Answer:
There is a 38.97% probability that this student earned an A on the midterm.
Step-by-step explanation:
The first step is that we have to find the percentage of students who got an A on the final exam.
Suppose 13% students earned an A on the midterm. Of those students who earned an A on the midterm, 47% received an A on the final, and 11% of the students who earned lower than an A on the midterm received an A on the final.
This means that
Of the 13% of students who earned an A on the midterm, 47% received an A on the final. Also, of the 87% who did not earn an A on the midterm, 11% received an A on the final.
So, the percentage of students who got an A on the final exam is
To find the probability that this student earned an A on the final test also earned on the midterm, we divide the percentage of students who got an A on both tests by the percentage of students who got an A on the final test.
The percentage of students who got an A on both tests is:
The probability that the student also earned an A on the midterm is
There is a 38.97% probability that this student earned an A on the midterm.
Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
Answer:
He'll need 288 cups to make a waffle on his 24 foot diameter circular griddle.
Step-by-step explanation:
In order to find out how much batter Danny needs we first need to compute the area of the first pans, since it is a circular pan their area is given by A = 2*pi*r. So we have:
Area of the first pan = 2*pi*(6/2) = 18.84 square inches
Area of the second pan = 2*pi*(24/2) = 75.36 square foots
We now need to convert these values to be in the same unit, we'll convert from square foots to square inches:
Area of the second pan = 75.36 * (12)^2 = 10851.84 square inches
We can now use a proportion knowing that the batter and the thickness of the waffles are the same. If 0.5 cup of flour can make a waffle on 18.84 square inches then x cup of flour can make a waffle on 10851.85 square inches. Writing this in a mathematical form, we have:
0.5/x = 18.84/10851.84
18.84x = 0.5*10851.85
x = 10851.85*0.5/18.84 =288 cups
Answer:
56 cm
Step-by-step explanation:
We need ro find the GCD of these numbers. In finding the GCD, we list the multiples of the number, beginning with the smallest number. Here, the
The factors of 616=2*2*2*7*11
The factors of 448 =2*2*2*2*2*2*7
Common factors in both are 2*2*2*7=56
Therefore, the greatest possible length is 56 cm
