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3 years ago

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Katelyn did a survey of 200 randomly selected gym members, and found that 72 of them are interested in yoga classes. The gym has

1,000 members. About how many gym members would be interested in yoga?

1 answer:

Georgia [21]3 years ago

7 0

Answer:

the answer is

360 members

that means out of 1000 members only 360 take yoga classes

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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

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3 years ago

38% of the animals are dogs. 40% of the animals are spotted. 12% of the animals are spotted dogs. What percent of the animals in

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Step-by-step explanation:

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Step-by-step explanation:

$\frac{ {4}^{8} }{ {4}^{5} } = {4}^{3}$

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Step-by-step explanation:

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mario62 [17]

Answer: choice A) 7017

==========================================================

Work Shown:

The first term is a_1 = 24 and we go up by 7 each time.
The common difference is d = 7

The nth term formula we'll use is
a_n = a_1 + (n-1)*d
a_n = 24 + (n-1)*7

----------

The 1000th term corresponds to n = 1000

Replace every n with 1000
Then use the order of operations (PEMDAS) to simplify

a_n = 24 + (n-1)*7
a_1000 = 24 + (1000-1)*7
a_1000 = 24 + (999)*7
a_1000 = 24 + 6993
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