Nokea
(x/y) - z = nw. Solve for x in the equation above.
- A. x = y(nw + z)
- B. x = y(2 + rw)
- C. x = yw + yz
- D. x = y(nw - z)
Correct Answer: A
Rationale: To solve for x, first add z to both sides: (x/y) = nw + z. Then multiply both sides by y to isolate x: x = y(nw + z).
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A circle has an area of 49π square inches. What is the circumference of the circle in terms of π?
- A. 7Ï€ in
- B. 14Ï€ in
- C. 28Ï€ in
- D. 3.5Ï€ in
Correct Answer: B
Rationale: To find the circumference of a circle in terms of π, we first determine the radius using the formula for the area of a circle, A = πr^2. Given that the area is 49π square inches, we have 49π = πr^2, which simplifies to r = 7. The circumference of a circle is calculated using the formula C = 2πr. Substituting r = 7, we get C = 2π(7) = 14π. Therefore, the circumference of the circle is 14π inches.
A gumball machine contains red, orange, yellow, green, and blue gumballs. Twenty percent of the gumballs are red, 30% are orange, 5% are yellow, 10% are green, and the rest are blue. If there are a total of 120 gumballs, how many more blue gumballs are there than yellow gumballs?
- A. 48
- B. 36
- C. 30
- D. 42
Correct Answer: B
Rationale: First, calculate the number of gumballs of each color: Red = 0.20 x 120 = 24 gumballs, Orange = 0.30 x 120 = 36 gumballs, Yellow = 0.05 x 120 = 6 gumballs, Green = 0.10 x 120 = 12 gumballs. The total number of gumballs of the mentioned colors is 24 + 36 + 6 + 12 = 78 gumballs. Therefore, the number of blue gumballs is 120 - 78 = 42 gumballs. To find the difference between the number of blue and yellow gumballs, subtract the number of yellow gumballs from the number of blue gumballs: 42 - 6 = 36. Therefore, there are 36 more blue gumballs than yellow gumballs.
A consumer purchases a new sofa that is on sale for 10% off. The original price of the sofa is $950. Which of the following prices represents the sale price of the sofa before taxes are applied?
- A. $940
- B. $855
- C. $85
- D. $95
Correct Answer: B
Rationale: To find the sale price before taxes, you need to deduct 10% of the original price ($950) from the original price. This is calculated as follows: $950 - ($950 * 0.10) = $950 - $95 = $855. Therefore, the sale price of the sofa before taxes is $855. This calculation involves applying the 10% discount to the original price to determine the reduced sale price. The correct answer is $855.
The Americans with Disabilities Act (ADA) requires the slope of a wheelchair ramp to be no greater than 1:12. What is the minimum length of the ramp needed to provide access to a door that is 2.5 feet above the sidewalk?
- A. 25 feet
- B. 30 feet
- C. 32.5 feet
- D. 14.5 feet
Correct Answer: B
Rationale: To determine the minimum length of the ramp needed to provide access to a door elevated 2.5 feet above the sidewalk, we divide the vertical rise (2.5 feet) by the slope ratio (1:12). This calculation results in 2.5 feet divided by 1/12, which equals 30 feet. Therefore, a 30-foot ramp is required to meet the ADA requirement of a 1:12 slope, ensuring proper wheelchair access to a door elevated 2.5 feet above the sidewalk.
A consumer needs to purchase at least 50 soft drinks for a picnic. Which of the following combinations is the most cost-effective? 2 packs of Orange and 1 pack of Cream Soda; 2 packs of Root Beer and 1 pack of Cream Soda; 3 packs of Orange; 5 packs of Cream Soda.
- A. 2 packs of Orange and 1 pack of Cream Soda
- B. 2 packs of Root Beer and 1 pack of Cream Soda
- C. 3 packs of Orange
- D. 5 packs of Cream Soda
Correct Answer: A
Rationale: Option A, 2 packs of Orange and 1 pack of Cream Soda, provides 60 drinks for $23, resulting in the lowest cost per drink. Since the consumer needs a minimum of 50 soft drinks for the picnic, this combination offers the most cost-effective solution to meet the requirement within the specified budget. Choosing this combination allows the consumer to have a surplus of 10 drinks while keeping the cost per drink at a minimum, making it the optimal choice for the consumer's needs.