A man wins £7500 on the pools and decides to share it with his
family. He gives his wife2/5,his son 1/4and saves the rest for himself.
(a) How much does he give to his wife?
(b) How much does he give to his son?
(c) What fraction does he save for himself?

The sample space is all the cards in the deck if an experiment involves choosing one card from a deck of playing cards.

Given statement,

If an experiment is selecting a card from a deck of cards, then the sample space is,

For the given case,

The sample space in this case is " all the cards in the deck "

Therefore, If an experiment is selecting a card from a deck of cards, then the sample space is all the cards in the deck.

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Answer:

10 x squared minus 4 y + 2 x squared minus y

Step-by-step explanation:

9x^2-2y+3x^2-3y

Collect like terms

9x^2+3x^2-2y-3y

=12x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

Collect like terms

10x^2+2x^2-4y-y

=12x^2-5y

9x^2-2y+3x^2-3y is equivalent to

10x^2-4y+2x^2-y

Check all the options

6 x squared minus y + 6 x squared minus 5 y

6x^2-y+6x2-5y

12x^2-6y

6 x squared minus y + 3 x squared minus 4 y

6x^2-y+3x^2-4y

9x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

12x^2-5y

11 x squared + 2 y + x squared minus 3 y

11x^2+2y+x^2-3y

12x^2-y

Answer:

C.) 12x squared- 2y- 3y

Step-by-step explanation:

i'm not 100 percent on this but it is the only logical answer, i will comment if i am right or not :) good luck luvs

Answer:

  d is true

Step-by-step explanation:

Linear dimensions are multiplied by the scale factor. Area dimensions are multiplied by the square of the scale factor.

__

False

The area of the new garden will be (4/5)² = 16/25 of the area of the original garden.

__

False

see (a)

__

False

see (d)

__

True.

Perimeter is a linear dimension, measured in length units. The perimeter of the new garden will be 4/5 the perimeter of the old garden.

Answer: ≈ 196.53 m²

All work is shown in the picture.

Answer:

subtracting a negititive is the same as adding so -66.1+55.6

Hope This Helps!!!

Answer:

Johnson rode her bike 5 miles

Step-by-step explanation:

Answer:

3/25

Step-by-step explanation:

0.12 multiplied by 100 equals 12

which means 12/100 is 0.12

now simplify

6/50

3/25

The maximum strut load is 70.87 kN. The maximum strut load can be calculated using the following equation: Maximum strut load = 2 * unit weight * gravity * depth * sin(friction angle) * cos(friction angle)

In this case, the unit weight is 20 kN/m3, the gravity is 9.81 m/s^2, the depth is 7.5 m, and the friction angle is 36°. Plugging these values into the equation, we get the following:

Maximum strut load = 2 * 20 * 9.81 * 7.5 * sin(36°) * cos(36°) = 70.87 kN

Therefore, the maximum strut load is 70.87 kN.

The maximum strut load occurs at the first row of struts, which is installed at a depth of 0.5 m below ground surface. The strut load decreases with depth, and the maximum strut load is reached at the first row of struts.

The strut load is caused by the weight of the soil above the struts. The soil above the struts exerts a lateral force, which is resisted by the struts. The maximum strut load occurs when the lateral force is at its maximum.

The maximum strut load is an important design consideration for braced cuts. The strut load must be able to be safely carried by the struts. If the strut load is too high, the struts may buckle or fail.

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The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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\(n^{m}\) - \((n-1)^{m}\) * m + \((n-2)^{m}\) * (m choose 2) - \((n-1)^{m}\) * (m choose 3) + ... + \((-1)^{(n-1)}\) * \(1^{m}\) * (m choose n-1)

This formula gives the total number of ways to assign m jobs to n employees so that each employee is assigned at least one job.

What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects. It is concerned with the study of discrete structures, such as graphs, hypergraphs, and matroids, and their properties.

This problem is a classic example of applying the principle of inclusion-exclusion.

Let's start by assuming that we can assign any number of jobs to each employee, without the constraint that each employee must receive at least one job. In this case, the number of ways to assign m jobs to n employees would be n^m, since each job has n choices of employee to assign it to.

However, we need to subtract the number of cases where at least one employee is left without a job. This can happen in m different ways, since we can choose any of the m jobs to be unassigned. For each of these cases, there are \((n-1)^{m}\) ways to assign the remaining jobs to the n-1 remaining employees.

However, we have now "overcorrected" for cases where more than one employee is left without a job, since we have subtracted those cases twice (once for each pair of employees that are left out). To correct for this, we need to add back in the number of cases where at least two employees are left without a job. This can happen in (m choose 2) ways, since we can choose any pair of jobs to be unassigned. For each of these cases, there are \((n-1)^{m}\) ways to assign the remaining jobs to the remaining n-2 employees.

We continue this process of alternating subtraction and addition for all possible numbers of employees left without a job, up to n-1. The final answer is:

\(n^{m}\) - \((n-1)^{m}\) * m + \((n-2)^{m}\) * (m choose 2) - \((n-1)^{m}\) * (m choose 3) + ... + \((-1)^{(n-1)}\) * \(1^{m}\) * (m choose n-1)

This formula gives the total number of ways to assign m jobs to n employees so that each employee is assigned at least one job.

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The correct answer is B. Intention-to-Treat analysis of a clinical trial means that anyone randomized into one of the study groups must be included in the final analysis in the group to which they were originally randomized, regardless of whether they adhered to the protocol or not.

Intention-to-Treat (ITT) analysis is a fundamental principle in clinical trials that ensures the integrity of the study design and maintains the validity of the results. It aims to assess the treatment's effectiveness in real-world conditions, accounting for potential deviations from the protocol. In an ITT analysis, all subjects randomized into different study groups are included in the final analysis according to their original assignment, regardless of their adherence to the treatment or protocol.

This approach is important because it reflects the practical scenario where patients may not fully comply with the study requirements. Excluding non-compliant participants could introduce bias and compromise the generalizability of the results. By including all randomized subjects in the analysis, the ITT principle provides a more conservative estimate of treatment effects and offers a realistic representation of how the intervention may perform in a broader population. Therefore, answer B is the correct choice, reflecting the essence of the ITT analysis in clinical trials.

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Answer:

37.33 mph

Step-by-step explanation:

calculator soup app is good for this type of problem.

The rate when expressed in miles per hour gives us;

37.33 miles per hour

We are given;

28 miles in 3/4 hour

This means that a distance of 28 miles is covered in every 3/4 hour.

Now, we want to express it as a rate in miles per hour

Miles per hour simply means speed.

We know that formula for speed is;

Speed = distance/time

Speed = 28 miles/(3/4 hour)

Speed = (28 × 4)/3

Speed = 37.33 miles per hour

Thus, the rate when expressed in miles per hour is 37.33 miles per hour

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The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference.

Mathematicians use the term "radius" to label any line segment from the center of a circle to any point on the circle  is likely due to the historical development of geometry and the influence of Latin and Greek languages. and it helps to describe the size and properties of the circle.

The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference. It is a fundamental measurement in geometry and is used in various mathematical formulas and equations involving circles.

In geometry, the study of circles and their properties has a long history that dates back to ancient times. The ancient Greek mathematicians, including Euclid, made significant contributions to the development of geometry. The Greek language was widely used in mathematics during that period.

The term "radius" itself originates from Latin and means "spoke of a wheel." It refers to the line segment from the center of a circle to any point on the circle, which resembles the spoke of a wheel radiating outwards. The concept of the radius played a fundamental role in understanding the properties of circles and their relationships with other geometric figures.

When mathematicians formalized the study of circles and developed a standard terminology, the term "radius" was adopted to describe this important line segment. Since mathematics often draws from historical and cultural influences in naming concepts, it is likely that the term "radius" was chosen to maintain consistency with its historical usage and to evoke the visual image of lines radiating from a center.

While the term "radius" may have originated from the analogy to a wheel spoke, its adoption and usage in mathematics have become established conventions that provide a concise and universally understood way to refer to this key element of a circle.

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The speed is:

Work/explanation:

To find the train's speed, we use the formula:

\(\large\textsl{$Speed=\dfrac{distance}{time}$}\)

In our case, the distance is 400 miles, and the time is 2 hours.

So, I plug in the data:

\(\large\text{$Speed=\dfrac{400}{2}$}\)

\(\large\text{$Speed=200\:mph$}\)

Hence, the train's speed is 200 mph.

Answer:

200 mph (321.87 km/h)

Explanation:

If a train travels 400 miles in two hours, it would travel half of that in one hour (\(400\) ÷ \(2\)) which is 200 miles. To convert mph to km/h, just multiply by 1.61 (to be exact, 1.60934).

The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.



To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.

To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.

Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.

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Answer:

where's the triangle. I can try and help

Answer :-

Since here, no parameters are given to calculate the perimeter, we use the formula to state the perimeter of the triangle :-

Perimeter of a triangle is given as :-

P = a+b+c

where, a, b and c are the measurement of the sides of the triangle.

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The first quartile is the median of 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

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Step-by-step explanation:

the option A is the binomial.

hope this helps you.

Answer:

area of rectangle = length× width

Thus, there are several methods to receive a blue, red, or yellow ribbon, including: 32736 ways.

There are two methods for choosing an item from a set. The first is referred to as a combination, while the second as a permutation. These approaches all specify how to choose an item, however they only differ in terms of the order.

An arrangement when the order of the elements is important is known as a permutation in mathematics. It differs from just a combination in that a combination doesn't care about the order.

Given data:

Number of horses = 33.

Awards: (with no repetitions)

blue --> 33 ways

red --> 32 ways

yellow ---> 31 ways

Number of ways to presents ribbons as award:

= 33 x 32 x 31

= 32736 ways.

Thus, there are several methods to receive a blue, red, or yellow ribbon, including: 32736 ways.

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Complete question:

There are 33 horses competing in a show. in how many ways can the blue, red, and yellow ribbons be awarded?

The total elongation of the cable 300 mm.

To determine the total elongation of the steel cable, we need to consider the axial strain produced by both the weight of the cage and the weight of the steel cable.

Let's break down the problem step by step:

1. Calculate the elongation due to the weight of the cage:
  - Given the uniform axial strain of 260µm/m, we can calculate the elongation using the formula:

elongation = strain * original length.

  - The original length of the cable is 600 m.
  - Therefore, the elongation due to the weight of the cage is 260µm/m * 600 m = 156 mm.

2. Calculate the elongation due to the weight of the steel cable:
  - The additional axial strain produced by the weight of the cable is proportional to the length below the point.
  - We are given that the total axial strain at the upper end of the cable is 500µm/m.
  - The length of the cable is 600 m.
  - Using the formula: additional strain = total strain - uniform strain.

  - Therefore, the additional strain due to the weight of the cable is 500µm/m - 260µm/m = 240µm/m.
  - The elongation due to the weight of the cable can be calculated using the formula: elongation = strain * length.
  - The length below the upper end of the cable is 600 m.
  - Therefore, the elongation due to the weight of the cable is 240µm/m * 600 m = 144 mm.

3. Calculate the total elongation of the cable:
  - The total elongation is the sum of the elongations due to the weight of the cage and the weight of the cable

.
  - Total elongation = elongation due to the weight of the cage + elongation due to the weight of the cable.

  - Total elongation = 156 mm + 144 mm = 300 mm.

Therefore, the total elongation of the cable is 300 mm.

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Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.

Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.

Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.

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The.dimensions (length and width) of the poster include 10 inches and 2 inches.

Let the width be represented by w.

The length based on the information given will be: (w/2) + 9 = 0.5w + 9

The area is 20 inches²

It should be noted that length × width = area.

This will be:

= (0.5w + 9) × w = 20

0.5w² + 9w = 20

0.5w² + 9w - 20 = 0

Multiply through by 2

w² + 18w - 40 = 0

w² + 20w - 2w - 40 = 0

w(w + 20) - 2(w + 20)

(w - 2) = 0

w = 0 + 2

Width = 2 inches

Length = 0.5w + 9

= 0.5(2) + 9

= 1 + 9

= 10 inches.

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Answer:

C - 10

Step-by-step explanation:

I did the quiz and this is what I got, it said I was right.

Answer:

Answer:

c-10

Step-by-step explanation

the person above's right

Answer:

x>7

Step-by-step explanation:

-9x + 4 + 12 + 18x >79

9x+16>79

9x>79 - 16

9x > 63

x>7

Answer:

x= 4/5

y= 2/5

Step-by-step explanation:

3x-y=2

2x+y=5

solve them so that they are in y=mx+b form

3x-y-3x=2-3x

-y= -3x+2

y= 3x -2

2x+y -2x= 2-2x

y= -2x+2

now use the substitution method to get your points

3x -2= -2x+2

3x -2+2= -2x+2+2

3x= -2x+4

3x+2x= -2x+4+2x

5x=4

x= 4/5

now substitute x into any of the 2 equations

y= 3x -2

y= 3(4/5) -2

y= 2 2/5 -2

y= 2/5

Hope this helped!

The c is equal to half of the definite integral of the function over the interval [0, 2].

To determine c such that f(c) is the average value of the function on the interval [0, 2], we can use the formula for the average value of a function:

avg = 1/(b-a) * ∫(a to b) f(x) dx

In this case, a = 0 and b = 2, so the formula becomes:

avg = 1/2 * ∫(0 to 2) f(x) dx

We want to find the value of c such that f(c) = avg, so we can set these two expressions equal to each other and solve for c:

f(c) = avg
f(c) = 1/2 * ∫(0 to 2) f(x) dx

We can then use calculus to solve for c by finding the derivative of both sides with respect to c and setting them equal to each other:

f'(c) = 1/2 * (f(2) - f(0))

Solving for c gives us:

c = (1/2) * ∫(0 to 2) f(x) dx

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A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.

A ray is named using its endpoint first, and then any other point on the ray

Properties of ray:

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Please refer to the attachment for the answer and explanation! Hope it helps!!:))