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Diano4ka-milaya [45]
2 years ago
8

Which shows the length of the darkened arc? (The wierd symbol next to the answers is Pi)​

Mathematics
2 answers:
SashulF [63]2 years ago
8 0

Answer: 15 π

Step-by-step explanation:

The formula for determining the circumference of a circle is expressed as

Circumference = 2πr

Looking at the circle,

Diameter = 18 inches

Radius = diameter/2 = 18/2

Radius = 9 inches

Circumference = 2 × 9 × π = 18π

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r = 9 inches

θ = 60 degrees

Length of arc = 60/360 × 2 × π × 9

Length of arc = 3π

The length of the darkened arc is the circumference of the circle - the arc formed by 60 degrees. Therefore,

length of the darkened arc = 18π - 3π = 15π

fgiga [73]2 years ago
3 0

Answer:

15 pi

Step-by-step explanation:

The circumference of the circle is given by

C = pi * d

C = pi *18

We are subtracting part of the circumference that covers 60 degrees

The entire circle is 360 degrees

60/360 = 1/6

We are subtracting 1/6 of the circumference

1/6 *18pi = 3pi

We have 18pi and subtract 3pi = 15pi

The dark shaded arc is 15pi

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The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o
timurjin [86]

Answer:

a) Null hypothesis:\mu = 90000  

Alternative hypothesis:\mu \neq 90000  

b) p_v =2*P(t_{(24)}  

c) If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation  

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

The values obtained are:

\bar X=85272 represent the mean annual salary for the sample  

s=11039.23 represent the sample standard deviation for the sample  

n=25 sample size  

\mu_o =90000 represent the value that we want to test

\alpha=0.05 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)  

Part a: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:  

Null hypothesis:\mu = 90000  

Alternative hypothesis:\mu \neq 90000  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=25-1=24  

Since is a two sided test the p value would be:  

p_v =2*P(t_{(24)}  

Part c: Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0
3 years ago
One canned juice drink is 25​%orange​ juice; another is 10​%orange juice. how many liters of each should be mixed together in or
sertanlavr [38]
               Qty     ·     %      =      Total
Drink 1:    x            .25      =      .25x
Drink 2:   15 - x      .10      =      .10(15 - x)
Mixture:  15            .21     =       .25x + .10(15 - x)

                       (15)(.21)   =     .25x + 1.5 - .10x
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                           1.65      =     .15x
                               11     =       x

Drink 1 (25%) is 11 liters
Drink 2 (10%) is 15 - 11 = 4 liters
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Step-by-step explanation:

(a)

ii.

21 - 5 = 16 play only chess.

iii.

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5 play both.

that is 16+18+5 = 39 that play at least one of these games.

i.

so, 45 - 39 = 6 don't play any of these games.

(b)

we have 16+18 = 34 pupils out of 45 that play exactly one game.

so the probabilty to pick one of them is as usual

desired cases / total cases = 34/45 =

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