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Yakvenalex [24]
1 year ago
8

A circle with a radius of 12 inches has an arc that measures 8 pi inches. Find the measure of the central angle determined by th

is arc.
Mathematics
1 answer:
ivanzaharov [21]1 year ago
3 0
We know that

[length of a circle]=2*pi*r
r=12 in
[length of a circle]=2*pi*12--------------> 24pi in

if 360° (full circle)--------------------> has a length of 24pi in
X-------------------------------------------> 8pi

X=8pi*360/24pi-----------> 120°

the answer is 120°

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Mr. Barth is painting an arrow on the school parking lot. He draws the edges between the following points on the coordinate plan
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Answer:

<u>70 square units</u>

Step-by-step explanation:

<em>I have plotted the points on the coordinate system and connected roughly using a red line. Image is attached. </em>

The arrow created, consists of a TRIANGLE and a RECTANGLE. The area of the arrow would be:

Area of Arrow = Area of Triangle + Area of Rectangle

Area of Triangle = 0.5 * base * height

Base is 12 units

Height is 7 units, so

Area of Triangle = 0.5 * 12 * 7 = 42

Now,

Area of Rectangle = length * height

Length is 7

Height is 4

Area of Rectangle = 7 * 4 = 28

<u>Area of Arrow = 42 + 28 = 70 square units</u>

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GarryVolchara [31]
Dorothy and Gray live 8 miles from each other.
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The graph shows the linear relationship between the height of a plant (in centimeters) and the time (in weeks) that the plant ha
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I found a graph with the same problem, so I guess this is the graph to be based on. To find the rate, just determine the slope between any two points along the line. Suppose these points are: (30,10) and (50,20).

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Read 2 more answers
Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 35% plan to
DiKsa [7]

Answer:

a) Number = 60 *0.35=21

b) Since is a left tailed test the p value would be:  

p_v =P(Z  

c) If we compare the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.  

We can use as smallest significance level 0.044 and we got the same conclusion.  

Step-by-step explanation:

Data given and notation  

n=60 represent the random sample taken

X represent the business owners plan to provide a holiday gift to their employees

\hat p=0.35 estimated proportion of business owners plan to provide a holiday gift to their employees

p_o=0.46 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Part a

On this case w ejust need to multiply the value of th sample size by the proportion given like this:

Number = 60 *0.35=21

2) Part b

We need to conduct a hypothesis in order to test the claim that the proportion of business owners providing holiday gifts had decreased from the 2008 level:  

Null hypothesis:p\geq 0.46  

Alternative hypothesis:p < 0.46  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.35 -0.46}{\sqrt{\frac{0.46(1-0.46)}{60}}}=-1.710  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

Part c

If we compare the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.  

We can use as smallest significance level 0.044 and we got the same conclusion.  

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If the parent function is y = 3x, which is the function of the graph? y = 0.5(3)x y = 2(3)x y = −2(3)x y = −0.5(3)x
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Answer: If I remember correctly, the answer should be <em>y=-2(3)^x.  </em>

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