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1 year ago

In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number

Mathematics

1 answer:

katen-ka-za [31]1 year ago

7 0

Given the radius r and the tangent line AB, the length of the line OA is 24 units

<h3>How to determine the length OA?</h3>

The radius r and the tangent line AB meet at a right angle.

By Pythagoras theorem, we have:

AB² = OA² + r²

So, we have:

24² = OA² + 7²

Rewrite as:

OA² = 24² - 7²

Evaluate

OA² = 527

Take the square root of both sides

OA = 23

Hence, the length of OA is 24 units

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Osvoldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of

saw5 [17]

Answer:

Osvoldo did not meet his goal

Step-by-step explanation:

To know the percentage of carbohydrates that Osvoldo ate from grains with respect to the total, we simply have to divide the amount of carbohydrates he got with the grains by the total

55 / 220 = 0.25

then to express it as a percentage this number has to be multiplied by 100

0.25 * 100 = 25%

Osvoldo wanted to reach 30% and only got 25%

25% < 30%

4 0

3 years ago

Simplify (5^1/3)^3.

pentagon [3]

Answer:

The correct option is C. 5

Therefore,

$(5^{\frac{1}{3})^{3}\ =\ \d5$

Step-by-step explanation:

Simplify

$(5^{\dfrac{1}{3})^{3}=?$

Solution:

Using Identity

$(x^{a})^{b}=x^{(a\times b)}$

So in the given expression

$x = 5\\a=\dfrac{1}{3}\\\\b=3$

Therefore,

$(5^{\frac{1}{3})^{3}\ =\ \d5^{(\dfrac{1}{3}\times 3)}=\d5^{1}=\d5$

Therefore,

$(5^{\frac{1}{3})^{3}\ =\ \d5$

6 0

3 years ago

A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors

mezya [45]

<h3>Answer: 491,891,400</h3>

Delete the commas if necessary.

============================================================

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

$n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\$

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

15 ways to pick the freshmen
1287 ways to pick the sophomores
70 ways to pick the juniors
364 ways to pick the seniors

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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