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3 years ago

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In how many ways can a committee of 6 be formed from 18 people ? Assuming that, when people are chosen for a committee, the orde

r of the choices does not matter

1 answer:

Oksanka [162]3 years ago

4 0

Step-by-step explanation:

I think in 3 ways because total number of people is 18 and the committee should be of 6 so 18 ÷ 6 = 3

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The graphs of rational functions m and n have the same vertical asymptotes, and both have a single x-intercept at x = 5.

Hatshy [7]

Answer:

A

Step-by-step explanation:

We are given two rational functions m(x) and n(x) that have the same vertical asymptotes both with a single x-intercept at x = 5.

The correct choice will be A.

Recall the transformations of functions.

B represents m(x) being shifted up 5 units. If the function is shifted up, the vertical asymptotes will be the same, but the x-intercept will change.

C represents m(x) being shifted 5 units to the right. This changes both the x-intercept and the vertical asymptotes.

Likewise, D represents m(x) being shifted 5 units to the left. Again, this will change both the x-intercept and the vertical asymptotes.

Therefore, the only choice left is A. It represents a vertical stretch by a factor of 5. This preserves the x-intercepts and the vertical asymptotes. Consider the function:

$\displaystyle m(x)=\frac{x-5}{(x-3)(x-7)}$

If n(x)=5m(x), we can see that:

$\displaystyle n(x)=\frac{5(x-5)}{(x-3)(x-7)}$

So, the x-interceps and vertical asymptotes are preserved.

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3 years ago

Read 2 more answers

John flips three pennies. • amy peeks and sees that the first coin lands heads. what is the probability of getting all heads?

attashe74 [19]

The sample space would be 27. The probability of getting 3 heads if you flip 3 pennies is 1/27.
Hope it helps! :)

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3 years ago

Pls help me guys! This is super hard

natita [175]

I hope that this helps! Each dash represents a dot or whatever you have to put on there

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4 years ago

Ali is quite the baseball player. Forty two percent of her hits are home runs if Ali hit 150 balls last season how many of those

ra1l [238]

63 hits were home runs

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4 years ago

A diameter of a circle has endpoints p(-10,-2) and Q(4,6)

hodyreva [135]

Answer:

a. (-3,2)

b. sqrt65

c.

Step-by-step explanation:

a. To find the center of the circle, you can think of it just like finding the midpoint between the two endpoints. To find a midpoint between two endpoints, you take the average of the x values to get the x coordinate, and you take the average of the y values to get the y coordinate of the midpoint. Therefore, if (-10, -2) is (x1, y1) and (4, 6) is (x2, y2), the midpoint/center of the circle would be:

( (x1+x2)/2, (y1+y2)/2 ). When you plug in our x and y values, you get (-3, 2).

b. To find the radius of a circle, you need to know the center/midpoint of the circle which we solved for in part a. The formula for finding the radius of a circle with the center is (x-h)^2 + (y-k)^2 = r^2 for (h, k) as the center. The coordinates of the center that we found earlier for this circle are (-3, 2). With that, we just plug in our numbers into the formula, and we get:

(x+3)^2 + (y-2)^2 = r^2. Now, to get r, we can choose one of the original two endpoints given and plug in the x and y coordinates from that point into this equation. I like (4, 6), so I'm going to plug in 4 for x and 6 for y, and so we get (4+3)^2 + (6-2)^2 = r^2 which equals 49 + 16 = r^2 when simplified. 49 plus 16 is equal to 65, so we get 65 = r^2. To finally get r, we square root both sides of the equation to get r = sqrt65 which is already in the simplest radical form.

c. The circle equation is (x-h)^2 + (y-k)^2 = r^2, like I said in part b. Therefore, we already have our circle equation! We just plug in our center points and we get (x+3)^2 + (y-2)^2 = sqrt65. This is usually an equation a question will give you for a circle, and with this information, they will expect you to find the center (h, k) or the circle and it's radius, r.

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3 years ago