The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190
Answer: first number is 190
case 1,
Let the CP be ₹x,
SP = ₹2400
Profit = SP – CP
= 2400 – x
Profit % = {(2400–x)/ x} × 100%
According to the question,
{(2400–x)/ x} × 100 = 25
=> (2400–x)/ x= 25 /100
=> 100(2400–x) = 25x [ cross multiplication]
=> 240000 – 100x = 25x
=> 240000 = 25x + 100x
=> 240000 = 125x
=> 240000/125 = x
=> x = 1920
So, CP = ₹1920
case 2,
SP = ₹2040
Profit = SP – CP
= 2040 – 1920
= ₹120
profit % = 120/1920 × 100%
= 16%
<h3>Thus, his profit would be 16% if he had sold his goods for ₹2040.</h3>
Answer: 0.5898
Step-by-step explanation:
Given : J.J. Redick of the Los Angeles Clippers had a free throw shooting percentage of 0.901 .
We assume that,
The probability that .J. Redick makes any given free throw =0.901 (1)
Free throws are independent.
So it is a binomial distribution .
Using binomial probability formula, the probability of getting success in x trials :
, where n= total trials
p= probability of getting in each trial.
Let x be binomial variable that represents the number of a=makes.
n= 14
p= 0.901 (from (1))
The probability that he makes at least 13 of them will be :-
![=^{14}C_{13}(0.901)^{13}(1-0.901)^1+^{14}C_{14}(0.901)^{14}(1-0.901)^0\\\\=(14)(0.901)^{13}(0.099)+(1)(0.901)^{14}\ \ [\because\ ^nC_n=1\ \&\ ^nC_{n-1}=n ]\\\\\approx0.3574+0.2324=0.5898](https://tex.z-dn.net/?f=%3D%5E%7B14%7DC_%7B13%7D%280.901%29%5E%7B13%7D%281-0.901%29%5E1%2B%5E%7B14%7DC_%7B14%7D%280.901%29%5E%7B14%7D%281-0.901%29%5E0%5C%5C%5C%5C%3D%2814%29%280.901%29%5E%7B13%7D%280.099%29%2B%281%29%280.901%29%5E%7B14%7D%5C%20%5C%20%5B%5Cbecause%5C%20%5EnC_n%3D1%5C%20%5C%26%5C%20%5EnC_%7Bn-1%7D%3Dn%20%5D%5C%5C%5C%5C%5Capprox0.3574%2B0.2324%3D0.5898)
∴ The required probability = 0.5898
One square can be a 3 by 3 square, meaning each side is 3 units.The area for this would be 9.
Another one is the square can be a 9 by 9 square, meaning each side is 9 units. The area for this would be 81.
To add the two expressions, we can write it as:
4.6x-3 + (-5.3x+9)
We can distribute the plus sign (which means just drop the parenthesis in this case):
4.6x-3-5.3x+9
Now, we can simplify by combining like terms:
-0.7x+6
