7 are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

f(-8)=2(-8)^3+3(-8)^2-336(-8)

f(-8)=1856

f(7)=2(7)^3+3(7)^2-336(7)

f(7)=-1519

Therefore, (-8,1856) is a local maximum and (7,-1519) is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

f''(x)=6(2)x^{1}+6

f''(x)=12x+6

12x+6=0

12x=-6

\frac{12x}{12}=-\frac{6}{12}

x=-\frac{1}{2}

Therefore, x=-\frac{1}{2} is an inflection point of given function.

3 0
3 years ago
Which of the following measurements results in the largest circle?
AnnZ [28]

Answer:

A

Step-by-step explanation:

A) r = 8

B) r = 4

C) r = \sqrt{\frac{30}{\pi } } ~ 3.09

D) r = \frac{30}{2\pi} = \frac{15}{\pi } ~ 4.77

Circle A has the largest radius, and thus is the largest circle

5 0
2 years ago
Select the histogram that represents the given high temperatures.
Alisiya [41]

Step-by-step explanation:

Step 1: On the horizontal axis, we can choose the scale to be 1 unit = 11 lb.Since the weights in the table start from 65, not from 0, we give a break/kink on the X-axis. Step 2: On the vertical axis, the frequencies are varying from 4 to 10.Thus, we choose the scale to be 1 unit = 2.

4 0
3 years ago
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