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3 years ago

13

Which expressions are equivalent to (2^5)^-2

1 answer:

Aleonysh [2.5K]3 years ago

6 0

Answer: Choice B) 2^(-10) and 1/1024

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Explanation:

We'll use these two rules
Rule 1: (a^b)^c = a^(b*c)
Rule 2: a^(-b) = 1/(a^b)

Using rule 1 above, we can say
(2^5)^(-2) = 2^(5*(-2)) = 2^(-10)
So 2^(-10) is one of the answers

Now use rule 2 to convert 2^(-10) into...
2^(-10) = 1/(2^10) = 1/1024
so 1/1024 is the other answer

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Isabella save 2 nickels today, if she doubles the number of Nicole, she saves every day, how many days, including today, will it

Elden [556K]

Answer:

8 days

Step-by-step explanation:

On day 8, Isabella will save 256 nickels, bringing her total to 510.

_____

The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

_____

The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

__

The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...

an = a1·r^(n-1) = 2·2^(n-1) = 2^n

The sum of n terms of the sequence is ...

S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)

S = 2^(n+1) -2

__

We want S > 500, so ...

500 < 2^(n+1) -2

502 < 2^(n+1)

251 < 2^n

log(251) < n·log(2)

n > log(251)/log(2)

n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels

3 0

3 years ago

2) At the store Julie bought a shirt for $23.97, which was 25% off the original price. Which of these should she use to find x,

Scrat [10]

Answer:

0.75x = 23.97

Step-by-step explanation:

The total is 23.97. 0.25% is off so you have to subtracting 25% from 100% and you will get 75% if you convert it to decimal you will get 0.75.

5 0

3 years ago

What is the cube root of 216x18?

Vikentia [17]

Answer:

<u>The correct answer is 15.72 or 6 ∛18</u>

Step-by-step explanation:

Let's calculate the cube root of 216 * 18

∛(216 * 18)

216 = 8 * 27

8 = 2³; 27 = 3³

18 = 9 * 2 or 3² * 2

∛(8 * 27 * 18)

Simplifying:

∛(2³ * 3³ * 3² * 2)

∛(2³ * 3³ * 3² * 2)

2 * 3 ∛(3² * 2

<u>6 * 2.62 = 15.72 or 6 ∛18</u>

8 0

3 years ago

11x + 12 = 8x - 9 ... please

Marat540 [252]

Assignment: $\bold{\Solve \ Equation: \ 11x+12=8x-9}$

<><><><><><><>

Answer: $\boxed{\bold{x=-7}}$

<><><><><><><>

Explanation: $\downarrow\downarrow\downarrow$

<><><><><><><>

[ Step One ] Subtract 12 From Both Sides

$\bold{11x+12-12=8x-9-12}$

[ Step Two ] Simplify

$\bold{11x=8x-21}$

[ Step Three ] Subtract 8x From Both Sides

$\bold{11x-8x=8x-21-8x}$

[ Step Four ] Simplify

$\bold{3x=-21}$

[ Step Five ] Divide Both Sides By 3

$\bold{\frac{3x}{3}=\frac{-21}{3}}$

[ Step Six ] Simplify

$\bold{x=-7}$

<><><><><><><>

$\bold{\rightarrow Mordancy \leftarrow}$

4 0

3 years ago

Read 2 more answers

3/5 of juice is poured equally into 6 glasses. How much juice is in each glass?

olasank [31]

Answer:

1/10 or 0.1

Step-by-step explanation:

3/5 of juice split into 6 glasses can be written as

3/5 ÷ 6

See the attached image for help with dividing fractions.

4 0

3 years ago

Read 2 more answers