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trapecia [35]
3 years ago
6

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 2; B: the numbers add to 5

; C: at least one of the numbers is 2; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.] At least one of the numbers is 2, or the numbers add up to 5. C ∪ B
Mathematics
1 answer:
maxonik [38]3 years ago
6 0

Answer:

C \cup B =[(x,y),:x=2  \:Or\:  y=2 \:Or\: x+y=5, 1 \leq x \leq  6,1 \leq y \leq  6 ]\\

Step-by-step explanation:

Let the outcome from the two dice be (x,y) where x is the outcome from the red die and y is the outcome from the green die.

Event A: the red die shows 2

A=[(x,y), x=2,1 \leq y \leq  6 ]

Event B: the numbers add to 5

B=[(x,y),:x+y=5, 1 \leq x \leq  6,1 \leq y \leq  6 ]

Event C: at least one of the numbers is 2;

C=[(x,y),:x=2 \quad Or  \quad y=2, 1 \leq x \leq  6,1 \leq y \leq  6 ]

Event D: the numbers do not add to 9;

D=[(x,y),:x+y\neq 9, 1 \leq x \leq  6,1 \leq y \leq  6 ]

Therefore:

C \cup B =[(x,y),:x=2  \:Or\:  y=2 \:Or\: x+y=5, 1 \leq x \leq  6,1 \leq y \leq  6 ]\\

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3 years ago
11. A wave has a wavelength of 125 meters is moving at a speed of 20 m's. What is its frequency?
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Answer:

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3 years ago
The surface area of the solid is about ____ inches squared
Dafna11 [192]

Answer:

Surface area of the whole figure=  320.28inch^2

Step-by-step explanation:

The surface area of the figure :

Surface area of the cylinder(excluding top)+Surface area of the cone(excluding bottom)

Radius of the cylinder=3 inch     and  Height of cylinder=13 inch

Surface area of the cylinder with one circular face

                                    =2\pi rh+\pi r^2

As,     \pi =\frac{22}{7}= 3.14

   =(2*3.14*3*13)+(3.14*3*3)\\\\=244.92+28.26\\\\=273.18inch^2

Surface area of the cone excluding  base:

                =\pi *r*l

l= slant height=5 inch       r= radius= 3 inch

Surface area of the cone =3.14*3*5

                                        =47.1inch^2

Total surface area of the whole figure=273.18+47.1

                                                           =  320.28inch^2

5 0
3 years ago
Luke started a weight-loss program. The first week, he lost X pounds. the second week he lost 3/2 pounds less then 3/2 times the
irga5000 [103]

Luke started a weight-loss program.

The first week, he lost X pounds.

the second week he lost 3/2 pounds less then 3/2 times the pounds he lost the first week. so, he lost 3/2 x - 3/2

The third week, he lost 1 more pound than 3/4 of the pounds he lost the first week. so, he lost 3/4 x + 1

So, over 3 weeks he lost :

x + (3/2 x - 3/2) + (3/4 x + 1) = 13/4 x - 1/2

=========================================================

Liam started the program when Luke did.

The first week, he lost 1 pound less than 3/2 times the pounds luke lost the first week. so, he lost (3/2 x - 1)

The second week, he lost 4 pounds less than 5/2 times the pounds luke lost the first week. so ,he lost (5/2 x - 4)

The third week, he lost 1/2 more than 5/4 times the pounds luke lost the first week. so, he lost, ( 5/4 x + 1/2)

The expression for Liam's weight loss over the three weeks is =

= (3/2 x - 1) + (5/2 x - 4) + ( 5/4 x + 1/2) = 21/4 x - 9/2

=============================================================

Assuming they both lost the same number of pounds over the three weeks

So, equating the number of pounds lost by each one of them

so,

13/4 x - 1/2 = 21/4 x - 9/2

solve for x

13/4 x - 21/4 x = -9/2 + 1/2

-2x = -4

divide both sides by -2

so,

x = -4/-2 = 2

so,

The number of pounds luke lost in the fist week is 2 pounds

=============================================================

4. The number of pounds luke and liam each lost over the three weeks is

= 13/4 * 2 - 1/2 = 6 pounds

7 0
1 year ago
Derek has $20 to spend on used
goldfiish [28.3K]
5x+2y = 20

For every hardcover book (x) you will be charged 5$.

For every paperback book (y) you will be charged 2$.

The amount of both types of books you buy has to be under or equal to 20$
5 0
3 years ago
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