William Sealy Gosset worked at the Guinness Brewery in Dublin and made substantial contributions to the practice of statistics. In his work at the brewery, he collected and analyzed a great deal of data. Archives with Gosset’s handwritten tables, graphs, and notes have been preserved at the Guinness Storehouse in Dublin. In one study, Gosset examined the change in the double stout market before and after World War I (1914‑1918). For various regions in England and Scotland, he calculated the ratio of sales in 1925, after the war, as a percent of sales in 1913, before the war. Here are the data:

Region Ratio
Bristol 94
Cardiff 112
English Agents 78
English O 68
English P 46
English R 111
Glasgow 66
Liverpool 140
London 428
Manchester 190
Newcastle‑on‑Tyne 118
Scottish 24

(a) Compute the mean for these data. Give your answer to two decimal places.
⎯⎯⎯=
(b) Compute the median for these data. Give your answer to two decimal places.
=
(c) Which measure describes the center of this distribution the most accurately? Explain your answer.

The mean represents the center of the data most accurately because the mean incorporates all of the individual values, whereas the median depends more on the order of the values than their actual amounts.

The mean and the median should both be used. By comparing the mean and median, you can tell if the data are skewed.

The median represents the center of the data most accurately because the mean is more affected by extreme values.

The mean and the median are equally as accurate because the distribution of the data is approximately symmetical.
Region RelativeTo1913 RelativeToPast4
Bristol 94 82
Cardiff 112 80
English Agents 78 83
English O 68 88
English P 46 99
English R 111 99
Glasgow 66 78
Liverpool 140 106
London 428 105
Manchester 190 107
Newcastle-on-Tyne 118 115
Scottish 24 78

Answer:

26 and 27

Step-by-step explanation:

If the smaller integer is represented using the variable n, then the next consecutive integer is n + 1

3 times the smaller => 3n

2 times the larger => 2(n + 1 = 2n + 2

We are given 3 times the larger exceeds twice the smaller by 24 which can be represented as:

3n - (2n + 2) = 24

3n - 2n - 2 = 24

n - 2 = 24

n = 24 + 2 = 26

So the integers are 26 and 27

The required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
From the data select 1 pair of values,
x = 0, when h(0) = -2

Now, put this pair in each quadratic equation, since the equation that satisfies this fair will be the required quadratic equation.

A,
h(x) = (x − 1)² + 1
h(0) = (0 − 1)² + 1
h(0) =  2

B.
h(x) = (x − 1)² + 3
h(0) = 4

C.
h(x) = (x + 1)² - 1
h(0) = 0

D.
h(x) = (x + 1)² - 3

h(0) = 1 - 3 = -2
h(0) = -2

Thus, the required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

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Answer: C

Step-by-step explanation: If you solve each of them (1 x 4=4, 2x4=8, 3x4=12, 6x4=24), You can see that the are rational.

The operation statement is given as 3*(a + 5)

3 is the value of multiplication.

Inputs are the data that are entered into a program, whether manually by the programmer or digitally. These inputs are utilized to run the program and are saved as variables. A programmer may decide to incorporate outputs to keep the user updated on what is occurring inside the program.

I/O is the exchange of information between a computer or other information processing system and the outside world, which might include people or other information processing systems. The system's inputs are the signals or data it receives, and its outputs are the signals or data it sends.

Output is simply what occurs after all the code has been completed, the final outcome. It is what is entered into the console when all calculations have been completed. Basically, it's what is released.

The given Input is :

a x 3

The output it is giving is 3a + 15

One variable is a

The operation that is done is 'x' multiplication.

The operation statement is given as 3*(a + 5)

3 is the value of multiplication.

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Answer:

-2x^2+5y^3+

Step-by-step explanation:

The resulting image of the triangle ABC after the transformations is given by the image presented at the end of the answer.

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

First we have the reflection across the line x = 1, which is a vertical line, meaning that:

Hence the vertices after the reflection are given as follows:

A'(2,2), B'(-1,2), C'(0,7).

For example, a coordinate of 0 is one unit left of x = 1, hence the coordinate of the image will be one unit right, at x = 2.

The dilation with a scale factor of 2 centered at the origin means that the coordinates are multiplied by 2, hence:

A''(4,4), B''(-2,4), C''(0,14).

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

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Answer:

t = [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

t - [tex]\frac{4}{3}[/tex] = 1 ( multiply through by 3 to clear the fraction )

3t - 4 = 3 ( add 4 to both sides )

3t = 7 ( divide both sides by 3 )

t = [tex]\frac{7}{3}[/tex]

The number of children and adults that swan at the public pool that day would be = 208 and 209 respectively.

The number of people that swam on the summer day = 485 people.

The price paid for children = $1.25

The price paid for adults = $2.00

The total amount of money paid for the admission = $677.50.

The amount paid only for adults;

= 2/2+1.25 × 677.50/1

= 1355/3.25

= $416.92

The number of adults that swam ;

= 416.92/2

= 208.46

= 209 (approximately).

The amount paid for children;

= 1.25/3.25 × 677.50/1

= 846.875/3.25

= $260.58

The number paid for children alone;

= 260.58/1.25

=208.464

= 208 (approximately).

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Answer:

Area =312cm²

Step-by-step explanation:

since two rectangle are joined together you will find each area of the diagram and finally you add the two rectangle.

so the value for A1

A1 × Length × width.

A1 =16 ×17

A1 =272cm²

the value for A2

A2 Length × width

A2 = 14 × 3

A2 =42cm²

The area of the diagram

=A1 + A2

=272 + 42

=312cm².

The total area of the given figure is 468 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the given figure,

Larger rectangle has length=30 cm and width=14 cm.

Smaller rectangle has length=16 cm and width=3 cm.

We know that, the area of a rectangle is Length×Width

Area of Larger rectangle is

30×14 = 420 cm²

Area of Smaller rectangle is

16×3 = 48 cm²

Total area = 420+48 =468 cm²

Therefore, the total area is 468 cm².

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Answer:

-34 - 24i

Step-by-step explanation:

To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...

So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)

= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4

= -16 - 24i + 18i^2

= -16 - 24i -18

= -34 - 24i

Answer:

30%.

Step-by-step explanation:

Ayo earns 50,000 monthly and he spends 35,000 altogether, so he saves the rest of his income. To find the percentage of his savings, we can divide his savings by his total income and multiply by 100.

His total income is 50,000

His total expenditure is 35,000

His savings = total income - total expenditure = 50,000-35,000 = 15,000

So the percentage of his savings = (savings / total income) x 100 = (15,000 / 50,000) x 100 = 0.3 x 100 = 30%

Therefore, Ayo's savings percentage is 30%.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112

The equation is solved and the values of a and b is simplified as

a) The possible values of ab = 4

b) The possible values of a + b = 4

c) The possible values of a and b = 2

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

(a)

To find all possible values of ab, we can use the identity:

a⁴ + b⁴ = (a² + b²)² - 2a²b²

Substituting the given values, we have:

16 = (a² + b²)² - 2a²b²

We also know that a + b=4, which means that b = 4 - a.

Substituting this into the equation above, we have:

16 = (a² + (4-a)²)² - 2a²(4-a)²

Simplifying, we get:

16 = (2a² - 8a + 16)² - 32a² + 64a³ - 32a⁴

Expanding, we get:

16 = 4a⁴ - 64a³ + 288a² - 512a + 272

Rearranging and factoring, we get:

4a⁴ - 64a³ + 288a² - 512a + 256 = 0

Dividing by 4, we get:

a⁴ - 16a³ + 72a² - 128a + 64 = 0

This is a quartic equation, which can be factored as:

(a-2)⁴ = 0

Therefore, the only possible value of a is 2, which means that the only possible value of b is 2 as well.

So, ab = 2 x 2 = 4

(b)

We know that a + b = 4, and since a = 2, we have b = 4 - a = 2

Therefore, the only possible value of a + b is 4

(c)

From part (b), we know that the only possible value of a + b is 4. From part (a), we know that the only possible values of a and b are both equal to 2.

Therefore, the only possible solution is a = 2 and b = 2

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Answer:

you could fit 7776 people on the gym floor for an event.

Step-by-step explanation:

The Locust Grove gymnasium has an area of 54 yd x 40 yd = 2160 square yards. To find the number of people that can fit on the gym floor, we need to convert the area of the gym floor to square feet and divide it by the number of square feet each person takes up.

We know that 1 yard = 3 feet, so we have to convert the area of the gymnasium in square yards to square feet by multiplying it by (3*3) = 9.

So the area of the gymnasium in square feet is 2160*9 = 19440 square feet.

To find the number of people that can fit on the gym floor, we divide the area of the gym floor by the number of square feet each person takes up.

19440 square feet / 2.5 square feet/person = 7776 people

The length of the bottom diagram in the final tape diagram is 5.04 units.

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 calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The top diagram length is 60 units.

20 % of the 60 units is carried down, the length of the new section is:

20/100 * 60 = 12units.

60% of the next 12 units are carried down, the length of the new section is:

60/100 * 12 = 7.2 units

Similarly, when 70% of the section is carried down the length of the new section is:

70/100 * 7.2 = 5.04 units.

Hence the length of the bottom diagram is 5.04 units.

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The cyclist's average speed is

14.93

mph.

Total

distance

covered is=2+8=10

Total time =10+30=40

=40/60 min

=.0.67 hours.

Convert miles per min to miles per hour,

average speed= 10 miles/0.67 hours,

=14.93 mph.

The average speed is =4.93 mph

The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is

10 miles / 0.67 hours = 14.93 mph

The average speed is =14.93 mph

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Answer:

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

Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9

Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45

Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.

x-y = 9

x = y+9

Step 4: Now we can substitute the value of x in the second equation

4(y+9) + 0.5y = 45

4y + 36 + 0.5y = 45

4.5y + 36 = 45

4.5y = 9

y=2

Step 5: We can substitute the value of y in one of the equation, to find the value of x

x-2 = 9

x = 11

Final Answer: The two numbers are 11 and 2.

Answer:

--------------------------------

Consecutive exterior angles are supplementary.

It proves a and b are parallel.

Corresponding angles are congruent.

It proves a and b are parallel.

Given two vertical angles showing the relation between one line and the transversal and not a reason to state the lines are parallel.

Given two angles of same value. Since they are alternate interior angles, it proves the lines a and b are parallel.

Given two angles with the sum of 180. They are same side interior angles. It proves the lines a and b are parallel.

Given two angles of same value. They are alternate exterior angles but in relation to one of the lines and it proves the two transversals are parallel but not the lines a and b.

Answer:

Step-by-step explanation:

2 x 12 - (9 - 3) x 2 / 2

Answer:

  369,287 in the US

  3.69287×10⁵ in the UK

Step-by-step explanation:

Given the number (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1), you want it written in standard form.

The "standard form" of a number is different depending on your local culture.

In the US, the standard form of this number can be had by performing the indicated addition.

  (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1)

  = 80 +60,000 +300,000 +200 +9,000 +7

  = 300,000 +60,000 +9,000 +200 +80 +7 . . . . more useful order

  = 369,287

In the UK, "standard form" of a number refers to "scientific notation". The leading digit is shown to the left of the decimal point, and the multiplier is the power of 10 corresponding to that digit's place value.

  = 3.69287×10⁵

Using the details given, the area of the triangle in which the angles lies between the two sides is 90.3 units²

The area of a triangle can be calculated using the formula A = 1/2bh, where b is the base of the triangle and h is the height. Area of a triangle can be calculated using the formula: Area = (base x height) / 2, where base is the length of one side and height is the length of the side that forms the angle. In order to use this formula, you must know the length of two sides and the measure of the angle between them. However, this formula is subjective to details given

The area of a triangle can be calculated by

A = a×b×sinθ

a = 15

b = 8.1

θ = 132°

Substituting the values into the formula

A = 15 × 8.1 × sin 132

A = 90.3 units²

The area of the triangle is 90.3 units²

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Answer:

  see attached 0 ⇒ 0–6

Step-by-step explanation:

Given a table of ages and weights, you want the average rate of change (per month) for consecutive pairs of table values.

The average rate of change is the change in weight divided by the change in age. For example, in the interval 0–6 months, it is ...

  (17.4 -7.8)/(6 -0) = 9.6/6 = 1.6 . . . . . pounds per month

The calculations are conveniently done for the rest of the table by a spreadsheet. The results are attached. The value on each line is the average over the interval from that age to the next.

Answer: The function f(x) = || is the absolute value function of x, which is defined as f(x) = |x|. The graph of this function is a "V" shape, with the vertex at the origin (0,0) and the lines x = 0 and y = 0 as the asymptotes. The graph of f(x) starts at the origin and increases as x increases or decreases, but never reaches x-axis.

The function g(r) = (-1)|r| is the absolute value function of r, multiplied by -1. The effect of multiplying the function by -1 is to reflect the graph of f(x) across the x-axis. So the graph of g(r) will be a "V" shape, with the vertex at the origin, and the lines x = 0 and y = 0 as the asymptotes. The graph of g(r) starts at the origin and decreases as r increases or decreases, but never reaches x-axis.

In summary, the effect of the change on the graph of f(x) = || is that it will be reflected across the x-axis.

Step-by-step explanation:

The solution to the expression 5 2 (3x4) divided by 3-5 is -312

Fractions are simply described as part of a whole number or variable.

There are different types of fraction which includes;

PEMDAS is a mathematical acronym used to give the order of operations to be followed in solving expressions.

It stands for;

Given the expression;

52(3×4)/3 - 5

expand the parentheses

52(12)/-2

624/-2

Divide the values

-312

Hence, the values is -312

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3/2 does not have any factors because it is a fraction and factors are integers that can divide a number evenly. Only integers can have factors, fractions cannot.

Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.

A number is considered to be a factor if the division of that number by that number results in no residue. If we get a product when we multiply two whole numbers, then the numbers we are multiplying are factors of the product since they are divisible by the product. In other words, we get a product when we multiply two whole numbers. Multiplication and division are the two techniques that may be used to discover factors.

Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.

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Answer:

The interest earned is $92.40

The amount in the bank is 92.40 + 700 = $792.40

Step-by-step explanation:

I do not see a number line

Interest = principle x rate x time

Interest = 700 x .033 x 4

Interest = 92.40

Answer:

8:39 is the answer.

The rest, when simplified, change to 1:5.