isabella collected a bunch of dimes and quarters for her school fundraiser she collected a total of 211 coins and a total of 37.
1 answer:
Answer:
103 dimes and 108 quarters
Step-by-step explanation:
Given
Required
Determine the number of each coin collected
Represent dimes with D and quarters with Q.
So:
--- Value
--- Amount
Make D the subject in
Substitute 211 - Q for D in
Open brackets
Collect Like Terms
Make Q the subject
Substitute 108 for Q in
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Hi,
You just have to change z^25 to z^24 or z^27.
To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (
):
We can replace the variables in this equation with the values from the points we have been given, (
) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair
and the 
in the first ordered pair 
.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.
Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as
and we can change the improper fraction in the numerator into a mixed number for ease of addition.
And here, we can add, since it's made simple for us.
Finally, to get the slope we can complete the fraction by dividing.
The slope of this equation,, is 7, and so far, our equation looks like this:
Now, to find y-intercept.
To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.
Let us substitute in our values.
Now, we can solve by multiplying the 7 and 2.
Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with
which can be flipped around to show
The y-intercept of this line is 0.
Now, we can make this known in our equation like this:
Or, for neatness' sake, we can just say
which is your final equation.
The line through () and (2, 14) in slope-intercept form is <span>.
Hope that helped! =) </span>
We can replace the variables in this equation with the values from the points we have been given, (
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.
Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as
and we can change the improper fraction in the numerator into a mixed number for ease of addition.
And here, we can add, since it's made simple for us.
Finally, to get the slope we can complete the fraction by dividing.
The slope of this equation,
Now, to find y-intercept.
To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.
Let us substitute in our values.
Now, we can solve by multiplying the 7 and 2.
Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with
which can be flipped around to show
The y-intercept of this line is 0.
Now, we can make this known in our equation like this:
Or, for neatness' sake, we can just say
which is your final equation.
The line through (
Hope that helped! =) </span>
Answer:
a) There is a probability of 42% that the person will feel guilty for only one of those things.
b)There is a probability of 46% that a randomly selected person will not feel guilty for either of these reasons
Step-by-step explanation:
This probability problem can be solved by building a Venn like diagram for each probability.
I say that we have two sets:
-Set A, for those people that will feel guilty about wasting food.
-Set B, for those people that will feel guilty about leaving lights on when not in a room.
The most important information is that there is a .12 probability that a randomly selected person will feel guilty for both of these reasons. It means that
The problem also states that there is a .39 probability that a randomly selected person will feel guilty about wasting food. It means that P(A) = 0.39. The probability of a person feeling guilty for only wasting food is PO(A) = .39-.12 = .27.
Also, there is a .27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. So, the probability of a person feeling guilty for only leaving the lights on is PO(B) = 0.27-0.12 = 0.15.
a) What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room?
This is the probability that the person feels guilt for only one of those things, so:
P = PO(A) + PO(B) = 0.27 + 0.15 = 0.42 = 42%
b) What is the probability that a randomly selected person will not feel guilty for either of these reasons
The sum of all the probabilities is always 1. In this problem, we have the following probabilies
- The person will not feel guilty for either of these reasons: P
- The person will feel guilty for only one of those things: PO(A) + PO(B) = 0.42
- The person will feel guilty for both reasons: PB = 0.12
So
`P + 0.42 + 0.12 = 1
P = 1-0.54
P = 0.46
There is a probability of 46% that a randomly selected person will not feel guilty for either of these reasons