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2 years ago

can anyone explain to me what ratios and rates are with examples? I really need help i have a retake.

Mathematics

1 answer:

uysha [10]2 years ago

8 0

Answer:

Explanation on ratio and rates.

Step-by-step explanation:

So rates are when you compare two things. For example let's say there are 12 boys and 10 girls. The ratio would be 12:10 or 6:5. Rates is also comparing two things but in fraction format. For example if you drive 30 miles in 3 hours the rate would be 30/3. 10 miles per hour is a unit rate since it is 1 hour, 10/1. I hope this helps you, have a good day.

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Carlos is filling a spherical balloon with water. if he increases the volume of the balloon from 4,188.79 cubic centimeters to 1

Harrizon [31]

We know that the volume of a sphere of radius r is given by

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

Now, we have been given the initial volume was 4,188.79 cubic centimeters. Let us find the radius at this time.

Substituting the value of volume in the above equation, we get

$4,188.79=\frac{4}{3}\pi r^3\\
\\
4\pi r^3=4,188.79 \times 3\\
\\
r^3=\frac{4188.79 \times 3}{4\pi}\\
\\
r^3=1000\\
\\
r=10$

Now, the final volume is given by 14,137.167 cubic centimeters. Thus, we have

$14137.167 =\frac{4}{3}\pi r^3\\
\\
4\pi r^3=14137.167 \times 3\\
\\
r^3=\frac{14137.167\times 3}{4\pi}\\
\\
r^3=3375\\
\\
r=15$

Now, let us find the surface areas for these two radii.

For $r=10$

Surface area is given by

$S=4\pi r^2\\
\\
S=4\times 3.14 \times (10)^2\\
\\
S=1256 \text{ square centimeters}$

Similarly, for

$r=15\\
\\
S=4\times 3.14\times (15)^2\\
\\
S=2826 \text{ square centimeters}$

Therefore, the increase in the surface area is given by

$\Delta S= 2826-1256= 1570 \text{ square centimeters}$

Hence, the average rate at which the surface area is changing is given by

$\frac{1570}{12}=130.8$

Therefore, the average rate at which the surface area is changing is given by 130.8 square centimeters per second.

7 0

3 years ago

Show work only do those 32,34,36,38,40

Free_Kalibri [48]

Answer: see below

Step-by-step explanation:

$32)\quad \dfrac{3}{5}(x-12)>x-24$

3(x - 12) > 5(x - 24)

3x - 36 > 5x - 120

-5x -5x

-2x - 36 > -120

+36 +36

-2x > -84

÷ -2 ↓ ÷ -2

x < 42

Graph: ←------------o

34) 6[5y - (3y - 1)] ≥ 4(3y - 7)

6[5y - 3y + 1] ≥ 4(3y - 7)

6{2y + 1] ≥ 4(3y - 7)

12y + 6 ≥ 12y - 28

-12y -12y

6 ≥ -28

TRUE so the solution is All Real Numbers

Graph: ←-----------------------→

36) BC + AC > AB

4 + 8 - AB > AB

12 - AB > AB

+AB +AB

12 > 2AB

÷2 ÷2

6 > AB

AB < 6

$38)\quad \dfrac{1}{2}(y-16)\geq y+2\quad ;\text{claim}\ y\leq 20$

Check: let y = 16

then $\frac{1}{2}$ (16 - 16) ≥ 16 + 2

0 ≥ 18

FALSE so the claim is wrong

40) question not provided in the image so I cannot give a solution.

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2 years ago

The day after payday you have $300.

RUDIKE [14]

Answer:19.25

Step-by-step explanation:

300 subtract 146=154 divide by 8=19.25

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