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3 years ago

7

A population of kangaroos is growing at a rate of 2% per year, compounded continuously. If the rate continues, how many years wi

ll it take of the population to reach 150% of its current size according to the exponential growth function?

1 answer:

OlgaM077 [116]3 years ago

3 0

Answer:

75 years.

Step-by-step explanation:

Divide 150 by 2, that gives you the years.

You might be interested in

The distance in miles from Mercury to the Sun in scientific notation is 3.6 × 10

natka813 [3]

Answer:

wouldnt it be 4.2 ?

Step-by-step explanation:

7 0

3 years ago

Josie took a long multiple-choice, end-of-year vocabulary test. The ratio of the number of problems Josie got incorrect to the n

FrozenT [24]

Answer:

A. Josie got 36 correct answers.

B. Josie got 90 correct answers.

C. 8:36 and 20:90

D.6:27, 12:54, 30:135, among others.

e. Multiply both numbers on the ratio by the same constant integer, thereby ensuring that the resulting numbers form a ratio equivalent to the original.

Step-by-step explanation:

Very well, so the statement is that Josie got 2 problems incorrect for every 9 that she got correct. First the ask how many questions she got correct given that she missed 8 question. First, we divide the 8 question she missed by 2. Now have 4 pairs of questions that Josie missed and for every pair that she failed; Josie got 9 questions correctly. Therefore, we multiply 4 pairs of incorrect questions times 9 correct questions. So, if Josie had 8 incorrect questions, she also had 36 correct answers on her test.

In the case that Josie missed 20 questions, we divide them by two again in order to obtain the number of pairs that Josie missed. Now have 10 pairs of questions that Josie missed and for every pair that she failed; Josie got 9 questions correctly. Therefore, we multiply 10 pairs of incorrect questions times 9 correct questions. So, if Josie had 8 incorrect questions, she also had 90 correct answers on her test.

With the information we collected, we can affirm that the ratios 8:36 and 20:90 are equivalents to the original 2:9 that was stated. Other examples of equivalents ratios could be 6:27, 12/54, 30:135, among many others.

To find the equivalent ratios what we need to do is find common multiples of the numbers that conform the ratio. To do so, we can multiply both numbers by the same constant integer, thereby ensuring that the resulting numbers form a ratio equivalent to the original.

Have a nice day! :D

6 0

4 years ago

Help asap will give brainliest!!!!

GarryVolchara [31]

Answer:

C

Step-by-step explanation:

ley y = f(x) and rearrange making x the subject

y = $\frac{1}{x+5}$ - 1 ( add 1 to both sides )

y + 1 = $\frac{1}{x+5}$ ( multiply both sides by (x + 5)

(y + 1)(x + 5) = 1 ← expand factors using FOIL

xy + 5y + x + 5 = 1 , that is

xy + x + 5y + 5 = 1 ( factor first/second and third/fourth terms on left side )

x(y + 1) + 5(y + 1) = 1 ← factor out (y + 1) from each term on left side

(y + 1)(x + 5) = 1 ( divide both sides by (y + 1) )

x + 5 = $\frac{1}{y+1}$ ( subtract 5 from both sides )

x = $\frac{1}{y+1}$ - 5

Change y back into terms of x with x = $f^{-1}$ (x) , then

$f^{-1}$ (x) = $\frac{1}{x+1}$ - 5 where x ≠ - 1

7 0

3 years ago

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2.5 over 5 and 59 hundredths. Triangles XYZ

adell [148]

Dilation involves changing the size of a shape

<h3>How to determine the relationship between the trigonometry ratios</h3>

From the question, we understand that:

The dilation of triangle XYZ gives triangle ACB

This means that, the following are corresponding points

Points X and A
Points Y and C
Points Z and B

The above means that:

The relationships between the trigonometry ratios of both triangles are:

cos(X) = cos(A), cos(Y) = cos(C) and cos(Z) = cos(B)

<h3>How to determine the measures of segments AC and AB</h3>

In (a), segments XY and XZ corresponds to the segments AC and AB

So, the product of the lengths of XY and XZ and the scale factor will result in the lengths of AC and AB,

i.e.

AC = 2 * XY and AB = 2 * XZ

Read more about dilation at:

brainly.com/question/26332230

5 0

2 years ago

Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches. He st

o-na [289]

Answer: Exactly square root 58 inches

Step-by-step explanation: The dimensions given for the right angled triangle are 7 inches and 3 inches respectively. The third side is yet unknown. However what we know is that a right angled triangle can be solved by using the Pythagoras theorem which states that,

AC^2 = AB^2 + BC^2

Where AC is the longest side. The question requires us to calculate the longest side and with the other two sides already known, the Pythagoras theorem now becomes,

AC^2 = 7^2 + 3^2

AC^2 = 49 + 9

AC^2 = 58

Add the square root sign to both sides of the equation

AC = square root 58 inches

5 0

3 years ago

Read 2 more answers