In A fith grade class 3/4 of th students like to go to the movies. Of the students who like to go to the movies 2/3 of them like
1 answer:
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Fraction of students that like movies:
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Fraction of the students like action movies :
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Fraction of the students who like action and comedy movies:
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Answer:
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Fraction of students that like movies:
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Fraction of the students like action movies :
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Fraction of the students who like action and comedy movies:
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Answer:
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The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deep
The maximum volume is
(80/3 in)²(20/3 in) = 4740 20/27 in³
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deep
The maximum volume is
(80/3 in)²(20/3 in) = 4740 20/27 in³
If you have any questions on what I did, just leave a comment.
I tried to add my second image but it won't allow me. So, the base is 6 that you're missing for question 6. Good luck.
I tried to add my second image but it won't allow me. So, the base is 6 that you're missing for question 6. Good luck.
Answer:
The fifth integer in row 10 using the number tree pattern is 515.
Step-by-step explanation:
The attached picture is instrumental to understanding the solution to this. There are different methods to approach this problem. But we will use observations to solve the problem.
Looking at the tree diagram, we see that the first row has 1 integer, the second has 2, the third has 4 and the fourth has 8. From here, we can see that a row has 2^n numbers where n = 0, 1, 2, 3, 4, . . .
Row 1 = 2^0 = 1 number
Row 2 = 2^1 = 2 numbers
Row 3 = 2^2 = 4 numbers
Row 4 = 2^3 = 8 numbers. And so on.
Also we notice that the last number in row 4 is 14. This can be gotten by adding the total number of numbers from row 1 to row 4 which is
1 + 2 + 4 + 8 = 15 but the first number on the chart is 0 which means we have to take out the first integer to get the last integer on row 4. Doing this, we have 14.
Since our aim is to know the fifth number in row 10, then we need to know the last number in row 9 then count from the first number in row 10 to the fifth. Using 2^n to get the number of numbers in each row like we've done above we can add the number of numbers to know the total numbers we have from row 1 to row 9 as follows:
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 = 511
As we've said previously, 0 is the first integer in the tree and should be removed to know the last number in row 9. This would be 510.
If 510 is the last number in row 9 is 510, then the first number in row 10 would be 511. Counting to the fifth number we get to 515. Thus the fifth number in row 10 using the number tree pattern is 515.
