8. The graph shows the relationship between the United States dollar and
the euro, the currency of the European Union, in December 2011. Part A:
What is the constant of proportionality shown in the graph?*
Exchange Rate (December 6, 2011)
YA
(400, 300)
300
Number of euros
200
(250, 187.50)
100
(120, 90)
0
100 200 300 400
Number of US dollars
Your answer

The claim states that if 1 is a rational number and x is an integer, then the result of squaring x is also an integer. This implies that if a natural number does not have an integer square root, its square root must be irrational.

Let's assume that 1 is a rational number, which means it can be expressed as the ratio of two integers, p and q, where q is not equal to zero. So, we have 1 = p/q. Now, let's consider squaring an integer x, resulting in x^2. Since x is an integer, it can be expressed as a fraction with a denominator of 1. Therefore, x = r/1, where r is an integer. Now, if we square x, we get (x^2) = (r/1)^2 = (r^2)/1 = r^2, which is also an integer.

This claim shows that if 1 is a rational number and x is an integer, then the square of x is an integer as well. Consequently, if a natural number does not have an integer square root, its square root must be irrational because rational numbers squared will always yield rational results. For example, if we take the square root of 6 (√6), which is irrational, and square it, we get (√6)^2 = 6, which is rational. Thus, the claim provides a proof for the fact that natural numbers without an integer square root must have an irrational square root.

Learn more about rational number here:

https://brainly.com/question/17450097

#SPJ11

Answer:

A. 7

b. 14

c. 16

Step-by-step explanation:

A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

Read more on z-values here: brainly.com/question/4302527

#SPJ4

Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

The probability should be set so that the game is as evenly matched as feasible in order to maximize the anticipated number of games played. Setting p = q = 1/2 will allow you to attain this goal by increasing the anticipated number of games played.

Let's write down the likelihood that team 1 will win a game as p and the likelihood that team 2 will win a game as q. Since one of the sides must prevail in each match, p + q = 1.

(A) A geometric distribution can be used to determine the anticipated number of games that will be played if the series finishes when one of the sides has won two games. Up until one of the sides wins two games, let X be the total number of games played.

For more such questions on Probability

https://brainly.com/question/13604758

#SPJ4

A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

To know more about research,

https://brainly.com/question/24250717

#SPJ4

The stream function, denoted by ψ, can be determined from the velocity potential, denoted by ф, by taking the partial derivatives with respect to the coordinates. In this case, the velocity potential is given as ф = \(3xy^2 - x^3\). To find the stream function, we will calculate the partial derivatives and rearrange the equations.

The stream function, denoted by ψ, is related to the velocity potential through the following equations:

ψ_x = -ф_y   and   ψ_y = ф_x

Taking the partial derivative of ф with respect to y, we have:

ф_y = \(3x(2y) - 0 = 6xy\)

Equating this to -ψ_x, we get:

-ψ_x = \(6xy\)

Integrating this equation with respect to x yields:

ψ = \(-3xy^2 + g(y)\)

Here, g(y) represents an arbitrary function of y that arises due to the integration process.

Similarly, taking the partial derivative of ф with respect to x, we have:

ф_x = \(3y^2 - 3x^2\)

Equating this to ψ_y, we get:

ψ_y = \(3y^2 - 3x^2\)

Integrating this equation with respect to y yields:

ψ = \(y^3 - 3xy^2 + f(x)\)

Here, f(x) represents an arbitrary function of x.

Combining the two expressions for ψ, we have:

ψ = \(-3xy^2 + g(y) = y^3 - 3xy^2 + f(x)\)

Since g(y) and f(x) are arbitrary functions, we can set them to zero.

Therefore, the stream function for the given flow field is:

ψ = \(y^3 - 3xy^2\)

Learn more about Integrating here:

https://brainly.com/question/31744185

#SPJ11

The number of individuals in Chicago that will respond positively to Program 2 is 22 out of 25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Given that the chances of a positive response from Chicago residents to two government programs are 65.9% for Program 1 and 87.5%  for Program 2, the likelihood of a positive response for Program 2 given that the person is from Los Angeles must be calculated as follows:

87.5 100 = X

43.75 / 50 = X

21.875 / 25 = X

Therefore, 22 out of 25 individuals in Chicago  will respond positively to Program 2.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

Answer:

4

Step-by-step explanation:

1) 16-(-6)= -10

2) Absolute value of -10 is 10

3) 10(2/5)=4

4) Point Q=4

This means that \(n^2\) is an even number, which implies that n is also even. However, this contradicts our assumption that p and q have no common factors. Therefore, our initial assumption that \(sqrt(2)\) is rational

To prove that \(sqrt(2)\) is irrational using strong induction, we first need to establish two base cases:

Base case 1: n = 1

We need to show that sqrt(2) is irrational when n = 1. This is a well-known result and can be proven using a proof by contradiction. Assume that sqrt(2) is rational, then it can be expressed as a fraction p/q, where p and q are positive integers with no common factors. Squaring both sides of the equation, we get:

\(2 = p^2/q^2\)

Multiplying both sides by \(q^2\), we get:

\(2q^2 = p^2\)

This means that \(p^2\) is an even number, which implies that p is also even. Let p = 2k, where k is a positive integer. Substituting in the equation above, we get:

\(2q^2 = (2k)^2 = 4k^2\)

Dividing both sides by 2, we get:

\(q^2 = 2k^2\)

This means that q^2 is an even number, which implies that q is also even. However, this contradicts our assumption that p and q have no common factors. Therefore, our initial assumption that sqrt(2) is rational must be false, and sqrt(2) is irrational when n = 1.

Base case 2: n = 2

We need to show that sqrt(2) is irrational when n = 2. This is already established in the first base case, since n = 2 is a specific case of n = 1.

Now, we assume that sqrt(2) is irrational for all positive integers up to some positive integer k, and we want to show that it is also irrational when n = k + 1.

Assume that sqrt(2) is rational when n = k + 1, so it can be expressed as a fraction p/q, where p and q are positive integers with no common factors. We can write this equation as:

\(sqrt(2) = p/q\)

Squaring both sides of the equation, we get:

\(2 = p^2/q^2\)

Multiplying both sides by q^2, we get:

\(2q^2 = p^2\)

This means that p^2 is an even number, which implies that p is also even. Let p = 2m, where m is a positive integer. Substituting in the equation above, we get:

\(2q^2 = (2m)^2 = 4m^2\)

Dividing both sides by 2, we get:

q^2 = 2m^2

This means that q^2 is an even number, which implies that q is also even. We can write q = 2n, where n is a positive integer. Substituting in the equation above, we get:

(2n)^2 = 2m^2

Simplifying the equation, we get:

2n^2 = m^2

This means that m^2 is an even number, which implies that m is also even. Let m = 2p, where p is a positive integer. Substituting in the equation above, we get:

Dividing both sides by 2, we get:

\(n^2 = 2p^2\)\(2n^2 = (2p)^2 = 4p^2\)

To know more about  irrational   here

https://brainly.com/question/11663368

#SPJ4

Gloria walked  500500 Miles from nearest bus stop to home.

How to convert yards into miles ?

To convert a yard measurement to a mile measurement, divide the length by the conversion ratio.

Since one mile is equal to 1,760 yards, you can use this simple formula to convert:

miles = yards ÷ 1,760

The length in miles is equal to the yards divided by 1,760.

Given:

Gloria traveled : 888 miles

1 Mile = 1760 yards

880880880 yards = 500500 Miles

So she walked  500500 Miles from nearest bus stop to home.

Learn more about Unit conversion at:

https://brainly.com/question/97386

#SPJ1

Caroline saved $3. 84 on a discounted item that was marked down 15% off of the original price of the item. What was the original price of the item before the discount, the original price of the item was $4.52 before the discount.

Let the original price of the item be $x. The item was marked down by 15%, so the discounted price is 85% of the original price. This is equivalent to saying that the discounted price is 100% - 15% of the original price. Mathematically, we can write this as: 0.85x = discounted price

Since Caroline saved $3.84 on the discounted item, we can write an equation that equates the amount she paid for the item to the discounted price minus the amount she saved. Mathematically, we can write this as:

0.85x - 3.84 = amount paid

Solving for x (the original price) requires us to rearrange the equation to isolate x. Mathematically, we can write this as:

x = (amount paid + 3.84) / 0.85

Substituting in the given values gives: x = ($0.00 + $3.84) / 0.85 = $4.52

You can learn more about discounts at: brainly.com/question/28720582

#SPJ11

Answer:

50 by 50 meter pool

Step-by-step explanation:

since a 100 by 100 meter pool won’t fit the only option is a 50 by 50 meter pool

100x50=5000

5000/2=2500

50x50=2500

Hopes this helps please mark brainliest

The allowed error in the angle measurement would be 0%, as the ft measurement is considered 100% accurate.

To find the allowed error in the angle measurement, we can use the concept of percent error.
First, let's determine the  answer to the question. The calculated height needs to be accurate within a certain percentage.

Now, let's answer the question by considering the given information. The surveying team set up the equipment ft from the base of the tree. From ground level, they measured the angle of elevation to be .

To find the allowed error in the angle measurement, we can calculate the percent error. The percent error is given by the formula:

Percent Error = (Measured Value - True Value) / True Value * 100

In this case, the measured value is the angle of elevation obtained by the surveying team, and the true value is the actual angle of elevation.

Since we don't have the true value of the angle of elevation, we cannot directly calculate the allowed error in the angle measurement. However, we are given that the ft measurement is 100% accurate.

Therefore, we can assume that the ft measurement is the true value. In this case, the allowed error in the angle measurement would be 0%, as the ft measurement is considered 100% accurate.

In conclusion, the allowed error in the angle measurement is 0%.

To know more about Percent Error  visit:

brainly.com/question/30545034

#SPJ11

We can then use the first or second derivative test to determine whether each value represents a local maximum or a local minimum. We can also use the sign of the derivative to determine intervals of increase or decrease.

Find approximate x values for any local maximum or local minimum points. The graph of the function f(x) = x³ - x shows a local maximum point at (-1, 0) and a local minimum point at (0, -1). ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals. Find approximate x values for any local maximum or local minimum points. The graph of the function f(x) = -(x-3)(x+1)(1-x) shows a local maximum point at (1, 0) and local minimum points at (-1, -4) and (2, -2).ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals Here is the table showing the intervals of increase or decrease and the slope of the tangent on those intervals

The approximate x values for any local maximum or local minimum points for the given function have been calculated and the table showing intervals of increase or decrease and the slope of the tangent on those intervals has been set up. The table of values showing "x" and its corresponding "slope of tangent" for at least 7 points has been set up. The graph of the derivative using the table of values has also been sketched. To find the local maximum or local minimum points, we calculate the derivative of the function and set it equal to zero. For the given function, the derivative is 3x² - 1. Setting it equal to zero, we get x = ±√(1/3). We can then use the first or second derivative test to determine whether each value represents a local maximum or a local minimum. We can also use the sign of the derivative to determine intervals of increase or decrease.

To know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11

The linear function for the given statement is y = (-1/2)x + 6.

To write a linear function for the statement "A candle is 6 inches tall and burns at a rate of 1/2 inch per hour," we will need to use the slope-intercept form of a linear function, which is y = mx + b. In this case, y represents the remaining height of the candle, m represents the rate of burning, x represents time in hours, and b represents the initial height of the candle.

Step 1: Identify the initial height (b). The candle is 6 inches tall, so b = 6.

Step 2: Identify the rate of burning (m). The candle burns at a rate of 1/2 inch per hour, so m = -1/2 (negative because the height decreases as time passes).

Step 3: Write the linear function using the slope-intercept form y = mx + b. Substitute the values of m and b:
y = (-1/2)x + 6

Thus, we can state that the linear function for the given statement is:

y = (-1/2)x + 6.

To learn more about linear functions visit : https://brainly.com/question/15602982

#SPJ11

Answer:

\(\frac{1}{81}\)

Step-by-step explanation:

Key skills: Exponents + Fractions

Use the negative exponent property. If your number is x^-y then it would be the same as 1/x^y

3^-4 is the same as \(\frac{1}{3^{4}}\)

3^4 is 81, so your answer would be 1/81.

Hope you have a nice day and understood this!

The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

Learn more on trapezoid:

https://brainly.com/question/1410008

#SPJ4

This Graph represents all the real numbers which are less than or equal to 8.(Please see the attached image.)

Graphing Inequalities -

While graphing inequalities, we have to keep the following things in mind.

If the endpoint is included(i.e., incase of ≤ or ≥ ) use a closed circle.

If the endpoint is not included (i.e., in case of < or >), use an open circle.

Use open circle at either ∞ or -∞ .  

Draw a line from the endpoint that extends to the right side if the variable     is greater than the number.

Draw a line from the endpoint that extends  to the left side if the variable is lesser than the number.

Writing Inequality in Interval Notation-

If the endpoint is included (i.e., in case of ≤ or ≥) use the closed brackets '[' or ']'.

If the endpoint is not included(i.e., in case of < or > ), use the open brackets '(' or ')'

Use always open bracket at either ∞ or - ∞

inequality form = q ≤ 8

interval notation = ( -∞, 8]

It means q = (-∞......................... -4,-3,-2,-1,0,1,2,3,4,5,6,7,8] (Please see the attached image).

Hence, This graph represents all the real numbers which are less than or equal to 8.

Learn more about Inequality here https://brainly.com/question/25275758

#SPJ9

The total distance for path C is 960 meters.

Path C consists of three segments: C1, C2, and C3.

C1: From the starting point, path C moves horizontally to the right for three blocks, which equals a distance of 3 blocks × 120 meters/block = 360 meters.

C2: At the end of C1, path C turns left and moves vertically downwards for two blocks, which equals a distance of 2 blocks × 120 meters/block = 240 meters.

C3: After C2, path C turns left again and moves horizontally to the left for three blocks, which equals a distance of 3 blocks × 120 meters/block = 360 meters.

To find the total distance for path C, we sum the distances of the three segments: 360 meters + 240 meters + 360 meters = 960 meters.

Learn more about distance

brainly.com/question/13034462

#SPJ11

The required angles are :

corresponding angles:  ∠7=∠5

alternate interior angles: ∠4 = ∠2 and∠3 = ∠1

alternate exterior angles: ∠7 = ∠6

same side interior angles: ∠7 = ∠8

alternate interior angles

alternate exterior angles

same side interior angles

Corresponding angles:

one that hold the same relative position as another angle somewhere in figure.

Alternate interior angles:

Alternate interior angles are the angles formed on the opposite sides of the transversal.

Alternate exterior angles:

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Same side interior angles:

The theorem states that the same-side interior angles must be supplementary given the lines intersected by the transversal line are parallel.

corresponding angles:

∠7=∠5

alternate interior angles:

∠4 = ∠2

∠3 = ∠1

alternate exterior angles:

∠7 = ∠6

same side interior angles:

∠7 = ∠8

To learn more about geometry , visit:

https://brainly.com/question/28899589

#SPJ1

Answer:

This Is CORRECT

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/2 slope

just took the test

Answer:

36 is 257% of 14.

Step-by-step explanation:

36/14 = 2.57,

so 36 is 257% of 14.

Answer:

the third one

Step-by-step explanation:

\(\color{plum}\tt\bold{ A = 1.69 \pi \: mm²}\)

Given :

Circumference of a circle = 2.6π mm

We know that :

\(\color{hotpink}\tt \: circumference \: of \: a \: circle\color{plum} = 2\pi r\)

Which means :

\( =\tt 2 \times r \times \pi = 2.6\pi\)

\( =\tt r\pi = \frac{2.6}{2} \)

\( =\tt r \pi = 1.3 \: mm\)

Thus, the radius of this circle = 1.3 mm

The area of this circle :

\( =\tt \pi {r}^{2} \)

\( =\tt 1.3 \times 1.3 \times \pi\)

\(\color{plum} = \tt1.69\pi\)

Thus, the area of this circle = 1.69π

▪︎Therefore, the correct option is ○ A = 1.69π mm²

Answer:

w = -20

Step-by-step explanation:

8-3=5

-w/4=5

5*4=20

-w=20

-1/20=-20

w=-20

(x+a)(x+3a)= x²+bx+75

x²+4a+3a²=x²+bx+75

by comparing 3a²=75 and b= 4a

a= ±5

possible values of b= ±20

Two possible values of b are 20 and -20.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The mathematical expression as;

(x + a)(x + 3a) = x² + bx + 75​

Now,

The mathematical expression is;

(x + a)(x + 3a) = x² + bx + 75​

Solve the expression as;

(x + a)(x + 3a) = x² + bx + 75​

x² + 3ax + ax + 3a² = x² + bx + 75

x² + 4ax + 3a² = x² + bx + 75

After comparison we get;

4a = b  ... (i)

And, 3a² = 75  .. (ii)

Solve the second equation for a as;

3a² = 75

Divide by 3;

a² = 25

Take square root both side, we get;

a = ± 5

So, By equation (i) we get;

b = 4a

Substitute a = 5;

b = 4 x 5

b = 20

And, Substitute b = -5;

b = 4 x -5

b = -20

Thus, Two possible values of b are 20 and -20.

Learn more about the quadratic equation visit:

https://brainly.com/question/24034973

#SPJ2

Answer: ok

Step-by-step explanation: I THINK it E2

Answer:

-6

Step-by-step explanation:

2x-8=-6x-11

Answer:

24 SUV's

Step-by-step explanation

18 divided by 3=6

6 times 4 is 24

24 SUV's sold

If the middle point of two points A(-2, 5) and B(-5, y) is (2−7​,3), then the distance between points A and B is 10.67 (rounded to two decimal places).

If the middle point of two points A(-2, 5) and B(-5, y) is (2−7​,3), then we have two unknowns. We will have to use the distance formula to solve the question. Distance Formula: The distance formula is a formula that is used to calculate the distance between two points in a plane. The formula is given as follows: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Now let's find the missing coordinate value. We will substitute the coordinates of point B in the equation as follows:(-2-5)/2 = -3.5y = -6 - 7 = -13

Now we can find the distance between points A and B by substituting their respective coordinates in the distance formula:d = √[(-5 - (-2))² + (-13 - 5)²]d = √[(-3)² + (-18)²]d = √(9 + 324)d = √333d = 10.67

Therefore, the distance between points A and B is 10.67 (rounded to two decimal places).

You can learn more about the middle point at: brainly.com/question/24111285

#SPJ11

The total number of students appeared in the examination is 488.

Number of students passed in English = 0.7x

Number of students passed in Mathematics = 0.75x

Number of students failed in both subjects = 0.1x

Number of students passed in at least one subject = 0.9x

Number of students passed in both subjects = 220

We know that the total number of students appeared in the examination is x.

So, the number of students who failed in both subjects will be:

0.1x = (number of students failed in English) + (number of students failed in Mathematics) - 220

0.1x = (0.3x) + (0.25x) - 220

0.1x = 0.55x - 220

0.45x = 220

x = 488

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ4

Answer:

$20.75

Step-by-step explanation:

The answer is $21.50

Explain:

$8.60 / 4 = $2.15

$2.15 x 10 = $21.50

Could I have brainliest?