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almond37 [142]
2 years ago
5

Mrs. Cooper hosts an annual art contest for kids. She has records of the number of entries for the last 9 years. She received 30

entries in the first year. Over the next 3 years, the number of entries increased by 10 kids per year. In the next 2 years after that, there were 60 entries each year, and in the last 3 years, the number of entries increased by 15 kids per year. Which graph models the piecewise function for the given situation, where x represents time after the first year and y represents the number of entries in that year?
Mathematics
1 answer:
Zanzabum2 years ago
8 0

To graph this situation we must take into account the data and the organization of each of them on the X axis and Y axis.

<h3>How to graph this situation?</h3>

To graph this situation we must take into account the data we have:

  • Years
  • Tickets

Based on these data, we assign the horizontal axis to count years and the vertical axis to count tickets per year. We must continue the pattern of increased attendance over the years.

Learn more about graph in: brainly.com/question/16608196

#SPJ1

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How long does it take for an investment to quadruple in value if it is invested at 11% compounded
defon

Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:

100 * (1+1.07)x = 400

Then we will take 400 and divide it by 100 getting:

1.07X = 4

Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X

Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.

2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula

where:

P (principal) is equal to hypothetical $100

E (e) is a mathematical constant, which is approximately 2.718

R (rate) is the interest rate, in our case it is 5.5%

T (time) is the time required for money to grow

A (amount) is the final amount desired, which is 4 times larger of $100, thus $400

We have the following:

400 = 100 * e0.055t

400/100 = e0.055t

4 = e0.055t

Then we will apply natural log to both sides of the equations and get the following:

ln(4) = ln(e0.055t)

Since e is the base of ln(x) the equation simplifies to:

ln(4) = 0.055t

Using the calculator to find ln(4) we are getting:

1.38629 = 0.055t

Lastly find t

t = 1.38629/0.055

t = 25.20535202

Plug the answers back to the original equation to verify the answers.

1st part of the question answer: t = 20.4895

2nd part of the question answer: t = 25.20535202

3 0
3 years ago
In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In ad
zysi [14]

Answer:  a) 0.0792   b) 0.264

Step-by-step explanation:

Let Event D = Families own a dog .

Event C = families own a cat .

Given : Probability that families own a dog : P(D)=0.36

Probability that families own a dog also own a cat : P(C|D)=0.22

Probability that families own a cat : P(C)= 0.30

a) Formula to find conditional probability :

P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\\Rightarrow P(A\cap B)=P(B|A)\times P(A)   (1)

Similarly ,

P(C\cap D)=P(C|D)\times P(D)\\\\=0.22\times0.36=0.0792

Hence, the probability that a randomly selected family owns both a dog and a cat : 0.0792

b) Again, using (2)

P(D|C)=\dfrac{P(C\cap D)}{P(C)}\\\\=\dfrac{0.0792}{0.30}=0.264

Hence, the conditional probability that a randomly selected family owns a dog given that it owns a cat = 0.264

5 0
3 years ago
Which expression is equivalent to<br> 128x8,329 ? Assume y20 and 720
kaheart [24]

Answer:767600640

Step-by-step explanation: If 720 equals x, you multiply 128 by 720, and multiply the answer by 8,329.

8 0
2 years ago
Sum of numbers 12-111
liubo4ka [24]

Answer:

12-111=-99

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The legs of a right triangle measure 6 inches and 9 inches. If is the angle between the 6-inch leg and the hypotenuse, sin = ___
mr Goodwill [35]
First find the length of the hypotenuse using pythagorean theorem
<span>c^2 = 5^2 + 7^2
c^2 = 25 + 49
c^2 = 64
c=8 (take the square root in both sides)
Since sin = opposite/hypotenuse,
sin = 5/8 = 0.625</span>
3 0
3 years ago
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