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2 months ago

Point B is in the interior of ∠AOC, m∠AOC = 108°, m∠AOB = 3m∠BOC. Find m∠AOB.

2 answers:

6 0

Assuming point B lies within <AOC, then m<AOB plus m<BOC equals m<AOC (angle addition postulate), represented as equation 1. Thus, the equation 3m<BOC plus m<BOC equals m<AOC as m<AOB is 3m<BOC, yielding 4m<BOC = 108. Therefore, m<BOC equates to 27. Then, referring back to m<AOB plus m<BOC gives m<AOC with m<AOB substituting in yields m<AOB resulting in a value of 81.

zzz [12.3K]2 months ago

5 0

The measure at point B is 36 degrees. Since point B originates from within angle AOC, we take AOC's measure and divide it by 3, leading to a result of 36. The associated formula is 3x=108, yielding x=36.

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WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the

Inessa [12570]

Answer:

a) $P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

$P(z>1.43)=1-P(z$

b) $P(X$

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

$P(z$

c) $P($

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

$P(-1.43$

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

$X \sim N(15,3.5)$

Where $\mu=15$ and $\sigma=3.5$

We seek the probability:

$P(X>20)$

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

$z=\frac{x-\mu}{\sigma}$

By applying this formula, we can find the probability:

$P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

$P(z>1.43)=1-P(z$

Part b

$P(X$

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

$P(z$

Part c

$P($

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

$P(-1.43$

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2 months ago

Two parallel lines are crossed by a transversal. Parallel lines x and y are cut by transversal w. On line x where it intersects

AnnZ [12381]

Answer:

118.2°

Step-by-step explanation:

Dos líneas paralelas x e y son cortadas por la transversal w (ver el diagrama adjunto).

Se forman 8 ángulos (denominados 1, 2, 3, 4, 5, 6, 7 y 8).

Los ángulos 1 y 6 son ángulos del mismo lado cuando dos líneas paralelas x e y son cortadas por la transversal w.

Dos ángulos del mismo lado son suplementarios (suman 180°). Esto significa

$m\angle 1+m\angle 6=180^{\circ}$

Dado $m\angle 1=61.8^{\circ},$ por lo que

$m\angle 6=180^{\circ}-61.8^{\circ}=118.2^{\circ}$

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2 months ago

Read 2 more answers

A trust fund worth $25,000 is invested in two different portfolios, this year, one portfolio is expected to earn 5.25% interest

Leona [12618]

Answer:

A sum of $12,000 should be allocated at an interest rate of 5.25%, while $13,000 should be put in at 4%.

Step-by-step explanation:

Recall that

The simple interest formula is given by

$I=P(rt)$

where

I represents the total interest earned,

P is the initial investment,

r stands for the interest rate, and

t is the number of time periods.

Define

x as the amount invested at 5.25%,

and (25,000 - x) as the amount put in at 4%.

From the problem,

$t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150$

Plugging these into the formula:

$I=P_1(r_1t)+P_2(r_2t)$

$1,150=x(0.0525*1)+(25,000-x)(0.04*1)$

Now, isolate x:

$1,150=0.0525x+1,000-0.04x$

$0.0525x-0.04x=1,150-1,000$

$0.0125x=150$

$x=\$12,000$

$|$25,000-x=\$13,000$

Hence, investing $12,000 at 5.25% and $13,000 at 4% meets the required interest condition.

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3 months ago

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1 month ago