algebra
If -30 + k = 22, what is the value of k ?
52
Find the area of a triangle with a base of 10 units and a height of 6 units.
30 square units
A set of five consecutive integers has a mean of 18. What is the smallest integer in the set?
16
Simplify (8!)/(5!*3!)
56
2x + 4y = 15
2x + 4y = 13
Consider the given system of equations. How many (x, y) solutions does this system have?
no solutions
In the right triangle ABC, angle C is 90 degrees. The length of AC =4 and the length of AB =10. What is the length of BC?
2 √21
The median of a data set is 30, and the mean is 40. If one more data point of 100 is added, what happens to the median and mean?
The median remains 30, and the mean increases.
If 3x-y=12 and 2x+y=3, find x
x=3
The Silver Lake Reservoir in California is being drained to make way for an underwater pipeline. The reservoir holds 400 million gallons of water, and it is estimated that the drainage will take at least 25 days. If the water is drained at a constant rate, what is the maximum rate of drainage, in millions of gallons per day?
16 million gallons per day
What is the radian measure that equals to 45 degrees?
π/4
In a survey, 60% of participants prefer Product A, 30% prefer Product B, and the remainder prefer Product C. If 200 people were surveyed, how many preferred Product C?
20
The sum of two numbers is 50, and their product is 576. Find the numbers.
32 and 18
Roberto plans to start a new job. In preparation, he decides that he should spend no more than 30 hours per week on the job and homework combined. If Roberto wants to have at least 2 homework hours for every 1 hour at his job, what is the maximum number of hours that he should spend at his job each week?
10 hours
A circle in the xy plane has its center at (-2.8,6.1) and radius 4.2. What is an equation of the circle?
(x+2.8)2 + (y-6.1)2 = 17.64
In a survey of smartphone owners, 64% of a random sample of younger adults aged 18-29 used their phones to listen to music or podcasts, compared to 21% of a random sample of older users who did so. Based on the results of this survey, which of the following conclusions are valid?
I : Younger adults are more likely to listen to music or podcasts on their smartphones than are older adults.
II : Older adults like music less than younger adults.
III : Older adults do not listen to music on their smartphones because they find it inconvenient.
IV : Younger adults are more likely than older adults to own smartphones.
I only
The quadratic equation x2 - 8x + 15 = 0 has two roots. What is the sum of their reciprocals?
8/15
The graph of a line in the xy-plane passes through the points (-2, 0) and (8, -2). The graph of a second line has a slope of -2 and contains the point (1, 3). If the two lines intersect at the point (a, b), what is the value of a + b?
2
The angles of a triangle are in the ratio 3:4:5. Find the measure of the largest angle.
75 degrees
The ages of students in a class are: 12, 13, 13, 14, 15, and x. If the mean age is 14, find x.
x = 17
A box contains 4 red balls, 3 green balls, and 2 blue balls. If two balls are drawn at random without replacement, what is the probability that both are green?
1/12