Answer:
nCr = n! / (r!)(n-r!).
Step-by-step explanation:
That would be nCr = n! / (r!)(n-r!).
A quick way of working these out is as follows:
Take 7C4:
this is 7*6*5*4/4*3*2*1 Cancelling out the 4 and 3*2:
= 7*5
= 35.
15C12 = 15C(15-12)
= 15C3
= 15*14*13 / 3*2*1
= 5*7*13
= 455.
Complete question :
A welder drops a piece of red-hot steel on the floor. The initial temperature of the steel is 2,500 degrees Fahrenheit. The
ambient temperature is 80 degrees Fahrenheit. After 2 minutes the temperature of the steel is 1,500 degrees. The function
f(t) = Ce^-kt + 80 represents the situation, where t is time in minutes, C is a constant, and k is a constant.
After 2 minutes the temperature of the steel is 1,500 degrees. After how many minutes will the temperature of the steel be
100 degrees and therefore safe to pick up with bare hands? Round your answer to the nearest whole number, and do not.
include units.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the exponential function :
f(t) = Ce^(-kt) + 80
t = time in minutes ; k = constant ; C = constant; Initial temperature = 2500 = temperature at t = 0
Hence,
2500 = Ce^k*0 + 80
2500 = C + 80
C = 2500 - 80
C = 2420
Temperature after 2 minutes ; t = 2 minutes
1500 = 2420e^-k*2 + 80
1500 = 2420e^-2k + 80
1500 - 80 = 2420e^-2k
1420 = 2420e^2k
1420 / 2420 = e^-2k
0.58677 = e^-2k
Take the In of both sides
In(0.58677) = - 2k
−0.533122 = - 2k
k = 0.533122 / 2
k = 0.2665
k = 0.2667
Time at which temperature falls to 100
f(t) = Ce^(-kt) + 80
100 = 2420 * e^(-0.267t) + 80
100 - 80 = 2420 * e^(-0.267t)
20 = 2420 * e^(-0.267t)
Divide both sides by 2420
0.0082644 = e^(-0.267t)
Take In of both sides
−4.795790 = - 0.267t
Divide through by - 0.267
t = 17.96176
t = 17.96 minutes
Answer:
The required equation is:
0.23x = 52
Hence, option A is true.
Step-by-step explanation:
Given
Let 'x' be the initial depth
The snow is now 52 inches deep and it is a 77% decrease.
Let the initial 'x' depth be represented as 100%.
x → 100%
Given the current 52 inches is a 77% decrease. So, we need to decrease the 77/100 or 0.77 from the initial depth, so
[100% - 77%] of x = 52
[100/100 - 77/100] × x = 52
[1 - 0.77] × x = 52
0.23x = 52
Therefore, the required equation is:
0.23x = 52
Hence, option A is true.
Answer:
The answer is 84%
Step-by-step explanation:
The total amount of grocery shoppers that was at the shop was 700, you take the number that did not buy the candy bar and divide it by 700, so 588/700 = .84 move over the decimal by 2 to get your percentage and there you go.
