Answer:
1. 41/45.
2. x/(x^2+3x+6)
Step-by-step explanation:
1.
So first we fill the ven diagram.
There are 240 in band, so we fill that. 60 students are in both, we put that in the middle, and there are 110 people in choir.
now, since we want the probability that a student is chosen that is in band, and choir, and both. We add all this up
240 + 60 + 110 = 410.
The total possible outcome is 410, and the total outcome is 450, so the answer is
410/450 = 41/45
2.
First, to get the total outcomes, we have to add all the expressions together.
x(x-2) + x + 2x+8 = x^2 - 2 + x + 2x + 8 = x^2 - 2 + 3x + 8 = x^2 + 3x + 6.
Since that is the total outcome, we have to find the possible outcomes.
The problem wants BOTH from the 20th century and British, so it is x.
x/(x^2+3x+6). We cannot simplify any further, thus x/(x^2+3x+6) is our answer
Answer: If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.
Step-by-step explanation:
Let x = Number of weeks.
As per given question ,
Weight of Frank after x weeks = 160+2x (pounds)
Weight of John after x weeks = 208-3x (pounds)
When Weight of Frank= Weight of John



Weight of Frank after 9.6 weeks = 160+2(9.6) = 179.2 pounds
Weight of John after 9.6 weeks = 208-3(9.6)=179.2 pounds
Hence, If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.
So I think maybe the example for the first problem created some confusion, and you may want to have your child take another look.
If we numbered the top half 1 to 9 going from left to right, numbers 1, 2, 6, 7 and 8 are right. They worked because the top number (numerator) perfectly fit into the bottom number (denominator). This is not true for the rest.
The key is to find the largest number that you can think of that will go into BOTH the top and the bottom evenly.
So for number 3: 18/24; 18 does not fit evenly into 24. The highest number that will fit into both is 6, so you divide both top and bottom by 6 and your answer is 3/4.
Number 4: 45/54; the highest number that goes into both is 9, so you divide both top and bottom by 9 and your answer is 5/6.
Number 5: 55/66; the highest number that can go into both is 11, so the answer is 5/6.
Is this making sense?
The bottom, numbering 1 to 9 from left to right. The correct ones are 1, 6 and 9.
For 2: 14/41 is about 15/40. Both can be divided by 5, so the answer is 3/8.
For 3: 20/81 is about 20/80, and 2/8 is close, but can still be divided by 2, so the answer is 1/4.
For 4: 24/49 is closer to 25/50 than 20/50. 25/50 can be divided by 25, so the answer is 1/2.
For 5: it was all correct, but the answer can be further reduced from 2/8 to 1/4.
For 7: 23/72 is about 25/75, and 25 goes into both, so it reduces to 1/3.
For 8: 13/21 is about 15/20, and 5 goes into both, so the answer is 3/4.
As your child continues to learn this, remember that if he or she gets an answer like 2/6 or 6/12, they should ask themselves if they can further reduce the fractions- 2/6 reduces to 1/3, and 6/12reduces to 1/2. I know it's confusing, but they do get the hang of it with practice
To measure and classify our triangle we are going to perform the following steps:
Step 1. Open GeoGebra or GeoGebra geometry and enter the input of the three points of our triangle.
Step 2. In the measure menu, choose the distance tool and select tow points in our triangle to measure the distance of one side; repeat the process for the other two sides.
Step 3. In the measure menu, choose the angle tool and select three points in our triangle to measure the angle between the three points; repeat the process for the other two angles.
Step 4. After performing the previous steps, we end with a triangle of three equal sides of 5.8 units and three equal angles of 60°. Since all the sides and angles in our triangle are equal, we have an equilateral triangle.
We can conclude that the triangle with coordinates <span>(10, 14), (15, 11.11), and (10, 8.22) is an
equilateral triangle.</span>