Answer:
He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.
Step-by-step explanation:
After n consecutive serves, his total number of serves is going to be n+8, since he has already served 8 times. In the best case, his number of successful first serves is n+2.
His percentage of succesful first serves is the division of the number of succesful first serves divided by the total number of serves. So
We want 
. So
He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.
As you can see in the picture above, there are six faces of a rectangular prism; two are formed with dimensions width and height, two are formed by the dimensions length and width, and two are formed by the dimensions length and height. So, if you know the length, width, and height of the rectangular prism, then the formula for the surface area is
=(2⋅ℎ⋅ℎ)+(2⋅ℎ⋅ℎℎ)+(2⋅ℎ⋅ℎℎ)
Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
Answer:
The correct option is:
The student should have switched the direction of the inequality sign to get –5> x for a final answer
Step-by-step explanation:
The students has made a mistake in the 3rd step.
We know that when we multiply or divide any negative number on both sides of the inequality, the sign of inequality reverse its direction.
In step 3 the student divided 25 by -5 but did not switch direction of the inequality sign.
Therefore the correct option is: The student should have switched the direction of the inequality sign to get –5> x for a final answer
