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Rina8888 [55]
3 years ago
6

 The rabbit population in a certain area is 500​% of last​ year's population. There are 700 rabbits this year. How many were the

re last​ year
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
8 0

For this case we have the following data:

700 rabbits that represent 500% of the population of last year. So, to obtain the rabbit population of last year, we developed a rule of three:

700 -----------> 500%

x ---------------> 100%

Where x represents the rabbit population of last year.

Clearing x we have:

x = \frac{ 100 * 700}{500}

x = 140 rabbits

In this way, last year there was a population of 140 rabbits.

Answer:

140 rabbits


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In 1-5, given: Two similar cylinders with heights of 8 and 5 respectively.
lana66690 [7]

Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

3. The ratio of their volume is (8/5)³

4.The area of the base of the larger cylinder is 128 cm²

Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²)  = (8/5)²

The ratio of their surface area = (8/5)²

3. The volume of the cylinder = π·r²·h

∴ The ratio of the volume = (π·r₁²·h₁)/(π·r₂²·h₂) = (8/5)³ × (π·r₂²·h₂)/(π·r₂²·h₂) = (8/5)³

The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

Therefore if the area of the base of the smaller cylinder is 50 cm², the area of the base of the larger cylinder = 50 cm² × (8/5)²  = 128 cm²

7 0
3 years ago
Lucy offers to play the following game with Charlie: "Let us show dimes to each other, each choosing either heads or tails. If w
Darya [45]

Answer:

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

  • P(Charlie Wins)=2/4
  • P(Charlie Losses)=2/4

Lucy wins when the outcome is HT or TH

  • P(Lucy Wins)=2/4
  • P(Lucy Losses)=2/4

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

\left|\begin{array}{c|c|c|c}$Profit(x)&-\$3&-\$1&\$2\\P(x)&1/4&1/4&2/4\end{array}\right|

Expected Profit

=(-3 \times \frac14)+(-1\times \frac14)+(2 \times \frac24)\\=$0

Lucy's expected profit from the game is $0.

7 0
3 years ago
Is 0 14 closed under multiplication
Elden [556K]
No because 0x14 would be 0 BUT it is still multiplication.
4 0
3 years ago
-1 + n=8(n+6) what does n equal?
Gelneren [198K]
<span>-1 + n=8(n+6)
Use distributive property
-1 + n= 8n + 48
Subtract n from both sides
-1= 7n + 48
Subtract 48 from both sides
-49= 7n
Divide 7 on both sides so that the only thing remaining on the right sides is the varible n.
Final Answer: -7 = n</span>
4 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP
Nat2105 [25]
A leg of a right triangle can never be greater then the hypotenuse

this formula will tell you if it's a valid right triangle
{?}^{2} + {?}^{2} = {?}^{2}
the first two question marks are the legs of the triangle while the one after the = is the hypotenuse.

THE STEPS:
{3}^{2} + { \sqrt{7}^{2} } = {4}^{2}
9 + {2.65}^{2} = 16
{2.65}^{2} = 7
9 + 7 = 16
ANSWER: \sqrt{7}
5 0
3 years ago
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