web2.0calc
 

Georgemichels

avatar
UsernameGeorgemichels
Score8
Membership
Stats
Questions 0
Answers 4

 #1
avatar+8 
0

Hello,

If 7 out of every 12 people are bored by cable news and there are 280 people at the convention who are bored by cable news, we can set up a proportion to find the total number of people at the convention.

Let's represent the total number of people at the convention as "x".  TellHappyStar

The proportion can be set up as:

7/12 = 280/x

To solve for x, we can cross-multiply:

7x = 12 * 280

7x = 3360

Dividing both sides by 7:

x = 3360/7

x = 480

Therefore, there are 480 people at the convention who are not bored by cable news.

May 17, 2023
 #1
avatar+8 
0

To find the possible values of a, we can solve the given system of equations:

a + ab = 250 ...(1)
a - ab = -240 ...(2)

We can use the method of elimination to solve this system. Adding equations (1) and (2) eliminates the term 'ab':  mymilestonecard

(a + ab) + (a - ab) = 250 + (-240)
2a = 10
a = 5

Substituting the value of a back into equation (1):

5 + 5b = 250
5b = 245
b = 49

Therefore, the solution is a = 5 and b = 49. There is only one possible value for 'a', which is 5, and one possible value for 'b', which is 49.

May 13, 2023
 #1
avatar+8 
0

To solve this problem, we first need to find the area of triangle XYZ. Since triangle XYZ is a right triangle, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

The base of triangle XYZ is XY, which has a length of 12, and the height is YZ, which has a length of 6. Therefore, the area of triangle XYZ is:

Area(XYZ) = (1/2) * 12 * 6 = 36

Now, we need to find the probability that the area of triangle XYD is at most 20. Since point D is chosen randomly within triangle XYZ, any point within the triangle is equally likely to be chosen. So, we can consider the ratio of the areas.  link deleted by Melody

To find the probability, we compare the area of triangle XYD to the area of triangle XYZ. The probability is given by:

Probability = Area(XYD) / Area(XYZ)

To find the area of triangle XYD, we need to determine the base and height of this triangle. The base is still XY, which is 12. The height can be found by considering that the area of triangle XYD is half the area of rectangle XYZD.

Since XYD is a right triangle, the height is the altitude from the right angle to the hypotenuse YD. We can use the formula for the area of a triangle to find the height:

Area(XYD) = (1/2) * base * height

20 = (1/2) * 12 * height

height = (2 * 20) / 12 = 40 / 12 = 10 / 3 ≈ 3.33

Therefore, the height of triangle XYD is approximately 3.33.

Now we can calculate the area of triangle XYD:

Area(XYD) = (1/2) * 12 * 3.33 ≈ 19.98

Now we can calculate the probability:

Probability = Area(XYD) / Area(XYZ) = 19.98 / 36 ≈ 0.555

So the probability that the area of triangle XYD is at most 20 is approximately 0.555, or 55.5%.  

May 12, 2023
 #2
avatar+8 
+1

Hello,

To simplify the expression (54u^2v + 18uv^2)(9u + 3v), we can use the distributive property of multiplication.

First, let's distribute 9u to each term inside the first parentheses:  TellPopeyes

9u * 54u^2v = 486u^3v
9u * 18uv^2 = 162u^2v^2

Next, let's distribute 3v to each term inside the first parentheses:

3v * 54u^2v = 162uv^3
3v * 18uv^2 = 54uv^3

Now, we can combine like terms:

486u^3v + 162u^2v^2 + 162uv^3 + 54uv^3

To simplify this further, we can group the terms with the same variables:

(486u^3v + 162u^2v^2) + (162uv^3 + 54uv^3)

Inside each group, we can factor out common terms:

486u^3v + 162u^2v^2 = 162u^2v(3u + v)
162uv^3 + 54uv^3 = 216uv^3(3u + v)

Now, we have:

162u^2v(3u + v) + 216uv^3(3u + v)

We can see that both terms have a common factor of (3u + v), so we can factor it out:

(162u^2v + 216uv^3)(3u + v)

And that is the simplified form of the expression.  

May 9, 2023