There are 7,315 different combinations, thus, the correct option is c
<h3>
How many combinations are there?</h3>
If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:
In this case we have K = 4 and N = 22, replacing that, we get:
So there are 7,315 different combinations, thus, the correct option is c.
If you want to learn more about combinations:
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1. The information given in the problem is:
- <span>The length of a rectangular garden is 8 feet longer than the width.
- </span><span>The garden is surrounded by a 4-foot sidewalk.
- The area of the sidewalk is 320 ft</span>².
2. So, the length of the rectangular garden is:
L1=8+W1
3. The formula for calculate the area of the sidewalk, is:
A2=L2xW2
"A2" is the area of the sidewalk (A2=320 ft²).
"L2" is the length of the sidewalk.
"W2" is the widht of the sidewalk.
4. The length of the sidewalk (L2) is:
L2=L1+4+4 (4 feet on each side)
L2=L1+8
5. When you substitute L1=8+W1 into the equation L2=L1+8, you obtain:
L2=8+W1+8
L2=W1+16
6. The widht of the sidewalk is:
W2=W1+4+4
W2=W1+8
7. Now, you must substitute the length and the widht of the sidewalk into the formula A2=L2xW2:
A2=L2xW2
A2=(W1+16)(W1+8)
320=W1²+16W1+8W1+128
W1²+16W1+8W1+128-320=0
W1²+16W1+8W1-192=0
8. When you solve the quadratic equation, you obtain the value of W1:
W1=16.97 ft
9. Finally, you must substitute the value of W1 into the formula L1=8+W1:
L1=8+W1
L1=8+16.97
L1=24.97 ft
10. Therefore, the dimensions of the garden are:
L1=24.97 ft
W1=16.97 ft
$6462.5
Simple Interest = (Principal × Rate × Time) / 100
SI = (P×R×T) / 100
P = 5500
R = 3.5
T = 5
[substitute the values into the formula]
SI = (5500 × 3.5 × 5) / 100
SI = 96250 / 100
SI = 962.5
Total = Principal + Simple Interest
T = P + SI
T = 5500 + 962.5
T = 6462.5
The total value of the account after 5 years will be $6462.5
Answer:
$8
Step-by-step explanation:
Each pack includes one pack of popcorn and one pack of candy. Since Jenny bought 4 packs, and it cost $32 in total, the equation will look like:
4x = 32
To solve this you divide 4 into each side of the equation:
4x = 32
---- ----
4 4
x = 8
The answer is 8.
Hope this helped.
Just add 360 to -800 until you end up with an angle between 0 and 360:
-800+360=-440
-440+360=-80
-80+360=280
So the angle is 280 degrees.
