Dan is playing a game where he selects a card from a deck of four cards, labeled 1 , 2, 3, or 4. The possible cards and probabilities are shown in the probability distribution below. What is the expected value for the card that Dan selects?
3.5
2.0
2.5
1.0

Train A takes 20 hours to get to Chicago from Washington whereas Train B takes 16 hours, making a 20: 16 ratio between the two trains.

Given: Time taken by Train A = 16 hours

Time taken by train B = 20 hours

We need to find, the ratios of speeds of trains A and B

The distance exists same (Chicago to Washington) and to finding the speed of train A.

Let the equation be

Speed [tex]$=\frac{\text { Distance }}{\text { time }}$[/tex]

Let the distance between Chicago and Washington be x

Speed [tex]${(\text {train } \mathrm{A})}=\frac{\mathrm{x}}{16} \mathrm{~km} / \mathrm{h}$[/tex]

Hence, speed of train [tex]$A=\frac{x}{16} \mathrm{~km} / \mathrm{h}$[/tex]

To find the speed of train B

Speed [tex]${({train~B})}=\frac{\mathrm{x}}{20} \mathrm{~km} / \mathrm{h}$[/tex]

[tex]$\mathbf{S}_{(\{train~A})}: \mathrm{S}_{(\{train} B)} \\[/tex]

[tex]$& \longrightarrow \frac{\mathrm{x}}{16}: \frac{\mathrm{x}}{20} \\[/tex]

= 20 : 16

Therefore, the ratio of train A and train B be 20 : 16.

The complete question is:

Train a take 16 hour to reach Chicago from Washington while train b take 20 hour, the ratio of the speed of both the train.

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Answer:

2

Step-by-step explanation:

Let ( x1, y1) represent the first point (0,0)  and  (x2, y2) represent the second point (2,4). Slope (m) (y2 - y1) / ( x2 - x1)= (4 - 0) / (2-0) =2

Their total determines which angles are equivalent. Alternative Corresponding Angles Parallel Corresponding angles

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No, the length of any pair of sides added together is not necessarily longer than the length of the third side.

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It is true three side lengths of 23, 32, and 45 units will form exactly one unique triangle.

The complete question is

Three side lengths of 23, 32, and 45 units will form exactly one unique triangle. true /false.

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Answer:259

Step-by-step explanation:

3+256=269

Answer: 259

Step-by-step explanation: 3 + 256 = 259

The answers for all triangle problems are:

10. ΔABC is a equilateral triangle, then:

∠A = ∠B = ∠C = 8x - 44

3 (8x - 44) = 180

24x - 132 = 180

24x = 48

x = 2

11. ΔRST is an isosceles triangle, then:

∠R = ∠T

15x - 31 = 9x + 11

6x = 42

x = 7

∠S + ∠R + ∠T = 180°

∠S + 2∠T = 180°

∠S + 2( 9x + 11) = 180°

∠S + 2(9(7) + 11) = 180°

∠S + 2 (63 + 11) = 180°

∠S + 2 (74) = 180°

∠S = 180 - 144

∠S = 36°

12. Based on the given data:

∠P = 5x - 14

∠Q = x - 5

∠R = 2x - 9

Since ΔPQR is a triangle, then:

∠P + ∠Q + ∠R = 180°

(5x - 14) + (x - 5) + (2x - 9) = 180°

8x - 28 = 180°

8x = 208

x = 26

∠P = 5x - 14 --> 5(26) - 14 = 116°

∠Q = x - 5 --> (26) - 5 = 21°

∠R = 2x - 9 --> 2(26) - 9 = 43°

13. ΔJKL is a triangle, where:

∠J = ∠L - 7

∠K = 2∠L - 21

∠J + ∠K + ∠L = 180

(∠L - 7) + (2∠L - 21) + ∠L = 180°

4∠L - 28 = 180°

4∠L = 208

∠L = 51°

∠J = ∠L - 7 --> (51) - 7 = 44°

∠K = 2∠L - 21 --> 2(51) - 21 = 81°

14. In a triangle ΔBCD:

BD = BD

∠B = 13x - 35

∠C = 5x - 19

∠D = 2x + 14

Since BC = BD; then:

∠C = ∠D

5x - 19 = 2x + 14

3x = 33

x = 11

∠C = ∠D = 2x + 14 --> 2(11) + 14 = 36°

∠B + ∠C + ∠D = 180°

∠B + 36° + 36° = 180°

∠B = 108°

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If 2/9 of the students in a school are in sixth grade.

then 20 students  sixth graders are there if the school has 90 students.

6 students sixth graders are there if the school has 90 students

If the school has a students then 2x/9 the number of sixth graders in terms of x.

Part of a full number and a means of dividing a numbers into equal pieces are represented by fractions. The denominator is the total number of components in the whole, while the numerator is the fraction of equal portions being counted.

a. From the details of the question, we have 2/9 of the students in the school in sixth grade. Hence;

Number of students in sixth grade = 2/9 × 90 = 20 sixth grade students

b. If the school has 27 students, number of sixth graders =  2/9 ×  27 = 6 sixth grade students

c. If we have x students in the school, the number of sixth graders =  2/9 × x = 2/9x students

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The probability that a plain pencil from the first box and a color pencil from the second box are selected is 3/8.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A box contains 5 plain pencils and 5 pens.

A second box contains 3 color pencils and 1 crayon.

One item from each box is chosen at random.

The probability that a plain pencil from the first box and a color pencil from the second box are selected,

= 5/10 x 3/4

= 3/8

Therefore, the probability is 3/8.

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The number of planes manufactured by the aeroplane company will be 432.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that an aeroplane factory made 36 aeroplanes per month. The number of aeroplanes made in a year will be calculated as:-

Number = 36 x Months in a year

Number = 36 x 12

Number = 432

Therefore, the number of planes will be 432.

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The statement is True: the null space of a is the solution set of the equation ax = 0.

The collection of all solutions to the homogeneous equation makes up a matrix's null space. Any matrix's null space contains the zero vector at all times. The null space is denoted as Null A.

We know that The null space of an m × n matrix A, written as Nul A, is the set of all solutions to the homogeneous equation Ax = 0.

Hence, the statement is True: the null space of a is the solution set of the equation ax = 0.

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For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et. The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

c = -1: y = e-t

c = 0: y = 0

c = 1: y = et

For c = -1, we have f(t,y) = -y = -1. Rearranging this equation yields y = -1, which simplifies to y = e-t.

For c = 0, we have f(t,y) = -y = 0. Rearranging this equation yields y = 0.

For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et.

The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

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Answer:

3a - 7.5

Step-by-step explanation:

4.5a−1.5(a+5)

4.5a - 1.5a - 7.5

3a - 7.5

So, the answer is 3a-7.5

Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.

let,

Pete is standing 4 feet away from a mirror on the ground.

Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.

We can say two triangles are formed are similar,

So if the mirror is 20 feet away from the base of the tree

After talkig the similarity theorem we get,

[tex]\frac{6}{4} = \frac{x}{20}[/tex]

So x = 6*5

x = 30 feet.

The height of the mirror is 30 feet.

Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).

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Answer: $75

Step-by-step explanation:

Price for one person: $4.50+$8

Price for six people: 6($4.50+$8)=$75

The minimum length of the third side must be greater than 16 feet.

The minimum length of the third side can be determined using the Triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. The Triangle Inequality Theorem can be expressed by the following inequality: a + b > c, where a, b, and c are the lengths of the three sides of the triangle. In this case, we have two sides of 4 feet and 12 feet, so the inequality can be written as 4 + 12 > c, which simplifies to 16 > c. Solving for c yields c > 16, which means that the minimum length of the third side must be greater than 16 feet.

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The limit does not exist if the graph features a vertical asymptote with one side going toward infinity and the other toward negative infinity.

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£479.42 is  the income tax Angela gets deducted each month.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Angela earns £35 240 a year. She has to pay income tax. She is allowed to earn £6475 before paying tax. She pays 20% tax on the rest.

So,

taxable income = 35,240-6,475

taxable income = 28,765

Since She pays 20% tax

Thus,

The Total tax = 28,765 * 20%

the total tax = 5,753

Since Her employer deducts the income tax each month.

so,

Income tax deducted each month =  5,753/12

Income tax deducted each month =  479.417

Therefore, the income tax Angela gets deducted each month is £479.42.

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The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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Line of fit go through (1, 10) and (10, 1) to best fit the data.

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Line of best fit of the scatterplot should go through as many points as possible of the graph.

If we draw a line passing through the pair of points given in the options, the line passing through (1, 10) and (10, 1) passes through (9, 2), (7, 4) and (3, 8).

No other line drawn through points in the options passes through 5 points.

Hence the line of best fit is the line passing through (1, 10) and (10, 1).

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The volume of the solid is approximately 54.8 cubic cm.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

The paraboloid z = 8 - 2x² - 2y² can be written in polar coordinates as z = 8 - 2r². The volume of the solid can be found by using the double integral of the height of the paraboloid over the region defined by the polar coordinates.

In polar coordinates, the region is defined by 0 <= r <= √4 and 0 <= θ <= [tex]\frac{\pi }{2}[/tex]The volume of the solid is given by:

V=[tex]\int\limits \int\limits {(8-2r^{2} )} r\, dr dy[/tex]

= [tex]\int\limits^0_\frac{\pi }{2} {} \, dx\int\limits^0_\sqrt{4} \,}(8-2r^{2})r }dr[/tex]

= [tex]\int\limits^0_\frac{\pi }{2} dx[ {4r^{2} -\frac{2}{3}r^{3} }] \,[/tex] from 0 to sqrt(4)

= [tex]\frac{\pi }{2} [4(4)-(\frac{2}{3}4^{\frac{3}{2} } ][/tex]

= [tex]\frac{\pi }{2}[16-\frac{2}{3}(16^{\frac{1}{2} } )][/tex]

= [tex]\frac{\pi }{2}[16-8({\frac{2^{} \frac{1}{2} }{3} }) ][/tex] cubic cm

So the volume of the solid is approximately 54.8 cubic cm.

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The requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

1 GEL and 25 tetris = 1.25
1 GEL and 5 tetris = 1.05

We can set up two equations to find the unknown values of x and y:

1.25 = 5x + 2y  - - - - - -(1)

1.05 = 2x + 3y  - - - - - (2)

To solve the system of equations, we can substitute the value of y in the first equation using the second equation:

y = (1.25 - 5x) / 2

Substituting this value of y in the second equation:

1.05 = 2x + 3((1.25 - 5x) / 2)

x = 0.15

Now,
Put x = 0.15 equation 1,
e get
y = 0.25

Thus, the requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.

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The coordinate of point C' after transformation is; C'(4, 4)

Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller. That is a reduction or an enlargement.

Usually when we dilate an object by a scale factor, what we simply do is to multiply the original coordinates by the scale factor to get the new dilated coordinates.

Since the quadrilateral is dilated by a scale factor of 2, we will multiply the original coordinate of point C by 2.

Coordinate of C = (2, 2)

Thus;

Dilated coordinate; C' = (2*2, 2*2) = 4,4

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The lengths of the diagonals of rectangle is 66 units

The properties of a rectangle is given as;

From the information given, we have that;

$WY=14x+10

$XZ=11x+22

Since the diagonals are of the same length, we have;

WY = XZ

14x + 10 = 11x + 22

collect like terms

14x - 11x = 22 - 10

subtract the like terms

3x = 12

Make 'x' the subject of the formula

x = 4

WY = 54 + 10 = 66

XZ = 66

Hence, the values are 66

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The statement using the specified property i.e  Associative Property of Multiplication will be 14y.

One's identity property is its capacity for multiplication.

7(2y)

The phrase is given as follows:

7(2y)

=14y

The one has the multiplication property, which says:

Any number or expression that is multiplied by one doesn't alter in any way.

The result is: 1xa=a

The identification property is another name for this particular attribute.

The general rule is shown as follows:

Examples include

1 * 2 = 2

1 * x = x

1 * ab = ab

and so forth

So, the property of multiplying by one is an identity property.

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Answer:

deductive reasoning

Step-by-step explanation:

On the map, the two towns are 17 centimeters apart.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

The scale on a map is stated as 1 : 200000.

A main road connects two towns which are 34 kilometers apart.

34 kilometers in centimeters,

= 3400000

So, the road on the map = 3400000/200000

The road on the map = 17 centimeters.

Therefore, the value is 17 centimeters.

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Answer:

$2280

Step-by-step explanation:

38000*6% =2280

The approximate value of the correlation coefficient for the given graph is D. -1.

The correlation coefficient is a statistical measure that indicates the strength and direction of the linear relationship between two variables. A correlation coefficient of -1 indicates a perfect negative linear relationship, meaning that as the value of one variable increases, the value of the other variable decreases at a constant rate. In this case, as the number of years increases, the price of the car decreases, so the correlation coefficient is negative.