Answer:
x = 1, y = 60
Step-by-step explanation:
Value of new-releases (x) = $20 each
Value of classic (y) = $8 each
Total budget = $500
Equation : 20x + 8y = 500
The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.
Lets assume the librarian buys at least one new-release DVD.
x=1
20x + 8y = 500
8y + 20(1) = 500
y = 60
<em>Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.</em>
!!
<span>Number line refers to a mathematical process of
solving the equation with the use of lines.
=> 235 + 123
Starting from 0 you count 1 up to 235. Then starting from 235 you additionally
count another 123.
Then from zero start counting the total number to the line you stopped when
adding 123 to 235.
This simply equals to
=> 235 + 123
=> 358.
Pls. see attached image for illustration of number line.</span>Answer here
Answer:
10
Step-by-step explanation:
If there is a direct relation between two variables x and y then it can be represented as
y = kx ,
where y is dependent variable
x is independent variable
k is constant of variation
_____________________________
First condition
y = 400
x = r
using y = kx then relationship will be
400 = kr
finding k here
k = 400/r
Second condition
y = r
x = 4
using y = kx then relationship will be
r = 4k
finding k
k = r/4
since in both condition equation is same
thus, value of k will also be same
thus,
400/r = r/4
=> 400*4 = r*r
=> 1600 = r^2

Thus, 40 is the value of r
k = r/4 = 40/4 = 10
Thus, constant of variation is 10 which is correct choice.
To cross validate
k = 400/r = 400/40 = 10
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
Answer:
<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29
Step-by-step explanation:
Let Marge's present age be = M
Dan's present age [D] : 14 years elder than Marge = M + 14
Marge Age = M - 8
Dan's Age = D - 8 = (M + 14) - 8 = M + 6
{Given} : Dan's age = 3 times Marge's age
M + 6 = 3 (M - 8)
M + 6 = 3M - 24
6 + 24 = 3M - M
30 = 2M
M = 30/2
M = 15 [Marge's present age]
Dan's present age [D] = M + 14 = 29