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2 years ago

8

A fair die is rolled once. Let A be the event of rolling an even number, and let B be the event of rolling a number greater than

3. Find A ∩ B

1 answer:

IRISSAK [1]2 years ago

3 0

Answer:

A ∩ B = {4, 6}

Step-by-step explanation:

A die had 6 faces

S = {1, 2, 3, 4, 5, 6}

If A be the event of rolling an even number, then;

A = {2, 4, 6}

If B be the event of rolling a number greater than 3, then;

B = {4, 5, 6}

A ∩ B are the values that are common to both sets

A ∩ B = {4, 6}

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

3 years ago

Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24

Nat2105 [25]

Answer:

E. 16 min 12 sec

Step-by-step explanation:

Let x represent total time taken to complete the exercise.

We have been given that Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session.

When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. This means that 90% time of exercise is equal to 24 minutes and 18 seconds.

18 seconds will be equal to 0.3 minutes.

Let us find total time of exercise as:

$\frac{90}{100}x=24.3$

$0.90x=24.3$

$\frac{0.90x}{0.90}=\frac{24.3}{0.90}$

$x=27$

To find readout when Dara had completed 40% of her exercise session, we need to find 60% of total time.

$\frac{60}{100}(27)=0.60(27)=16.2$

Since our time in in minutes, so we will convert 0.2 minutes to seconds by multiplying by 60.

$0.20(60)=12$

Therefore, the readout will indicate 16 minutes 12 seconds, when Dara had completed 40% of her exercise session.

8 0

3 years ago

What is the value of x? Help me please

Basile [38]

168 degrees
180-12=168

5 0

3 years ago

Andrej [43]

The distance between the bottom of the lighthouse and the boat is 77.6m.

<h3>What is the distance between the bottom of the lighthouse and the boat?</h3>

The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The distance between the top of the lighthouse and boat would be the hypotenuse. The distance between the bottom of the lighthouse and the boat would be the base.

In order to determine the required distance, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:
a = length
b = base
c = hypotenuse

125² = 98² + b²

b² = 125² - 98²

b = √(25² - 98² )

b = 77.6m

To learn more about Pythagoras theorem, please check: brainly.com/question/14580675

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3 0

2 years ago

June and her brother Jason both read for the same amount of time at their own constant rates.When June has read 35 pages Jason h

Wewaii [24]

I think about 41 pages

6 0

3 years ago