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SSSSS [86.1K]
3 years ago
11

Kallie wants to invite Ainsley, Alysse, Bre, Becky, and Darla to a movie, but her mom will only allow her to invite two friends.

She writes the name of each friend on a piece of paper and places them in a bag. She randomly selects two papers from the bag. What is the probability that the names of the two friends she selects start with the same letter? Show your work.
Mathematics
1 answer:
Lana71 [14]3 years ago
5 0

Answer:

The probability that Kallie will select two friends whose names starts with the same letter is \frac{1}{5}.

Step-by-step explanation:

There are a total of 10 different outcomes of selecting two friends without caring about order. Out of the 10 possible outcomes, only 2 of them meet the requirement of the names of her friends starts with the same letter. So the probability that Kallie will select two friends whose names starts with the same letter is \frac{2}{10} or \frac{1}{5}.

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The Pythagorean's Theorem for our situation would look like this:

shortleg^2+longleg^2=hypotenuse^2

So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:

s^2+(2s+4)^2=(2s+6)^2

And of course we have to expand. Doing that will leave us with

s^2+4s^2+8s+8s+16=4s^2+12s+12s+36

Combining like terms we have

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Our job now is to get everything on one side of the equals sign and solve for s

s^2-8s-20=0

That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!

6 0
3 years ago
Please help me please
Gnoma [55]
Eq1
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3 years ago
Please Help. ASAP!!
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Answer:

Equation:   x + (x+ 1) = 67

Step-by-step explanation:

We want to find two consecutive integers.

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