A scale drawing has a scale of 1/4 in. :6ft.find the length of the drawing for each actual length.

? A mug can hold 13.46 oz of coffee without overflowing. The radius of the mug is 3 cm. Given that 1 cm3 equals 0.034 oz, what i

Elan Coil [88]

Answer:

14 cm

Step-by-step explanation:

Given:

A mug can hold 13.46 oz of coffee.

The radius of the mug is 3 cm.

Given that 1 $cm^{3}$ equals 0.034 oz.

Question asked:

What is the height of the mug to the nearest centimeter ?

Solution:

Given that 1 $cm^{3}$ equals 0.034 oz.

By unitary method:

0.034 oz = 1 $cm^{3}$

1 oz = $\frac{1}{0.034}$

13.46 oz = $\frac{1}{0.034}\times13.46 =395.88 \ cm^{3}$

A mug can hold 13.46 oz of coffee means volume of cylinder is given which is 395.88 $cm^{3}$ . Now we can find the height of the mug by using volume of cylinder formula:

volume of cylinder = $\pi r^{2} h$

$395.88=\frac{22}{7} \times3\times3\times \ h\\395.88=\frac{198 \ h}{7}$

By cross multiplication:

$395.88\times 7 =198\ h\\2771.16= 198\ h$

By dividing both side by 198

$h = 13.99$ $cm$

Therefore, height of the mug to the nearest centimeter is 14 cm.

6 0

3 years ago

Read 2 more answers

8 less than the product of 5 and -4

Karolina [17]

The answer would be:
5(-4) - 8
-20 - 8
-28

4 0

2 years ago

Solve <img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D

Nostrana [21]

Answer:

$\displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}$

Step-by-step explanation:

we would like to solve the following equation for x:

$\displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x}$

to do so isolate $\frac{1}{x}$ to right hand side and change its sign which yields:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x}$

simplify Substraction:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)}$

get rid of only x:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)}$

simplify addition of the left hand side:

$\displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)}$

divide both sides by q+p Which yields:

$\displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)}$

cross multiplication:

$\displaystyle x(p + q + x) = - pq$

distribute:

$\displaystyle xp + xq + {x}^{2} = - pq$

isolate -pq to the left hand side and change its sign:

$\displaystyle xp + xq + {x}^{2} + pq = 0$

rearrange it to standard form:

$\displaystyle {x}^{2} + xp + xq + pq = 0$

now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so

factor out x:

$\displaystyle x( {x}^{} + p ) + xq + pq = 0$

factor out q:

$\displaystyle x( {x}^{} + p ) +q (x + p)= 0$

group:

$\displaystyle ( {x}^{} + p ) (x + q)= 0$

by Zero product property we obtain:

$\displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}$

cancel out p from the first equation and q from the second equation which yields:

$\displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}$

and we are done!

3 0

2 years ago

Solve for x, -3x = -15

Goshia [24]

Answer:

x=5

Step-by-step explanation:

so to isolate the x you dived the -3 to both sides

so it will now be

x=5 because a negative times or divided by a negative equals a positive so to prove that x=5

-3(5)=-15

which is true

5 0

2 years ago

Read 2 more answers

The+pie+chart+shows+the+age+distribution+in+a+village+of+120+a)+how+many+people+are+older+than+60+=+120+B)+What+percentage+of+th

AleksandrR [38]

Answer:

if the village is of 120 people and 120 people are over the age of 60 then 0 people are under the age of 25.

Step-by-step explanation:

5 0

2 years ago