Kevin is travelling from Manchester to Oxford tomorrow.
(b) Complete the probability tree diagram to show the outcomes of Kevin's seating on the two
trains.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.
315
Seat on the
first train
with a
table
without
a table
Seat on the
second train

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.

A cone has a radius of 5.1 m and a slant height of 10.9 m. So the surface area of the cone is 87.3834 π m².

These are the specified parameters:

Radius (r) = 5.1 m

Cone height (h) = 10.9 m

Find the length of the cone painter's line (s)

s² = r² + h²

   = 5.1² + 10.9²

   = 26.01 + 118.81

   = 144.82

s = √144.82

s = 12.034

Find the surface area of the cone

A = πr (r + s)

   = π × 5,1 (5.1 + 12.034) m²

   = 5.1 π (17.134) m²

   = 87.3834 π m²

Which would increase the cone's surface area more is doubling the radius.

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The probability of getting 1st even and second odd is 9/36 = 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.

Number of outcomes with 1st even and second odd is 9

Total number of outcomes = 36

So, the probability of getting 1st even and second odd is 9/36 = 1/4

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Answer:

To solve this problem, we will use the following steps:

Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).

Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.

Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.

Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.

Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.

Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.

Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.

Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.

5/18 = 0.278

Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.

Answer: 18

unclear but appears its 18.

Step-by-step explanation:

Because x is 7; 4x+8/2 = 36.

but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.

The area of the given prism is equal to 1,920 in³.

What is a rectangular prism?

A rectangular prism is simply a three-dimensional solid shape which with six faces that are rectangles.

We have given,

length l = 8  in.

width w = 12 in,

height h = 20 in.

The volume of a prism is defined as the total space occupied by the three-dimensional object.

The volume of a rectangular prism is given by A = l * w * h,

where 'l' is the length of the prism, 'w' is the width, and 'h' is the height.

so, A = 8 * 12 * 20 = 1,920 in³.

A = 1,920 in³.

Therefore, the area of the given prism is equal to 1,920 in³.

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The inverse function of y = 2(x - 5)² is  [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Let, y = 2(x - 5)².

y/2 = (x - 5)².

Solving for 'x'.

[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].

[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]

Now, We have to interchange the positions of x and y.

[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

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Think of a bracelet made of five different coloured beads. Be sure to account for flipping and rotating. Check to see whether your solution is right by applying the same logic to a bracelet with four beads of four different colours.

Properties. The form with the biggest area for a given perimeter is a circle (see Isoperimetric inequality). The circle has excellent spherical shape around the centre for all angles and every line thru the centre generates a path of reflection symmetry.

My response is: There are (n-1)!/2 potential bracelets for n different colours, as in our example. Therefore, there are 4!/2=12 various bracelets that might be made for n=5.

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Answer: 25q and 3d

Step-by-step explanation:

23 dimes and 17 quarters equal $6.55.

To find the number of dimes and quarters which equals $6.55, we can use the following method:

Let D = number of dimes

Let Q = number of quarters

40 coins  ==>  D + Q = 40  ==>  D = 40 - Q

$6.55 total  ==>  10*D + 25*Q = 655

After the value for D is substituted in the second equation,

10*(40 - Q) + 25*Q = 655

400 - 10*Q + 25*Q = 655

15*Q = 255

Q = 17

i.e., D = 40 - 17 = 23

Check:  23 dimes = $2.30

           17 quarters = $4.25

           Total = $6.55 

Therefore, 23 dimes and 17 quarters equal $6.55.

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The system of inequalities that models this situation is given as follows:

One possible solution is given as follows:

(9,4).

Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.

The variables for the system of inequalities in this problem are given as follows:

The number of hours cannot be negative, hence the first two restrictions are given as follows:

He can work a maximum of 14 total hours, hence:

x + y ≤ 14.

He must earn no less than $180, hence, considering the rates for each job, we have that:

18x + 10y ≥ 180.

Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:

The shaded region represents all possible solutions for the system of inequalities.

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Answer:

.

Step-by-step explanation:

Answer: C - The statement is false.

Step-by-step explanation: Rhombuses also have perpendicular diagonals.

The next year's population will be 140,014. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

For all real numbers, there are four fundamental mathematical operations that are:

1. The sum of the numbers is achieved through addition ('+').

2. Subtraction with the sign "-," which yields the numbers' differences.

3. Multiplication('×') when the result is the product of the numbers.

4. Division ('÷'), which yields the numbers' quotient.

We are given that the population of a city increases by 2.2% per year and this year's population is 137,000.

Let the population of next year be 'x'

So, we get

⇒137,000 + 137,000(2.2%) = x

⇒137,000 + 3014 = x

⇒140,014 = x

Hence, the next year's population will be 140,014.

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Answer:

$60 / 6 barbecue sticks = $x / 1 barbecue stick

Where x is the value of 1 barbecue stick.

To find the value of x, we can cross-multiply and divide by 6:

$60 = 6 barbecue sticks * $x/1

$60 = $6x

$x = $10

So, $10 will equal 1 barbecue stick, if $60 = 6 barbecue sticks.

We know that you earned $300, so we can substitute that into the proportion:

$60 / 6 barbecue sticks = $300 / n barbecue sticks

We can cross-multiply and divide by 60:

6 barbecue sticks * $300 = $60 * n barbecue sticks

n barbecue sticks = $300 * 6 / $60

n barbecue sticks = 30

Therefore, you sold 30 barbecue sticks.

A function can be obtained from the table provided with the values of x and y in the form of a y=mx+b equation.

The above equation can be solved by plotting the graph or from table itself and after calculating its y-intercept, the value of y in the form of y= mx+ b can be obtained. Suppose the table has values of x and y as follows:

x: 0   1   2  3

y: 2  4   6  8

However, it can be seen that when x=0, y= 2, so the y-intercept i.e. the value of y obtained at x=0 is 2. And the slope can be calculated as:

m=[tex]\frac{change in y}{ change in x}[/tex]

m= [tex]\frac{4-2}{1-0}[/tex]

m=2

So the function can be written as y=2x+2

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Data set 2 is not a function, while data set 1 is a function. To turn the data set that is not a function into a function, the point (3,0) can be changed so the x-value is not equal to 1, 3, 5 or 7.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

In input-output format, the points in these relations are given as follows:

(x,y).

Hence a data-set will represent a function if each value of x is mapped to a single value of y.

This means that data-set 1 represents a function, while data-set 2 does not, as the value of x = 3 is mapped to both y = 2 and y = 0.

The data-set 2 will represent a function if one of the x-coordinates of 3 is changed to another x-coordinate, that is also different of the other x-coordinates of the table.

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If the graph only touches the x-axis at the x-intercept, then it is said to "touch" the x-axis. This indicates that the graph does not pass through the x-axis at the x-intercept, but rather just touches it.

The x-intercept of a graph is the point at which the graph crosses the x-axis. It is also known as the abscissa. The x-coordinate of the x-intercept is the value where the graph intersects the x-axis.

The x-intercept of a graph is the point at which the graph crosses (or, in some cases, touches) the x-axis. A graph can have one or more x-intercepts. If the graph only crosses the x-axis once, then it has only one x-intercept. If the graph crosses the x-axis twice or more, then it has multiple x-intercepts. In either case, the x-intercepts can be described as either "crosses" or "touches" the x-axis.

If the graph crosses the x-axis at the x-intercept, then it is said to "cross" the x-axis. This indicates that the graph passes through the x-axis at the x-intercept.

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Answer: x= 337/70 or 4 57/70

Step-by-step explanation:

The square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

Square is a two-dimensional shape with four equal sides and four right angles. It is one of the most common shapes in geometry. Squares have many practical uses, such as in forming grids, creating patterns, and making tiling. Squares are also used in art and architecture, as well as in construction, mathematics, and science.
To solve this problem, we will use the formula for the volume of a rectangular box, V = lwh. We can substitute the given values to solve for x. First, we will find the length and width of the box after the square corners are cut out:

Length = 20 - 2x

Width = 14 - 2x

Now, substituting these values into the volume formula, we get:

288 = (20 - 2x)(14 - 2x)h

Expanding and simplifying, we get:

288 = 280 - 56x + 4x^2

Subtracting 280 from both sides, we get:

8 = -56x + 4x^2

Solving for x, we get:

4x^2 - 56x + 8 = 0

Using the quadratic equation, we get x = 2.4 or x = 0.4

Since x must represent a length, we can discard the negative solution, x = 0.4. Therefore, the square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

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Answer:

4 I think

Step-by-step explanation:

A vertex is a point where two or more edges meet (i.e the sharp points of the figure).

A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.

The tens digit of k when sum of its digits is 5 and tens digit of k + 6 is 3.

Let tens digit of k be x and units digit be y. Then

k = 10x + y

The sum of the tens digit of k and the units digit of k is 5, that is

x + y = 5

So possible combinations of (x, y) is (1, 4), (2, 3), (3, 2), (4, 1) and (5, 0).

The tens digit of k+6 is 3.

So x<=3.

14 + 6 = 20

23 + 6 = 29

32 + 6 = 38

So k is 32.

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Answer: 8.7

Step-by-step explanation:

The remaining interior angle is [tex]95^{\circ}[/tex].

[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]

The measurement that you can use in your future career depends on the exact career and there are many more options.

Depending on the exact career but measurements are plentiful in the healthcare business. First, you'll most likely deal with weight and height... since that's part of most healthcare consultations. Then, if you deal with medication, you'll use grams, milligrams, milliliters, and liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes. There are countless ways you'll use mathematics and measurements in the healthcare sector.  

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The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC

the table shows the statement and the reasons for the proves of congruency of the angles and triangles

The table appears as follows

sn                  Statement                               Reason

1                     AD = RE                                 Given

2                   <A ≅<R                                    Given

3                     <AMD ≅<RMC                      Vertically opposite angles

4                     ΔMAD≅ΔMRC                      Congruent by ASA or SSA

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I) we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

II) The 30th term of this arithmetic sequence is 29.

To solve this problem, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant.

(i) Let's call the common difference d. Then we can set up the equation:

x + d = 2x + 1

d = x - 1

Since we know that x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence, we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

(ii) To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the number of the term we want to find.

Substituting the known values into this formula:

a30 = x + (30 - 1)d

a30 = 0 + (29)(1)

a30 = 29

So the 30th term of this arithmetic sequence is 29.

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The expressions that are equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

All of the following expressions are equivalent to 9/7x−3/4:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

When you multiply or divide both the numerator and denominator of a fraction by the same non-zero number, the fraction remains equivalent.

Hence, the expressions that equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

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Answer:

Step-by-step explanation:

Unfortunately, without more information, it is not possible to accurately predict the number of pounds someone would be overweight if they spent 8 hours per day using a computer. The graph provided does not provide enough data to make an accurate prediction. It is possible, however, to make an educated guess based on the graph. Looking at the graph, it appears that someone who spends 8 hours per day on the computer would likely be somewhere between 20 and 40 pounds overweight.

The width and length of the rectangle is 4.5ft and 12ft.

Width of a rectangle = b = x ft.

Length of a rectangle = l = (2x+3) ft.

Area of the rectangle = l×b = 54 sq.ft.

                                    = x (2x + 3) = 54

                                    = 2x² + 3x = 54

                                      (2x-9)(x+6) = 0

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.

 It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

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Answer:

Step-by-step explanation:

Quadratic: binomial

Cubic: trinomial

Quartic: four terms

Quintic: five terms

8th degree: six terms

Answer:

Coupon A

Step-by-step explanation:

Coupon A takes 40% off

51 x .40= $20.40

Coupon B only gives a rebate for $18

Coupon A is $2.40 less than the price with coupon B