14. Use mental math to simplify (4.55 +27) + 5.45. 32 13 18 37

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a

belka [17]

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s

4 0

3 years ago

Read 2 more answers

What percent is equivalent to 8/40 ? 8% 20% 25% 40%

Nikitich [7]

First you have to get the number on the right 40 to equal 100 so do 40x2=80- +40x1.5= 100

Then do the same thing to the first number 8 so 8x2=16+8x1.5=20

then you have 20/100 right so then that number over 100 is the percent that you get ^-^ 20%

7 0

3 years ago

Read 2 more answers

Please help me on this!

yanalaym [24]

Answer:

${9}^{ - 8}$

Step-by-step explanation:

$\frac{ {9}^{ - 5} }{ {9}^{3} }$

${9}^{ - 5 - (3)}$

${9}^{ - 5 + (- 3)}$

${9}^{ - 8}$

6 0

3 years ago

Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actual

NISA [10]

Answer:

Randy is 48 years old

Sandy is 12 years old

Todd is 27 years old

Step-by-step explanation:

Given

Represent their ages with the first letters of their names:

$R + S + T = 87$

$R = 4 * S$

$T = 15 + S$

Required

Determine their individual ages

We'll solve the above equations using substitution method of simultaneous equations

Substitute 15 + S for T and 4 * S for R in $R + S + T = 87$

This gives:

$4 * S + S + 15 + S = 87$

$4 S + S + 15 + S = 87$

Collect Like Terms

$4 S + S + S = 87 - 15$

$6S = 72$

Divide through by 6

$S = 72/6$

$S = 12$

This implies that Sandy is 12 years old

Substitute 12 for S in $R = 4 * S$ and $T = 15 + S$

$R = 4 * 12$

$R = 48$

$T = 15 + 12$

$T = 27$

This implies that Randy is 48 years old and Todd is 27

7 0

3 years ago

A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the groun

vovangra [49]

You have to go at this in a round-about fashion...by finding the length of the leg across from the 67 degree angle. This is found by using the tangent ratio...Tan(67)=x/137; x=137tan(67) = 322.8. Now you can use this in one of two ways: use Pythagorean's Theorem to find the length of the hypotenuse OR you could use the sin67=322.8/x. Up to you. Either way, make sure you have your calculator in degree mode!

4 0

3 years ago

14. Use mental math to simplify (4.55 +27) + 5.45.32131837​

14. Use mental math to simplify (4.55 +27) + 5.45.32131837