David was in need for some money so he decided to clean out the water fountain at the mall he found 20 nickels and quarters. The
1 answer:
Answer:
David find <u>8</u> quarters.
Step-by-step explanation:
Given:
David was in need for some money so he decided to clean out the water fountain at the mall he found 20 nickels and quarters.
The collection of nickels and quarters totaled to 2.6.
Now, to find the quarters David find.
Let the number of nickels be
And the number of quarters be
Thus, the number of nickels and quarters he found:
⇒ .........( 1 )
The totaled of nickels and quarters:
(As 1 nickel=$0.05 and 1 quarter=$0.25)
Now, putting the equation ( 1 ) in the place of we get:
⇒
⇒
<em>Subtracting both sides by 1 we get:</em>
⇒
<em>Dividing both sides by 0.20 we get:</em>
⇒
So, the quarters = 8.
Therefore, David find 8 quarters.
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A 52-card deck is made up of an equal number of diamonds, hearts, spades, and clubs. Because there are 4 suits, there is a 1/4 chance to draw one of them, in our case, spades.
There are 4 aces in a 52-card deck, so the chance of drawing one is 4/52, or 1/13.
The question asks for the probability of drawing an ace or a spade. Because it uses the word "or," we add the probabilities together. This is because there is a chance of drawing either of the cards; it doesn't have to meet both requirements to satisfy the statement.
However, if the question were to say "and," we would multiply the two probabilities.
Let's add 1/4 and 1/13. First, we can find a common denominator. We can use 52 because both fractions can multiply into it (since the ratio came from a deck of 52 cards as well).
Now we can add them together.
This cannot be simplified further, so the probability is 17 in 52, or 33%.
hope this helps!
Answer:
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)
Step-by-step explanation:
Notation and definitions
n=50 represent the sample size
represent the sample mean
represent the sample standard deviation
m represent the margin of error
Confidence =88% or 0.88
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in R using the following formulas:
qt(0.06,49)
[1] -1.582366
qt(1-0.06,49)
[1] 1.582366
The critical value
Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
With R we can do this:
m=1.582366*(5.83/sqrt(50))
m
[1] 1.304639
Calculate the confidence interval
The interval for the mean is given by this formula:
And calculating the limits we got:
Using R the code is:
lower=27.02-m;lower
[1] 25.71536
upper=27.02+m;upper
[1] 28.32464
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)