Answer:
Number of dimes = 28
Step-by-step explanation:
Given that:
Worth of coins = $6.30 = 6.30 * 100 = 630 cents
Let,
x be the number of dimes
y be the number of quarters
According to given statement;
x = 2y Eqn 1
10x+25y = 630 Eqn 2
Putting x = 2y in Eqn 2
10(2y) + 25y = 630
20y + 25y = 630
45y = 630
Dividing both sides by 45
Putting y=14 in Eqn 1
x = 2(14)
x = 28
Hence,
Number of dimes = 28
Answer:
The inverse function is:
{(1,8), (2,-1), (5,10), (-3,-3)}
Step-by-step explanation:
When a function is represented in the form of ordered pairs, the first element of each ordered pair is the input and the second element in each ordered pair is the output. In the inverse of a function the input becomes output and the output becomes input.
Given function is:
{(8,1), (-1,2), (10,5), (-3,-3)}
Reversing the order of elements of ordered pairs will given us the inverse function.
The inverse function is:
{(1,8), (2,-1), (5,10), (-3,-3)}
Answer: The percentage of legal quarters will be rejected by the vending machine = 2.275%
Step-by-step explanation:
Given: The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram.
Let x be the weights of legal U.S. quarters .
Required probability: 
![=P(\dfrac{x-\mu}{\sigma}\dfrac{5.81-5.67}{0.07})\\\\=P(z2)\approx0.02275 \ \ \ [By\ P-value\ calculator]](https://tex.z-dn.net/?f=%3DP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3C%5Cdfrac%7B5.33-5.67%7D%7B0.07%7D%29%2BP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3E%5Cdfrac%7B5.81-5.67%7D%7B0.07%7D%29%5C%5C%5C%5C%3DP%28z%3C-4.857%29%2BP%28z%3E2%29%5Capprox0.02275%20%20%20%20%5C%20%5C%20%5C%20%5BBy%5C%20%20P-value%5C%20calculator%5D)
The percentage of legal quarters will be rejected by the vending machine = 2.275%
Lets say that the two unknown integers are
and
.
We know the following things about
and
:
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of
and
, which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
