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3 years ago

In how many ways can you arrange 3 out of 5 books (a, b, c, d, and

Mathematics

1 answer:

soldi70 [24.7K]3 years ago

3 0

Yes bro...
the easiest way is to use 5C3
= 5! /(5-3)!3!
= 5(5-1)(5-2)(5-3)!/ (5-3)!3!
= 5×4×3×2/3×2
= 5×4 = 20ways

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The measures of the angles of a triangle are shown in the figure. solve for x

yuradex [85]

Answer:

solution,

x+41+59=180⁰ ( the sum of total angle of triangle is 180⁰)

or, x+ 100=180

or, X=180-100

so , X=80

Step-by-step explanation:

let us check

59+41+80=180

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2 years ago

What are the coordinates of the vertex of the parabola described by the

ICE Princess25 [194]

Step-by-step explanation:

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3 years ago

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In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted tha

siniylev [52]

Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

Step-by-step explanation:

Since we have given that

Probability that students attend class on Fridays = 70% = 0.7

Probability that who went to class on Fridays would pass the course = 95% = 0.95

Probability that who did not go to class on Fridays would passed the course = 10% = 0.10

Let A be the event students passed the course.

Let E be the event that students attend the class on Fridays.

Let F be the event that students who did not attend the class on Fridays.

Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30

P(A|E) = 0.95, P(A|F) = 0.10

We need to find the probability that they did not attend on Fridays.

We would use "Bayes theorem":

$P(F\mid A)=\dfrac{P(F).P(A\mid F)}{P(E).P(A\mid E)+P(F).P(A\mid F)}\\\\P(F\mid A)=\dfrac{0.30\times 0.10}{0.70\times 0.95+0.30\times 0.10}\\\\P(F\mid A)=\dfrac{0.03}{0.695}=0.043$

Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

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3 years ago

The variables x and y vary directly. Use the given values to write an equation that relates x and y: x = 4, y = -16

Gnesinka [82]

Vary Directly: y = k*x

Vary Inversely: y = k/x

Because x and y vary directly, our equation will look like the first one.

y = k*x

With the inputted values:

-16 = k * 4

Now, to find k, isolate the variable

k = -16/4 = -4

Your final equation will then look like this:

y = -4 * x

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3 years ago

A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 101 million kilometers.

Elden [556K]

Kepler's third law described the relation between semi-major axis (or average distance to the star) and the orbital period (how long it takes to complete one lap) as follows:
a^3 / p^2 = constant
In the case of our Solar system the constant is 1
This means that, for this problem:
a^3 / p^2 = 1
p^2 = a^3
p = a^(3/2)
The semi major axis is given as 101 million km. We need to convert this into AU where 1 AU is approximately 150 million Km
101 million Km = (101x1) / 150 = 0.67 AU

Now, we substitute in the equation to get the orbital period as follows:
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3 years ago