MAT 108 Social Science Mathematics Exam 1 Review

Flashcards created from the MAT 108 Social Science Mathematics exam review notes covering applications of linear equations, ratio and proportion, the rectangular coordinate system, and set theory.

What is the linear equation to find the number that satisfies "The difference of a number and 8 is the same as 46 less the number"?

Let x be the number. The equation is x - 8 = 46 - x.

If a storehouse has 450 different inventory items, and 3/5 of these items are perishable, how many items are perishable?

The number of perishable items is 270.

What are the capacities of Center City East and West Garage given that Center City East has a capacity of 253 cars more than West, and together they hold 1231 cars?

Center City East: 742 cars, Center City West: 489 cars.

How many marbles are in the second bag when dividing 30 marbles among three bags with specific ratios?

There are 15 marbles in the second bag.

For a car rental costing $29.95 per day and $0.19 per mile, how many whole miles can you drive for $200 if you rent for 2 days?

You can drive 737 whole miles.

What is the unit price of a 1.5-lb package of grapes that costs $3.95?

The unit price is $2.63 per pound.

If Dr. Wong can see 12 patients in 3 hours, how long would it take her to see 72 patients?

It would take 18 hours.

What is the ratio of the number of women to the number of men on a committee with 13 people total, 8 of whom are women?

The ratio is 8:5.

Given the equation 3x - 1 = 7x + 2, what is the solution for x?

The solution for x is 13/4.

How many applications should Sarah expect from a 13-oz bottle of self-tanning lotion if a 4-oz bottle provides five applications?

Sarah should expect 16 applications.

What is the slope of the line that contains the points (6, -9) and (-1, 1)?

The slope is -10/7.

What is the graphing equation of the line represented by -4x - 24y - 24 = 0 in slope-intercept form?

The equation in slope-intercept form is y = 1/6x + 1.

What is the slope of the line represented by the equation 3x + 2y = 6?

The slope is -3/2.

What formula can be used to predict the total number of balloons blown up by the homecoming committee as a function of hours?

The linear equation is y = 60x + 30.

In roster notation, how do you represent the set {x | x ∈ Ν and x > 24}?

The set is {25, 26, 27, 28, …}.

Is the statement "3 ∉ {6, 9, 12, 15, 18}" true or false?

The statement is true.

What is the cardinal number of the set Β = {eight}?

The cardinal number n(Β) is 1.

How do you determine if {6, 26, 31} is a subset or not of {17, 26, 31, 41}?

The correct answer is ⊈.

Using a Venn diagram, how do you find B′ given the sets?

B′ = {p, q, r, w, x}.

Identify the intersection of crops grown in both Alabama and Arkansas using the sets provided.

The intersection A ∩ K includes {h, s, w}.

For the union A ∪ B, what is the resulting set using the lists provided?

The union A ∪ B is {e, b, j, h, m, t}.

How do you compute A' ∩ (B′ ∪ C') using defined sets?

A' ∩ (B' ∪ C') = {25, 35}.

In what way can you represent the set A' ∪ B using envelope or set notation?

A' ∪ B is represented as {q, r, s, t, v, x, y, z}.

What does the Venn diagram for the desserts show regarding how many people ordered cake?

According to the Venn diagram, 28 people ordered cake.

How many customers did not order caller ID based on the telephone features outlined in the Venn diagram?

67 customers did not order caller ID.

Using survey data, how many tourists plan to visit only the Art Museum?

12 tourists plan to visit the Art Museum only.

How many backpacks contained none of the three writing instruments based on the findings from examining 38 backpacks?

2 backpacks contained none of the three writing instruments.