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Arlecino [84]
3 years ago
11

What is the minimum number of selections from the set { 1, 3, 5, 7, 9, 11, 13, 15 } that we need to guarantee that at least one

pair of those numbers adds up to 16?
Mathematics
1 answer:
anygoal [31]3 years ago
3 0
Perhaps I don't understand the question. You only need to choose one pair that adds to 16, any of {1, 15}, {3, 13}, {5, 11}, {7, 9}.

You can choose up to 4 numbers without getting a pair that adds to 16, so if you choose any 5 numbers, at least one pair of them will add to 16.
You might be interested in
Original price $65.00; Markdown: 12%
MAVERICK [17]
65 x .12 = 7.865 - 7.8 = 57.2

8 0
3 years ago
The combustion of one gallon of automobile fuel produces about 5 pounds of carbon (in CO₂). Two autos are making a trip of 600 m
rewona [7]

Answer:

Approximately 50 pounds less carbon (in CO₂) will be produced by the second auto on this trip.

Step-by-step explanation:

We have been given that the combustion of one gallon of automobile fuel produces about 5 pounds of carbon (in CO₂). Two autos are making a trip of 600 miles.

Let us find amount of fuel used by autos by dividing the total distance by their mileage.

\text{Fuel used by 1st auto}=\frac{\text{ 600 miles}}{\frac{\text{ 20 miles}}{\text{gallon}}}

\text{Fuel used by 1st auto}=\frac{\text{ 600 miles}}{\text{ 20 miles}}\times \text{gallon}

\text{Fuel used by 1st auto}=30 \text{ gallons}

\text{Fuel used by 2nd auto}=\frac{\text{ 600 miles}}{\frac{\text{ 30 miles}}{\text{gallon}}}

\text{Fuel used by 2nd auto}=\frac{\text{ 600 miles}}{\text{ 30 miles}}\times \text{gallon}

\text{Fuel used by 2nd auto}=20 \text{ gallons}

Let us find the difference of fuel used by both autos.

\text{Number of gallons that 2nd auto used less than 1st auto}=30-20

\text{Number of gallons that 2nd auto used less than 1st auto}=10

Since one gallon of automobile fuel produces about 5 pounds of carbon, so 10 gallons of fuel will produces 5\times 10=50 pounds of carbon.

Since 2nd auto used 10 gallons less than 1st auto, therefore, 2nd auto will produce 50 pounds less carbon than 1st auto.

8 0
3 years ago
A real estate agent has 12 properties that she shows. She feels that there is a 30% chance of selling any one property during a
Ronch [10]

Answer:

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property, which means that the binomial probability distribution is used 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.

A real estate agent has 12 properties that she shows.

This means that n = 12

She feels that there is a 30% chance of selling any one property during a week.

This means that p = 0.3

Compute the probability of selling no more than 2 properties in one week.

2 or less sold, which is:

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

In which

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

P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138

P(X = 1) = C_{12,1}.(0.3)^{1}.(0.7)^{11} = 0.0712

P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678

Then

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0138 + 0.0712 + 0.1678 = 0.2528

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

8 0
3 years ago
Which graph shows a line with positive slope that passes through the point (r, s)?
Nadusha1986 [10]

r is the x coordinate and s is the y coordinate. Positive slopes go from lower left to upper right, like going up stairs or up a hill. The line that goes through (r, s) that is positive is line B.

5 0
3 years ago
What is a equivalent fraction of 10/25, 6/8, 3/5, 1/10​
user100 [1]

Answer:

Step-by-step explanation:

10/25=20/50=40/100

6/8=3/4=12/16

3/5=6/10=60/100

1/10=10/100

6 0
3 years ago
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