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3 years ago

Will a ratio be able to determine a percentage

Mathematics

1 answer:

AnnyKZ [126]3 years ago

7 0

Yes, to convert the ratio into the percentage, divide, the multiply the result by 100, and there is your answer !!.

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

Evaluate (104)^3 using suitable identity

egoroff_w [7]

Answer:

1124864

Step-by-step explanation:

7 0

3 years ago

How can you use estimation to find

KATRIN_1 [288]

Well you can add to find out that 9 x 5 = 45 and 1/2 x 5 = 2 1/2 so the correct answer is 47 1/2 to estimate it just do 9 x 5 = 45 Hope this helps! :D

4 0

3 years ago

Read 2 more answers

An airplane has 29 seats. The price for a coach seat is $600 in the price for a first class seat is $1050. The airline collected

In-s [12.5K]

Answer:

19 coach seats

Step-by-step explanation:

let the number of coach seats be C and number of first class seats be F

given that the total number of seats is 29,

C + F = 29 ---------(eq 1)

also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,

600C + 1,050F = 21,900 -------(eq 2)

we have 2 equations and 2 unknowns, we can solve the system of equations by elimination

(eq 1) x 1,050 gives us:

1,050 (C + F) = 1,050(29)

1,050C + 1,050F = 30,450 ----- (eq 3)

by elimination, subtract eq 2 from eq 3

(1,050C + 1,050F) - (600C + 1,050F) = 30,450 - 21,900

1,050C - 600C = 8,550

450C = 8550

C = 855 /450

C = 19

7 0

3 years ago

Q # 15 please Graph the equation .y = 4x - 3

murzikaleks [220]

Answer: Please, see the attached file.

Thanks.

Solution:

We can graph using the intercepts:

(1) y-intercept, when x=0

y=4x-3→y=4(0)-3→y=0-3→y=-3

Point=(x,y)=(0,-3)

(2) x-intercept, when y=0

y=4x-3→0=4x-3

Solving for x: Adding 3 both sides of the equation:

0+3=4x-3+3

3=4x

Dividing both sides of the equation by 4:

3/4=4x/4

3/4=x

x=3/4=0.75

Point=(x,y)=(3/4,0)=(0.75,0)

With these pair of points (0, -3) and (0.75,0) we can draw the right line

4 0

3 years ago