<span>10!/5! =10*9*8*7*6=30,240;;
If order is not considered, 10C5 =10!/5!5!=252 </span>
Asa has 15 dimes and 32 quarters.
Step-by-step explanation:
Given,
Total coins = 47
Worth of coins = $9.50 = 9.50*100 = 950 cents
1 dime = 10 cents
1 quarter = 25 cents
Let,
Number of dimes = x
Number of quarters = y
According to given statement;
x+y=47 Eqn 1
10x+25y=950 Eqn 2
Multiplying Eqn 1 by 10
![10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=10%28x%2By%3D47%29%5C%5C10x%2B10y%3D470%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 3 from Eqn 2
![(10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480](https://tex.z-dn.net/?f=%2810x%2B25y%29-%2810x%2B10y%29%3D950-470%5C%5C10x%2B25y-10x-10y%3D480%5C%5C15y%3D480)
Dividing both sides by 15
![\frac{15y}{15}=\frac{480}{15}\\y=32](https://tex.z-dn.net/?f=%5Cfrac%7B15y%7D%7B15%7D%3D%5Cfrac%7B480%7D%7B15%7D%5C%5Cy%3D32)
Putting y=32 in Eqn 1
![x+32=47\\x=47-32\\x=15](https://tex.z-dn.net/?f=x%2B32%3D47%5C%5Cx%3D47-32%5C%5Cx%3D15)
Asa has 15 dimes and 32 quarters.
Keywords: linear equation, elimination method
Learn more about elimination method at:
#LearnwithBrainly
Answer:
1/128 * (3 - 4cos2x + cos4x)
Step-by-step explanation:
See attachment for steps
Answer as a compound inequality: ![-4 \le y < 2](https://tex.z-dn.net/?f=-4%20%5Cle%20y%20%3C%202)
Answer in interval notation: [-4, 2)
=============================================
Explanation:
The range is the set of all possible y outputs of a function. When dealing with a graph like this, we just look at the highest and lowest points to determine which y values are possible.
The lowest point occurs when y = -4. We include this value. So far we have
which is the same as ![-4 \le y](https://tex.z-dn.net/?f=-4%20%5Cle%20y)
The upper ceiling for the y value is y = 2. We can't actually reach this value because of the open hole at (-3,2). So we say that ![y < 2](https://tex.z-dn.net/?f=y%20%3C%202)
Combine
and
to get the compound inequality ![-4 \le y < 2](https://tex.z-dn.net/?f=-4%20%5Cle%20y%20%3C%202)
This says y is between -4 and 2, including -4 but excluding 2.
To convert this to interval notation, we write [-4, 2) where the square bracket says to include the endpoint and the curved parenthesis says to exclude the endpoint.
Answer:no
Step-by-step explanation:
it’s equal to -10 + 10h by the commutativity of addition and subtraction