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Kaylis [27]
3 years ago
8

2. (09.01 MC) In circle A shown below, the measure of ∠BAD is 148°: Circle A with angle BAD measuring 148 degrees; points B, C,

D lie on Circle A. If m Arc BC is 96°, what is m Arc CD ? (3 points) 96° 22° 52° 148°

Mathematics
1 answer:
n200080 [17]3 years ago
3 0

Answer:

Measure of arc CD will be 52°.

Step-by-step explanation:

In the given circle A, measure of central angle intercepted by the arc BCD at the center = 148°

And points B, C and D lie on the given circle.

m(\widehat {BCD}) = 148°

m(\widehat {BCD})=m(\widehat{BC})+m(\widehat {CD})

148° = 96° + m(\widehat{CD})

148 - 96 = m(\widehat{CD})

m(\widehat{CD}) = 52°

Therefore, measure of arc CD will be 52°.

Option (3) will be the answer.

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Amanda [17]

Answer:

t=\frac{33.9-36}{\frac{4.1}{\sqrt{22}}}=-2.402    

df = n-1= 22-1=21

t_{\alpha/2}= -2.08

Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old

Step-by-step explanation:

Data given

\bar X=33.9 represent the sample mean

s=4.1 represent the sample standard deviation

n=22 sample size  

\mu_o =26 represent the value that we want to test

\alpha=0.025 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is less than 36 years old, the system of hypothesis would be:  

Null hypothesis:\mu \geq 36  

Alternative hypothesis:\mu < 36  

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

And replacing we got:

t=\frac{33.9-36}{\frac{4.1}{\sqrt{22}}}=-2.402    

Now we can calculate the critical value but first we need to find the degreed of freedom:

df = n-1= 22-1=21

So we need to find a critical value in the t distribution with df =21 who accumulates 0.025 of the area in the left and we got:

t_{\alpha/2}= -2.08

Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old

3 0
3 years ago
Valarie used a laser to measure the average thickness of a human hair which is 0.0032 meters thick. A grain of sand is 0.0024 me
fredd [130]

Answer:

A human hair is 0.0008 meters thicker.

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Step-by-step explanation:

3 0
3 years ago
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For women aged 19-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation
Mrac [35]

Answer: p = 0.00714

Step-by-step explanation:

Since the population standard deviation of the distribution is known, the z test ( which produces the z score) is the perfect test for finding the probability of the data set in the question.

From the question,

Population mean (u) = 114.8

Sample mean (x) = 121.5

Population standard deviation (σ) = 13.1

Sample size (n) = 23

The z score formulae is given below as

Z = x - u/σ/√n

Z = 121.5 - 114.8/(13.1/√23)

Z = 6.7/(13.1/√23)

Z = 6.7/2.731

Z = 2.45.

The question is interested in knowing the probability of mean systolic blood pressure greater than 121.5.

This implies that we are looking for the probability at which our z score is greater than 2.45: P(z>2.45)

The z score (z=2.45) has divided the distribution into two regions, z< 2.45 ( area to the left of the distribution) and z>2.45 ( area to the right of distribution).

Hence, p(z>2.45) + p(z<2.45) = 1

To get a the probability, we have to use a standard normal distribution table.

The table we have here gives probability of the distribution to the left ( that's area towards the left), hence we need to find p(z<2.45) first

From the table p(z<2.45) = 0.99286

But p(z>2.45) = 1 - p(z<2.45)

p(z>2.45) = 1 - 0.99286

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3 years ago
Convert the equation − x − 2 y = 8 from standard to slope-intercept form
Molodets [167]

Answer:

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Step-by-step explanation:

We have our equation in standard form: -x - 2y = 8. We can use simplifying rules to isolate y on one side of the equation and give us our y = mx + b format. I'll begin by adding x to both sides.

-x - 2y = 8

-2y = x + 8

Now that we have y on one side, we can divide everything by -2.

-2y/-2 = x/-2 + 8/-2

y = -1/2x - 4

That looks like y = mx + b form.

If you have any further questions or need clarification on anything, let me know!

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loris [4]

Answer:

V = PI*r2h

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Here is a step-by-step case that illustrates how to find the volume of a cylinder with a radius of 3 inches and a height of 5 inches. In this example PI will be 3.14.

V = pi * r2 * h

= pi * 32 * 5

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= 141.37 cubic inches

Step-by-step explanation:

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm.

6 0
2 years ago
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