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Nat2105 [25]
3 years ago
15

Suppose we pick three people at random. For each of the 2.32 The following questions, ignore the special case where someone migh

t be born on February 29th, and assume that births are evenly distributed throughout the year.(a) What is the probability that the first two people share a birthday?(b) What is the probability that at least two people share a birthday?
Mathematics
1 answer:
inn [45]3 years ago
7 0

Answer:

(a) 1 in 365 or 0.2740%

(b) 0.8227%

Step-by-step explanation:

(a) For any given birthday date of the first person, there is a 1 in 365 chance that the second person shares the same birthday, therefore the probability that the first two people share a birthday is:

P = \frac{1}{365}=0.2740\%

(b) There are four possibilities that at least two people share a birthday, first and second, first and third, second and third, all three share a birthday. Therefore, the probability that at least two people share a birthday is:

P =3* \frac{1}{365}+ (\frac{1}{365})^2\\ P=0.8227\%

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PLEASE HELPPP!!!
Tems11 [23]

Answer:

a) -16t^{2}+64t\geq40

b)[2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}]

(see attached picture for the number line)

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) h_{max}=64ft

d) t=2s

Step-by-step explanation:

a)

Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:

-16t^{2}+64t\geq40

this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.

b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:

-16t^{2}+64t =40

we can move the 40 to the other side of the equation so we get:

-16t^{2}+64t-40=0

we can factor the equation so it's easier to solve, so we get:

-8(2t^{2}-8t+5) =0

which simplifies to:

2t^{2}-8t+5=0

and we can use the quadratic formula to solve this equation, so we get:

t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}

so we get:

t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}

which yields:

2\pm \frac{\sqrt{6}}{2}

and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:

(-\infty, 2-\frac{\sqrt{6}}{2}]  for a test value of 0

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

[2+\frac{\sqrt{6}}{2},\infty) for a test value of 4

so next we test each of the values in the original inequality and see if the inequality is true:

(-\infty, 2-\frac{\sqrt{6}}{2}] for a test value of 0

-16(0)^{2}+64(0)\geq40

0\geq40 false

so this is not an answer.

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

-16(1)^{2}+64(1)\geq40

48\geq40

true, so this is an answer.

[2+\frac{\sqrt{6}}{2}, \infty) for a test value of 4

-16(4)^{2}+64(4)\geq40

-16(16)+64(4)\geq40

-256+256\geq40

0\geq40

false, so this is no answer.

So the answer is the interval:

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}]

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)

so we can use the following formula to find the t-value for this maximum height:

t=-\frac{b}{2a}

so we substitute the corresponding values:

t=-\frac{64}{2(-16)}

which yields:

t=2s

next, we can substitute this time into the original function to find the maximum height, so we get:

h=-16(2)^{2}+64(2)

which yields:

h=64 ft

d) We found the answer for d on the previous part where we got that t=2s

6 0
3 years ago
Please help me no bs
Nataly_w [17]

Answer:

what do you need help with? and thank you for the points! Once you tell me what you need help with I will write the answer in the comments!

Step-by-step explanation:

3 0
2 years ago
Rochelle bought 4 pieces of ribbon to finish a project. Each puece was 1 5/12 yards long. What is the combined length of the rib
dusya [7]

Answer:

is it 15/12 or a mixed fraction

6 0
3 years ago
4.2×10 to the negative 2 power divided by 2×10 to the 2nd power
xxTIMURxx [149]
8.4 is the answer i believe
6 0
3 years ago
Read 2 more answers
Help me please!! I’m in a hurry!! 15pts!!
Nikolay [14]

Answer:

300 times

Step-by-step explanation:

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3 years ago
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