Answer:
Leslie has 13 quarters and 23 half-dollars.
Step-by-step explanation:
You can write the following equations from the information given and considering that a quarter is $0.25 and half-dollar is $0.50:
x+y=36 (1)
0.25x+0.50y=14.75 (2), where:
x=amount of quarters
y=amount of half-dollars
First, you can isolate x in (1):
x=36-y (3)
Then, you can replace (3) in (2):
0.25(36-y)+0.50y=14.75
9-0.25y+0.50y=14.75
0.25y=5.75
y=5.75/0.25
y=23
Finally, you can replace the value of y in (3) to find the value of x:
x=36-23
x=13
According to this, the answer is that Leslie has 13 quarters and 23 half-dollars.
In order to solve a negative exponent, you have to consider the multiplicative inverse of the base:
![a^{-m}=\dfrac{1}{a^m}=\left(\dfrac{1}{a}\right)^m](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cdfrac%7B1%7D%7Ba%5Em%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7Ba%7D%5Cright%29%5Em)
So, if we solve the negative exponent on the left hand side, we have
![2^{-\frac{1}{2}}=\dfrac{1}{2^\frac{1}{2}}=\left(\dfrac{1}{2}\right)^{\frac{1}{2}}](https://tex.z-dn.net/?f=2%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cdfrac%7B1%7D%7B2%5E%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
which is the right hand side.
If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
<h3>
Length across the other axis</h3>
Using Pythagoreans theorem formula
a²=b²+c²
Where:
c=16 feet
a=40/2=20 feet
Hence:
20²=b²+16²
b²=20²-16²
b²=400-256
b²=√144
b=12
2b=12×2
2b=24 feet
Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
The complete question is are:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Learn more about Length across the other axis here:
brainly.com/question/2005046
brainly.com/question/16492329
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Answer:
2.28% of faculty members work more than 58.6 hours a week.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average full-time faculty member in a college works an average of 53 hours per week. Standard deviation of 2.8 hours.
This means that ![\mu = 53, \sigma = 2.8](https://tex.z-dn.net/?f=%5Cmu%20%3D%2053%2C%20%5Csigma%20%3D%202.8)
What percentage of faculty members work more than 58.6 hours a week?
The proportion is 1 subtracted by the p-value of Z when X = 58.6. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{58.6 - 53}{2.8}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B58.6%20-%2053%7D%7B2.8%7D)
![Z = 2](https://tex.z-dn.net/?f=Z%20%3D%202)
has a p-value of 0.9772
1 - 0.9772 = 0.0228
0.0228*100% = 2.28%
2.28% of faculty members work more than 58.6 hours a week.
my answer is 232.2 i got it by adding 50, 220, 250, 410 which would be 930 and then you divide it by 4 because that is how many numbers there are so the answer would be 232.2 that is the average.
hope this helps if that is what the question asked.