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RUDIKE [14]
3 years ago
8

Due to gravity, an object falls 16t² feet in t seconds. You drop a backpack from a window that is 100 feet above the ground. Wil

l the backpack hit the ground in 3 seconds?
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

the backpack will be on the ground in 3 seconds but it will first make contact with the ground in 2.5 seconds

Step-by-step explanation:

the equation would be:  y = -16t² + 100

if you solve for 't' then you will find the amount of time until it lands

0 = -16t² + 100

-100 = -16t²

100/16 = t²

t = √100/16

t = 10/4 = 2.5

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At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper
Korvikt [17]

Answer:

90.67% probability that John finds less than 7 golden sheets of paper

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.

This means that p = 0.3

14 of these containers of paper.

This means that n = 14

What is the probability that John finds less than 7 golden sheets of paper?

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{14,0}.(0.3)^{0}.(0.7)^{14} = 0.0068

P(X = 1) = C_{14,1}.(0.3)^{1}.(0.7)^{13} = 0.0407

P(X = 2) = C_{14,2}.(0.3)^{2}.(0.7)^{12} = 0.1134

P(X = 3) = C_{14,3}.(0.3)^{3}.(0.7)^{11} = 0.1943

P(X = 4) = C_{14,4}.(0.3)^{4}.(0.7)^{10} = 0.2290

P(X = 5) = C_{14,5}.(0.3)^{5}.(0.7)^{9} = 0.1963

P(X = 6) = C_{14,6}.(0.3)^{6}.(0.7)^{8} = 0.1262

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0068 + 0.0407 + 0.1134 + 0.1943 + 0.2290 + 0.1963 + 0.1262 = 0.9067

90.67% probability that John finds less than 7 golden sheets of paper

7 0
3 years ago
How pure is 16-karat gold?
natta225 [31]

Answer:

here

Step-by-step explanation:

16 karat gold is 16 parts gold to 8 parts other material for a pure gold percentage of 67%.

3 0
3 years ago
Read 2 more answers
A person invested $6,000, some at 7% and the rest at 5%. The income from the 7% investment is equal to the income from the 5% in
8090 [49]

Answer:

The person invested $3500 at 7% and $2500 at 5%

Step-by-step explanation:

We can say that 0,07x+0,05x=6000 because the investment is equal both in one as in another, where x is the income from the investment.

Solving the equation we have:

0,12x=6000\\x=50000

Then to get the incomes:

At 7%: I=0.07*50000\\I=$3500

And at 5%: I=0.05*50000\\I=$2500

Finally we can demonstrate the answer because the  income at 7% + income at 5% are 3500+2500=$6000

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3 years ago
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3,5

1 across and 1 down pattern
find the halfway point
5 0
3 years ago
What does this mean I need help?
chubhunter [2.5K]

Answer:

Step-by-step explanation:

x > 3 reads x is greater than three. This includes all numbers to the right of three, but not three itself.    |₋₋|₋₋|₋₋₀---|---|---|---|---|---|----->

                                             0 1  2  3  4  5  6  7  8  9

x ≤5  reads x is less than or equal to five. This includes all numbers to the left of and including the number 5    <--|---|---|---|---|---|---|--•₋₋₋|₋₋|₋₋₋|₋₋₋|₋₋₋₋

                                                           -2 -1  0  1  2  3  4  5  6  7  8  9

x ≥ -4 reads x is greater than or equal to minus four. This includes all numbers to the right of and including -4.    

 |₋₋₋|₋₋₋|₋₋₋•---|---|---|---|---|---|---|-->

-7 -6  -5  -4 -3 -2  -1  0  1  2  3

6 0
3 years ago
Read 2 more answers
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