MATHEMATICS HIGH SCHOOL

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t^2 + 48t + 100

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answers

Answer 1
Answer: f(x)=-16t^(2) +48t+100
Average rate of change from t = 3 to t = 5 = (f(5)-f(3))/(5-3)= (( -16(5^(2))+48(5)+100)-(-16(3^(2))+48(3)+100))/(2)= ((-16(25)+240+100)-(-16(9)+144+100))/(2)=((-400+240+100)-(-144+144+100))/(2)= (-60-100)/(2)=(-160)/(2)=-80

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The area of the garden is 160 meter squared.Suppose the length of the garden is 3m more than twice its width.What is the length of the garden?

Answers

w-width\n\n2w+3-length\n\n160m^2-area\ of\ the\ garden\n\nw\time(2w+3)-area\ of\ the\ garden\n\nw(2w+3)=160\n\n2w^2+3w-160=0

a=2;\ b=3;\ c=-160\n\n\Delta=b^2-4ac\to\Delta=3^2-4\cdot2\cdot(-160)=9+1240=1249\n\nw_1=(-b-\sqrt\Delta)/(2a);\ w_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(1249)\approx35.34\n\nw_1=(-3-35.34)/(2\cdot2) < 0;\ w_2=(-3+35.34)/(2\cdot2)=(32.34)/(4)=8.085\ (m)\n\nlength\approx2\cdot8.085+3=19.17\ (m)

Jared recently purchased a new pair of running shoes. He got a 20% discount, which saved him $9.00

Answers

If you are looking for the total price of the shoes its really quite simple, if 20% is $9 then you can just multiply that by 5 and get $45 so the total cost of the shoes would be $45        But- if you are looking to see what he actually paid then it would be $36

A deck of 52 cards contains four aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player?

Answers

Answer:

The probability that all four aces will be received by the same player is approximately 0.01.

Step-by-step explanation:

Of the 52 cards the four  aces can be selected in 52\choose4 ways.

If any one of the players receives all the four aces then that player can be selected in 4\choose1 ways.

Now for the selected player to receive all the four aces, the four ace cards must be placed among the 13 cards the player receives. This can be done in 13\choose4 ways.

Then the total number of ways such that all the four aces is received by one player is 413\choose4.

Then the probability that all four aces will be received by the same player is:

4*\frac{{13\choose4}}{{52\choose4}}=4*(715)/(270725) =0.01056\approx 0.01

Thus, the probability that all four aces will be received by the same player is approximately 0.01.

Final answer:

The probability that all four aces will be received by the same player in a game of 52 card deck distributed among four players is given by the formula P(E) = 4 * C(48, 9) / C(52, 13), derived through principles of combinatorics.

Explanation:

This is a probability problem that can be solved using combination and permutation principles in mathematics. Specifically, the subject involves combinatorics.

First, we note that each of the four players is dealt 13 cards from a 52 card deck. Hence, for a single player, the total number of ways 13 cards can be chosen from 52 is given by the combination formula C(n, r) = n! / [(n-r)!r!], where ! denotes factorial. In our case, n=52, and r=13.

The total number of ways to deal these 13 cards is thus C(52, 13).

Next, we need to consider the specific case where all four aces end up with one player. This means this player has 9 other cards that are not aces, from the remaining 48 cards (52 total cards - 4 aces). This can happen in C(48, 9) ways.

Therefore, the probability that a specific player gets all four aces is P(E) = C(48, 9) / C(52, 13).

To find the probability that any of the four players gets all four aces, we multiply this result by 4, because there are four players.

So, the final probability is P(E) = 4 * C(48, 9) / C(52, 13).

Learn more about Probability here:

brainly.com/question/22962752

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Answers

Answer:

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Step-by-step explanation:
I’m pretty sure it’s 70

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Answers

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Answers

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Step-by-step explanation:

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