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3 years ago

In this particular arithmetic sequence, a8 = 28 and a16 = 108. What is the value of a24?

Mathematics

1 answer:

kap26 [50]3 years ago

5 0

In this sequence d=10. Therefore, a24=188.

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Suppose you have 60 red marbles and 40 blue marbles in a

andrew-mc [135]

Answer: The required probability is 0.26.

Step-by-step explanation: Given that there are 60 red marbles and 40 blue marbles in a box 10 marbles are picked without replacement.

We are to find the probability of selecting 6 red marbles.

Since the marbles are picked up without replacement, so it is a situation of combination.

Let S denote the sample space of the experiment of drawing 10 marbles and E denote the event that 6 marbles are red.

So,

$n(S)=^{100}C_{10}=\dfrac{100!}{10!(100-10)!}=\dfrac{100!}{10!90!}=17310309456440,\\\\\\n(E)=^{60}C_6\times^{40}C_4=\dfrac{60!}{6!54!}\times\dfrac{40!}{4!36!}=50063860\times91390.$

Therefore, the probability of event E is given by

$P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.$

Thus, the required probability is 0.26.

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3 years ago

Examine the system of equations.

earnstyle [38]

Answer:

The correct answer is B(2)

Step-by-step explanation:

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3 years ago

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3 years ago

Calculate the area.

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d. 91.61 cm^2

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a student walks 8 steps east 6 steps northeast 9 steps north west what is her displacement? include magnitude and direction

kati45 [8]

The displacement is 18.03 steps, and the direction is 47.25°

<h3>How to get the displacement?</h3>

We know that displacement is the difference between the final position and the initial position.

We assume the initial position (0, 0). Let's define the positive x-axis as the east and the positive y-axis as the north.

First, the student moves 8 steps east, so she is at:

(0 + 8, 0)

Then she moves 6 steps northeast, so the new position is:

(6*cos(45°) + 8, 6*cos(45°))

Finally, she moves 9 steps due north, so we have:

(6*cos(45°) + 8, 6*cos(45°) + 9)

Then the final position is:

(12.24, 13.24)

So the displacement is:

D = (12.24, 13.24) - (0, 0) = (12.24, 13.24)

The magnitude of the displacement is:

$|D| = \sqrt{12.24^2 + 13.24^2} = 18.03$

So the magnitude is 18.03 steps.

And the direction is given by the arctangent of the quotient between the y-component and the x-component:

$\theta = Arctg(13.24/12.24) = 47.25 \°$

If you want to learn more about displacements:

brainly.com/question/4931057

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2 years ago