Brian asked a group of people their favourite holiday destination.
The results are summarised in the table.

Destination UK Europe USA Africa Other
Frequency 204 84 36 204 12


How many degrees does one person represent?
Give your answer as a fraction in its simplest form.

The slope of the line representing that relationship in the coordinate plane is -5.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

A container of fuel dispenses fuel at the rate of 5 gallons per second.

If y represents the amount of fuel remaining in the container, and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship.

The linear equation is,

y = -5x.

And the slope is -5.

Therefore, the slope is -5.

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Population model: Y = β0 + β1X + ε, where Y is the SAT score, X is the number of hours spent in the preparation course, β0 is the intercept, β1 is the causal effect (the effect of hours on SAT), and ε is the error term.

To estimate the causal effect of hours of preparation on the SAT score, we would structure a controlled experiment as follows:

Population model: Y = β0 + β1X + ε, where Y is the SAT score, X is the number of hours spent in the preparation course, β0 is the intercept, β1 is the causal effect (the effect of hours on SAT), and ε is the error term. This model assumes that the causal relationship between hours and SAT score is linear and that the effect of hours on SAT score is constant for all students in the population.

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Answer:

hi !!!

Step-by-step explanation:

Vcylinder = pi*radius*radius*height= pi*25*9= 706.5 cubic milimeters = 7.065 cubic centimenter

The given expression can be written as in the simplified form, 5/3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

[tex]1 + \frac{1}{1+ \frac{1}{1+1} }[/tex]

It can be solved by various steps,

First step,

1/(1+1) can be written as 1/2

[tex]1 + \frac{1}{1+ \frac{1}{2} }[/tex]

Second step,

1 + 1/2 can be written as 3/2

[tex]1 + \frac{1}{\frac{3}{2} }[/tex]

Now, 1/(3/2) can be written as 2/3

[tex]1 + \frac{2}{3}[/tex]

Further, it can be written as,

5/3

Hence, the simplified form is 5/3

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In the right triangle ABC the value of x will be 24.7 and this can be determined by using the trigonometric function.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

Given :

The right-angle triangle ABC.

AB = x

BC = 9

now,

The Trigonometric function can be used to determine the value of 'x'. The tangent function is an important trigonometric function that can be used to determine the value of 'x'.

The tangent function is given by the equation:

tanФ = P/B

where P is the perpendicular and B is the base of the given triangle.

Now, substitute the values of P, Ф, and B in the above equation.

tan 20 = 9/x

solving we get,

x = 24.72

(to the nearest tenth)

So, by using the trigonometric ratio the value of x is 24.7.

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The price of a round-trip ticket to Las Vegas on Southwest this week is 175 after applying a 12.5% discount.

The formula used to calculate the price of a round-trip airline ticket to Las Vegas on Southwest this week is Price = Original Price - Percentage Discount x Original Price. The original price of the ticket is $200 and it is 12.5% off this week. Therefore, the calculation of the price of the ticket this week is Price = 200 - 0.125 x 200 = 175. This means that the price of the round-trip ticket to Las Vegas this week is 175.

The 12.5% discount is calculated by taking the percentage discount and multiplying it by the original price. This result is then subtracted from the original price to get the discounted price. For example, if the original price of the ticket is 200 and the discount is 12.5%, then the calculation is 200 - 0.125 x 200 = 175. Therefore, the discounted price of the ticket this week is 175.

In conclusion, the price of a round-trip ticket to Las Vegas on Southwest this week is 175 after applying a 12.5% discount. The discount is calculated by taking the percentage discount and multiplying it by the original price, and then subtracting that result from the original price.

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When one alternative stochastically dominates another, it means that the first alternative has a higher probability of leading to a better outcome than the second alternative, regardless of the decision maker's attitude towards risk.

In other words, one alternative stochastically dominates another when, for any level of payoff that the decision maker might find acceptable, the first alternative has a higher probability of achieving that level of payoff than the second alternative.

This concept is often used in decision-making under uncertainty, such as in the field of economics. It can help decision makers to compare different alternatives and choose the one that is more likely to lead to a desirable outcome. Stochastic dominance is a concept that is commonly used in decision theory and is based on the idea of probability. It refers to the relationship between two alternatives with respect to their probability distributions.

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- 4.2 explain in your own words what it means when one alternative stochastically dominates another?

Answer:

The number 9.3488 rounded to the nearest tenth is; 9.3

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

The percentage of the students who did not go on the trip will be 40%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a school has 120 students. On Friday, 72 students went on a field trip.

The number of the students who did not go to the trip are:-

N = 120 - 72 = 48

The percentage will be calculated as:-

Percentage  = 48 / 120

Percentage = 0.4 x 100

Percentage = 40%

Therefore, the total of 40% of the students will not have attended the trip.

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The probability of your friend getting a lemon-lime-flavored drink and you getting an orange-flavored drink is 5/18.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The first bottle you grabbed had a 5/10 chance of being lemon-lime and a 5/10 chance of being orange.

After you gave your friend a lemon-lime, there were 4 lemon-lime drinks and 5 orange drinks left in the cooler. So, the probability of you grabbing an orange drink was 5/9.

Multiplying these probabilities gives the final answer of (5/10) × (5/9) = 25/90 = 5/18.

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The question seems incomplete, the complete question would be as:

A cooler contains ten bottles of sports drinks: five lemon-lime flavored and five orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. Your friend gets a lemon-lime and you get an orange.

What is the probability of this happening?

David paid a total amount of 19.05 in dollars.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Cost of the food = $15

Sales tax = 7%

Cost of food with sales tax = 15 + (7% × 15) = $16.05

He tipped the waiter 20% of the cost of the food.

Total cost = $16.05 + (20% × 15) = $16.05 + 3 = $19.05

Hence the total amount is $19.05.

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After performing dimensional analysis we get there are 89 decigrams in 8.9 grams

Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed.

Given that, we need to change the unit of 8.9 grams into decigram.

We know that,

1 g = 10 dg

Dimensional Analysis Formula

1 g × 10 dg / 1 g = 10 dg

Therefore,

8.9 g × 10 dg / 8.9 g

= 8.9 × 10 dg

= 89 dg

Hence, After performing dimensional analysis we get there are 89 decigrams in 8.9 grams

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Answer: i believe its D

Step-by-step explanation:

The first one is a reflection - witch is the answer so D

The dependent variable in this research question is the birth rate in Phoenix, AZ.

This can be represented mathematically as B, where B represents the birth rate in Phoenix, AZ. We can calculate the birth rate by taking the total number of live births in Phoenix, AZ (L) and dividing it by the total population in Phoenix, AZ (P), and then multiplying by 1,000. B = (L/P) * 1000.

For example, if there were 10,000 live births in Phoenix, AZ in a given year, and the population of Phoenix, AZ in that same year was 2,500,000, then the birth rate in Phoenix, AZ would be dependent variable as follows: B = (10,000/2,500,000) * 1000 = 4. This would mean that the birth rate in Phoenix, AZ is 4 births per 1,000 individuals.

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Complete question:If the researcher's question is "What are the reasons for an increase in the birth rate in Phoenix, AZ?", then the dependent variable is the birth rate in Phoenix, AZ.

Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.

Here,

Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.

Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.

The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.

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Because of gravity, the item accelerates continuously. The ball took 2 seconds to reach the ground, hence option (d) is accurate.

The metric system and the International Systems in Units both use the metre (m), also spelt as meter, as the basic unit of length (SI). Inside the British Imperial & American Customary systems, it is equivalent to around 39.37 inches.

Metric is the preferred word outside of North America for the measuring unit that is equivalent to about 1.094 yards, with American spelling being meter. Metric in American English and Metric everywhere else are terminology used in music and poetry respectively.

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any cylindrical shape that has the r²h equal to 160 will have an equal volume.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Right circular cylinder A has a volume of $160pi cubic feet.

The product of a cylinder's base area and height provides the formula for calculating the cylinder's volume. A cylinder's volume is equal to πr²h cubic units.

Where r is the radius

and h is the height

In our case volume = 160 * pi

By comparing,

r²h = 160

So we can state that any cylindrical shape that has the r²h equal to 160 will have an equal volume.

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If you roll a fair six-sided die, you will receive the indicated number of points. After one roll, 3.5 points should be expected.

A six-sided cube with the digits 1-6 printed on the faces is the most popular type of die. The value of the roll is indicated by the number of "spots" that are visible at the top. The opposite faces on the six-sided die are positioned so that they always add up to seven. The word "die" is derived from Old French and Latin datum, which means "anything provided or played." The names of the numbers are preferable, but some seasoned gamblers still refer to the different sides of the dice by using the terms ace, deuce, trey, cater, cinque, and dice.

Add up all of the die's pips., [tex]1+2+3+4+5+6=21[/tex].

The likelihood of a specific face being up on any roll of a single die is [tex]1/6[/tex].

After one roll, the anticipated number of points is [tex]21/6= 3.5[/tex]

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The solution of the system of equation are y=4/9x-5 and 1/9x-2y=-4 is x=18 and y=3.

Two or more expressions with an Equal sign is called as Equation.

The system of equation are:

y=4/9x-5..(1)

1/9x-2y=-4..(2)

Substitute 1 in equation 2

1/9x-2(4/9x-5)=-4

1/9x-8/9 x+10=-4

x/9(1-8)+10=-4

x/9(-7)+10=-4

Substitute 10 on both sides

-7x/9=-4-10

-7x/9=-14

-7x=-126

Divide both sides by 7

x=126/7

x=18

Now plug in x value in equation 1

y=4/9(18)-5

y=8-5

y=3

Hence, the solution of the system of equation are y=4/9x-5 and 1/9x-2y=-4 is x=18 and y=3.

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The value of h in the equation five eighths plus h equals eleven over eight is six eighths

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

Given the equation five eighths plus h equals eleven over eight, it is represented as:

(5/8) + h = 11/8

multiply the both sides of the equation by 8:

(5/8) * 8 + h * 8 = (11/8) * 8

5 + 8h = 11

subtract 5 from both sides:

5 + 8h - 5 = 11 - 5

8h = 6

divide both sides by 8:

8h/8 = 6/8

h = 6/8

The value of h is 6/8

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Answer:

Step-by-step explanation:

y=10

The nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors that lie in the plane.

Let's find the vectors PQ and PR, which can be found by subtracting the coordinates of P from the coordinates of Q and R:

PQ = Q - P = (-2, 1, 3) - (1, 0, 1) = (-3, 1, 2)

PR = R - P = (4, 2, 5) - (1, 0, 1) = (3, 2, 4)

Next, we'll take the cross product of these two vectors to find a vector orthogonal to the plane:

n = PQ x PR =

[(1)(4) - (2)(2), (2)(-3) - (3)(1), (3)(3) - (2)(-2)]

= [-8, -8, -12]

This vector is orthogonal to the plane through the points P, Q, and R. To make it a nonzero vector, we can scale it to have magnitude 1:

n = [-8, -8, -12] / sqrt((-8)^2 + (-8)^2 + (-12)^2) = [-8/13, -8/13, -12/13]

So, the nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

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The equation of the line through the points (-1, -2) and (4, 3) is y = x + 3.

The equation of a line can be found using the point-slope form, where the slope of the line is determined from the two given points and the equation is written in the form y = mx + b, where m is the slope and b is the y-intercept.

Given the points (-1, -2) and (4, 3), the slope of the line can be calculated as (3-(-2))/(4-(-1)) = 5/5 = 1.

Plugging in the coordinates of one of the points and the slope into the point-slope form, we have:

y - -2 = 1(x - -1)

Simplifying, we get:

y = x + 3 is the required equation of the line.

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The expression for F in terms of d is F = 108 / d².

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s.

Inversely proportional means, when one quantity increases, other decreases.

Given that,

The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the distance, d cm, between the magnets.

F ∝ 1 / d²

This can be written as, for some constant k,

F = k (1 / d²)

When d = 1.5, F = 48.

48 = k (1 / (1.5)²)

48 = k / 2.25

k = 48 × 2.25

k = 108

So the expression relating F and d can be written as,

F = 108 / d²

Hence the required expression is F = 108 / d².

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The true statement on probability is C. The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 23 over 50.

The theoretical probability of an occurrence indicates its propensity to occur. The theoretical probability of receiving heads is 1/2 since we know that flipping a coin has an equal chance of landing heads or tails. The frequency of an event actually occurring in an experiment is referred to as its experimental probability.

The theorectical probability of swimming is 1 / 2 because it is either heads or tails. However, the experimental probability of swimming is:

= Number of swimmers / Total number of students

= 23 / 50

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The proportional equation that represents the salary of each person after the raise is given as follows:

y = 1.12x.

The raise to the salary of each staff member is given as follows:

12%.

Hence the percentage of the salary after the raise is given as follows:

100 + 12 = 112%.

Meaning that the multiplier is of:

1.12.

Then the equation is given as follows:

y = 1.12x.

In which:

The problem asks for the proportional equation that represents the salary of each person after the raise.

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When digitizing a recording of a musical performance, two strategies that will result in a more accurate digital representation of the original music are:

Increasing the sampling rate of the music being digitized: The sampling rate is the number of samples of the analog audio waveform taken per second. The higher the sampling rate, the higher the frequency range that can be captured, resulting in a more accurate representation of the original sound.

Increasing the bit depth of the music being digitized: The bit depth is the number of bits used to represent each sample of the audio waveform. The higher the bit depth, the greater the number of possible levels of amplitude that can be captured, leading to a more accurate representation of the original analog waveform and a clearer, more dynamic digital audio file.

Increasing the volume of the music being digitized and increasing the speed of the music that is being digitized do not necessarily result in a more accurate digital representation of the original music.

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Amounts that have with Lisa, Aldo, and Miguel in their wallets are $35, $25, and $100 respectively.

Lisa, Aldo, and Miguel have a total of $160 in their wallets.

Miguel has 4 times what Aldo has.

Lisa has $10 more than Aldo.

Let the amount that the Aldo has to be $x

Then according to the given question.

The amount that the Lisa has $(x+10)

The amount that the Miguel has $(4x)

So the total amount can be resulted as the sum of the amounts of the three each individual.

x + x + 10 + 4x = 160

6x + 10 = 160

6x = 160 - 10

6x = 150

x = 25

Therefore the amount in the Aldo wallet is $25

Hence, the amount in the Lisa's wallet is:

x + 10 = 25 + 10 = $35

Hence, the amount in the Miguel's wallet is:

4x = 4(25) = $100

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Lisa, Aldo, and Miguel have a total of $160 in their wallets. Miguel has 4 times what Aldo has. Lisa has $10 more than Aldo. how much does each have?

Answer:

the largest possible value for x is 6

the smallest possible value for x is 1

Step-by-step explanation: