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I am Lyosha [343]
3 years ago
7

1. State if each scenario involves a permutation or a combination. Then find the number of possibilities:(a) Castel and Joe are

planning trips to three countries this year. There are 7 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks.(b) You are setting the combination on a three-digit lock. You want to use the numbers 123 but don't care what order they are in.(c) A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
Mathematics
1 answer:
BaLLatris [955]3 years ago
5 0

Answer:

a) This is a permutation, there are 210 ways to do it

b) This is a permutation with 6 possibilities

c) This is a combination with a total of 1081575 possibilities

Step-by-step explanation:

a) Here the order does matter bacause it is not the same that they go to France in the weak trip than they go there for 2 days, as a result, this scenario is a permutation.

You need to pick 3 countries from a total of 7, but the order matters, so the total amount of ways to do this is

{7 \choose 3} * 3! = \frac{7!}{(7-3)!} = 210

b) Here each permutation of 123 will give you a possible (and a different one from the others) lock-combination, so this is again a permutation.

The total amount of ways we have to do the selectio of the lock-combination is the total amount of permutations of a set of 3 elements, in other words, it is 3! = 6.

c) If you only cares about who advances to the finals, then the order doesnt matter here, you just want 8 people out of the 25 available. This is therefore a combination, and the total amount of possible cases are

{25 \choos 8} = 1081575 .

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boyakko [2]

The slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.

<h3>What is Slope?</h3>

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the given containing ordered paid A(2,-5) and B(-2,6) is:

Slope = 6+5/-2-2 = 11/-4

Hence, the slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.

Learn more about Slope of Line:

brainly.com/question/14511992

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1 year ago
Helpppp pweeseee, i cant figure this out, it has something to do with slope intercept form
andrew-mc [135]

Answer:

The answer should be B) The initial fee of $25

Step-by-step explanation:

The equation for slope-intercept form is y = mx + b, with b being the y-intercept. In this equation, b = 25. The question is asking to interpret the y-intercept, so you would have to reread the question and see that it says the company charges your team with "an initial fee of $25". So, the answer is B.

7 0
2 years ago
Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from t
Mandarinka [93]
Parameterize the intersection by setting x(t)=t, so that

x^2=2y\iff y=\dfrac{x^2}2\implies y(t)=\dfrac{t^2}2
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The length of the path C is then given by the line integral along C,

\displaystyle\int_C\mathrm dS

where \mathrm dS=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt. We have

\dfrac{\mathrm dx}{\mathrm dt}=1
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and so the line integral is

\displaystyle\int_{t=0}^{t=2}\sqrt{1^2+t^2+\dfrac{t^4}4}\,\mathrm dt

This result is fortuitous, since we can write

1+t^2+\dfrac{t^4}4=\dfrac14(t^4+4t^2+4)=\dfrac{(t^2+2)^2}4=\left(\dfrac{t^2+2}2\right)^2

and so the integral reduces to

\displaystyle\int_{t=0}^{t=2}\frac{t^2+2}2\,\mathrm dt=\dfrac{10}3
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3 years ago
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lubasha [3.4K]

Answer:

Try typing into a scientofic calculator I reccomed the site desmos

Step-by-step explanation:

7 0
3 years ago
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xxTIMURxx [149]
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