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2 years ago

15

Elijah gave out a survey to some students in his school about their favorite color. 392 of those surveyed said their favorite co

lor was red. If 56% of the students surveyed said their favorite color was red, how many students were surveyed in total?

1 answer:

Softa [21]2 years ago

6 0

Answer:

700

Step-by-step explanation:

It was right on my test lol

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A square has a side that is (x-3) units long. If the area of the square is 126.5625 sq units, what is the value of x?

Kitty [74]

Answer:

14.25 units

Step-by-step explanation:

Area of a square= $l*b= (x-3)(x-3)=x^{2}-3x-3x+9=x^{2}-6x+9$

$x^{2}-6x+9=126.5625$

$x^{2}-6x-117.5625$

Solving the equation using quadratic equation then as attached

x=14.25 units

To prove

x-3=14.25-3= 11.25 units

area=11.25*11.25=126.5625 sq units

4 0

3 years ago

Tony separates a number of paintbrushes, x, into 3 equally sized groups. He claims that this is the same as making a group 1/3 t

DochEvi [55]

Answer:

Size of each group = $\frac{x}{3}$

Step-by-step explanation:

Total number of paint brushes = x

Since each the three groups are equally sized, to get the number of paintbrushes in a group, we will have to divide the total number of paint brushes by 3

∴ We have, number of paint brushes in a group = $\frac{Total number of paintbrushes}{3}\\$

= $\frac{x}{3}$

this is also the same thing as saying $\frac{1}{3}$ × $\frac{x}{1}$

This shows that the size of the new group is the same as $\frac{1}{3}$ the size of the original group

4 0

3 years ago

I’m need help with the question in general.

navik [9.2K]

Answer:

I Cant See

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

Enjoy the points :D eeeeeeeeeeeeee

balandron [24]

The answer is 4/8 because half of 16 is 8 and half of 8 is 4, therefore they are equivalent

3 0

3 years ago

Read 2 more answers