the five-number summary calculated in part C to create a box plot representing the data. Draw a box plot representing the following data. Be sure to mark the outlier. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Lines Shapes Fill: Line: Width: 2 pt

The number of ways that the dancers can line up is; 518400 ways

The fundamental counting theorem is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n1 * n2 * n3.....*nₙ

Total = 12

Dancers on Green = 6

Dancers on blue = 6

Number of ways for those wearing green = 6!

Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.

Number of ways to arrange those wearing blue = 6!

Thus;

Number of ways that the dancers can line up = 6! * 6! = 518400 ways

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See below for the values of the probabilities

The probabilities of the whole events

For event A, the probability of the whole event is calculated using

P(A) = n(A)/Total

Using the table of values, we have:

P(F) = 130/200 = 0.65

P(M) = 70/200 = 0.35

P(L) = 60/200 = 0.30

P(S) = 40/200 = 0.20

The probabilities of the intersection events

For events A and B, the probability of the intersection events is calculated using

P(A n B) = n(A n B)/Total

Using the table of values, we have:

P(F n E) = P(E n F) = 60/200 = 0.30

P(F n L) = P(L n F) = 40/200 = 0.20

P(F n S) = P(S n F) = 30/200 = 0.15

P(M n E) = P(E n M) = 40/200 = 0.20

P(M n L) = P(L n M) = 20/200 = 0.10

P(M n S) = P(S n M) = 10/200 = 0.05

The probabilities of the Union (OR) disjoint events

For events A and B, the probability of the union (OR) disjoint events is calculated using

P(A u B) = P(A) + P(B)

Using the table of values, we have:

P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70

P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80

P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1

P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1

The probabilities of the Union (OR) joint events

For events A and B, the probability of the union (OR) joint events is calculated using

P(A u B) = P(A) + P(B) - P(A n B)

Using the table of values, we have:

P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85

P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55

The probabilities of the conditional probabilities

For events A and B, the conditional probability is calculated using

P(A/B) = P(A n B)/P(B)

Using the table of values, we have:

P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75

P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60

P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25

P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33

P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23

P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46

P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14

P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29

The multiplication of dependent events

For events A and B, the conditional probability is calculated using

P(A n B) = P(A) * P(B/A)

Using the table of values, we have:

P(F n L) = P(F) * P(L/F)

This gives

P(F n L) = 0.65 * (0.20/0.30)

Evaluate

P(F n L) = 0.43

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Answer: Either Rohmbus or Parallelogram...

Step-by-step explanation: Your picture is a bit small, sry

Reason:

The angles x and 71 are opposite the congruent sides. We call these the base angles. The base angles are congruent for any isosceles triangle. Therefore, x = 71.

It might help to rotate the triangle so that the angles x and 71 are flat along the ground (rather than tilted).

The critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

We want to find the two tail critical values.

This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.

Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.

However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.

From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;

z = 1.41

Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

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The graphed system of inequalities is:

So the correct option is the third one.

On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).

We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:

Only with that, we conclude that the correct option is the third option:

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Using the cosine double angle formula,

[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Using the Pythagorean identity,

[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

The distance at t = 3.5 hours can be obtained as illustrated below:

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

The length of third side of triangle is 4 or 14.

According to the statement

we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.

So, For this purpose, we know that the

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.

And

We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.

So, The length of third side of triangle is 4 or 14.

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Answer:

  76/165

Step-by-step explanation:

The difference of fractions can be found using the formula ...

  a/b -c/d = (ad -bc)/(bd)

Using the given values in the formula, we have ...

  [tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]

Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.

The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.

Answer:

Step-by-step explanation:

76/165 is the answer

The cost of goods sold using LIFO is $99.

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]

[tex]s = 4120.00[/tex]

Answer:

A

Step-by-step explanation:

Triangle side length rule says any two sides added together must be greater than third side .... '6' is the only side length that will work

Answer:

[tex]\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

Step-by-step explanation:

Given expression:

[tex]-2x^{-3}y(5yx^5+8xy-4y^2x^2)[/tex]

Distribute:

[tex]\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)[/tex]

Multiply the constants and collect like terms:

[tex]\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2[/tex]

Remember that a = a¹.

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}[/tex]

[tex]\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

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Answer:

788,000 =

788 x 10^3

78.8 x 10^4

7.88 x 10^5

.788 x 10^6

and so on

This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

The total amount of interest that is paid for the term loan is $383,385.54

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

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[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787

Answer:

Răspuns: 88=>rezultatul

Explicație pas cu pas:

a+2b =18/×3

b+3c=17/×2

3a+6b =54 ^

2b+6c=34 | +

3a+(6b+2b)+6c=54+34

3a+8b+6c=88

Step-by-step explanation:

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the amount of money invested in stocks, y represent bonds and z represent CDs, hence:

x + y + z = 215000     (1)

Also:

0.0225z + 0.02y + 0.092x = 8087.5    (2)

And:

y = 15000 + z    (3)

The solution of the equation is:

x = 50000, y = 90000 and z = 75000

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

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Answer:

60

Step-by-step explanation:

60 + y + y = 180

2y = 120

y = 60

The target cost for Model J20 is $2000.

The required cost reduction is $30.

The total saving will be $30.3.

The target cost will be:

= Sales price - (100% × Target cost)

= 400 - (100% × Y)

Y + Y = 400

2Y = 400

Y = 400/2 = 200

Target cost = $200

Therefore, the target cost is $200.

The required cost reduction will be:

= $230 - $200

= $30

The required cost reduction is $30.

The three engineering improvements together will be:

Direct labor reduction = 7.5

Additional inspection = 17

Injection molding = 5.8

Total savings = 30.3

The total savings is $30.3.

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The surface area of the cylinder is 48π inches².

Surface area of a cylinder = 2πr(r + h)

where

Therefore,

Surface area of the smaller cylinder = 2 × π × 2(2 + 10)

Surface area of the smaller cylinder = 4π(12)

Surface area of the smaller cylinder = 48π

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The solutions for the Questions are

a) Given that, the minimum requirement is 58 out of 75.

a=0.7733

b) For  16 out of a total of 75

b=0.2133

c)  For 11 out of a total of 75

c =0.1466

Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.

Therefore, let's assume that:

- In Set A, I watched one of the Naruto episodes.

Set B: Observed a new segment of the anime series Death Note.

Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that

(A intercept B) equals 23.

In addition to this, it is a given that 42 has seen one episode of Death Note.

This indicates that B is equal to 42.

This pertains to us:

[tex]B = (B-A)+(A \cap B)[/tex]

In this case, members of B through A are individuals who have only viewed Death Note. So

42=(B−A)+23

(B-A) = 11

Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.

Therefore, the value of A is 39.

A=(A−B)+(A intercept B)

39=(A−B)+23

(A−B)= 16

(A union B)= 42+ 39- 23

(A union B)=58

In conclusion, the total number of pupils is:

58 with at least one and 17 with none, for a total of 75

a) Given that, the minimum requirement is 58 out of 75.

a=58*100/75

a=0.7733

b) For  16 out of a total of 75

b= 16/75*100

b=0.2133

c)  For 11 out of a total of 75

c= 11/75*100

c =0.1466

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The length of the arc of the circle is 3.67 meters

The arc of a circle is a part of the circumference that makes up the circle

From the question, we have the following parameters

Diameter, d = 14 meters

Central angle = π/6 radians

Start by calculating the radius of the circle using

Radius, r = Diameter/2

This is so because radius is half the diameter

So, we have

r = 14 meters/2

Evaluate the quotient of 14 meters and 2

r = 7 meters

The length of the arc of the circle is then calculated using

L = Radius * Central angle

Substitute known values in the above equation

L = 7 meters * π/6

Evaluate the product of 7 and π/6

L = 3.67 meters

Hence, the length of the arc of the circle is 3.67 meters

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Answer: 44

Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.

Considering the given discrete probability distribution, the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

The range of a random variable is the set of all values that the variable can assume.

From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

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The slopes of OA, OB and OC are integer values.

According to the statement

we have given that the some points on the graph and we have to find that the slopes of these points have integer value or not.

So, For this we know that the

If a line passing through two points then the slope of the line is

So, [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Then

The slope of line OA is 4 because 8/2 = 4.

And

The slope of line OB is 3 because 9/3 = 3.

And

The slope of line OC is 2 because 8/4 is 2.

And

The slope of line OD is 8/5 because it is 8/5.

And

The slope of line OE is 7/6 because it is 7/6.

And

The slope of line OE is 6/7 because it is 6/7.

From all this it is clear that

So,The slopes of OA, OB and OC are integer values.

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