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jeyben [28]
3 years ago
6

You have a set of cards labeled 1-10. Set A is drawing an even card. Set B is drawing a 8 or higher.  What is the  P ( A ∪ B ) ?

 Express your answer as a decimal and explain how you got your answer please.
Mathematics
1 answer:
creativ13 [48]3 years ago
5 0

set A = {2, 4, 6, 8, 10}   (only even cards)

set B = {8, 9, 10}    (8 or higher)

( A ∩ B ) means the numbers which are common in both sets .

They both have 8 & 10 in common. 

So the answer is: P(A ∩ B) = {8,10}

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Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *
Luda [366]

Answer:

The answer to your question is   \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1          

Step-by-step explanation:

Data

Foci  (-2, 2)  (4, 2)

Major axis = 10

Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

                  2c = 6

                    c = 6/2

                    c = 3

3.- Determine a

                  2a = 10

                    a = 10/2

                    a = 5

4.- Determine b using the Pythagorean theorem

                   a² = b² + c²

-Solve for b

                   b² = a² - c²

                   b² = 5² - 3²

                   b² = 25 - 9

                   b² = 16

                   b = 4

5.- Find the center (1, 2)  From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

                      \frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1

                       \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1                

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3 years ago
Which of the following numbers is NOT a solution<br> of the inequality 3x – 5&gt;_4x – 3 ?
Arte-miy333 [17]

Answer:

A)-1

Step-by-step explanation:

3x-5≥4x-3

3x-4x≥-3+5

-x≥2

x≤-2

(-infinity,-2]

-1 x

-2,-3,-5 ✓

8 0
3 years ago
This is the longest side of a right triangle. It is also the side directly across from the 90-degree angle of a right triangle.
muminat

Answer:

hypotenuse

Step-by-step explanation:

the other sides are known as legs

7 0
3 years ago
Does 2^8 equal (3sqrt{16})^6
ale4655 [162]

Answer:

Does 2⁸ = (3√16)⁶? No.

Step-by-step explanation:

2⁸ = (3√16)⁶

Evaluate 2⁸. This can simply be written out as:

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4 * 2 * 2 * 2 * 2 * 2 * 2

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16 * 2 * 2 * 2 * 2

32 * 2 * 2 * 2

64 * 2 * 2

128 * 2

256.

256 = (3√16)⁶

Evaluate √16.

256 = (3*4)⁶

Multiply 3 and 4.

256 = 12⁶

Evaluate 12⁶. This can be rewritten as:

12 * 12 * 12 * 12 * 12 * 12

144 * 12 * 12 * 12 * 12

1728 * 12 * 12 * 12

20736 * 12 * 12

248832 * 12

2985984.

Since 256 ≠ 2985984, the answer to this question is no.

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18 pieces total.......
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