Find the circumference of the circle.Use 3.14 pi

Looks like pizza
13in

We just need to find the area of the parallelogram and the triangle, and then add.

Parallelogram: The area is base times height. So, we can write 4 * 6 = 24 in^2.

Triangle: The area is base times height divided by two. So, it's 4 * 6 / 2 = 12 in^2.

24 + 12 gives us an answer of 36 inches squared.

Answer:

36 inches squared

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

if m increases n increases too and vice versa

please like and Mark as brainliest

Answer:

38ft

Step-by-step explanation:

I'm assuming that you mean that the dimensions are 8ft by 11ft

If so, you need to add all the sides together, there should be two 8ft sides and two 11ft sides

8*2 = 16 (or 8+8

11*2= 22 (or 11+11

16+22 = 38

Answer:

No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed

Completed question;

Max travels to see his brother's family by car. He drives 216 miles in 4 hours. What is his rate in miles per hour? Suppose he makes two stops of 10 minutes each during his journey. Will he be able to reach the town in 4 hours if he keeps the speed the same?

Step-by-step explanation:

Average speed = total distance travelled/time taken

Given;

Total distance travelled= 216 miles

Total time taken = 4 hours

Average speed v = 216/4 = 54 miles per hour

v = 54 mph

Suppose he makes two stops of 10 minutes each during his journey.

Total time on stops = 2 × 10 = 20 minutes = 0.33 hours

Total time spent on motion = 4 - 0.33 hours = 3.67 hours

Total distance covered in 4 hours with two stops;

d = 3.67 × 54 mph = 198.18 miles

Since d < 216 miles

No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed

Answer:

[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]

Step-by-step explanation:

Here is one example:

[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]

[tex]\sin 0.5x \cdot \cos 0.5x + \cos 0.5x\cdot \sin 0.5x[/tex]

[tex]\sin (0.5x + 0.5x)[/tex]

[tex]\sin x[/tex]

The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.

Step-by-step explanation:

The given is,

               Radius of pentagon - 7 cm

Step:1

              Ref the attachment,

              The pentagon contain 10 right angled triangle.

                        Angle of Right angle triangle = [tex]\frac{360}{10}[/tex] = 36°        

              From the right angle OPQ triangle,

                                        sin ∅ = [tex]\frac{Opp}{Hyp}[/tex]

              Where,  ∅ = 36°  

                          Radius = Hyp = 7 cm

              Trigonometric ratio becomes,

                                 sin 36° = [tex]\frac{b}{7}[/tex]          

                                0.5878 = [tex]\frac{b}{7}[/tex]                  (∵ sin 36° = 0.5878 )

                                           b = ( 0.5878 × 7 )

                                           b = 4.115 cm

                From the right angle OPQ triangle,

                                    cos ∅ = [tex]\frac{Adj}{Hyp}[/tex]

                Where, Adj = h

                                   cos 36° = [tex]\frac{h}{7}[/tex]

                                0.809017 = [tex]\frac{h}{7}[/tex]

                                              h = ( 0.809017 × 7 )

                                              h = 5.663 cm

Step:2

                Area of triangle OPR,

                                             [tex]A = \frac{1}{2} (Height )(Base)[/tex]

              Where, Height, h = 5.663 cm

                                  Base = b + c = 4.115 + 4.115 = 8.23 cm

              Area of OPQ becomes,

                                       A = [tex]\frac{1}{2}[/tex] (8.23)(5.663)

                                          =  [tex]\frac{1}{2}[/tex] ( 46.6065)

                                     A = 23.30324 squared centimeters

Step:3

              Pentagon contain 5 triangles,

                         Area of pentagon = 5 × Area of triangle

                                                        = 5 × 23.30324

                                                        = 116.516 squared centimeters

                        Area of pentagon = 116.516 squared centimeters

Result:

          The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.

Answer:

The probability that dist(Ada,Bob)>(Ada,Cathy)  is very small as there is very large number of range to choose the product ==4.7*10^-9.

Step-by-step explanation:

Given:

Ada ,bob and cathy purchase electronics carries

Ada and bob commonly take 3 products and 7 independently.

And Cathy take 10  products on its own .

To Find:

probability that    dist(Ada,bob)>dis(Ada,Cathy)?

Solution:

Using Euclidean distance  is distance formula used in coordinate geometry simply known as Distance formula,

this problem is related to Euclidean Distance and Jaccard Similarity in Data mining.

1st calculate probability for x such that ,

[tex]3\leq x\leq 10[/tex]   as there are 3 common products.

P([tex]3\leq x\leq 10[/tex])

=[tex]\frac{7C(x-3)*990C(10-x)}{997C7}[/tex].............. where x=3,4,5....10. ..........(equation 1).

Now calculate for each term,we get

When

x=3,P(x=3)=0.95

x=4,P(x=4)=[tex]6.8*10^{-3}[/tex]

x=5,P(x=5)=[tex]4.1*10^{-5}[/tex]

x=6,P(x=6)=2.1*10^-7

x=7,P(x=7)=8.5*10^-10

x=8,P(x=8)=2.6*10^-12

x=9,P(x=9)=5.2*10^-15

x=10,P(x=10)=5.3*10^-18.

Now calculating the Euclidean distance,

It is distance between two points ,

So there are total of 2 points as Ada and bob

they have 3 products in common

and 7 independent products ,7  Ada and 7 bob

Total of 17 products .

1,2,3,4,5,6..........,16,17.

Consider each product number as distance between them ,

(Suppose 5 product and 1 product distance will be 4)

Similarly,

Suppose Ada is at 3rd number at the  3 product (as they have 3 product same.)

and bob  at product 17.

Hence when 3 products are similar distance between Ada and bob will be of 14.

Euclidean distance =[tex]\sqrt{14}[/tex].

Hence the Jaccard similarity =(Ada intersection Bob)/(Ada union bob)

=3/14

When 4 products are same means both will selected 6 and 6 independent product so that  the each one will get 10 products i.e. starting condition should remain same .

Hence now  bob will be at 16th term as it will take one more same product in between them

So no of same products will be 4,

Hence Ada will be at 4th term and bob will be at 16

So Euclidean distance =[tex]\sqrt{12}[/tex].

Similar For Next terms we can conclude as follows:

When

X=5 , dist(ada,bob)=[tex]\sqrt{10}[/tex],

X=6,dist(Ada,Bob)=[tex]\sqrt{8}[/tex]

X=7,dist(Ada,Bob)=[tex]\sqrt{6}[/tex]

X=8,dist(Ada,Bob)=[tex]\sqrt{4}[/tex]

X=9,dist(Ada,Bob)=[tex]\sqrt{2}[/tex]

X=10,dist(Ada,Bob)=[tex]\sqrt{0}[/tex].

Now for( Ada and cathy)

Here X ranges different but use same concept as above

Each term analog to the distance between them

Suppose 1st and 3rd term distance will be 2

First calculate

P([tex]1\leq x\leq 10[/tex]) as Cathy selects 10 products with no common between them.

P([tex]1\leq x\leq 10[/tex])

=[tex]\frac{10Cx*990C(10-x)}{1000C10}[/tex]..................equation (2)

Calculate for each term As x=1,2,3...8,9,10.

Hence

P(X=1)=9.23*10^-3  P(X=5)=3*10^-11     P(X=9)=3.8*10^-21

P(X=2)=8.4*10^-5   P(X=6)=1.5*10^-13   P(X=10)=3.8*10^-21

P(X=3)=6.9*10^-7   P(X=7)=6.1*10^-16

P(X=4)=4.9*10^-9   P(X=8)=1.9*10^-18

So Ada will have 10 products and Cathy will have 10 products

Namely,

1,2,3,4,5.......18,19,20.

So suppose 1 product is same between them will be ,

both will have 1 product so remaining will be 19 products.

Jaccard similarity =1/19

Distance to reach 1 to 19th product will be 18

So Euclidean distance =[tex]\sqrt{18}[/tex]

For next when they will 2 products in same remaining will be 18

Jaccard similarity =2/18

And Distance to reach  2 to 18 th product will be  16

Euclidean distance =[tex]\sqrt{16}[/tex]

Similar for  other

When

x=3 dist(Ada, Cathy)=[tex]\sqrt{14}[/tex]

x=4 dist(Ada, Cathy)=[tex]\sqrt{12}[/tex]

x=5  dist(Ada, Cathy)=[tex]\sqrt{10}[/tex]

x=6  dist(Ada, Cathy)=[tex]\sqrt{8}[/tex]

x=7  dist(Ada, Cathy)=[tex]\sqrt{6}[/tex]

x=8  dist(Ada, Cathy)=[tex]\sqrt{4}[/tex]

x=9  dist(Ada, Cathy)=[tex]\sqrt{2}[/tex]

x=10  dist(Ada, Cathy)=[tex]\sqrt{0}[/tex]

This sqrt(0) means both are holding same products hence they are at same point on the graph so distance with itself will be zero.

Now the Probability of distance of dist(Ada,Bob)>dist(Ada,cathy) will be

=multiplying both the probabilities equations (Adding each term probabilities and multiplying )

=Equation(1) *Equation( 2).

=Summation Of P(3≤x≤10)*summation of P(1≤x≤10)

=4.7*10^-9.

In larger number of product event of in large space ,it is difficult( less likely)  that they will chose same product .

This question involves complex probability in high dimensional spaces, making it difficult to provide an exact mathematical solution. Using a simulated method like Monte Carlo simulations could potentially provide an estimated answer, but it's key to remember that these are just approximations.

This question involves a complex application of probability and distance in a high dimensional space (analogous to the recommendation system in e-commerce). The Euclidean distance between Ada and Bob would be zero for the first three products. For the other seven products that Ada and Bob independently purchase, the probability that they choose the same product would influence the Euclidean distance between them. However, getting an exact mathematical model for this is quite complex. The distance between Ada and Cathy is even more complicated because Cathy is selecting products randomly from all 1000 products.

Because of the randomness and high dimensionality involved, this question may not have an exact solution but could be estimated using simulations. In settings like these, Monte Carlo simulations, which involve running many trials with randomized inputs and calculating the averages, can be useful. However, it's important to remember these are only estimates and not exact mathematical solutions.

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Answer:

The answer is A.histogram

Step-by-step explanation:

Statistical data can be represented on charts such as histograms, box plots, etc.

The (a) histogram shows the number of values within series of a range

From the question, we understand that:

The chart that supports the above highlights is the histogram.

This is so because, it can be used to illustrate grouped data (i.e. data in series of a range), while others are not suitable for grouped data.

Hence, the chart is (a) histogram

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Answer:

We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Step-by-step explanation:

We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.

We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Let p = proportion of Americans who only use their cell phones to access the internet

SO, Null Hypothesis, [tex]H_0[/tex] : p = 38%  {means that the proportion of Americans who only use their cell phones to access the internet is same as that of Chinese proportion of 38%}

Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 38%  {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}

The test statistics that will be used here is One-sample z proportion statistics;

                 T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of cell phone owners who browse the internet

                 exclusively on their phone in a survey of 2,254 adults = 17%

          n  = sample of adults = 2,254

So, test statistics = [tex]\frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }[/tex]

                            = -26.542

Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Answer:

Step-by-step explanation:

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . false

There is no value of x that will make this true, hence NO SOLUTION.

_____

Comment on the other choices

3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.

Answer:

Answer:

[tex]P(X\geq 3.4)=0.0228[/tex]

Step-by-step explanation:

Given the mean is 3.2, standard deviation is 0.8 and the sample size is 64.

-We calculate the  probability of a mean of 3.4 as follows:

#First determine the z-value:

[tex]z=\frac{\bar X -\mu}{\sigma/\sqrt{n}}\\\\=\frac{3.4-3.2}{0.8/\sqrt{64}}\\\\=2.000[/tex]

#We then determine the corresponding probability on the z tables:

[tex]Z(X\geq 3.4)=1-P(X<3.4)\\\\=1-0.97725\\\\=0.0228[/tex]

Hence, the probability of obtaining a sample mean this large or​ larger is 0.0228

To find the probability of obtaining a sample mean of 3.4 pounds or larger, calculate the z-score and find the corresponding probability using the standard normal distribution table.

To find the probability of obtaining a sample mean of 3.4 pounds or larger, we need to calculate the z-score for the sample mean and then find the corresponding probability using the standard normal distribution table.

First, calculate the z-score using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we have: z = (3.4 - 3.2) / (0.8 / √64) = 0.2 / (0.8 / 8) = 0.2 / 0.1 = 2.

Next, we can find the probability by looking up the z-score of 2 in the standard normal distribution table. The probability of obtaining a sample mean of 3.4 pounds or larger is approximately 0.0228 or rounded to four decimal places.

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0.000000452 in scientific notation would be 4.52 × [tex]10^{-7}[/tex]

Answer:

Step-by-step explanation:

Hello!

You have the information about the number of red lights a commuter pass on her way to work and the probability of them stoping her:

Be x: number of red lights

X: 0,         1,        2,       3,      4,      5

hi: 0.05, 0.25, 0.30, 0.20, 0.15, 0.05

a. What is the expected number of red lights at which she will stop on her way to work?

The expected number of red lights is the sample mean, you can calculate it using the following formula:

[tex]X[bar]= sum Xi*hi= (0*0.05)+(1*0.25)+(2*0.30)+(3*0.20)+*(4*0.15)+(5*0.05)=2.3[/tex]

She's expected to be stopped by 2.3 red lights on the way to work.

b. Suppose each red light delays the commuter 1.8min. What is the standard deviation od the number of minutes that she is delayed by red lights?

If each light delays the commuter 1.8 min then you can determine a new variable of interest:

Be Y: the time a commuter is delayed by red lights on the way work, then Y= X*1.8min

Meaning if X= 0, then Y=0 (the commuter will be delayed 0 min), if X=1, then Y= 1.8min, if X=2, then Y= 3.6min and to on....

The properties of variance state that if

Y= X*k (Where K= constant)

Then the sample variance of Y will be

V(Y)= V(X*k)= k²*V(X)

Then the standard deviation of Y will be the constant k by the standard deviation of X:

Sy= k*Sx= 1.8 * 1.27= 2.286

I hope it helps!

Answer:

The correct option is (A).

Step-by-step explanation:

The (1 - α)% confidence interval for difference in proportion formula is,

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

The given information is:

n₁ = n₂ = 200,

X₁ = 1062,

X₂ = 900.

Compute the sample proportion as follows:

[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{1062}{2000}=0.531\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{900}{2000}=0.45[/tex]

For the 95% confidence level, the z-value is,

z₀.₀₂₅ = 1.96

*Use a z-table.

Compute the 95% confidence interval for the difference in proportion as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

     [tex]=(0.531-0.45)\pm1.96\sqrt{\frac{0.531(1-0.531)}{2000}+\frac{0.45(1-0.45)}{2000}}[/tex]

     [tex]=0.081\pm 0.031\\=(0.050, 0.112)[/tex]

Thus, the 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.050, 0.112).

The correct option is (A).

Answer:

Triangle F G H is similar to Triangle K L J

Step-by-step explanation:

Angle H = Angle J

Angle G = Angle L

Angle F = Angle K

KLJ is similar to FGH

If the lengths are also equal, then they're congruent

Triangle FGH is similar to triangle JKL.

To express the relationship between the two triangles using a similarity statement, we need to match corresponding angles.

Since the triangles are similar, corresponding angles are congruent.

In triangle FGH,

the angles are 65° , 24°  , and 91 °

In triangle JKL,

the angles are 24° ,91°  , and 65°

We see that the angles 24°  , 91°, and 65° in triangle JKL match the angles in triangle FGH respectively.

So, the similarity statement expressing the relationship between the two triangles is:

Triangle FGH is similar to triangle JKL.

To find the probability that y is between 6.2 and 6.9 hours, calculate the z-scores and use the standard normal distribution table.

To find the probability that y is between 6.2 and 6.9 hours, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table. The formula to calculate the z-score is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 6.2 hours: z = (6.2 - 6) / 2 = 0.1
For 6.9 hours: z = (6.9 - 6) / 2 = 0.45

Using the standard normal distribution table, the probability that y is between 6.2 and 6.9 hours is P(0.1 ≤ z ≤ 0.45). Thus, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 4.02 and x = 0.89 in the z table which has an area of 0.99997 and 0.81327 respectively.}

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183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members.

Step-by-step explanation:

The given is,

                Members of an online gaming group is 75

                Increasing by 25% every year

Step:1

                Formula to calculate the members in gaming group after few years with an rate of increase,

                                   [tex]F = P(1+r)^{t}[/tex].......................(1)

             Where, F - Members in gaming group after 4 years

                          P - Members in gaming group in initially

                           r -  Rate of increase in year

                           t - No. of years

Step:2

             From the given,

                        P = 75 members

                        r = 25 %

                        t = 4 years

             Equation (1) becomes,

                                  [tex]F = 75(1+0.25)^{4}[/tex]

                                      [tex]= 75(1.25)^{4}[/tex]

                                      = ( 75 ) ( 2.441406 )

                                      = 183.105

                                 F ≅ 183 members

Result:

          183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members

Answer:

Step-by-step explanation:

The set that represents the notation Ø is E ∩ O

Venn diagrams are used to represent sets and the relationship between them using diagrams

The sets are given as:

O = Odd

E = Even

P = Prime

The notation Ø represents an empty set.

In the number system, a number cannot be even and odd at the same time

Hence, the set that represents Ø is E ∩ O

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Answer:

Step-by-step explanation:

1.

1/4 cup x 13 and 1/2 cup x 1

2.

1/2 cup x 7 1/4 cup x 1

Answer:

Why do they delete your question and answers too??

Step-by-step explanation:

Step-by-step explanation:

A=8B  

A+B=180

8B+B=180°

9B=180°

B=20°

so  

angle A =8×20=160°

angle B= 20°

The requried measures of angles A and B are 160° and 20° respectively.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
Angle A and angle B are supplementary angles and angle A is eight times as large as angle ​B,
The sum of the supplementary angle is 180°
A + B = 180
8B + B = 190
B = 20

Now,
A = 8B
A = 160°

Thus, the requried measure of angles A and B are 160° and 20° respectively.

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Answer:

the answer will be 15

Step-by-step explanation:

If it took her 52 minuets in total, then 7 questions she solved.

Two or more expressions with an Equal sign is called as Equation.

Let x be number of equations.

From the given information, we know that Kate took 3 minutes to solve each equation, so the total time she spent on equations is 3x minutes.

We also know that it took her 7 minutes to solve the word problem.

So, the total time she spent on equations and the word problem is:

3x + 7

According to the problem, this total time is 52 minutes:

3x + 7 = 52

Subtracting 7 from both sides, we get:

3x = 45

Dividing both sides by 3, we get:

x = 15

Therefore, Kate solved 15 equations.

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Answer:

One sample t-test for population mean would be the most appropriate method.

Step-by-step explanation:

Following is the data which botanist collected and can use:

We have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:

One sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.

Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.

Therefore, One-sample t-test for population mean would be the most appropriate method.

Answer:

  c. A line of credit against which additional debt may be drawn

Step-by-step explanation:

A line of credit is "open" if there are no specific payoff requirements (except perhaps a minimum payment according to the balance). There is usually a limit to the available credit, but as long as the amount borrowed is less than that limit, additional funds may be borrowed at any time.

A credit card is an example of an open line of credit.

Consider a circle with radius [tex]r[/tex] centered at some point [tex](R+r,0)[/tex] on the [tex]x[/tex]-axis. This circle has equation

[tex](x-(R+r))^2+y^2=r^2[/tex]

Revolve the region bounded by this circle across the [tex]y[/tex]-axis to get a torus. Using the shell method, the volume of the resulting torus is

[tex]\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx[/tex]

where [tex]2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}[/tex].

So the volume is

[tex]\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx[/tex]

Substitute

[tex]x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt[/tex]

and the integral becomes

[tex]\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt[/tex]

Notice that [tex]\sin t\cos^2t[/tex] is an odd function, so the integral over [tex]\left[-\frac\pi2,\frac\pi2\right][/tex] is 0. This leaves us with

[tex]\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt[/tex]

Write

[tex]\cos^2t=\dfrac{1+\cos(2t)}2[/tex]

so the volume is

[tex]\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}[/tex]

Answer:

[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]  

[tex]p_v =2*P(z>3.998)=0.0000639[/tex]  

With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5

Step-by-step explanation:

Information given  

n=297 represent the random sample of male taken

X=183 represent the  men who said yes, they had driven a car when they probably had too much alcohol

[tex]\hat p=\frac{183}{297}=0.616[/tex] estimated proportion of men who said yes, they had driven a car when they probably had too much alcohol

[tex]p_o=0.5[/tex] is the value that we want to test

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Hypothesis to test

We need to conduct a hypothesis in order to test the claim that the majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, and the system of hypothesis are:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

After replace we got:

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

[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]  

Decision

We have a right tailed test so then the p value would be:  

[tex]p_v =2*P(z>3.998)=0.0000639[/tex]  

With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5

Answer:

The treasure is hidden under 95.

Step-by-step explanation:

The numbers are:

[tex]1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\\21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40\\41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60\\61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80\\81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,100[/tex]

Clue A:Start at 3. The rule is: Subtract 2, and then add 5.

3-2+5=6

6-2+5=9

Therefore, this rule eliminates all multiples of 3.

[tex]1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20\\22, 23, 25,26, 28, 29, 31, 32, 34, 35, 37, 38, 40\\41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, \\61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80\\82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100[/tex]

Clue B:Start at 2. The rule is: Add 6.

The numbers are:2,8,14,...

We have left:

[tex]1, 4, 5, 7, 10, 11, 13, 16, 17, 19, \\22, 23, 25, 28, 29, 31, 34, 35, 37, 40\\41, 43, 46, 47, 49, 52, 53, 55, 58, 59, \\61, 64, 65, 67, 70, 71, 73, 76, 77, 79, \\82, 83, 85, 88, 89, 91, 94, 95, 97, 100[/tex]

Clue C: Start at 5. The rule is: Add 12.

The numbers are: 5,17,29,...

We have left:

[tex]1, 4, 7, 10, 11, 13, 16, 19, \\22, 23, 25, 28, 31, 34, 35, 37, 40\\ 43, 46, 47, 49, 52, 55, 58, 59, \\61, 64, 67, 70, 71, 73, 76, 79, \\82, 83, 85, 88, 91, 94, 95, 97, 100[/tex]

Clue D: Start at 83. The rule is: Subtract 12.

The numbers are 83,71,59,...

We have left:

[tex]1, 4, 7, 10, 13, 16, 19, \\22, 25, 28, 31, 34, 37, 40\\ 43, 46, 49, 52, 55, 58, \\61, 64, 67, 70, 73, 76, 79, \\82, 85, 88, 91, 94, 95, 97, 100[/tex]

Clue E: Start at 1. The rule is: Add 3.

The numbers are 1,4,7,...

We are left with:

[tex]95[/tex]

The treasure is hidden under 95.

We're given the following probabilities:

[tex]P(A_1)=0.30[/tex]

[tex]P(A_2)=0.55[/tex]

[tex]P(A_1\cap A_2)=0[/tex]

[tex]P(B\mid A_1)=0.20[/tex]

[tex]P(B\mid A_2)=0.05[/tex]

(a) Yes, [tex]A_1[/tex] and [tex]A_2[/tex] are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.

(b) Use the definition of conditional probability to expand:

[tex]P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06[/tex]

[tex]P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275[/tex]

(c) By the law of total probability,

[tex]P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875[/tex]

(d) Bayes' theorem says

[tex]P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686[/tex]

[tex]P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314[/tex]

Using probability concepts, it is found that:

a) Since [tex]P(A1 \cap A2) = 0[/tex], events A1 and A2 are mutually exclusive.

b) P(A1 ∩ B) = 0.06, P(A2 ∩ B) = 0.0275.

c) P(B) = 0.0875.

d) P(A1|B) = 0.6857 and P(A2|B) = 0.3143.

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Conditional Probability  

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

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Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which

-----------

Item a:

-----------

Item b:

To compute these probabilities, we use conditional probability.

A1 and B:

[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]

Since [tex]P(A1) = 0.3, P(B|A1) = 0.2[/tex]

[tex]0.2 = \frac{P(A1 \cap B)}{0.3}[/tex]

[tex]P(A1 \cap B) = 0.2(0.3) = 0.06[/tex]

Thus P(A1 ∩ B) = 0.06.

A2 and B:

[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]

Since [tex]P(A2) = 0.55, P(B|A1) = 0.05[/tex]

[tex]0.05 = \frac{P(A2 \cap B)}{0.55}[/tex]

[tex]P(A2 \cap B) = 0.05(0.55) = 0.0275[/tex]

Thus P(A2 ∩ B) = 0.0275.

-----------

Item c:

P(B) can be written as:

[tex]P(B) = P(A1)P(B|A1) + P(A2)P(B|A2) = 0.3(0.2) + 0.55(0.05) = 0.06 + 0.0275 = 0.0875[/tex]

Thus P(B) = 0.0875.

-----------

Item d:

Applying Bayes Theorem, first for A1 given B.

[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.3(0.2)}{0.0875} = 0.6857[/tex]

Then for A2 given B.

[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.55(0.05)}{0.0875} = 0.3143[/tex]

Thus P(A1|B) = 0.6857 and P(A2|B) = 0.3143.

A similar problem is given at https://brainly.com/question/22428992

Answer:

x = 4

x = -4

Step-by-step explanation:

bro i dont know but i hope this help a little, sorry

OK, let's try with no figure.  We have an isosceles triangle sides s,s, and b.

Opposite b is angle t.

Draw the altitude h to bisect t.  We have two right triangles, legs b/2 and h, hypotenuse s.  The angle opposite b/2 is t/2 so

sin(t/2) = (b/2)/s = b/2s

So we arrived at the first part,

b = 2s sin(t/2)

The area of a triangle with sides s,s and included angle t is

A = (1/2) s² sin t