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
denis-greek [22]
3 years ago
10

Hannah and Francine have $120. Hannah and Peter have $230. Peter has 6 times as much money as Francine. How much money does Hann

ah have?
Mathematics
1 answer:
aivan3 [116]3 years ago
5 0
x-Francine's\ money\\6x-Peter's\ money\\120-x-Hanna's\ money\\\\120-x+6x=230\\-x+6x=230-120\\5x=110\ \ \ |:5\\x=22\\\\6x=6\cdot22=132\\\\120-22=98\\\\Hanna\ has\ \$98
You might be interested in
Please solve please and thank you
Dahasolnce [82]
(2x+2)(3x+1)
2x*3x+2x*1+2*3x+2*1
6x^2+2x+6x+2
6x^2+8x+2

Hope this helped
6 0
3 years ago
Read 2 more answers
An amusement park recently increased the cost of a family season pass. The original price was $150. The new price is $183. What
viva [34]

Answer:

1.22%

Step-by-step explanation:

150 x 1.22 = 183

6 0
2 years ago
2)
Elenna [48]

Parallel lines are in the same plane, never intersect, and have the same slope.

7 0
3 years ago
What the distance between points 3,2 & 9,5??
Georgia [21]

Answer:

the difference is 1 and 4

Step-by-step explanation:

hope this helps

5 0
2 years ago
Uninhibited growth can be modeled by exponential functions other than​ A(t) ​=Upper A 0 e Superscript kt. For ​ example, if an i
laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than A(t)=A_{0}e^{kt}. for example, if an initial population P₀ requires n units of time to triple, then the function P(t)=P_{0}(3)^{\frac{t}{n} } models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form P(t)=P_{0}(3)^{\frac{t}{n} } that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form A(t)=A_{0}e^{kt}.

Answer: a) P(t)=50(3)^{\frac{t}{30} }

              b) P(t) = 280 insects

              c) t = 74 days

             d) A(t)=50e^{0.037t}

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

P(t)=50(3)^{\frac{t}{30} }

b) In t = 47 days:

P(t)=50(3)^{\frac{t}{30} }

P(47)=50(3)^{\frac{47}{30} }

P(47)=50(3)^{1.567}

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

750=50(3)^{\frac{t}{30} }

\frac{750}{50}=(3)^{\frac{t}{30} }

(3)^{\frac{t}{n} }=15

Using the property <u>Power</u> <u>Rule</u> of logarithm:

log(3)^{\frac{t}{30} }=log15

\frac{t}{30}log(3)=log15

t=\frac{log15}{log3} .30

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

A(t)=A_{0}e^{kt}

3A_{0}=A_{0}e^{30k}

3=e^{30k}

Use Power Rule again:

ln3=ln(e^{30k})

ln3=30k

k=\frac{ln3}{30}

k = 0.037

Equation for exponential growth will be:

A(t)=50e^{0.037t}

3 0
3 years ago
Other questions:
  • 24 is 120% of what number?
    5·1 answer
  • At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard dev
    7·1 answer
  • Mike mowed the lawn for 1 1/2 hours. He charged $12. How much did he charge per hour?
    11·1 answer
  • One lap around the track is 400 meters.if you run 10 laps around the track,how many miles would you run?Round your answer to the
    7·1 answer
  • Why is it valid to say that both a function and its inverse describe the same relationship
    5·1 answer
  • Daniel buys a video game, which is on sale for 30% off the regular price of $69.98. The combined taxes are 15%. How much does Da
    11·2 answers
  • Can someone please help me
    6·1 answer
  • Find Value of x. The diagram is not to scale.
    13·1 answer
  • A dinosaur park cost $5.00 to enter plus $0.75 taxes. How much does it cost if a family of 4 went to the park
    7·1 answer
  • Joy is making hand-painted ornaments for her family this year. Yesterday, she made 2 ornaments in 6 hours. This weekend, she pla
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!