Find the hypotenuse of a right triangle (in cm) if one leg measures 7 cm and the other leg measures 11 cm. Round to the nearest thousandth. ____________ cm

median=order them and find the middle=6

mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4

range= the difference between the smallest and largest number=9-3=6

mode= the one that appears the most= 7

The median, mean, range and mode will be 6, 5.4, 9 and 7.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Answer:

Dy/Dx=1/√ (2x+3)

Yeah it's correct

Step-by-step explanation:

Applying differential by chain differentiation method.

The differential of y = √(2x+3) with respect to x

y = √(2x+3)

Let y = √u

Y = u^½

U = 2x +3

The formula for chain differentiation is

Dy/Dx = Dy/Du *Du/Dx

So

Dy/Dx = Dy/Du *Du/Dx

Dy/Du= 1/2u^-½

Du/Dx = 2

Dy/Dx =( 1/2u^-½)2

Dy/Dx= u^-½

Dy/Dx=1/√ u

But u = 2x+3

Dy/Dx=1/√ (2x+3)

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

D

Step-by-step explanation:

Solution:-

The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:

                                   f ( x ) = sin ( w*x ± k ) ± b

Where,

                 w: The frequency of the cycle

                 k: The phase difference

                 b: The vertical shift of center line from origin

We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).

We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.

The resulting sinusoidal waveform can be expressed as:

                           f ( x ) = sin ( 2x )  ... Answer

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Answer:

a. Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. P(at least B) = 0.330

c. P(pass) = 0.855

Step-by-step explanation:

Professor Sanchez has been teaching Principles of Economics for over 25 years.

He uses the following scale for grading.

Grade     Numerical Score      Probability

A                       4                            0.090

B                       3                            0.240

C                       2                            0.360

D                       1                            0.165

F                       0                            0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

The cumulative probability distribution is given by

Grade = F

P(X ≤ x) = 0.145

Grade = D

P(X ≤ x) = 0.145 + 0.165 = 0.310

Grade = C

P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670

Grade = B

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910

Grade = A

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1

Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

At least B means equal to B or greater than B grade.

P(at least B) = P(B) + P(A)

P(at least B) = 0.240 + 0.090

P(at least B) = 0.330

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the course means getting a grade of A, B, C or D

P(pass) = P(A) + P(B) + P(C) + P(D)

P(pass) = 0.090 + 0.240 + 0.360 + 0.165

P(pass) = 0.855

Alternatively,

P(pass) = 1 - P(F)

P(pass) = 1 - 0.145

P(pass) = 0.855

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Answer:

21=2w+2w+3    18=4w     w=4.5

Answer:

  1

Step-by-step explanation:

The lateral area of a cylinder is ...

  LA = 2πrh

The total area is that added to the areas of the two circular bases:

  A = 2πr² +2πrh

We want the ratio of these to be 1/2:

  LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr

Multiplying by 2(r+h) gives ...

  2h = r+h

  h = r . . . . . subtract h

So, the desired ratio is ...

  h/r = h/h = 1

The ratio between height and radius is 1.

Answer:

Use a graphing calc.

Step-by-step explanation:

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

Answer:

33%

Step-by-step explanation:

let fraction be x/y

numerator increased by 60%

=x+60%ofx

=8x

denominator increased by 20%

=y+20%of y

so the increased fraction is 4x/3y

let the fraction is increased by a%

then

x/y +a%of (x/y)=4x/3y

or, a%of(x/y)=x/3y

[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]

therefore a=33

anda%=33%

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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Answer:

The right Riemann sum is 21.5.

The left Riemann sum is 29.5.

Step-by-step explanation:

The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:

[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].

To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].

Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]

Now, we just evaluate the function at the right endpoints:

[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]

Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]

The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:

[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].

To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].

Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]

Now, we just evaluate the function at the left endpoints:

[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]

Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

Answer:

B. 1788

Step-by-step explanation:

The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by

length * height * width

The volume for current object is :

12 * 28 * 5

= 1788 cubic yards.

Answer: 1778

Step-by-step explanation:

because Ik I had the question

Answer:

Option C

Step-by-step explanation:

The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.

It tests the claim that the row and column variables are independent of each other.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Answer:

Experimental Study

Step-by-step explanation:

In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.

These studies are usually randomized ie subjects are group by chance.

As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6

Answer:

C and D

Step-by-step explanation:

khan acedemy

An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the given equation v²=25/81 can be found as shown below.

v²=25/81

Taking the square root of both sides of the equation,

√(v²) = √(25/81)

v = √(25/81)

v = √(5² / 9²)

v = ± 5/9

Hence, the solutions of the given equation are A, B, and C.

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Answer:  [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

Inversely proportional means a x b = k   --> b = k/a

Given that a₁ = 2   --> b₁ = k/2

Given that a₂ = 3   -->  b₂ = k/3

[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]

The area bounded by region between the curve [tex]y = x^2- 24[/tex]  and [tex]y = 1[/tex] is

[tex]0[/tex] square units.

To find the Area,

Integrate the difference between the two curves over the interval of intersection.

Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .

The point of Intersection is the common point between the two curve.

Value of [tex]x[/tex] and [tex]y[/tex] coordinate  will be equal for both curve at point of intersection

In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].

[tex]1 = x^2-24[/tex]

Rearrange, like and unlike terms:

[tex]25 = x^2[/tex]

[tex]x =[/tex]  ±5

The point of intersection for two curves are:

[tex]x = +5[/tex]  and  [tex]x = -5[/tex]

Integrate the difference between the two curve over the interval [-5,5] to calculate the area.

Area =   [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]

Simplify,

[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]

Integrate,

[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]

Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.

[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]

= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]

[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]

[tex]= 0[/tex]

The Area between the two curves is [tex]0[/tex] square  units.

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we just have to use the Pythagoras theorem and then calculate the value of x and y.

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

Answer:

Betty should use T = 2.571 to construct the confidence interval

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571

Betty should use T = 2.571 to construct the confidence interval