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3 years ago

Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x^3 + 2.

Mathematics

1 answer:

den301095 [7]3 years ago

7 0

Step-by-step explanation:

step 1. we will denote the average rate of change as r.

step 2. r = (f(5) - f(3))/(5 - 3)

step 3. r = (375 - 81)/2

step 4. r = 294/2

step 5. r = 147.

step 6. note: this is just like finding m. m = (y2 - y1)/(x2 - x1)

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A new crew of painters can paint a small apartment in 12 hours. an experienced crew can paint the small apartment in 6 hours. ho

Yakvenalex [24]

This is the concept of proportionality, we are required to calculate for the number of hours two crews can use to paint the house altogether.
Here proceed as follows;
number of hours new crew can paint=12 hrs
portion of work painted by new crew in 1 hour= 1/12

number of hours experienced crew can paint=6 hours
Portion of work painted by experienced crew in 1 hour=1/6

Portion of work painted by the two crews altogether in 1 hour will be:
1/6+1/12=1/4

thus the total amount of hours that the two painters will take to paint will be:
4 hours

6 0

3 years ago

Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on

Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.
If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by = $\frac{^{3}C_2 }{^{47}C_2}$ {∵ one king is already there}

= $\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}$ {∵ $^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{3}{1081}$ = 0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = $\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}$

= $\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}$

= $\frac{6}{1081}$ = 0.0055

Now, probability that he ends up with a full house = $\frac{3}{1081} + \frac{6}{1081}$

= $\frac{9}{1081}$ = <u>0.0083</u>.

3 0

3 years ago

Read 2 more answers

PLEASE I NEED HELP!!!!!

AVprozaik [17]

Answer:

113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1

7 0

3 years ago

Solve the equation 5x-2x^2+1

Pani-rosa [81]

Answer:

Step-by-step explanation:

If you call "5x-2x^2+1" an "equation," then you must equate 5x-2x^2+1 to 0:

5x-2x^2+1 = 0

This is a quadratic equation. Rearranging the terms in descending order by powers of x, we get:

-2x^2 + 5x + 1 = 0. Here the coefficients are a = -2, b = 5 and c = 1.

Use the quadratic formula to solve for x:

First find the discriminant, b^2 - 4ac: 25 - 4(-2)(1) = 25 + 8 = 33

Because the discriminant is positive, the roots of this quadratic are real and unequal.

-b ± √(discriminant)

Applying the quadratic formula x = --------------------------------

we get:

-5 ± √33 -5 + √33

x = ----------------- = --------------------- and

2(-2) -4

-5 - √33

---------------

-4

5 0

3 years ago

Find the volume of a cone with a radius of 8 cm and height 15 cm? Round to the nearest tenth. Please show work.

Nonamiya [84]

You multiply radius by 3.14 by the height if you plug it in your equation is 8×3.14×15 which equals 1005.31 which rounds to 1005, the answer is 1005! :D

4 0

3 years ago