Byron has 72 coins in his piggy bank. The piggy bank contains only dimes
2 answers:
Answer:
(3)
Step-by-step explanation:
Let d represent number of dimes and q represent number of quarters.
We have been given that Byron has 72 coins in his piggy bank. We can represent this information in an equation as:
We are also told that the value of all coins is $14.70.
Value of d dimes: .
Value of q quarters: .
From equation (1), we will get:
Substitute this value in equation (2):
Therefore, the equation can be used to determine q, the number of quarters.
You might be interested in
Answer:
Probability that the sample will have a mean that is greater than $52,000 is 0.0057.
Step-by-step explanation:
We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.
We select a random sample of 1,000 people.
<em>Let </em><em> = sample mean</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = $50,000
= population standard deviation = $25,000
n = sample of people = 1,000
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample will have a mean that is greater than $52,000 is given by = P( > $52,000)
P( > $52,000) = P(
>
) = P(Z > 2.53) = 1 - P(Z
2.53)
= 1 - 0.9943 = 0.0057
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>
Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.
A generic odd number can be written as
Since there is an odd number every two numbers, three consecutive odd numbers will be
Now let's make up the equations: the sum of the first two is
And 27 less than 3 times the largest is
These two must be the same, so we have
Subtracting 4k and 3 from both sides gives
Which means that the problem has no solution.
To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even
On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).
So, the left hand side is even, and the right hand side is odd. They can't be the same number.