I believe the answer is cos^2 theta. Sec^2 theta on the right side of the equation is the inverse of Cos^2 theta, so multiplying the two together will get you 1. Cos^2 theta * Tan^2 theta = Sin^2 theta, and Cos^2 theta * 1 = Cos^2 theta. This all leads to the third and last step in the picture above.
Total cards with cat = 5
Total cards with dog = 6
Total cards = 5 + 6 = 11
He removed a card with dog.
Total cards with dog = 6 - 1 = 5
Total number of cards = 11 - 1 = 10
P(dog) = 5/10 (Answer C)
Answer:
8
Step-by-step explanation:
On the first day, they traveled for 10 hours with an average speed of 60 mph. Which means on the first day they traveled 600 miles.
Since the total distance is 1023 miles and presumably they will be going at a speed of 60 mph. We divide the miles by the rate:
1023/60 = 17.05
So it will take 17.05 hours to drive the whole way to Florida.
Answer: Either 2, 5, or 8
This means the number 426 is divisible by 6. So are 456 and 486
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Explanation:
A number is divisible by 6 if both of the following are true
- The number is divisible by 2
- The number is divisible by 3
This is simply because 6 = 2*3. So if 6 is a factor of a number, then 2 and 3 must be factors.
- To have 2 be a factor, the units digit must be in the set {0,2,4,6,8} which is the case here (the units digit is 6 in this case). Therefore we know the number is a multiple of 2 regardless of what the other digits are.
- To have 3 be a factor, the digits must add up to a multiple of 3. Through trial and error, we see that 0 doesn't work because 4+0+6 = 10 which is <u>not</u> a multiple of 3. Same goes for 4+1+6 = 11, but 4+2+6 = 12 is a multiple of 3.
Therefore, 426 is a multiple of 6
Increment that middle digit 2 by 3 and we jump from 426 to 456. Those three digits add to a multiple of 3 as well (4+5+6 = 15). Following that line of logic, we go from 456 to 486 as the last possible three digit number that has these conditions of having 4 first and 6 last, and the number is a multiple of 6.
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In short,
The numbers 426 and 456 and 486 are all multiples of 6 since they are multiples of 2 and 3 at the same time.
So we could replace that middle digit with either 2, 5 or 8.
