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3 years ago

For f(x) = 3x - 5 and g(x) = x2 + 2, find (f+ g(x).

Mathematics

1 answer:

Vladimir [108]3 years ago

8 0

Answer:

Step-by-step explanation:

hello :

f(x) = 3x - 5 and g(x) = x² + 2

(f+ g)(x)= f(x)+g(x) = 3x-5 +x²+2

(f+ g)(x).= x²+3x-3

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4(5+ab) where a=-3.5 and b-0.8

lozanna [386]

Answer:

31.2

Step-by-step explanation:

4(5 + (- 3.5 × - 0.8)

4(5 + 2.8)

4(7.8)

31.2

6 0

2 years ago

Pyramid A is a right square pyramid with a height of 100 m and a square base with a perimeter of 356 m. Pyramid B has a square b

Tomtit [17]

Answer:

The volume of pyramid B is 3.5 times greater than the volume of pyramid A

Step-by-step explanation:

The area of squared based a pyramid is given by:

$Area = \frac{1}{3}*s*s*h$

Where 's' the length of the side of the base and 'h' is the height.

For pyramid A:

h= 100 m

s= 356/4 = 89 m

$Area_A = \frac{1}{3}*89*89*100\\Area_A=264,033.33\ m^3$

For pyramid B:

h= 215 m

s= 456/4 = 114 m

$Area_B = \frac{1}{3}*114*114*215\\Area_B=931,380\ m^3$

Pyramid B has a greater volume and the ratio between volumes is:

$\frac{Area_B}{Area_A} =\frac{931,380}{264,033.33}\\\frac{Area_B}{Area_A} =3.5$

3 0

3 years ago

Harrison Water Sports has two retail outlets: Seattle and Portland. The Seattle store does 60 percent of the total sales in a ye

Anna11 [10]

Answer: P = 0.75

Step-by-step explanation:

Hi!

The sample space of this problems is the set of all the possible sales. It is divided in the disjoint sets:

$S_s = {\text{sales made in Seattle }}\\S_p={\text {sales made in Portland}}$

We have also the set of sales of boat accesories $S_b$ , the colored one in the image.

We are given the data:

$P(S_s) = 0.6\\P(S_b | S_s) = \frac{P(S_b\bigcap S_s)}{P(S_s)}=0.4\\P(S_b|S_p) =\frac{P(S_b\bigcap S_p)}{P(S_p)}=0.2$

From these relations you can compute the probabilities of the intersections colored in the image:

$pink\;set:\;P(S_b \bigcap S_s) =0.6*0.4=0.24\\blue\;set\;:P(S_b \bigcap S_p)=(1-0.6)*0.2 =0.08$

You are asked about the conditional probability:

$P(S_s|S_b) = \frac{P(S_s \bigcap S_b)}{P(S_b)}$

To calculate this, you need $P(S_b)$ . In the image you can see that the set $S_b$ is the union of the two disjoint pink and blue sets. Then:

$P(S_b)=P((S_b \bigcap S_s)\bigcup(S_b \bigcap S_p)) = 0.24 + 0.08 = 0.32$

Finally:

$P(S_s|S_b) = \frac{0.24}{0.32}=0.75$

4 0

3 years ago

a culture started with 2000 bacteria. after 4 hours it grew to 2200. predict how many bacteria will be present after 9 hours. ro

Sati [7]

First you will divide;
200÷4=50
Then you multiply;
50×9=450
Last you add;
2000+450=2450

4 0

3 years ago

Read 2 more answers

04.03 HC)

faust18 [17]

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.

(b) Explain why one rate of change is greater than the other.

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.

6 0

2 years ago