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aleksklad [387]

3 years ago

7

A brother and a sister are in the same math class. There are 8 boys and 10 girls in the class. One boy and one girl are randomly

chosen What
is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form

1 answer:

Anon25 [30]3 years ago

6 0

Answer:

1/80

Step-by-step explanation:

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If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

When the function below is graphed, how many x-intercepts does it have?y = 4x2 - 12x + 9?

Sladkaya [172]

Only x-intercept because if you want to know about x-intercepts so y will be zero (y=0)
then 0 =4x^2 -12x + 9
0=(2x-3)(2x-3)
0=2x-3
so x=3/2 that is x-intercept

7 0

3 years ago

Read 2 more answers

(45pts) An elevator holds at most 1,400 pounds. A team of movers and their cart have a combined weight of 1,200 pounds. If each

emmainna [20.7K]

Let $x$ be the number of boxes the team brings with them. Their weight combined with the boxes can't exceed the capacity of 1400. Assuming the elevator runs fine at that exact weight, you want to find the number of boxes, each of which contributes 40 pounds. This is given by the equation

$1400=1200+40x$

Solving for $x$ , you have

$1400=1200-40x$
$200=40x$
$x=5$

So the team can bring *at most* 5 boxes at a time.

4 0

3 years ago

Subtract j from 9, then subtract 3 from the result

Lera25 [3.4K]

Answer:

(9-j)-3

Step-by-step explanation:

Let's start from the beginning and subtract j from 9. Because the word "from" is used, 9 will be the first number and j will be the second number.

We have 9-j

Now, we have to subtract 3 from the final answer. So, we have (9-j)-3

7 0

4 years ago

What is the solution set of x2 + 5x - 5 = 0?

Llana [10]

If you're completing the square the answer is in the image.

expression

x^2 + 5x - 5=ax^2+bx+c

a=1, b=5, c=-5, and you can solve it that way.

4 0

3 years ago