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3 years ago

15

you can buy popcorn at the village theater in small, medium, or large sizes. the pop corn can be buttered or plain. if all the c

hoices are equally likely, what is the probability that a customer chooses a medium size with butter

1 answer:

timama [110]3 years ago

3 0

Answer:

Step-by-step explanation:

Close to none because they are all the same price

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

2 years ago

Broccoli tastes bitter to some people. This bitterness is inherited through the TAS2R38 gene. About 52% of the population has th

Eddi Din [679]

Answer:

271 people

Step-by-step explanation:

Margin of error = critical value × standard error

At 90% confidence, the critical value is 1.645.

Standard error for a proportion is s = √(p (1 − p) / n).

0.05 = 1.645 √(0.52 (1 − 0.52) / n)

n = 271

3 0

2 years ago

PLEASE HELP!!!!<br><br> Question below.

aleksley [76]

Step-by-step explanation:

Answer is in the pic above

5 0

2 years ago

I need help! If you can help me with this I can mark you!

Alina [70]

Answer:

I think it is 82 degrees or 102 degrees depend if you pick the 10s or 100s

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

What is the measure of arc AC?

8_murik_8 [283]

If Im not mistaken, the answer should be d because if you add all the degrees up, then you would get 222. And if you subtract 360 from 222 you get 138. I hope this helps. :)

7 0

3 years ago