Q1)
the bus has to travel a total distance of 300 km. Average speed of the whole ride is 90 km/h
average speed is calculated by dividing total distance by total time taken.
Since we know speed and totat distance we can find out the total time for the trip taken.
average speed = total distance/total time
90 km/h = 300 km/total time
total time = 300/90 = 10/3 hours
for the first half of the trip -speed is 75 km/h and distance is 150 km, as half of 300 km is 150 km.
time taken for the first half = 150 km/75 km/h = 2 hours
then for the second trip, distance is 150 km
time taken - (10/3 - 2) hours
speed = 150 / (10/3 - 2)
=
=
speed = 112.5 km/h
answer is B
Q2)
the wood used covered 2 triangle sides and 1 rectangle side.
area of 1 triangle = 1/2 x base x height
= 1/2 x 8.25 x 3 = 12.375
surface area of 2 triangles = 12.375 x 2 = 24.75 ft²
to find surface area of rectangle , length should be found out.
we can find the length as it is the hypotenuse of the right angle triangle.
hypotenuse - H can be found out using the following equation,
H² = 8.25² + 3²
H = √77.06
H = 8.78 ft
area of rectangle - 8.78 x 6 = 52.68
total area = 52.68 + 24.75 = 77.4 ft²
correct answer is J
Q3)
the number of peanut pounds she buys - x
number of raisin pounds - y
peanuts cost per pound - $5.50
raisins cost per pound - $4
she needs to make 10 pounds
therefore,
x+y = 10
we need to find y
x = 10 -y
each pound of snack mix costs $4.90, therefore 10 pounds - $49.0
5.5x + 4y = 49
substituting x = 10 - y
5.5 (10-y) + 4y = 49
55 - 5.5y + 4y = 49
-1.5y = -6
y = 4
answer is B - 4 lb
Q4)
the number of red delicious apples - x
since red delicious apples are same as yellow delicious apples
number of yellow delicious apples - x
number of jonathon is twice as much as red delicious
then number of jonathon is 2x
then she buys macintosh twice as much as jonathon
number of macintosh - 4x
then total number of apples - x + x + 2x + 4x = 8x
since there are 2x number of jonathon apples,
probability of picking jonathon is 2x/8x = 1/4 = 0.25
answer is G
Q5)
as this is a right angle triangle, we can use trigonometry ratios
for angle x, opposite side is 20 ft and adjacent side is 70 ft.
therefore we can find
tan θ = opposite side / adjacent side
since we know the sides we need to calculate inverse of tan to find the angle
tan θ = 20/70
θ = tan⁻¹ 20/70
θ = 15.9 °
Answer is D
Q6)
width of the rectangle - x yards
length of the rectangle is 3 yards more than twice its width
twice the width - 2x
therefore length = 2x + 3
perimeter is sum of all 4 sides of the rectangle
Perimeter = 2*length + 2* width
Perimeter = 2(2x + 3) + 2(x)
= 4x + 6 + 2x
perimeter is 72 yards
4x + 6 + 2x = 72
6x + 6 = 72
6x = 66
x = 11 yards
correct answer is F
