Question 1: Where x is 4 and y is -2.35, calculate 1.13x + 21.5y + 13.22.

• 68.265
• 1
• —38.825
• —32.785 (Correct answer)

Correct answer: —32.785

To calculate the expression, substitute x=4 and y=-2.35: 1.13(4) + 21.5(-2.35) + 13.22. This simplifies to 4.52 - 50.525 + 13.22. Performing the arithmetic operations yields -32.785.

Question 2: Ariel is comparing the costs of two different brands of paper towels, Brand A and Brand B. At $1.74 per roll, Brand B is the more affordable option. Brand A comes in 8-packs, whereas Brand B comes in 12-packs. The cost of a pack of Brand Bis is the same as the cost of a pack of Brand A. How much does Brand A cost each roll?

• $2.53
• $3.00
• $1.07
• $2.61 (Correct answer)

Correct answer: $2.61

First, calculate the total cost of a Brand B pack: 12 rolls * $1.74/roll = $20.88. Since a pack of Brand A costs the same, an 8-pack of Brand A also costs $20.88. To find the cost per roll for Brand A, divide the pack cost by the number of rolls: $20.88 / 8 rolls = $2.61 per roll.

Question 3: For $115, a combat veteran and a senior citizen each purchase the identical vacuum cleaner model. They're both going to use their coupons, which say, "Veterans enjoy 20% off all store purchases!" and "senior discount 550!" respectively. Who has the better bargain?

• The senior citizen (Correct answer)
• The war veteran
• They both get an equal price

Correct answer: The senior citizen

The veteran's discount is 20% of $115, which is $23, making their final price $115 - $23 = $92. Assuming 'senior discount 550!' is a typo for '$55 off', the senior citizen pays $115 - $55 = $60. Since $60 is less than $92, the senior citizen receives the better bargain.

Question 4: 3 lbs. of ground beef costs $11.52 at one grocery. ”34 per ounce of ground beef,” reads a mistake on a price tag. What is the percentage increase in the price of 3 lbs. ground beef if the buyer calculates his price based on the wrong tag instead of the true price? To the nearest hundredth of a percent, round up.

• 5.25%
• 29.41%
• 41.67% (Correct answer)
• 29.00%

Correct answer: 41.67%

First, convert 3 lbs to ounces (3 lbs * 16 oz/lb = 48 oz). The true price per ounce is $11.52 / 48 oz = $0.24/oz. The mistaken price is $0.34/oz. The percentage increase is calculated as ((Mistaken Price - True Price) / True Price) * 100%, which is (($0.34 - $0.24) / $0.24) * 100% = ($0.10 / $0.24) * 100% = 41.666...%, rounding up to 41.67%.

Question 5: Find the answer to x: 5 (x+3) = 3 (x—5)

• x = -1
• x = -15 (Correct answer)
• x = 4
• All of the above

Correct answer: x = -15

To solve the equation 5(x+3) = 3(x-5), first distribute the numbers on both sides: 5x + 15 = 3x - 15. Next, subtract 3x from both sides to get 2x + 15 = -15. Then, subtract 15 from both sides, resulting in 2x = -30. Finally, divide by 2 to find x = -15.

Question 6: Illuminate for the variable: 3x — (2x+3)2 = 5

• x = 11
• x = -11 (Correct answer)
• x = 1
• x = -1

Correct answer: x = -11

To solve 3x - (2x+3)2 = 5, first distribute the 2 into the parentheses: 3x - (4x + 6) = 5. Then, distribute the negative sign: 3x - 4x - 6 = 5. Combine like terms: -x - 6 = 5. Add 6 to both sides: -x = 11. Finally, multiply by -1 to get x = -11.

Question 7: Someone's unattended luggage slides out of an open hatchway aboard a helicopter at 30,000 feet. How much time does a recovery crew have to catch the luggage before it lands? (Assume the baggage is falling at 145 feet per second at its final velocity.)

• 3 minutes and 27 seconds (Correct answer)
• 3 minutes and 7 seconds
• 2 minutes and 45 seconds
• 2 minutes

Correct answer: 3 minutes and 27 seconds

To find the time it takes for the luggage to fall, divide the total distance by the falling speed. Time = Distance / Speed = 30,000 feet / 145 feet/second. This calculation yields approximately 206.896 seconds. Converting this to minutes and seconds (206.896 / 60) gives 3 minutes and approximately 26.9 seconds, which rounds to 3 minutes and 27 seconds.

Question 8: Is this a geometric or arithmetic sequence? <br> 0,2,4,6,8,..

• Arithmetic (Correct answer)
• Geometric
• Both
• Neither

Correct answer: Arithmetic

An arithmetic sequence is characterized by a constant difference between consecutive terms. In the given sequence (0, 2, 4, 6, 8...), each term is obtained by adding 2 to the previous term (e.g., 2-0=2, 4-2=2). A geometric sequence, in contrast, involves a constant ratio between terms.

Question 9: In the following sequence, extrapolate the 15th value. <br> 0, 2, 4, 6, 8...

• 30
• 25
• 32
• 28 (Correct answer)

Correct answer: 28

This is an arithmetic sequence with a first term (a_1) of 0 and a common difference (d) of 2. The formula for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d. For the 15th term (n=15), substitute the values: a_15 = 0 + (15-1) * 2 = 0 + 14 * 2 = 28.

Question 10: x = 10 and y = 35 in a straight variant. Write a formula for this relationship.

• y = x + 3.5
• y = 10x +35
• y = 3.5x (Correct answer)
• y = 350x

Correct answer: y = 3.5x

A 'straight variant' implies a direct variation, which is represented by the formula y = kx, where k is the constant of proportionality. Given x = 10 and y = 35, substitute these values into the formula: 35 = k * 10. Solving for k, we get k = 35 / 10 = 3.5. Therefore, the formula for this relationship is y = 3.5x.

Question 11: What is the y-intercept and what does it represent in the following equation that predicts the revenue of a pizza store over time? <br> y = 120x + 1500

• y = 120, it is the beginning revenue before the shop has had any sales
• y = 120, it is the time elapsed before each dollar is earned
• y = 1500, it IS the beginning revenue before the shop has had any sales
• y = 1500, it is the time elapsed before each dollar is earned (Correct answer)

Correct answer: y = 1500, it is the time elapsed before each dollar is earned

In a linear equation of the form y = mx + b, 'b' represents the y-intercept. In the equation y = 120x + 1500, the y-intercept is 1500. The y-intercept occurs when x (time) is 0, and in this context, it represents the initial revenue of the pizza store before any sales have been made.

Question 12: Solve the system of linear equations below. <br> 5.5x + 2 = ~15x ~3 + 4y <br> 6x + 32y = 3

• x = ~.218, y = .135 (Correct answer)
• x = ~.234, y = .050
• x = -.274, y = .192
• x = -2.34, y = .5

Correct answer: x = ~.218, y = .135

First, simplify the first equation to 20.5x - 4y = -5. Then, use elimination or substitution with the second equation, 6x + 32y = 3. Multiplying the first simplified equation by 8 yields 164x - 32y = -40. Adding this to the second equation gives 170x = -37, so x ≈ -0.218. Substituting x back into an original equation and solving for y yields y ≈ 0.135.

Question 13: Who do you think would be the least biased source for an article headed "Are casinos hurting our town?"

• The district gambling commissioner
• The local casino manager
• A regular casino patron
• A man walking past the casino

A man walking past the casino has no direct personal or financial stake in the casino's operations or its impact on the town. Unlike the other options (gambling commissioner, casino manager, or regular patron), his perspective is least likely to be influenced by personal gain, loss, or professional obligations, making him the least biased source.

Question 14: Simon rides his motorcycle around a 4-meter-diameter circular track. His motorcycle wheels are meter in diameter. How many revolutions have his wheels made if he goes around 10 times?

• 50 revolutions
• 30 revolutions
• 90 revolutions
• 80 revolutions (Correct answer)

Correct answer: 80 revolutions

First, calculate the circumference of the track (C_track = π * 4 meters) and the circumference of the motorcycle wheel (C_wheel = π * 0.5 meters). For one lap, the number of wheel revolutions is C_track / C_wheel = (4π) / (0.5π) = 8 revolutions. Since Simon goes around the track 10 times, the total revolutions are 8 revolutions/lap * 10 laps = 80 revolutions.

Question 15: Calculate the mean and median of the following collection of numbers: <br> 17.6, 114.3, 13.2, 15.6, 15.7, 16.2, 899.5, <br> 615.2, 1.5

• 190, 16.2 (Correct answer)
• 16.2, 190
• 190, 17.6
• 17.6, 190

Correct answer: 190, 16.2

To find the mean, sum all 9 numbers (1708.8) and divide by 9, which equals approximately 189.87, rounding to 190. To find the median, arrange the numbers in ascending order: 1.5, 13.2, 15.6, 15.7, 16.2, 17.6, 114.3, 615.2, 899.5. The median is the middle value in the ordered list, which is the 5th number, 16.2.

Question 16: In the interval [0,6], which values are included?

• 0, ½ , 1, π (Correct answer)
• 1, π, 3, 2π
• -½ , 0, ½, 1
• ½, 1, π, 6

Correct answer: 0, ½ , 1, π

The notation [0,6] represents a closed interval, meaning it includes all real numbers from 0 up to and including 6. Option A contains 0, ½ (0.5), 1, and π (approximately 3.14159), all of which are real numbers that fall within this specified range. Other options include values outside this interval, such as -½ or 2π (approximately 6.28).

Question 17: Illuminate: 13 ≥ 3- |x+15|

• D) All real numbers (Correct answer)

Correct answer: D) All real numbers

First, rearrange the inequality 13 ≥ 3 - |x+15| to isolate the absolute value term: 10 ≥ -|x+15|. Multiplying by -1 and reversing the inequality sign gives -10 ≤ |x+15|. Since an absolute value expression is always non-negative (greater than or equal to zero), |x+15| will always be greater than or equal to -10 for any real number x. Therefore, the inequality holds true for all real numbers.

Question 18: For the interval [-2, 3) choose the suitable alternative notation.

• ~2 ≤ < 3 (Correct answer)
• ~2 ≤ x < 3
• ~2 < x < 3
• ~2 < x ≤ 3

Correct answer: ~2 ≤ < 3

The interval notation `[-2, 3)` signifies that the set of numbers includes -2 but excludes 3. The square bracket `[` denotes 'greater than or equal to' (≥), while the parenthesis `)` denotes 'less than' (<). Therefore, the suitable alternative notation is `-2 ≤ x < 3`, indicating that x is greater than or equal to -2 and less than 3.

Question 19: Which of the following functions best fits the data? <br> X Y <br> -8 20 <br> -7 13 <br> -6 8 <br> -5 6 <br> -4 3 <br> -3 7 <br> -2 12

• Quadratic (Correct answer)
• Exponential
• Cubic
• Linear

Correct answer: Quadratic

Observing the Y-values (20, 13, 8, 6, 3, 7, 12) as X increases, they initially decrease to a minimum point (around X=-4 or -5) and then begin to increase. This characteristic U-shaped pattern, where values decrease then increase, is typical of a quadratic function (parabola). Other function types like linear, exponential, or cubic would exhibit different trends across the given data points.

Question 20: Assess: <br> 8!/5!+6!_6!/2!

• 350
• 1,400
• 40,400
• 696 (Correct answer)

Correct answer: 696

To assess the expression `8!/5! + 6!/2!`, we first simplify each factorial division. `8!/5! = 8 * 7 * 6 = 336`, and `6!/2! = 6 * 5 * 4 * 3 = 360`. Adding these results together, `336 + 360` equals `696`.