On a quiz harry got 12 out of 15 items correct.what was his quiz score

There are 50 animals in a shelter. Sixty percent of the animals are dogs. Which equation can be used to find the number of dogs

svetoff [14.1K]

50*.6=30

so if you solve this equation it would be 30 dogs in the shelter

8 0

3 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

What number comes next in this pattern? 46, 49, 52, 55, 58,...

Ksenya-84 [330]

Answer:

61

Step-by-step explanation:

just add 3 to the next one

8 0

3 years ago

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One sixth of a jar of sweets contains 11 sweets. How many sweets does the jar contain when its full?

vivado [14]

Answer:

66 sweets

Step-by-step explanation:

all you need to do is multiply 11 by 6 to get your answer seeing that ⅙ of the jar is 11

5 0

2 years ago

Define a variable and write an equation to model each situation. Then solve. Show your work. Tickets to the county fair for four

Citrus2011 [14]

If x is the childrens ticket
$4(x + 1.5) + 5x = 33.30 \\ 4x + 6 + 5x = 33.3 \\ 9x = 33.3 - 6 \\ 9x = 27.3 \\ x = \frac{27.3}{6} \\ x = 4.55$
so that means that the adults ticket is
$x + 1.50 = 4.55 + 1.50 = 6.05$

4 0

3 years ago