The number of quarters she have 11.
<h3>What is a system of equations?</h3>
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let consider y = quarters; x = dimes
We know that there are 3 times as many dimes as quarters. So we can state that x = 3y.
Then, we say that 25y + 10x = 605
(Value of coin * amount of coins)
Then we substitute x=3y into the equation, yielding:
25y + 10(3y) = 605
25y + 30y = 605
55y = 605
605/55 = 11 = y
Therefore, the number of quarters she have 11.
Learn more about equations here;
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Answer:
-1/2
Step-by-step explanation:
Im not going to go into detail about how to compute sin30 and cos 30, but know that sine and cosine are just the ratios between the sides of a 30-60-90 triangle with a hypothenuse of 1.
With that being said:
sin^2 30 - cos^2 30
= (1/2)^2 - ((sqrt3)/2)^2
= 1/4 - 3/4
= -1/2
Answer:
μ = 235.38
σ = 234.54
Step-by-step explanation:
Assuming the table is as follows:
![\left[\begin{array}{cc}Savings&Frequency\\\$0-\$199&339\\\$200-\$399&86\\\$400-\$599&55\\\$600-\$799&18\\\$800-\$999&11\\\$1000-\$1199&8\\\$1200-\$1399&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7DSavings%26Frequency%5C%5C%5C%240-%5C%24199%26339%5C%5C%5C%24200-%5C%24399%2686%5C%5C%5C%24400-%5C%24599%2655%5C%5C%5C%24600-%5C%24799%2618%5C%5C%5C%24800-%5C%24999%2611%5C%5C%5C%241000-%5C%241199%268%5C%5C%5C%241200-%5C%241399%263%5Cend%7Barray%7D%5Cright%5D)
This is an example of grouped data, where a range of values is given rather than a single data point. First, find the total frequency.
n = 339 + 86 + 55 + 18 + 11 + 8 + 3
n = 520
The mean is the expected value using the midpoints of each range.
μ = (339×100 + 86×300 + 55×500 + 18×700 + 11×900 + 8×1100 + 3×1300) / 520
μ = 122400 / 520
μ = 235.38
The variance is:
σ² = [(339×100² + 86×300² + 55×500² + 18×700² + 11×900² + 8×1100² + 3×1300²) − (520×235.38²)] / (520 − 1)
σ² = 55009.7
The standard deviation is:
σ = 234.54
The answer to this is .15%
