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2 years ago

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Circle M is shown. Line segments H M, J M, and K M are radii. Lines are drawn from point H to point K, and from point J to point

K. Tangents K L and J L intersect at point L outside of the circle. Angle J M K is 131 degrees.
Which statements are true? Check all that apply.

The circumscribed angle L has a measure of 49°.
The circumscribed angle L has a measure of 65.5°.
If the measure of arc HJ is 98°, the measure of angle HMJ is 98°.
If the measure of arc HJ is 98°, the measure of angle HKJ is 98°.
If the measure of arc HJ is 98°, the measure of arc HK is 131°.

2 answers:

svp [43]2 years ago

8 0

Answer:

a,c,E

Step-by-step explanation:

Natasha2012 [34]2 years ago

4 0

Answer:

1,3,5

Step-by-step explanation:

You might be interested in

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Se

Ugo [173]

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 175$

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that $p = 0.467$ . So

$\mu = E(X) = np = 175*0.467 = 81.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6$

This probability, using continuity correction, is $P(X \geq 85 - 0.5) = P(X \geq 84.5)$ , which is 1 subtracted by the pvalue of Z when X = 84.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{84.5 - 81.725}{6.6}$

$Z = 0.42$

$Z = 0.42$ has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is $P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)$ , which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 81.725}{6.6}$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

X = 79.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{79.5 - 81.725}{6.6}$

$Z = -0.34$

$Z = -0.34$ has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that $p = 0.063$

$\mu = E(X) = np = 175*0.063 = 11.025$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141$

This probability, using continuity correction, is $P(X < 12 - 0.5) = P(X < 11.5)$ , which is the pvalue of Z when X = 11.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{11.5 - 11.025}{3.2141}$

$Z = 0.15$

$Z = 0.15$ has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that $p = 0.227$

$\mu = E(X) = np = 175*0.227 = 39.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54$

Using continuity correction, this probability is $P(X \leq 55 + 0.5) = P(X \leq 55.5)$ , which is the pvalue of Z when X = 55.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55.5 - 39.725}{5.54}$

$Z = 2.85$

$Z = 2.85$ has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

8 0

2 years ago

Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $

VMariaS [17]

Answer:

Her first coupon ti be used is $50 off a purchase above $300

Final purchase price= $340

Step-by-step explanation:

Marie has two coupons

one for a 15% discount and one for $50 off any purchase above $300.

The stores allow the two coupons to be combined and she spends a total of $450.

Her first coupon ti be used is $50 off a purchase above $300.

So Marie have $400 now

15% off $400= 400-(0.15*400)

15% off $400 = 400-60

15% off $400 =$ 340

6 0

2 years ago

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The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x(height) and y(arm span) is sho

abruzzese [7]

Answer:

27.385 cm longer would we expect Mike's arm span to be than George's.

Step-by-step explanation:

We have to find how many centimeters longer would we expect Mike's arm span to be than George's using the equation:

y= 4.5x + 0.977 x

where y= arm span

and x= height

Given:

Mike's height=x = 175 cm

so Mike's arm span= y= 4.5 x + 0.977 x

= 4.5* (175) + 0.977* (175)

= 787.5 + 170.975

= 958.475 cm

George's height = x = 170 cm

so George's arm span= y= 4.5 x + 0.977 x

= 4.5* (170) + 0.977* (170)

= 765 + 166.09

= 931.09 cm

Mike's arm span longer than George's = Mike's arm span - George's arm span

= 958.475 - 931.09

= 27.385 cm.

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2 years ago

Show a way to count from 170 to 410 using tens and hundreds. circle at least 1 benchmark number

Anastasy [175]

Benchmark are numbers that are used as standards to which the rest of the data is compared to. When counting numbers using a number line, the benchmark numbers are the intervals written on the axis. For benchmark numbers of 10, the number line on top of the attached picture is shown. Starting from 170, the tick marks are added by 10, such that the next numbers are 180, 190, 200, and so on and so forth. When you want to find 410, just find the benchmark number 410.

The same applies to benchmark numbers in intervals of 100. If you want to find 170, used the benchmark numbers 100 and 200. Then, you estimate at which point represents 170. For 410, you base on the benchmark numbers 400 and 500.

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2 years ago

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A spherical container has a radius of 9 centimeters. It is filled with a solution that costs $2.10 per cubic centimeters.

vitfil [10]

Hello! For this question, first, we have to find the area of the spherical container. The formula for finding the area of a sphere is 4/3πr³. We raise the radius to the 3rd power and multiply it by pi (3.14). The radius is 9 cm. 9³ is 729. There's that number. Now, we multiply 81 by 3.14 to get the total area of the square. 729 * 3.14 is 2,289.06. Now, multiply that by 4/3. 2,289.06/1 * 4/3 is 3,052.08. The volume of the sphere is 3,052.08 cubic centimeters. Which brings us to the next part. Now, we can find the price of the solution by multiplying the area by the price. 3,052.08 * 2.10 is 6,409.368 or 6,409.37 when rounded to the nearest cent. The total value of the solution in the container is $6,409.37.

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2 years ago

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