Additional Topics
A yogurt factory fills cylindrical containers 80% of the way. to the top, putting 6 ounces of yogurt in each cup. The containers are 4 inches tall and 2.5 inches wide. What is the approximate volume of one ounce of yogurt in cubic inches?
2.6
The ratio of freshmen to sophomores in an auditorium was 3 to 10. After an additional 270 freshmen and 120 sophomores entered the auditorium, the ratio of freshmen to sophomores was 6 to 5. No other students entered or left the auditorium. How many freshmen were in the auditorium before the additional students entered?
42
If (3/4)y=6-(1/3)c, the what is the value of 2c + (9/2)y?
36
In the equation x-2=3/(x-2), which of the following is a possible value of x-2?
A) (3)1/2
B) 2
C) 2 + (3)1/2
D) 3
A) +/- (3)1/2
A pizzeria's top-selling pizzas are The Works and The Hawaiian. The Works sells for $17, and The Hawaiian sells for $13. Ingredient costs for The Works are $450 per week, and ingredient costs for The Hawaiian are $310 per week. If x represents the number of each type of pizza sold in one week, and the weekly profit from the sale of each type of pizza is the same, what is the value of x?
35
What is the maximum value of y on the circumference of the circle defined by the equation x2 + y2 + 6x - 10y - 47 = 0?
14
All of the attendees at a symposium are either physicists. or biologists. If there are 123 physicists and 270 biologists, then how many additional physicists must arrive at the symposium in order for the ratio of physicists to total attendees to become 2 to 5?
57
V = (1/3)pi(d/2)2h.
A circle of rubber with a constant diameter, d, is placed on a table; its perimeter is anchored to the table and a string is attached to its center. When the string is pulled upwards, a cone is formed with height, h, and volume, V. The relationship between d, h, and V is represented above. Which of the following statements must be true?
I) As the volume of the cone decreases, the height also decreases.
II) If the diameter of the base of the cone is 6 centimeters, the height can be determined by dividing the volume by 3pi.
III) If the height of the cone triples, the volume must also triple.
I, II, and III
Your whole group must sing the chorus to KISHASH
Good job. A little off pitch but acceptable 😂
Malik starts a job at which his starting salary is $25,500 per year. He expects that his salary will increase by a constant dollar amount annually. In 12 years, his salary will be double his starting salary. Assuming salary increases take place only at the end of a full year, how many years must Malik wait until his salary is at least $40,000 annually?
7 years
The area of a right triangle is 35 square inches. If the longer leg is 3 inches longer than the shorter leg, what is the length of the hypotenuse, in inches?
(149)1/2
After the completion of the one-night study, the patient was monitored an additional four nights. Over the total number of nights that the patient spent at the clinic, he spent an average of 180 minutes in stage 3 sleep per night. If the patient slept an average of 175 minutes in stage 3 sleep on the second, third, and fourth nights, how many minutes did he spend in stage 3 sleep on the last night?
195
Which American artist sings this song?
"She like the way that I dance.
She like the way that I move.
She like the way that I rock
She like the way that I woo..."
Pop Smoke (R.I.P.) 🙏
If 30x3+45x2-10x is divided by 5x, what is the resulting coefficient of x?
9
The product of all the solutions of the equation 3v2 + 4v -2 = 0 is M. What is the value of M?
-(2/3)
If sinx=cos(13pi/6), which of the following could be a value of x?
A) pi/6
B) pi/4
C) pi/3
D) pi/2
C) pi/3
The owner of a miniature golf course wants to determine what color golf ball is most popular at the course. The owner asked 150 randomly surveyed children what color they prefer. Approximately 60% said they prefer red, while 30% of them said blue.
This data best supports which of the following conclusions?
A) Most people prefer a red gold ball when playing miniature golf.
B) Red golf balls are used twice as often as blue golf balls.
C) Most children at the course prefer a red golf ball.
D) Approximately 10% of players prefer a white golf ball.
C
At a certain toy store, tiny stuffed pandas cost $3.50 and giant stuffed pandas cost $14. If the store sold 29 panda toys and make $217 in revenue in one week, how many tiny stuffed pandas were sold?
18 tiny stuffed pandas, 11 giant stuffed pandas
4x - 12(x)1/2 + 9 = 16. If the equation is true, then what is the positive value of the expression 10(x)1/2 - 15?
20
Which of the following equations does NOT have any solutions that are real numbers?
A) x2 + 8x -12 = 0
B) x2 - 8x + 12 = 0
C) x2 - 9x + 21 = 0
D) x2 + 100x - 1 = 0
C
Which of the following is equivalent to (38 + 18i)/(4 + 6i)? (Note: i = (-1)1/2)
A) (11/13) - 3i
B) 5 - 3i
C) (19/2) + 3i
D) 44 + 300i
B) 5 - 3i
On a used vehicle lot, 50% of the vehicles are cars, 3/4 of which have automatic transmissions. Of the cars with automatic transmissions, 1/3 have leather interiors. If a vehicle is chosen from the lot at random, what is the probability that it will be a car with an automatic transmission and a leather interior?
1/8
Let a and b be numbers such that -a < b+1 < a. Which of the following must be true?
I) a>0
II) |b|<a
III) b>a+1
I and II only
Suppose a2 + 2ab + b2 and c - b = 4. Assuming c > 0, what is the value of a?
4
What is the positive difference between the x-intercepts of the parabola given by the equation g(x) = -2.5x2 + 10x - 7.5?
2