Step-by-step explanation:
Let the original speed of the train be x km/h.
Time taken to cover a distance of 360 km = 360/x hours.
New speed of the train = (x+5) km/h.
Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.
Since, the train takes 1 hour less time,
∴360/x - 360/ x+5 = 1
⇒360 (5) = x² + 5x
⇒1800 = x² + 5x
⇒x² + 5x - 1800 = 0
⇒x² + 45x - 40x - 1800 = 0
⇒x (x+45) - 40( x +45) = 0
⇒(x+45) (x-40) = 0
⇒x = (-45), 40
But since speed cannot be in negative.
∴x = 40 km/hr.
Hence, the original speed of the train is 40 km/h.
Answer:
We have a small circle, that is dilated by a factor of 5/3 creating a larger circle.
If the smaller circle has a diameter D, then after the dilation, the larger circle will have a diameter equal to: (5/3)*D
We know that the area of the larger circle is:
A = 100*pi cm^2.
And the area of a circle of diameter d, is:
a = pi*(d/2)^2
knowing that the diameter of the large circle is (5/3)*D, we can find the value of D.
A = pi*( (5/3)*D/2)^2 = 100*pi cm^2
let's solve this for D:
pi*( (5/3)*D/2)^2 = 100*pi cm^2
( (5/3)*D/2)^2 = 100 cm^2
( (5/3)*D/2) = √(100 cm^2) = 10cm
D/2 = (3/5)*10cm
D = 2*(3/5)*10cm = 12cm.
Then the area of the smaller circle will be:
a = pi*(D/2)^2 = pi*(12cm/2)^2 = pi*(6cm)^2 = pi*36 cm^2
and pi = 3.14
a = pi*36 cm^2 = 3.14*36cm^2 = 113.04 cm^2
You need to find the percent of the 125 surveyed students to find the number of estimated students that like pizza.
58/125 = .464 or 46.4%
1500*.464 = 696 students like pizza.
Hope this helps!
Answer:
a) 0.1587
b) 0.023
c) 0.341
d) 0.818
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 515
Standard Deviation, σ = 100
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Formula:
a) P(score greater than 615)
P(x > 615)
Calculation the value from standard normal z table, we have,
b) b) P(score greater than 715)
Calculating the value from the standard normal table we have,
c) P(score between 415 and 515)
d) P(score between 315 and 615)
Answer:
×1 = 3 : 8.
×2 = 6 : 16
×3 = 9 : 24
×4 = 12 : 32
Step-by-step explanation:
