1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrew-mc [135]
2 years ago
13

A population of penguins is given by Pt=P0⋅3t5 where t is the time in years, t≥0. How long does it take for the population to tr

iple its size?
Mathematics
1 answer:
PolarNik [594]2 years ago
5 0

Answer:

5 years

Step-by-step explanation:

If the population of penguins is given by the function:

P(t)=P_0\cdot 3^{t/5}

Initial Size =P_0

Triple its Initial Size, P(t)=3P_0

Therefore:

3P_0=P_0\cdot 3^{t/5}\\$Divide both sides by P_0\\3=3^{t/5}\\$Since they have the same base\\1=t/5\\Cross multiply\\t=5

It therefore takes 5 years for the penguin population to triple in size.

You might be interested in
Use the line graph to solve.
Ksenya-84 [330]
The answer is c. 0.10. Week 4 is plotted at 0.35 and Week 2 is plotted at 0.25. Difference means subtract. 0.35 - 0.25 = 0.10. Hope this helps!
4 0
3 years ago
At your job, you are paid $50 per week plus $3 per sale. At least how many sales do you need to make in order to have over $250
julsineya [31]

<span>0+3⋅c>250</span>

<span>50+3⋅c−50>250−50</span>

<span>3⋅c>200</span>

<span><span><span>3⋅c</span>3</span>><span>2003</span></span>

<span>c><span>66.7</span></span>

<span><span>so 67 sales rouned</span></span>

6 0
3 years ago
Lena is 10 years old. She asks her dad how old he is. He tells her that the lowest common multiple of their ages is 14 times the
Ksju [112]

Answer:

  35

Step-by-step explanation:

We know the factors of Lena's age are 2 and 5. The least common multiple must have these factors and the factors of 14, so will at least have factors of 2, 5, and 7.

Apparently, the dad's age is 5·7 = 35.

___

The GCF is 5; the LCM is 70 = 5×14.

_____

Sometimes, I use a little 3-part diagram to think about LCM and GCF. Here, it would look like ...

  (2 [5) 7]

where the numbers in curved brackets (2·5) and the numbers in square brackets [5·7] are factors of the two numbers of concern (Lena's age, her dad's age). The middle number in both brackets [5) is the greatest common factor, and the product of all three numbers is their least common multiple.

Here, the product of outside numbers, 2·7 = 14, represents the ratio of the LCM to the GCF. We know that Lena's age has factors of only 2 and 5, so the numbers in the diagram have to be (2[5)7], where 2 and 7 are on the ends and 5 is in the middle.

7 0
3 years ago
WILL GIVE BRAINLIEST!!! Given tan(theta) = 4/3 and pi &lt; theta &lt; (3pi)/2, find cos(2theta).
babymother [125]

Answer:  \cos 2 \theta = \dfrac{-7}{25}

Step-by-step explanation:

Given: \tan \theta = \dfrac{4}{3}  and  \pi < \theta< \dfrac{3\pi }{2}

To find: \cos 2 \theta

Now as we know

\cos 2x = \dfrac{1- \tan ^2 x}{1+ \tan ^2 x}

So we have

\cos 2 \theta = \dfrac{1-(\dfrac{4}{3} )^2}{1+(\dfrac{4}{3} )^2} \\\\\Rightarrow \cos 2 \theta = \dfrac{1- \dfrac{16}{9} }{1+ \dfrac{16}{9} } = \dfrac{\dfrac{9-16}{9} }{\dfrac{9+16}{9}} = \dfrac{-7}{25}

Therefore d. is the correct option

Hence , \cos 2 \theta = \dfrac{-7}{25}

3 0
3 years ago
Read 2 more answers
Neach row, colour the one with more number of pictures​
saul85 [17]

Answer

neach row, colour the one with more number of pictures

Step-by-step explanation:

neach row, colour the one with more number of pictures

5 0
3 years ago
Other questions:
  • Ginger is selling gym memberships. The first week she sold 5 memberships and each week for the next four weeks she sells 3 more
    9·1 answer
  • Factor 2x^2 - 50 completely.
    13·2 answers
  • Use properties of addition and subtraction to evaluate the expression <br> -42 - 29 - 28
    7·1 answer
  • A population has a mean muequals160 and a standard deviation sigmaequals20. Find the mean and standard deviation of the sampling
    15·1 answer
  • Hitung jarak di antara titik P(7, 1) dengan titik Q(7, 8) ​
    13·1 answer
  • Will give the BRAINLEST<br><br>Please help and show your work. Thank you.​
    13·1 answer
  • Can someone answer this please?
    7·1 answer
  • What is 15 out of 100 in simplest form
    9·1 answer
  • Choose 3 values that would make this inequality true. 8n + 4 ≤ 28 <br><br> Choices:3,6,13,2,5,14,1
    6·1 answer
  • Prove that it is congruent​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!