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Aleksandr-060686 [28]
3 years ago
11

One week, you tell two of your friends a secret. The next week, each of them tell two people the secret, and the next week, each

of those people tell two more people. So the first week, two new people know the secret; the second week, four new people know the secret; the third week, eight new people know the secret, etc. How many people find out the secret on the sixth week?
A. 32
B. 64
C. 128
D. 256
Mathematics
2 answers:
ozzi3 years ago
5 0

Answer:

B. 64

Step-by-step explanation:

The trick here is to recognize that the number of <u>new</u> people who learn this information each week is in powers of 2.

Week 0: 2^0 = 1

Week 1: 2^1 = 2

Week 2: 2^2 = 4 (2*2)

Week 3: 2^3 = 8 (2*2*2)

So following this pattern, we can just plug in 6 for week 6 and see what our answer is:

Week 6: 2^6 = 64 (2*2*2*2*2*2)

* A quick note in calculating powers:

calculating 2*2 six times is a lot of work. You know what isn't? 2*2*2 (8). You know what also isn't? 8*8. That's right, 8*8 is also 64! So instead of calculating 2*2*2*2*2*2, you can just calculate 2^3*2^3, or 8*8. :)

dusya [7]3 years ago
5 0

Answer:

B. 64 people.

Step-by-step explanation:

Each week the number who know the secret doubles so in the 4th week 8*2 = 16 ( = 2^4) new people know.

The number who find it out in the 6th week  is 2^6 = 64 people.

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The area of two similar triangles are 50dm^2 and 32dm^2. The sum of their perimeters is 117dm. What us the perimeters of each of
Kay [80]

Answer:

Perimeter of one triangle is 65 dm

Perimeter of other triangle is 52 dm

Step-by-step explanation:

Please remember the concept

If sides are in the ratio of a:b

Then the area in the ratio of a^{2} :b^{2}

It is given sum of their perimeter is 117.

Let the small triangle has perimeter as x.

So, perimeter of big triangle is 117-x.

So, we can set up equation as

\frac{50}{32} =\frac{x^{2} }{(117-x)^{2} }

Cross multiply

50(117-x)^2 =32x^2

Expand the left side

50(13689 -234x+x^{2} )=32x^{2}

Distribute the left side

684450-11700x+50x^{2}=32x^{2}

Subtract both sides 32x^{2} and rewrite it 18x^{2} -11700x+684450=0

Solve this quadratic for x.

Divide both sides of the equation by 18 to simplify.

x^{2}-650 x+38025=0

Now, if possible let's factor

Find two integers whose multiplication is 38025 but adds to -650.

-65 and -585 works.

So, we can rewrite it as

(x -65)(x-585) =0

Solve them using zero product property

x=65, x=585

So, x=65 works here.

So, perimeter of one triangle is 65 dm

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solong [7]

ANSWER

80%

EXPLANATION

Donovan got 20 questions correct and 5 questions incorrect.

This means that the total number of questions he attempted in the test is the sum of correct and incorrect questions:

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To find the percentage of correct answers, we have to divide the number of correct answers by the total number of questions attempted and multiply by 100 (per cent).

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\begin{gathered} \frac{20}{25}\cdot\text{ 100 = }\frac{4}{5}\cdot\text{ 100} \\ =\text{ 80\%} \end{gathered}

That is the percentage of correct answers.

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