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olchik [2.2K]
3 years ago
13

Roll one fair, six-sided die, numbered 1 through 6. Let A be the event you will roll an even number. Let B be the event you will

roll a prime number. Enter 1 for Yes, and enter 0 for No. = Yes = No 1 (a) Are A and B independent events? (b) Are A and B mutually exclusive events?
Mathematics
1 answer:
11111nata11111 [884]3 years ago
7 0

Answer:

a) not independent

b) not mutually exclusive

Step-by-step explanation:

Given:

- A 6 sided die is rolled

- Event A is rolling an even number

- Event B is rolling a prime number

Find

- (a) Are A and B independent events?

- (b) Are A and B mutually exclusive events?

Solution:

- We will find the probability of each event:

                       set(Even number: A) = {2, 4, 6} = 3 outcomes

                       set(Prime number: B) = {2 , 3, 5} = 3 outcomes

- The probabilities are:

                        P(A) = 3/6 = 0.5

                        P(B) = 3/6 = 0.5

- For Event A and B to be independent then the following condition must match:

                        P ( A & B ) = P(A)*P(B)

                        set (A&B) = {2} = 1 outcome

                        P(A&B) = 1/6

                        1 / 6 = 0.5*0.5

                        1/6 = 0.25         ...... NOT INDEPENDENT

- For Event A and B to be mutually exclusive then the following condition must match:

                        P(A&B) = 0

                        P(A&B) = 1/6

Hence, we can say the events are NOT MUTUALLY EXCLUSIVE

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mars1129 [50]

Answer:

84 cm^2

Step-by-step explanation:

Area of triangle + area of rectangle

Area of triangle = 1/2*l*b

= 1/2*8*3= 12 cm^2

Area of rectangle = l*b

= 12*6 = 72 cm^2

Total area= 72+12

= 84 cm^2

7 0
3 years ago
2a - 7 - 6a = 9<br> Pls help?
slavikrds [6]

Step-by-step explanation:

2a - 7 - 6a = 9

- 4a - 7 = 9

- 4a = 16

a = -4

3 0
3 years ago
¿Cuál es el área de un rectángulo, sabiendo que su perímetro mide 24 cm y que su base es el triple de su altura?
Brrunno [24]

Answer:

El área del rectángulo es:

27 cm²

Step-by-step explanation:

Consideración:

La formula del perímetro de un rectángulo es:

p = 2(altura + base)

Planteamiento:

24 = 2(a+b)

b = 3a

a = longitud de la altura del rectángulo

b = longitud de la base del rectángulo

Desarrollo:

sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:

24 = 2(a + 3a)

24/2 = 4a

12 = 4a

a = 12/4

a = 3 cm

de la segunda ecuación del planteamiento:

b = 3a

b = 3*3

b = 9 cm

Comprobación:

de la primer ecuación del planteamiento:

24 = 2(3+9)

24 = 2*12

Respuesta:

la formula del área de un rectángulo es:

A = base * altura

A = 9cn * 3cm

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5 0
3 years ago
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 cm. What is the distance the hula hoop rol
lidiya [134]

Answer:

Distance covered by hula hoop rolls in 4 full rotations is 880 cm .

Step-by-step explanation:

Formula

Perimeter\ of\ a\ circle = 2\pi r

Where r is the radius of the circle.

As given

Allison is rolling her hula hoop on the playground.

The radius of her hula hoop is 35 cm.

r = 35 cm

\pi = \frac{22}{7}

Putting the value in the formula

Perimeter\ of\ a\ hula hoop = 2\times \frac{22}{7} \times 35

                                             = 220 cm

As given

The hula hoop rolls in 4 full rotations.

Distance covered by hula hoop rolls in 4 full rotations =  220 × 4

                                                                                          = 880 cm

Therefore the Distance covered by hula hoop rolls in 4 full rotations is 880 cm .

6 0
3 years ago
in a xy-coordinate system line 1 has a slope of -3. If the points (2,16 and (5,t) are on line 1, what is the value of t?
Dimas [21]
We can use the formula y2-y1/x2-x1 to find our answer. So, we have : t-16/5-2 = -3. We simplify that to t-16/3 = -3. We can then multiply both sides by 3 to get t-16 = -9. Then we can add 16 to both sides to get t = 7.
8 0
3 years ago
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