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3 years ago

3. Given that a is 30% of b, find the value of a/4b

Mathematics

1 answer:

Karolina [17]3 years ago

6 0

Answer:

a/4b = 0.075

Step-by-step explanation:

a = 30% of b

a = 30/100 × b

a = 0.3b

The value of a/4b is calculated as:

= 0.3b/4b

= 0.075

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3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

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

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

$V=\frac{1}{3}\pi r^{2}h$

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

4 years ago

A company paid $72 for 2 cases of printer paper each case contained 12 packages of paper next month the company's office manager

Tems11 [23]

To figure out the cost for 180 packages, you must first calculate how many packages they bought for $72. Since each case holds 12 packages, for $72, the company bought 24 packages (12×2). Then you have to divide 24 into 180 to figure out the cost for those 180 packages and get 7.5. To get the cost of the 180 packages, you must multiply 7.5 (the number of 24 packages that go into 180) by 72 (the cost of one group of 24 packages). You then get 540. The company must pay $540 for the 180 packages.

7 0

3 years ago

What is the difference between 2.23 seconds and 3.13 seconds?

boyakko [2]

Answer:

0.9

Step-by-step explanation:

3.13-2.23=0.9

7 0

3 years ago

Read 2 more answers

Help me please :) .....

Gnom [1K]

Answer:

at + vi = vf

Step-by-step explanation:

In order to solve for vf, we need to isolate said variable.

a = vf - vi/t (Given)

at = vf - vi (Multiply t on both sides)

at + vi = vf (Add vi on both sides)

5 0

3 years ago

If you have no idea, don't answer please.

tino4ka555 [31]

Answer:

1) A 2) B 3) C 4) C 5) A 6) B

Step-by-step explanation:

1) Slope is calculated by the change in y over the change in x thus (5-3)/(2-(-1)) = 2/3

2) Since there is no change in y, there is no slope.

3) The change in x is given which is 10-2 so the change in y is y2-3. For the slope to be 3/4 y must equal 6. Therefore y2 is 9.

4) Cosine is adjacent over hypotenuse and Tangent is opposite over adjacent. Given 3/5 as A/H you can construct a right triangle with the adjacent as 3 and hypotenuse as 5. The Pythagorean theorem says the adjacent squared plus the opposite squared is equal to the hypotenuse squared.

3^2 + O^2 = 5^2

O=4

Therefore TanP is 4/3

5) Pythagorean theorem again. $\sqrt{3} ^2 +\sqrt{3} ^2= H^2$ Therefore your hypotenuse is equal to $\sqrt{6}$

6) Csc is the inverse of the Sin function. So it becomes 5/4.

4 0

2 years ago