Evaluate. 102+6⋅7+8 70142150190
2 answers:
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For A B and C, you just plug in the given number
A
B
C
And for D, you set the equation to 26 and solve for n
I had to use x instead of n, but for D n=7. :)
A
B
C
And for D, you set the equation to 26 and solve for n
I had to use x instead of n, but for D n=7. :)
Answer:
option: B () is correct.
Step-by-step explanation:
We are given the solution set as seen from the graph as:
(-4,2)
1)
On solving the first inequality we have:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>-2 and x<4
so we have the region as:
(-2,4)
Case 2:
and
i.e. x<-2 and x>4
Hence, we did not get a common region.
Hence from both the cases we did not get the required region.
Hence, option 1 is incorrect.
2)
We are given the second inequality as:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>2 and x<-4
Hence, we do not get a common region.
Case 2:
and
i.e. x<2 and x>-4
Hence the common region is (-4,2) which is same as the given option.
Hence, option B is correct.
3)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x>-2 and x>4
Hence, the common region is (4,∞)
Case 2:
and
i.e. x<-2 and x<4
Hence, the common region is: (-∞,-2)
Hence, from both the cases we did not get the desired answer.
Hence, option C is incorrect.
4)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x<2 and x<-4
Hence, the common region is: (-∞,-4)
Case 2:
and
i.e. x>2 and x>-4.
Hence, the common region is: (2,∞)
Hence from both the case we do not have the desired region.
Hence, option D is incorrect.
Answer:
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.
Step-by-step explanation:
The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
1 from a set of 2(Either Mrs. Vera or Mr. Jan).
3 from a set of 18 - 2 = 16. So
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.