67,107 rounded to the nearest ten-thousand

Step-by-step explanation:

it is really simple :

every x is increased by 2, every y is decreased by 4.

C = (-4, 2) -> C' = (-2, -2)

R = (-5, -1) -> R' = (-3, -5)

T = (-1, 1) -> T' = (1, -3)

Answer:

9/8 m = 21/8

or

9m/8 = 21/8

Step-by-step explanation:

3m = 7

3/8 × 3m = 3/8 × 7

9/8 m = 21/8

29 elements are there in total for sets A, B, and C

Since  we are provided the  values of pair-wise intersections which are: |A∩B|=|A∩C|=|B∩C|= 7 and  the  three sets have common is |A∩B∩C| = 2 and individual sets  were having |A|=19 ,|B|=|15 and |C|=14. The formula we are referring to for calculating the  total  elememets altogether is A∪B∪C|=|A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C|, where |A|,|B|,|C|quantity for individual sets,|A∩B|,|A∩C|,|B∩C| are the intersection subsets in a pairwise, and|A∩B∩C| is the intersection subset for the three sets altogether.

So substituting the  know values in the  above format, we get  

=> |A∪B∪C|= 19+15+14-7-7-7+2

=>|A∪B∪C|=29

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The most likely problem with the sample they gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".

Thus, the most likely problem with the sample lycos web site gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".

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[tex]\huge\mathcal{♨Answer♥}[/tex]

Answer is on the attachment...

☆...hope this helps...☆

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The equation p=5xy+q can be expressed in terms of p,q, and x as y = (p-q)/5x.

The equation p=7x+4q can be expressed in terms of p and q as x = (p-4q)/7x.

Given in the first equation, p = 5xy+q

p-q=5xy

y=(p-q)/5x

Here we need to express y in terms of p,q, and x so we need all these three variables on one side of the equation and y on the other side. Initially we more q to the left-hand side of the equation which makes it p-q=5xy. Now we divide the left-hand side and the right-hand side by 5x making the equation y = (p-q)/5x.

Similarly in the second equation, p = 7x+4q

p-4q = 7x

x = (p-4q)/7

Here we need to express x in terms of p and q so we need all these two variables on one side of the equation and the term x on the other side. First, we will move 4q to the left-hand side of the equation which will make it p-4q=7x. Now, we will divide the whole equation by 7 which will make the equation x = (p-4q) / 7.

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Answer:

C. Function, there is a unique x-value for each y-value

A) The value of the measure of angle x is; x = 55 degrees.

B) The way we got x is that the Internal angle between 2 parallel lines are equal and also that the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.

A) From the given image attached, we see that the angle RPB can be calculated as;

m∠RPB = 180 - 120 = 60 degrees.

This is because sum of angles on a straight line sums up to 180 degrees.

Now, by definition of alternate angles, we can say that angle BPR is equal to 60 degrees.

Thus, the value of angle x is;

x =  180 - 60 - 65

x = 55 degrees.

B) From the given diagram, we can say that;

m ∠RPB + m < PRD = 180 degrees

This is because Internal angle between 2 parallel lines are equal.

Secondly the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.

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Answer:

[tex]\boxed{\sf Slope( m)=-\cfrac{3}{4}}[/tex]

Step-by-step explanation:

To find the slope between two points we'll use the Slope formula:-

[tex]\boxed{\sf \mathrm{Slope(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]

______________

Given:-

Where,

[tex]\mathrm{\left(x_1,\:y_1\right)=\left(3,\:-4\right)}[/tex]

[tex]\mathrm{\left(x_2,\:y_2\right)=\left(-5,\:2\right)}[/tex]

[tex]\mathrm{m=\cfrac{2-\left(-4\right)}{-5-3}}[/tex]  ← Subtract

[tex]\sf m=-\cfrac{6}{8}[/tex]

[tex]\sf m=-\cfrac{3}{4}[/tex]

Therefore, the slope of the line is m = - 3/4.

______________________

Hope this helps!

Have a great day!

The difference between the distance between the two cities if of 14.842 latitudes.

The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.

Therefore, the earth has 181 latitudes.

Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.

Hence the distance covered by all 181 latitudes = 2 X radius of the Earth

= 2 X 6378 km

= 12756

Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be

12756/181

= 70.475 km

Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.

Therefore the difference in latitudes between the two cities is

1046/70.475

= 14.842 latitudes

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If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .

In the question ,

it is given that

the base area of the rectangular container is = 200 cm²

the total height of the container = 20 cm

the height at which the water if filled = 15 cm

the height of water that is needed to be filled = 20 - 15 = 5cm

So , the volume of water to be added is = base area × height

= 200 × 5

= 1000 cm³

= 1 Liter            .... because 1000cm³ = 1 Liter

Therefore , If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .

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The solution for u in the expression given as 7/u = 3/11 is u = 25.7

From the question, the algebraic expression is given as

7/u = 3/11

There is no constant to add to or subtract from the expression

So, the equation remains the same

7/u = 3/11

Multiply both sides of the equation by u

This gives

u * 7/u = 3/11  * u

Evaluate the products

So, we have the following equation

7 = 3/11u

Multiply both sides of the equation by 11/3

This gives

11/3 * 7 = 3/11u * 11/3

Evaluate the products in the above expression

77/3 = u

So, we have

25.6667 = u

Approximate

25.7 = u

Rewrite as

u = 25.7

Hence, the solution is u = 25.7

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Answer: [tex]f(a^2)=2a^2-4[/tex]

Step-by-step explanation:

Substituting [tex]a^2[/tex] for [tex]x[/tex], [tex]f(a^2)=2a^2-4[/tex].

The value of the expression 22 - (8 x 1) divided by (6 - 4) - 2 is 0.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

The expression given is:

22 - (8 x 1) divided by (6 - 4) - 2

= 22 - (8 x 1) ÷ (6 - 4) - 2

= [22 - 8] ÷ [2 - 2]

= 14 ÷ 0

= 0

The value is 0.

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Converse: If I get sick, I ate too much candy.

Inverse: If I don't eat too much candy, then I will not get sick

Contrapositive: If I do not get sick, I did not eat too much candy.

What is the conditional statement?

'If p, then q's statements are examples of conditional statements. In this case, "p" stands for "hypothesis" and "q" for "conclusion."

A converse statement is one that is produced by flipping a conditional statement's hypothesis and conclusion.

So, Converse: If I get sick, I ate too much candy.

An inverse assertion presupposes that each of the original claims is true.

So, Inverse: If I don't eat too much candy, then I will not get sick.

When you reverse the hypothesis and the conclusion in a statement, you have a contrapositive statement that refutes both propositions.

So, Contrapositive: If I do not get sick, I did not eat too much candy.

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The expression for the sum is (12 + n).

We are given two terms to add. The first number is 12, which is an integer. The second number is unknown. An integer is a number that has no decimal or fractional portion and can be negative or positive, including zero.

The second number is represented by a variable "n". A variable is a mathematical object's symbol and placeholder. A variable can, for example, represent an integer, a vector, or other data.

We need to write the expression for the sum of these two numbers. Let S represent the sum of these two numbers.

S = 12 + n

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What happens when the slope of a line is undefined is that, the line is a vertical line that crosses the x-axis.

The points could be (1, 5) and (1, 10)

It is known that linear equations have slopes

These slopes are the average rate of change of the function

The values of these slopes can be

When the slope is undefined, it means that the line is a vertical line

An example of the vertices on such line is (x, y) and (x, y + n)

See that the x coordinate remains constant, while the y coordinate changed

Take for instance, a line that passes through (1, 5) and (1, 10) would have an undefined slope

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The probability of getting an odd number when you roll a 6 sided die​ is 1/2

How does probability explain work?

Simple terms, probability is the probability that an event will occur. When we do not even understand how an event will come out, we can analyze the probability or likelihood from several outcomes. Statistical is the analysis of events which match a posterior distribution.

What is the likelihood that the result of a roll of a standard six-sided die will be an odd number?



A cube with six faces makes up a standard six-sided die. They have the following numbers: 1, 2, 3, 4, 5, and 6. Any integer that is not divisible by two is an odd number. The odd numbers in this situation are 1, 3, and 5. The number of successful outcomes divided by the total number of possible outcomes can be represented as a fraction to represent the likelihood that any event will occur.

There are three correct answers to this puzzle, or the three odd integers. Additionally, there are six potential outcomes, ranging from one to six. When using standard six-sided die, there is a three-sixths, or three from out six, chance that the outcome will be an odd number.

Three can be divided by both three and six. As a result, this fraction can be expressed as one-half. One is equal to three divided by three. Additionally, two is equal to six times three. One-half or one in two chances exist that the result is strange.


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Answer:

1. 130/6

2. 240/3

Step-by-step explanation:

make the whole numbers into a fraction by putting 1 as the denominator.

48/1.

then multiply together.

48 x 5 = 130

6 x 1 = 6

130/6

do the same with the other

120 x 2 = 240

1 x 3 = 3

240/3

Answer:

40

80

Step-by-step explanation:

5/6 × 48

5 × 48 = 240

240/6

= 40

120 × 2/3

120 × 2 = 240

240/3

= 80

Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.

Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:

X ~ N (12, 3²)

Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:

P (X ≤ K) = 0.15

When we transform this into a typical normal variable, we get:

P [Z ≤ (K - 12) / 3] = 0.15

From the common normal tables, we can deduce:

P (Z ≤ -1.036) = 0.15

Comparing the two equations above, we obtain:

(K - 12) / 3 = -1.036

K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892

As a result, 8.892 ounces of gold are needed.

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The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.

An equation with a function and one or more of its derivatives is referred to as a differential equation:

At the start, the tank contains A(0) = 30 g of salt.

Salt flows in at a rate of

(1 g/L) * (4 L/min) = 4 g/min

and flows out at a rate of

(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min

so that the amount of salt in the tank at time t changes according to

A'(t) = 4 - A(t)/50

So,

[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]

The solution of linear differential equation y' + ay = g(x) is in the form,

[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]

Now, putting the values,

[tex]a=\frac{1}{50} \\g(x)=4[/tex]

[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]

Now,

[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]

Putting the initial value,

[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]

So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

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The cost of an adult ticket is £17 and a child ticket is £9.

Let's assume 'a'  for an adult ticket and 'c' for a child ticket

The cost of tickets for the Smith family of 2 adults and 3 children is £61

Equating, [tex]2a+3c=61[/tex]

[tex]2a=61-3c[/tex]

Dividing by 2, [tex]a=30.5-1.5c[/tex]        (equation 1)

Now, the cost of tickets for the Jones family of three adults and five children is £96

Equating, [tex]3a+5c=96[/tex]                 (equation 2)

Using equation 1, [tex]3(30.5-1.5c)+5c=96[/tex]

[tex]91.5-4.5c+5c=96[/tex]

[tex]91.5+0.5c=96[/tex]

[tex]0.5c=96-91.5[/tex]

[tex]0.5c=4.5[/tex]

[tex]c = \frac{4.5}{0.5}[/tex]

[tex]c=9[/tex]

Similarly, putting the answer of equation 2 in equation 1

we get, [tex]a=30.5-1.5c[/tex]

[tex]a=30.5-1.5(9)[/tex]

[tex]a=17[/tex]

Therefore, adult tickets cost £17 and child tickets cost £9

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Functions to build an area function of the triangle , A = b2 + 2b.

According to our question-

Let b = the base

altitude = 2b + 4

A = b(2b+ 4)/2

A = b(b + 2)

A = b2 + 2b

Hence, Functions to build an area function of the triangle , A = b2 + 2b.

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For 200mg of Cesium-137, it will be 229 years which is less than 230 years until only 1 milligram remains.

The amount of time a radioactive item takes to decay is known as the material's half-life.

The first-order kinetics for a half-life is given as 0.693 / k.

Given half-life = 30 years,

k = rate-constant =?

30 = 0.693 / k

k = 0.0231 years ⁻¹

The integrated rate law for first-order kinetics is given as follows:

A = A₀[tex]e^{-kt}[/tex]

k = rate constant of the reaction

A₀ = Concentration of reactant initially = 200 mg

A = t = 1 mg

Putting all values in the equation will give,

t = 229 years.

Thus, Cesium takes 229 years to decay to reach from 200milligram to 1 milligram in weight.

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Jade and Jordan both have a total of 35 trading cards altogether.

Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.

As, Jade has 28 trading cards

Let Jordan has 'x' trading cards.

Now, as Jade has 4 times as many trading cards as Jordan.

So, 28 = 4x

4x = 28

x = 7

So, Jordan has 7 trading cards.

Now, they both have a total of 35 trading cards altogether.

Hence, Jade and Jordan both have a total of 35 trading cards altogether.

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Regarding the situation described, it is found that:

The total amount invested is of $25.

1. You start making a profit when 15x - 25 > 0.

2. You earned $215 with this work.

With the investment, you made money (option b).

The investment was as follows:

Hence the total amount invested was of:

10 + 15 = $25.

The profit is given by revenue subtracted by costs.

In the context of this problem, the revenue and the cost functions are given as follows:

Hence the profit function is:

P(x) = R(x) - C(x)

P(x) = 15x - 25.

You start making a profit when:

P(x) > 0.

15x - 25 > 0.

The amount you earned mowing 16 lawns is of:

P(16) = 15(16) - 25 = $215.

(positive profit, hence you made money).

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The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.

Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

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Caina anticipate in income next year  $14000.

What is an income?

The amount of money, property, and other value transfers received over a predetermined period of time in return for goods or services is often referred to as income.

We have,

A scholarship of $6000 and a grant of $3200 together are $9200

6000 + 3200 = 9200.

She will make another $400 per month working a part-time job, so for 12 months she will make $400 × 12 = $4800.

All together will be $9200 + $4800 = $14000.

Therefore, She anticipate in income next year  $14000.

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Step-by-step explanation:

imagine a circle with the center at the vertex of the angle x, and the radius 72 ft.

cos(x) = 28/72 = 7/18 = 0.388888888...

x = 67.11461952...° ≈ 67.1°

A linear function that describes the cost of a trip, c, in terms of the number of miles, n will be "c=0.60n+0.67n" and cost per mile is $0.6 and $0.67 and the flat fee is $50.

Once you are aware of your mileage and total expenses, calculating cost per mile becomes a straightforward equation. Your cost per mile is calculated by dividing your total expenses by the total number of miles you have driven. Your expenses per mile are influenced by your variable and fixed costs, so you should probably pay closer attention to how much you're shelling out for each mile your drivers cover. You can better understand your primary costs and produce more accurate bids for new contracts by knowing your expenses at this specific level.

Here,

cost per mile,

20/30=$0.67/mile

30/50=$0.60/mile

c=0.60n+0.67n

flat fee,

=$30+$20

=$50

The cost per mile is $0.6 and $0.67, and the flat rate is $50. A linear function that expresses the cost of a trip, c, in terms of the number of miles, n, will be "c=0.60n+0.67n".

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