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3 years ago

7

on a recent test matthew got 18 out of 40 problems correct at the same rate how many problems would matthew get correct if there

were 60 problems

1 answer:

Flauer [41]3 years ago

8 0

Answer:

27

Step-by-step explanation:

18/40 = 27/60

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A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

6 0

3 years ago

Which of the following correctly uses absolute value to show the distance between –60 and 11?

MissTica

Answer:

C) |–60 + 11| = |–49| = –49 units

Step-by-step explanation:

4 0

3 years ago

Fifteen times the square of a non-zero number is equal to 20 times number.What is the number? Its not 4/3

e-lub [12.9K]

The number is (2√3) / 3

To find the missing number, convert what it says in words to an equation:
$15 {x}^{2} = 20x$
Divide both sides by 15:
${x}^{2} = \frac{20}{15} \\ \\ {x}^{2} = \frac{4}{3}$
Take the square root:
$x = \sqrt{ \frac{4}{3} } \\ \\ x = \frac{2}{ \sqrt{3} } \\ \\ x = \frac{2 \sqrt{3} }{3}$

4 0

3 years ago

C. Make n subject of the formula<br>S= n/2 [2a + (n - 1)d]<br><br>please provide your working out

yKpoI14uk [10]

Answer:

$n=\frac{4as -2ds}{(1-2ds)}$

Step-by-step explanation:

$S= \frac{n}{2 [2a + (n - 1)d]}$

Simplifying the fraction by multiplying d into the (n-1) term,

$s=\frac{n}{2 [2a + (n - 1)d] } = \frac{n}{2[2a + dn - d] }$

Simplifying the fraction by multiplying 2 throughout,

$s= \frac{n}{4a + 2dn-2d}$

Multiply $(4a + 2dn-2d)$ on both sides

$(4a + 2dn-2d)s= \frac{n}{4a + 2dn-2d} (4a + 2dn-2d)$

Cancel the $(4a + 2dn-2d)$ on the right hand side

$(4a + 2dn-2d)s= n$

Multiply s to the terms,

$4as + 2dns-2ds= n$

Move $2dns$ to the right hand side by subtracting $2dns$ on both sides $4as + 2dns-2ds-2dns= n-2dns$

$4as -2ds= n-2dns$

On the right hand side of the equation, take out $n$

$4as -2ds= n(1-2ds)$

Divide Left hand side by $(1-2ds)$ ,

$n=\frac{4as -2ds}{(1-2ds)}$

6 0

4 years ago

Simplify: ⅕y - ⅗y + 5 - ⅖y - 8<br> pls

MrRissso [65]

Answer:

The answer is -(4/5)y - 3.

Step-by-step explanation:

The steps are :

$\frac{1}{5} y - \frac{3}{5} y + 5 - \frac{2}{5} y - 8$

$= ( \frac{1 - 3 - 2}{5} y) + (5 - 8)$

$= - \frac{4}{5} y - 3$

5 0

3 years ago

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