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k0ka [10]
3 years ago
10

The very busy Freshman class is selling tickets for an upcoming field hockey game. The class sells 20 more student tickets than

adult tickets. The adult tickets cost $4 and the student tickets cost $2. The class made a total of $280 from ticket sales. How many of each type of ticket did they sell? Elaborate and clarify your reasoning.
1a. Define the variables in this system
b. Create equations to describe the relationships in this system between the variables
Mathematics
1 answer:
mixer [17]3 years ago
7 0

Answer:

60 student tickets and 40 adult tickets were sold

Step-by-step explanation:

Let s represent student tickets and a adult tickets, then the system of equations can be written as

s - a = 20 →(1)

2s + 4a = 280 → (2)

Multiply (1) by 4 and add to (2) to eliminate a

4s - 4a = 80 → (3)

Add (2) and (3) term by term

6s = 360 ( divide both sides by 6 )

s = 60

Substitute s = 60 into (1)

60 - a = 20 ( subtract 60 from both sides )

- a = - 40 ( multiply both sides by - 1 )

a = 40

Thus

60 student and 40 adult tickets were sold.

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Question 13
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The amount to be invested today so as to have $12,500 in 12 years is  $6,480.37.

The amount that would be in my account in 13 years is $44,707.37.

The amount I need to deposit now is $546.64.

<h3>How much should be invested today?</h3>

The amount to be invested today = future value / (1 + r)^nm

Where:

  • r = interest rate = 5.5 / 365 = 0.015%
  • m = number of compounding = 365
  • n = number of years  = 12

12500 / (1.00015)^(12 x 365) = $6,480.37

<h3>What is the future value of the account at the end of 13 years?</h3>

Future value = monthly deposits x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

  • r = interest rate = 5.3 / 12 = 0.44%
  • n = 13 x 12 = 156

200 x [{(1.0044^156) - 1} / 0.0044] = $44,707.37

<h3>What should be the monthly deposit?</h3>

Monthly deposit = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

  • r = 6.7 / 12 = 0.56%
  • n = 2 x 12 = 24

$14,000 / [{(1.0056^24) - 1} / 0.0056] = $546.64

To learn more about annuities, please check: brainly.com/question/24108530

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2 years ago
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Answer:

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Alternate Hypothesis: H_1: \mu_A >\mu _B or \mu_A -\mu _B>0

Here to test Fertilizer A height is greater than Fertilizer B

Two Sample T Test:

t=\frac{X_1-X_2}{\sqrt{S_p^2(1/n_1+1/n_2)}}

Where S_p^2=\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}

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P value for Test Statistic of P(3.3524,26) = 0.0012

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Critical value of P : t_{0.025,26}=2.05553

We can conclude that Test statistic is significant. Sufficient evidence to prove that we can Reject Null hypothesis and can say Fertilizer A is greater than Fertilizer B.

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Step-by-step explanation:

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