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Statistics Chapter 11: Simulation Practice

Answer:

Horizontal and vertical lines are perpendicular. So angles B&E .All right angles are 90°.

i hope you're helped

Horizontal and vertical lines are perpendicular. So, angles B and E are right angle by definition of perpendicular lines. All right angles are 90°/congruent/equal.

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

Given are two triangles ABC and DEF.

Two triangles are similar if all the corresponding angles are equal and the corresponding sides are proportional.

Here, given that,

AB / DE = BC / EF = 1 / 2.

So, two corresponding sides are proportional.

SAS similarity postulate is that, if two corresponding sides of two triangles are proportional and the corresponding included angle is congruent, then the two triangles are similar.

So we have to prove included angle B and E are equal.

A horizontal and vertical lines are always perpendicular.

Here B and E are formed by a horizontal and a vertical line.

So they are right angles.

All right angles are 90°. So they are equal or congruent.

So Triangles ABC and DEF are similar by SAS.

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Answer:

Step-by-step explanation:

Has on the scale

Added

Total

Answer:

the total weight is 2550 grams

Step-by-step explanation:

2 1/2 kilograms=5/2×1000grams=2500grams

if 50 grams is added

total weight in grams =2500grams+50grams=2550grams

The most appropriate choice for matrix will be given by

Number of seats in orchestra section = 1650, Number of seats in loge section = 1175 and Number of seats in balcony section = 875.

What is a matrix?

Numbers arranged in the form of rows and column is called matrix.

Here,

a) Let the number of seats in orchestra section be x,

Number of seats in loge section be y

Number of seats in balcony section be z

Total number of seats  = 3650

x + y + z = 3650 ......... (1)

There are twice as many orchestra seats as balcony seats

x = 2z

x - 2z = 0 ......... (2)

The revenue from selling all 3650 seats is $213125

Charge for orchestra seat = $75

Charge for loge seat = $55

Charge for balcony seat = $30

Total charge = $(75x + 55y + 30z)

By the problem,

75x + 55y + 30z = 213125

5(15x + 11y + 6z) = 213125

15x + 11y + 6z = \(\frac{213125}{5}\)

15x + 11y + 6z = 42625.......... (3)

The augmented matrix is

\(\left[\begin{array}{cccc}1&1&1 & 3650 \\1 &0&- 2&0\\15&11&6& 42625\end{array}\right]\)

b) Let A = \(\left[\begin{array}{cccc}1&1&1 \\1 &0&- 2\\15&11&6\end{array}\right]\), X = \(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\), b = \(\left[\begin{array}{ccc}3650\\0\\42625\end{array}\right]\)

AX = b

X = A^1 b

Adjoint A =

\(\left[\begin{array}{ccc}\begin{vmatrix}0 & -2\\11 & 6 \end{vmatrix}&-\begin{vmatrix}1 & -2\\15 & 6 \end{vmatrix}& \begin{vmatrix}1 & 0\\15 & 11 \end{vmatrix}\\\\ -\begin{vmatrix}1 & 1\\11 & 6 \end{vmatrix}& \begin{vmatrix}1 & 1\\15 & 6 \end{vmatrix} & -\begin{vmatrix}1 & 1\\15 & 11 \end{vmatrix}\\ \\\begin{vmatrix}1 & 1\\0 & -2 \end{vmatrix}& -\begin{vmatrix}1 & 1\\1 & -2 \end{vmatrix}& \begin{vmatrix}1 & 1\\1 & 0 \end{vmatrix}\end{array}\right] ^{T}\)

\(\left[\begin{array}{ccc}22&-36&11\\5&-9&4\\-2&3&-1\end{array}\right]^T\)

\(\left[\begin{array}{ccc}22&5&-2\\-36&-9&3\\11&4&-1\end{array}\right]\)

Det A =

\(\begin{vmatrix}1 & 1 & 1\\1 & 0 & -2 \\ 15 & 11 & 6 \end{vmatrix}\)

1(0 x 6 - 11) x (-2)) - 1(1 x 6 - 15 x (-2) + 1 (1 x 11 - 0 x 15)
22 - 36 + 11
-3

\(A^{-1} = -\frac{1}{3} \left[\begin{array}{ccc}22&5&-2\\-36&-9&3\\11&4&-1\end{array}\right]\)

\(X = -\frac{1}{3} \left[\begin{array}{ccc}22&5&-2\\-36&-9&3\\11&4&-1\end{array}\right]\begin{bmatrix}3650\\0\\42625\end{bmatrix}\)

  \(= -\frac{1}{3}\begin{bmatrix}-4950 \\-3525\\-2475\end{bmatrix}\)

\(X =\begin{bmatrix}1650 \\1175\\825\end{bmatrix}\)

x = 1650, y = 1175, z = 825

Number of seats in orchestra section = 1650

Number of seats in loge section = 1175

Number of seats in balcony section = 875

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The answer is 3.5 pounds

The corresponding angle of ∠3 in the parallel line is ∠8.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate interior angles, alternate exterior angles, linear angles etc.

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

Corresponding angles are congruent.

Hence, the corresponding angle of ∠3 is ∠8.

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Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Answer:

\(\textsf{13.} \quad(x-1)^2+(y+2)^2=9\)

       center = (1, -2)

       radius = 3

\(\textsf{14.} \quad y=5 \cdot 3^x\)

\(\textsf{15.} \quad x=\dfrac{104}{3}, \quad x=-\dfrac{88}{3}\)

Step-by-step explanation:

Equation of a circle

\((x-a)^2+(y-b)^2=r^2\)

(where (a, b) is the center and r is the radius)

Given equation:

\(x^2+y^2-2x+4y-4=0\)

To rewrite the given equation in graphing form, first add 4 to both sides of the equation and rearrange the variables:

\(\implies x^2-2x+y^2+4y=4\)

Add the square of half the coefficients of the x and y terms to both sides:

\(\implies x^2-2x+\left(\dfrac{-2}{2}\right)^2+y^2+4y+\left(\dfrac{4}{2}\right)^2=4+\left(\dfrac{-2}{2}\right)^2+\left(\dfrac{4}{2}\right)^2\)

\(\implies x^2-2x+1+y^2+4y+4=9\)

Finally, factor both trinomials:

\(\implies (x-1)^2+(y+2)^2=9\)

Now compare the equation in graphing form to the general equation of a circle to find the center and radius:

⇒ a = 1  and  b = -2  ⇒ center = (1, -2)

⇒ r² = 9  ⇒ radius = √9 = 3

General form of an exponential function:

\(y=ab^x\)

(where a and b are constants to be found)

Given points on the curve:

Substitute the given points into the general form of the equation to create two equations:

\(\textsf{Equation 1}: \quad ab^4=405\)

\(\textsf{Equation 2}: \quad ab^9=98415\)

Divide Equation 2 by Equation 1 to eliminate a, then solve for b:

\(\implies \dfrac{ab^9}{ab^4}=\dfrac{98415}{405}\)

\(\implies \dfrac{b^9}{b^4}=243\)

\(\implies b^{9-4}=243\)

\(\implies b^5=243\)

\(\implies b=\sqrt[5]{243}\)

\(\implies b=3\)

Substitute the found value of b into one of the equations and solve for a:

\(\implies a(3)^4=405\)

\(\implies 81a=405\)

\(\implies a=\dfrac{405}{81}\)

\(\implies a=5\)

Therefore, the exponential equation that passes through (4, 405) and (9, 98415) is:

\(y=5 \cdot 3^x\)

Given equation:

\(\left|\dfrac{3}{2}x-4\right|+2=50\)

Isolate the absolute value by subtracting 2 from both sides:

\(\implies \left|\dfrac{3}{2}x-4\right|=48\)

Set the contents of the absolute value to positive and negative and solve for x:

Positive absolute value:

\(\implies \dfrac{3}{2}x-4=48\)

\(\implies \dfrac{3}{2}x=52\)

\(\implies x=52 \cdot \dfrac{2}{3}\)

\(\implies x=\dfrac{104}{3}\)

Negative absolute value:

\(\implies -\left(\dfrac{3}{2}x-4\right)=48\)

\(\implies -\dfrac{3}{2}x+4=48\)

\(\implies -\dfrac{3}{2}x=44\)

\(\implies x=44 \cdot -\dfrac{2}{3}\)

\(\implies x=-\dfrac{88}{3}\)

Therefore, the solution to the equation is:

\(x=\dfrac{104}{3}, \quad x=-\dfrac{88}{3}\)

Answer + Step-by-step explanation:

13.

x² + y² - 2x + 4y - 4 = 0

(x² - 2x) + (y² + 4y )- 4 = 0

x² - 2x = (x² - 2x + 1) - 1

           = (x - 1)² - 1

y² + 4y = (y² + 4y + 4) - 4

            = (y + 2)² - 4

Then

x² + y² - 2x + 4y - 4 = 0

⇔ (x - 1)² - 1 + (y + 2)² - 4 - 4 = 0

⇔ (x - 1)² + (y + 2)² = 9

⇔ (x - 1)² + (y + 2)² = 3²

Then

The center is (1 , -2)

The radius is  3

……………………………………………

14.

(4 , 405)  ;  (9 , 98415)

y = abˣ

The graph passes through (4 , 405) ⇒ 405 = ab⁴

The graph passes through (9 , 98415) ⇒ 98415 = ab⁹

We divide:

ab⁹÷ab⁴ = 98415 ÷ 405

⇔ b⁵ = 243

⇔ b⁵ = 3⁵

⇔ b = 3

Finding a :

405 = ab⁴

⇔ 405 = a3⁴ = 81a

⇔ a = 405/81 = 5

Conclusion:

The exponential equation is :

y = 5×3ˣ

………………………………………………

15.

|3/2x - 4| + 2 = 50

Then

|3/2x - 4| = 48

Then

3/2x - 4 = 48 or 3/2x - 4 = -48

Then

3/2x = 52 or 3/2x = -44

Then

x = 104/3 or x = -88/3

The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.

Descriptive statistics were used in the statement.

Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).

In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.

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Descriptive statistics were used in the statement.

Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.

Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.

Hence, Descriptive statistics were used in the statement.

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Answer:

17/16 OR \(1\frac{1}{16}\) minutes

Step-by-step explanation:

Since Jayla spent 1/16 of a minute AND one whole minute watching a millipede crawl, we'd need to first add the two numbers.

Since the given minute is out of 16, we can convert the one minute to 16/16.  This means we can add the other 1/16 of a minute.

This leaves us with Jayla watching the millipede for 17/16 OR \(1\frac{1}{16}\) minutes.

Hope this helps!! <3 :)

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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Answer:

\(\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }\)

Step-by-step explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as \((\left \{ {{159} \atop {n}} \right} )\)

since the residents are mutually independent and equally likely home locations hence there are : \(159^{n}\) ways for the residents to live in

therefore the probability = \(\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }\)

Answer:

The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

\(Cost = 51.275\)

Step-by-step explanation:

The given parameters can be summarized as:

\(\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}\)

Where: x = Soybeans and y = Oats.

So, the system of equations are:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

\(Cost = 21x + 7y\)

The best way to solve this, is using graph

Plot the following equations on a graph, and get the points of intersection:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

From the attached graph, we have:

\((x_1,y_1) = (1.636,2.545)\)

\((x_2,y_2) = (1.775,1.575)\)

\((x_3,y_3) = (2.023,1.256)\)

Substitute each of the values of x's and y's in the cost function to get the minimum cost:

\(Cost = 21x + 7y\)

\((x_1,y_1) = (1.636,2.545)\)

\(Cost = 21 * 1.636 + 7 * 2.545\)

\(Cost = 52.171\)

\((x_2,y_2) = (1.775,1.575)\)

\(Cost = 21 * 1.775 + 7 * 1.575\)

\(Cost = 48.3\)

\((x_3,y_3) = (2.023,1.256)\)

\(Cost = 21 * 2.023 + 7 * 1.256\)

\(Cost = 51.275\)

The values of x and y that gives the minimum cost is:

\((x_2,y_2) = (1.775,1.575)\)

and the minimum cost is:

\(Cost = 48.3\)

Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

answer is 9

Step-by-step explanation:

12/4=3

1/4=3

3/4=9

From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

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Answer:

Linear

Step-by-step explanation:

y-x=4

y=x+4

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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Answer:1 1/3

Step-by-step explanation:

There is your answer! :)

Answer:

54-150

Step-by-step explanation:

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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Answer:

2x - 5

Step-by-step explanation:

2x + 4 - 9

the 2x gonna stay

so you take 4 - 9 = -5

so the answers gonna be 2x - 5

bc the 5 is negative so you gonna subtract

I hope you understand my english...

Answer:

b. 7 x 2⁴

= 122

is correct..

\( \red{ \boxed{ \sf \: Solution}} \\ \to\sf{122}\)

Step-by-step explanation:

7 × 2⁴

7 × 2×2×2×2

= 122

Answer:

51,129

Step-by-step explanation:

x+x+78=180(supplementary angles are 180)

2x+78=180

2x= 102

x= 51

x+78 = 129

Answer:

7+y

Step-by-step explanation:

Answer:

5/28

Step-by-step explanation:

First of all, probability is defined as the number of ways a certain event can happen divided by the total ways of an event happening. In this scenario, we are asked to find the number of non-defective computers divided by the total ways that a sample of two can be chosen.

The number of ways to choose 2 computers from 8 can be written as \(8\choose2\), which is equal to \(\frac{8\cdot7}{2}\), which is 28. Now, there are 3 defective computers, for a total of 5 non-defective computers, so the probability is 5/28.

Answer:

Step-by-step explanation:

1/4

Answer: It would be 4

So what's happing in the table, is that numbers are being multiplied by 4.

1x4=4

2x4=8

3x4=12

4x4=16

hope I helped :)

The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Answer:

478

Step-by-step explanation:

559.45-457.41=102.04

102.04/559.45*100

approximately 478