Question

students at a local community college can study spanish or french. they also have a choice of band or chorus for their music classes. the table shows the results of surveying 100 students.
which is a correct statement about students who study spanish and students who choose band?
a there is no association because students who study spanish are no more or less likely than other students to choose band.
b there is no association because students who study spanish are less likely than other students to choose band.
c there is an association because students who study spanish are more likely than other students to choose band.
d there is an association because students who study spanish are less likely than other students to choose band.

spiral review

1. a chili cook-off has adult and child tickets. a group of visitors buys 3 adult tickets and 2 child tickets and pays a total of $26. another group buys 5 adult tickets and 3 child tickets and pays $42. write and solve a system of equations to find the price of each type of ticket.

1. without graphing, find the point of intersection of the lines $-x + 2y = -4$ and $2x + y = 3$.

1. the graph of a proportional relationship passes through the point (6, 21). what is the equation for the relationship?

Explanation:

First Question (Association between Spanish and Band)

Step1: Find % Spanish in Band

$\frac{16}{64} \times 100 = 25\%$

Step2: Find % non-Spanish in Band

$\frac{9}{36} \times 100 = 25\%$

Step3: Compare the two percentages

Both groups have the same 25% chance of choosing band, so no association exists.

Step1: Define variables

Let $a$ = adult ticket price, $c$ = child ticket price.

Step2: Set up system of equations

$3a + 2c = 26$
$5a + 3c = 42$

Step3: Eliminate $c$ (multiply equations)

Multiply first eq by 3: $9a + 6c = 78$
Multiply second eq by 2: $10a + 6c = 84$

Step4: Subtract equations to solve for $a$

$(10a + 6c) - (9a + 6c) = 84 - 78$
$a = 6$

Step5: Substitute $a=6$ to find $c$

$3(6) + 2c = 26$
$18 + 2c = 26$
$2c = 8$
$c = 4$

Step1: Rearrange second equation

$2x + y = 3 \implies y = 3 - 2x$

Step2: Substitute $y$ into first equation

$-x + 2(3 - 2x) = -4$

Step3: Solve for $x$

$-x + 6 - 4x = -4$
$-5x = -10$
$x = 2$

Step4: Substitute $x=2$ to find $y$

$y = 3 - 2(2) = 3 - 4 = -1$

Answer:

A. There is no association because students who study Spanish are no more or less likely than other students to choose band.

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Question 6 (Ticket Prices)