Arithmetic and counting
The sum of three consecutive even integers is 54. What are the integers?
Answer16,18,20
Simplify
(2+(3)^½)/(3-(3)^½)
Answer
3/2+ (5(3)^½)/6
A hospital needs to administer a medication dosed at 10 mg per kilogram of body weight, but the dose should be divided into three equal parts to be given at intervals. If a patient weighs 70 kg, how much medication should be given per dose?
Answer
233.33 mg per dose (700 mg ÷ 3)
Find the distance between the points A(2,3) and B(6,7)
Answer
The distance is 4(2)^½
What is the sum of the first 50 positive integers?
Answer
1275
8^2x-1=4^x+1
Answer
x=5/4
A lawyer charges an hourly rate of $150 for their services, with an additional flat fee of $500 for administrative costs. If the client negotiates a 10% discount on the total hourly fee but still pays the full administrative cost, how much will they owe if the lawyer works for 12 hours?
Answer
$1,920 (12 hours at $135/hour + $500)
Find the slope of the line passing through the points P(1,2) and Q(4,-3).
Answer
The slope is -5/3
At a team meeting, 30 people each shake hands with every other person exactly once. How many total handshakes occur?
Answer
435
Find all the rational roots of the polynomial f(x)=2x^3-5x^2+4x-4
Answer
X=2
A coffee shop measures the flow rate of coffee being brewed as it fills a large container. The flow rate r(t) (in liters per minute) changes over time as the machine starts up, and it’s given by r(t) = 4 - 0.2t , where t is time in minutes after the machine starts.How much coffee has been brewed during the first 10 minutes?
Answer
30 liters
Find the equation of the line passing through A(-2,3) and perpendicular to the line 2x+3y=6.
Answer
The equation of the line is y=3x/2 +6
How many distinct ways can you arrange the letters in the word “MATHS” ?
Answer
120
If z=1+i find z^10 in terms of a real number
Answer
z^10 =32i
“This integer leaves a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the smallest such integer?”
Answer
59
The equation of an ellipse is given as: x^2/25 +y^2/9 =1
Find the coordinates of the foci
Answer
The coordinates of the foci are (4,0) and (-4,0).
A bag contains 7 red balls, 5 blue balls, and 6 green balls. You draw two balls from the bag without replacement. What is the probability of drawing a red and blue ball (in any order)?
Answer
70/306->35/135
Given that the roots are α=1, β=2, and γ=3 find α^2+β^2+γ^2
Answer
The value of α^2+β^2+γ^2 is 14.
It’s Kaia’s Birthday, 6 of her friends stand in a line for a photo, how many different ways can they arrange themselves to take the photo of Kaia must be in the middle.
Answer
Since Kaia must be in the middle, her position is fixed at the 4th spot in the lineup (with 7 total spots). This leaves the other 6 positions for her 6 friends.
Find the equation of the circle passing through the points A(2,3),B(4,5), and C(6,3).
Answer
x^2 +y^2-5x-9y +12=0