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Mama L [17]
2 years ago
12

At Lincoln High​ School, 6 students are members of both the Chess Club and the Math Club. There are 20 students in the Math​ Clu

b, 12 students in the Chess​ Club, and 400 students in the entire school. Find the probability that a student chosen at random belongs to the Chess Club or the Math Club
Mathematics
1 answer:
Rama09 [41]2 years ago
6 0
P(C or M) = P(C) + P(M) - P(C and M)

= 12/400 + 20/400 - 6/400

= 26/400 or 0.065

The answer is: P(C or M) = 0.065

Hope this helps.
:)
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Step-by-step explanation:

This is called a scalene triangle, where all 3 sides are different lengths.

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PLEASE HELP!! I DO NOT UNDERSTAND THIS ONE BIT. PLEASE RESPOND!
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2 years ago
For how many real values of x is <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B120-%5Csqrt%7Bx%7D%7D%20" id="TexFormula1" title
leva [86]

A good place to start is to set \sqrt{x} to y. That would mean we are looking for \sqrt{120-y} to be an integer. Clearly, y\leq 120, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since \sqrt{x} is a radical, it only outputs values from [0,\infty], which means y is on the closed interval: [0,120].

With that, we don't really have to consider y anymore, since we know the interval that \sqrt{x} is on.

Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval [0,120], which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

\sqrt{120-\sqrt{x}}=k \implies \\ \sqrt{x}=k^2-120 \implies\\ x=(k^2-120)^2

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.

5 0
3 years ago
Question 1
arlik [135]

Answer:

30

Step-by-step explanation:

This problem can be done without the Distance Formula (which is a way to find the distance between any two points in the plane).

The attached image shows the points and segments joining them.

PQ = 5 because the points are on the same horizontal line, and you can count spaces between them (or subtract x-coordinates: 4 - (-1) = 5).

PR = 12 because the points are on the same vertical line; count spaces or subtract y-coordinates, 7 - (-5) = 12.

The triangle is a right triangle, so the Pythagorean Theorem can be used to find the length of the hypotenuse.

(\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2

(QR)^2=5^2+12^2=25+144=169\\QR=\sqrt{169}=13

The perimeter of the triangle is 5 + 12 + 13 = 30

6 0
3 years ago
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