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rewona [7]
3 years ago
9

What is the average rate of change of the function f(x)=4(2)^x from x = 0 to x = 2? Enter your answer in the box.

Mathematics
2 answers:
bekas [8.4K]3 years ago
3 0

average rate of change is just the slope from (0,f(0)) to (2,f(2))


basically, average rate of change=slope=\frac{f(2)-f(0)}{2-0}

evalaute each

f(2)=4(2)^2=4(4)=16

f(0)=4(2)^0=4(1)=4


so average rate of change=\frac{16-4}{2-0}=\fracc{12}{2}=6

average rate of change is 6

ycow [4]3 years ago
3 0

6 Just took the test. X)

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A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 2
Shalnov [3]

Answer:

The expected winnings for a person buying 1 ticket is -0.2.                  

Step-by-step explanation:

Given : A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 25 cents each, find the expected winnings for a person buying 1 ticket.

To find : What are the expected winnings?    

Solution :

There are one first prize, 2 second prize and 20 third prizes.

Probability of getting first prize is \frac{1}{20000}

Probability of getting second prize is \frac{2}{20000}

Probability of getting third prize is \frac{20}{20000}

A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each.

So, The value of prizes is

\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10

If 20000 tickets are sold at 25 cents each i.e. $0.25.

Remaining tickets = 20000-1-2-20=19977

Probability of getting remaining tickets is \frac{19977}{20000}

The expected value is

E=\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10-\frac{19977}{20000}\times 0.25

E=\frac{1000+600+200-4994.25}{20000}

E=\frac{-3194.25}{20000}

E=-0.159

Therefore, The expected winnings for a person buying 1 ticket is -0.2.

3 0
3 years ago
A photo album costs $10.49 before discount and tax.
Gemiola [76]

Answer:

Total after tax and discount is $7.78

Step-by-step explanation:

(10.49×0.3)= 3.15

10.49 - 3.15 = 7.34

(7.34×0.06)= 0.44

7.34 + 0.44 = 7.78

7 0
3 years ago
Using binomial theorem, expand (x+6)^8 <br><br> edit: You could use the help of combinations too.
Pavlova-9 [17]

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

<u>Explanation:</u>

We know

(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ

and ⁿCₐ = n! / ( a! ) . ( n-a )!

So,

(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸

         = ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ     46656 + 8x . 279936 + 1679616

         = x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

Thus, the expansion of ( x+6)⁸ using binomial theorm is

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

4 0
3 years ago
(See diagram) The gradient of the line joining the origin to the point A is 1/2. The distance between A and the origin is sqrt 2
GuDViN [60]

Answer:

(42, 21) or (–42, –21)

Step-by-step explanation:

let A(x, y), A on line 2y = x

distance

x² + y² = 2205

(2y)² + y² = 2205

y² = 441

y = ±21

x = ±42

3 0
3 years ago
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fenix001 [56]

Answer:

i dont know for shore but i think it is part 2

Step-by-step explanation:

3 0
3 years ago
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