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2 years ago

In the diagram of circle O, what is the measure of abc? 34° 45° 68° 73°

Mathematics

2 answers:

AlexFokin [52]2 years ago

8 0

Answer: 34

Step-by-step explanation:

Lady_Fox [76]2 years ago

5 0

Answer:

A. $m\angle ABC=34^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle ABC.

First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.

$\text{Measure of arc AC}=360^{\circ}-146^{\circ}$

$\text{Measure of arc AC}=214^{\circ}$

Now, we will use tangent-tangent angle theorem to solve for ABC.

Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.

$m\angle ABC=\frac{214^{\circ}-146^{\circ}}{2}$

$m\angle ABC=\frac{68^{\circ}}{2}$

$m\angle ABC=34^{\circ}$

Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.

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2 years ago

Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear e

qaws [65]

Answer:

Step-by-step explanation:

For each of the yp(x) we can deduce the characteristic polynomial of the differential equation

$yp(x)=Ax^2+Bx+C\\m^2=0\\y''=0$

$yp(x)=Ae^{2x}\\(m-2)m=0\\m^2-2m=0\\y''-2y=0$

$yp(x)=Acos2x+Bsin2x\\m_1=2i\\m_2=-2i\\y''+4=0$

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hope this helps!!

8 0

2 years ago

A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that t

Alina [70]

Answer:

75.76% probability that there will be 10 or more customers at this bank in one hour.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

A bank gets an average of 12 customers per hour.

This means that $\mu = 12$

Find the probability that there will be 10 or more customers at this bank in one hour.

Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then

$P(X < 10) + P(X \geq 10) = 1$

We want $P(X \geq 10)$

Then

$P(X \geq 10) = 1 - P(X < 10)$

In which

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-12}*12^{0}}{(0)!} \approx 0$

$P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001$

$P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004$

$P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018$

$P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053$

$P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127$

$P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255$

$P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437$

$P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655$

$P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874$

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424$

Then

$P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576$

75.76% probability that there will be 10 or more customers at this bank in one hour.

3 0

2 years ago

The nth term of a sequence is 20 - n2

maks197457 [2]

Answer:

Fifth term

Step-by-step explanation:

The third term is:

20 − (3)² = 11

If the term is negative:

20 − n² < 0

n² > 20

n > √20

n > 4.47

The first term to have a negative value is the fifth term.

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2 years ago

A total of 180 students went on a field trip. There were 3 buses. If each bus had the same number of students on it, how many st

yanalaym [24]

Answer:

Step-by-step explanation:

180 divided by 3 is 60

6 0

2 years ago

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