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2 years ago

What must be true for lines a and b to be parallel lines? Select two options.

Mathematics

1 answer:

Rasek [7]2 years ago

8 0

The expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10

<h3>Lines and angles</h3>

A line is the shortest distance between two points and the point where two lines meet is known as an angle

From the figure shown

m<2 = 58 degrees (alternate exterior angle)

Since the sum of angles on a straight line is 180 degrees, hence;

3x-1+<2 + 4x - 10= 180

3x-1 + 58 + 4x - 10 =180

7x + 47 = 180

7x = 180- 47

7x = 133

x = 19

Hence the expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10

Learn more on lines and angles here; brainly.com/question/25770607

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Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

7 0

3 years ago

Calculating area of rectangle

PSYCHO15rus [73]

Answer:

$Area = 216.108cm^2$ --- You

$Area = 216.940cm^2$ --- Another student

Reason: Because there is a variation in the given dimensions

Step-by-step explanation:

Given

Your measurement

$Length = 20.70cm; Width =10.44cm$

Another students'

$Length = 20.74cm; Width =10.46cm$

Solving (a): The area

Area is calculated as:

$Area = Length * Width$

For you

$Area = 20.70cm * 10.44cm$

$Area = 216.108cm^2$

For the other student

$Area = 20.74cm * 10.46cm$

$Area = 216.940cm^2$

Solving (b): Reason for the variation in the areas

The given measurements are estimates of the dimensions of the rectangle.

Since there is a variation in the estimates, there will be some level of variation in the calculated area.

4 0

3 years ago

Lily weighs 57.7 kg while her sister weighs 59.02 kg, how much more does Lily's sister weigh then her? Please provide the calcul

PilotLPTM [1.2K]

The answer is 1.32

For this calculation, assuming that no conversions are required, the calcitonin goes as follows:

All that is needed is to subtract 57.7 from 59.02.

59.02 - 57.7 = ?

59.02 - 57.7 = 1.32

Hope this helps! Have a great day.

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3 years ago

20 points 1. A drawing of a building is made using a scale of 2 centimetres representing 11 feet. How many centimetres tall will

alisha [4.7K]

Answer:

42cm

Step-by-step explanation:

so if for every 11 feet you get 2 inches then for every 5.5 feet you get 1 cm. so if you break up the total number of feet into 220+16 it will be easier to solve. because 11*20=220ft so then you know you can do 2*20=40cm. now you can simplify 16 into 11+5 and get 11*1=11ft and 2*1=2cm. now youre left with 5ft and 5.5ft is 1 cm so you know that you have just under 1 cm. now add them all up 220ft+11ft+5ft=236ft and 40cm+2cm=42 cm

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4 years ago

Mr Wiggins buys 100 bags of candy for $5. What is the cost per bag?

GaryK [48]

Answer:

Step-by-step explanation:

$5= 500cents

500÷100=5

5 cents per bag of candy

6 0

3 years ago

Read 2 more answers