What is the Distribution property of multiply addends of number,the add the products

siniylev [52]

The answer is a: 80%

6 0

3 years ago

There are approximately 40,000 people that live in a city. A sample of 20,000 people from that city are asked and 8,000 live in

Archy [21]

Answer:

16,000 people

Step-by-step explanation:

Let's write a ratio

8,000:20,000

Let's write another ratio

x:40,000

We can write a percent proportion.

$\frac{8,000}{20,000} =\frac{x}{40,000}$

We can see that the relationship between the denominators is multiplied by 2 so that means the relationship between 8,000 and x is x is 2 times greater than 8,000

Let me know if you have any questions.

8 0

3 years ago

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

Is 2 the solution to x to the third minus x minus 6 equals 0

Natali [406]

X actually equals the cube root of 6
${x}^{3} - 6 = 0 \\ {x}^{3} = 6 \\ x = \sqrt[3]{6}$

5 0

3 years ago

What is the slope intercept form of a linear function

aivan3 [116]

Answer:

In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. ... y=mx+b. Where m is the slope and b is the y-intercept.

Step-by-step explanation:<em> I hope this helps</em>

5 0

3 years ago

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