DIVIDE THE FOLLOWING INTEGERS. A. -78/ 12 B. - 155 /-5 C. 100 /-4
2 answers:
Answer:
A. -6.5
B. 31
C. -25
Step-by-step explanation:
A. Using long division, we know that 12 goes into 78 exactly 6 times without going over, so 12 times 6 is 72, but we get a remainder of 6. The remainder, 6, is half of 12. Half can be written as 0.5 in a decimal. So our answer is 6+0.5=6.5 but 78 is a negative and 12 is positive so 6.5 has to be negative. You can also just use a calculator.
B. Again, we could use long division to find how many times 5 goes into 155. The answer we got was that 5 goes into 155 exactly 31 times. This time, we didn't get a remainder but we have to watch out for the negatives. 155 and 5 are both negative, which means that the negative gets canceled out so our answer will be positive 31.
C. Lastly, we used long division to find out how many times 4 goes into 100. The answer that we got was 25 and we did not get a remainder but one of the numbers, 4, is a negative and when only one number is negative, the answer will also be negative. The final answer is negative 25.
Also, if you are wondering how long division works, I provided an example that shows all the steps.
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Answer:
b) No, it's not independent.
c) 0.02
d) 0.59
e) 0.57
f) 0.5616
Step-by-step explanation:
To answer this problem, a Venn diagram should be useful. The diagram with the information of Event 1 and Event 2 is shown below (I already added the information for the intersection but we're going to see how to get that information in the b) part of the problem)
Let's call A the event that she passes the first course, then P(A)=.73
Let's call B the event that she passes the second course, then P(B)=.66
Then P(A∪B) is the probability that she passes the first or the second course (at least one of them) is the given probability. P(A∪B)=.98
b) Is the event she passes one course independent of the event that she passes the other course?
Two events are independent when P(A∩B) = P(A) * P(B)
So far, we don't know P(A∩B), but we do know that for all events, the next formula is true:
P(A∪B) = P(A) + P(B) - P(A∩B)
We are going to solve for P (A∩B)
.98 = .73 + .66 - P(A∩B)
P(A∩B) =.73 + .66 - .98
P(A∩B) = .41
Now we will see if the formula for independent events is true
P(A∩B) = P(A) x P(B)
.41 = .73 x .66
.41 ≠.4818
Therefore, these two events are not independent.
c) The probability she does not pass either course, is 1 - the probability that she passes either one of the courses (P(A∪B) = .98)
1 - P(A∪B) = 1 - .98 = .02
d) The probability she doesn't pass both courses is 1 - the probability that she passes both of the courses P(A∩B)
1 - P(A∩B) = 1 -.41 = .59
e) The probability she passes exactly one course would be the probability that she passes either course minus the probability that she passes both courses.
P(A∪B) - P(A∩B) = .98 - .41 = .57
f) Given that she passes the first course, the probability she passes the second would be a conditional probability P(B|A)
P(B|A) = P(A∩B) / P(A)
P(B|A) = .41 / .73 = .5616
Answer:
A.
Step-by-step explanation:
This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -
We can then apply the power rule " ", where a = exponent ( in this case 4 ),
From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -
- Add the exponents,
- 5 & 5 cancel each other out,
- And now adding the constant we see that our solution is option a!