The following figure shows the entire graph
of a relationship.


Does the graph represent a function?

Answer:

(a)=1/4,(b)=1/512

Step-by-step explanation:

(a) The two dice each have four possible outcomes, and the total number of possible outcomes when the two dice are thrown is 4 x 4 = 16. To determine the most likely total score, we need to find the sum that has the highest probability of occurring.

To do this, we can create a table that shows all the possible outcomes and their corresponding probabilities:

Dice 1 Dice 2 Total Probability

1 1 2 1/16

1 2 3 1/8

1 3 4 1/16

1 4 5 1/8

2 1 3 1/8

2 2 4 1/16

2 3 5 1/8

2 4 6 1/16

3 1 4 1/16

3 2 5 1/8

3 3 6 1/16

3 4 7 1/8

4 1 5 1/8

4 2 6 1/16

4 3 7 1/8

4 4 8 1/16

From the table, we can see that the most likely total score is 5, which occurs with a probability of 1/8 + 1/8 = 1/4.

(b) The probability of obtaining a specific score on three successive throws is the product of the probabilities of obtaining that score on each throw, assuming that the dice are fair and independent. The most likely total score is 5, so we will calculate the probability of obtaining a total score of 5 on each throw and then multiply the probabilities together.

The probability of obtaining a total score of 5 on one throw is 1/8, as we can see from the table above. Therefore, the probability of obtaining a total score of 5 on three successive throws is (1/8) x (1/8) x (1/8) = 1/512.

Answer:

24s+ 200 ≥ 500

Step-by-step explanation:

Let s be the number of sales

200 + 24s is the amount that they will make

They want to make at least 500 so the  amount they make must be greater than or equal to 500

200 + 24s≥ 500

Changing the order on the left side

24s+ 200 ≥ 500

The value of the fraction is 3/-2

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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The projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

Explain the term projection

Projection is the process of representing a three-dimensional object or scene onto a two-dimensional surface. It involves the use of mathematical principles to create a flat image that accurately depicts the shape and position of the object or scene. Projections are widely used in fields such as engineering, architecture, and computer graphics to create visual representations of complex structures and designs.

According to the given information

The projection of a vector u onto a vector v is given by the formula proj_v(u) = (u•v)/(||v||²) * v, where u•v is the dot product of u and v, and ||v|| is the magnitude of v.

In this case, u = (-9,-5) and v = (-6,5). The dot product of u and v is u•v = (-9)(-6) + (-5)(5) = 54 - 25 = 29. The magnitude of v is ||v|| = √((-6)² + (5)²) =

√(36 + 25) = √61.

So the projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

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ZR is the altitude of the triangle, which can be calculated using the distance formula.

To calculate the distance between Z and R, we need to use the Pythagorean Theorem. The altitude of the triangle is equal to the square root of the sum of the squares of the sides of the triangle. This can be expressed as: ZR = √(NZ² + MZ²). Substituting the given values, we get: ZR = √(12² + 6²) = √(144 + 36) = √180 = 13.43.

ZV is the median of the triangle, which is equal to twice the area of the triangle divided by the length of the base. To calculate the area of the triangle, we can use Heron's formula. The area of the triangle is equal to the square root of the product of the semi-perimeter and the difference between the semi-perimeter and the side lengths. This can be expressed as: ZV = 2√((M + N + I)⁄2)((M + N + I)⁄2 - M)((M + N + I)⁄2 - N)((M + N + I)⁄2 - I). Substituting the given values, we get: ZV = 2√((6 + 12 + 18)⁄2)((6 + 12 + 18)⁄2 - 6)((6 + 12 + 18)⁄2 - 12)((6 + 12 + 18)⁄2 - 18) = 2√(24)(12)(6)(0) = 0.

YZ is the opposite side of the triangle to the angle Y, which can be calculated using the distance formula. To calculate the distance between Y and Z, we need to use the Pythagorean Theorem. The length of the side is equal to the square root of the sum of the squares of the sides of the triangle. This can be expressed as: YZ = √(MZ² + NZ²). Substituting the given values, we get: YZ = √(6² + 12²) = √(36 + 144) = √180 = 13.43.

NV is the side length of the triangle opposite the angle N, which can be calculated using the distance formula. To calculate the distance between N and V, we need to use the Pythagorean Theorem. The length of the side is equal to the square root of the sum of the squares of the sides of the triangle. This can be expressed as: NV = √(MZ² + YI²). Substituting the given values, we get: NV = √(6² + 18²) = √(36 + 324) = √360 = 18.97.

MR is the side length of the triangle opposite the angle M, which can be calculated using the distance formula. To calculate the distance between M and R, we need to use the Pythagorean Theorem. The length of the side is equal to the square root of the sum of the squares of the sides of the triangle. This can be expressed as: MR = √(NZ² + YI²). Substituting the given values, we get: MR = √(12² + 18²) = √(144 + 324) = √468 = 21.67.

IZ is the side length of the triangle opposite the angle I, which can be calculated using the distance formula. To calculate the distance between I and Z, we need to use the Pythagorean Theorem. The length of the side is equal to the square root of the sum of the squares of the sides of the triangle. This can be expressed as: IZ = √(MZ² + NZ²). Substituting the given values, we get: IZ = √(6² + 12²) = √(36 + 144) = √180 = 13.43.

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The function that will return the value of x, rounded to the nearest whole number is option (c) round(x)

This function rounds the value of x to the nearest integer. For example, if x = 3.4, round(x) will return 3, and if x = 3.6, round(x) will return 4.

Option (a) abs(x) returns the absolute value of x, which means it returns the positive value of x regardless of its sign. For example, if x = -3, abs(x) will return 3.

Option (b) fmod(x) returns the remainder of x divided by another number, so it does not round x to the nearest whole number.

Option (d) whole(x) is not a standard math function, so it is unclear what it would do.

Option (e) sqrt(x) returns the square root of x, so it does not round x to the nearest whole number.

Therefore, the correct answer to this question is option (c) round(x).

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Answer:

I'm not quite sure if this is correct, but If the given values are our X's or the inputs, then yes it would be a function as they're all different numbers.

Answer:

y = 75 - 9d

Step-by-step explanation:

y = amount of $ left

An algebraic expression to represent the amount of money left over is y = 75 - 9d

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol can also be used to indicate the logical syntax's order of operations and other features.

Given that You have $75 and need to buy 9 books at the bookstore and each book costs d dollars.

Let y be the amount of $ left

Therefore, the expression would be;

y = 75 - 9d

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Answer:

(0,4) (1,6) (2,8)

Step-by-step explanation:  

4-4=2(0)

6-4=2(1)

8-4=2(2)

(0,4) (1,6) (2,8) Hope this helped

Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.

Geometric mean annual increase for the period:

Let A be the initial value and B be the final value of the given data for the geometric mean annual increase for the period in the United States from 2000 to 2014.

A = 40,255,000 and B = 214,014,920.

To find the geometric mean annual increase for the period, we need to use the formula:

Geometric mean = (B/A)^(1/n), where n = the number of years elapsed.

Therefore, n = 2014 - 2000 = 14 years.

Substituting the values of A, B, and n in the above formula, we get:

Geometric mean = (214,014,920/40,255,000)^(1/14) ≈ 1.1802.

Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.

Answer: 1.18.

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I think its B. 7/20...........

Therefore, it will take approximately 11.67 years for the money to grow from $10,000 to $15,000 at an annual interest rate of 4.5% compounded continuously.

To solve this problem, we can use the continuous compounding formula: A = Pe^(rt), where A is the final amount, P is the initial principal, e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years. We want to find t when A = $15,000 and P = $10,000. Plugging in these values and solving for t, we get:
$15,000 = $10,000e^(0.045t)
1.5 = e^(0.045t)
ln(1.5) = 0.045t
t = ln(1.5)/0.045
t ≈ 11.67 years

Therefore, it will take approximately 11.67 years for the money to grow from $10,000 to $15,000 at an annual interest rate of 4.5% compounded continuously.

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Answer:

78.5

Step-by-step explanation:

add 1+2+3+4+5+6+7+100-56=78.5

Answer:

n = 12

Step-by-step explanation:

Given equation:

\(\dfrac{9}{n}=\dfrac{75}{100}\)

We can solve the equation for the unknown quantity, n, by cross-multiplying, which means multiplying both sides of the equation by the product of the denominators.

The denominator of a fraction is the part below the division bar.

The denominators of the given equation are n and 100, so their product is 100n.

Multiply both sides by 100n:

\(\implies \dfrac{9}{n} \cdot 100n=\dfrac{75}{100}\cdot 100n\)

Simplify and cancel the common factors:

\(\implies \dfrac{9\cdot 100n}{n} =\dfrac{75\cdot 100n}{100}\)

\(\implies 9\cdot 100 =75\cdot n\)

\(\implies 900 =75n\)

To solve for n, divide both sides of the equation by 75:

\(\implies \dfrac{900}{75} =\dfrac{75n}{75}\)

\(\implies 12=n\)

Therefore, the unknown quantity, n, is 12.

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given equation to us is ,

\(\longrightarrow \dfrac{9}{n}=\dfrac{75}{100} \\\)

Simplify the RHS of the equation. This can be done by dividing the numerator and denominator by 25 as it is the HCF of 75 and 100 . So we have;

\(\longrightarrow \dfrac{9}{n}=\dfrac{75\div 25}{100\div 25} \\\)

Simplify,

\(\longrightarrow \dfrac{9}{n} = \dfrac{3}{4} \\\)

Flip the numerator and denominator on both the sides , as ;

\(\longrightarrow \dfrac{n}{9} =\dfrac{4}{3} \\\)

Multiply both the sides by 9 as ,

\(\longrightarrow \dfrac{n}{9}\times 9 =\dfrac{4}{3}\times 9\\\)

Simplify,

\(\longrightarrow \boxed{\boldsymbol{ n = 12}} \\\)

Henceforth the value of n is 12 .

Answer: \(2\sqrt{22}\)

Step-by-step explanation:

Pythagorean theorem: \(a^{2} +b^{2} = c^{2}\), where a and b are the legs and c is the hypotenuse.

We can solve for x by only using the left side of the triangle. Since we're only using the left side of the triangle, we can reduce 18 by 2 to get 9. Now we plug in our information to the equation.

\(9^{2} +b^{2} = 13^{2}\)

\(81 +b^{2} = 169\)

Since we don't know what \(b^{2}\) is, we're going to isolate it by subtracting 81 on both sides

\(b^{2} = 88\)

We have to square root both sides in order to find out b (or x in the problem).

\(\sqrt{b^{2}} = \sqrt{88}\)

When you put this on a calculator it would result in \(2\sqrt{22}\) which is the answer d in the problem.

The addition is 5x - 2. We can find out our answer using simple arithmetic calculations.

What are arithmetic calculations?

Arithmetic calculations are mathematical operations used to solve equations and perform numerical calculations. They include addition, subtraction, multiplication, and division. Arithmetic is a fundamental part of mathematics, and it is an important part of everyday life. Arithmetic is used to solve problems in a variety of fields, such as engineering, finance, and science. It is also used in everyday tasks such as grocery shopping and budgeting. Arithmetic calculations are essential for most people and can help them understand and solve a variety of problems. By mastering basic arithmetic calculations, people can make more informed decisions and better understand the world around them.

In algebraic expressions ,

same variables are added together and constants together.

In given equation,

2x and 3x are added i.e. 5x

and 5 and -7 are added  i.e. -2

So, the equation is 5x-2.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer:

It is 3/4

Step-by-step explanation:

You take the 3/4 out of the 1 and are left with 1/4 and then add that to the 1/2 and you get 3/4

The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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We can use linear algebra to argue that there exists a polynomial q ∈ r[x] such that 5q ′′ 3q ′ = p. To do this, we can consider the vector space V of polynomials in r[x] of degree at most 2.

This vector space has a basis consisting of the polynomials 1, x, x2. Thus, any polynomial in r[x] can be written as a linear combination of these three basis polynomials.We can now consider the case where p = a1x2 + a2x + a3, where ai ∈ r. We can then write 5q ′′ 3q ′ = a1x2 + a2x + a3. To solve this equation, we can use the fact that the basis polynomials are eigenvectors of the left-hand side of the equation. Thus, we can find the eigenvalues of 5q ′′ 3q ′, and then solve for the coefficients in the linear combination of basis polynomials that is equal to p. This will give us the polynomial q such that 5q ′′ 3q ′ = p.

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The circumference of rectangular garden is 158 m.

The length is 5 meter more than width.

To find the width and length.

Let the width be x .

Then the length is

The perimeter of rectangle is

Substitute the values

The width is 37 m , find the length.

Hence the length is 42 m and width is 37 m.

In a real piping system there are always losses due to viscosity.

These losses cause a drop in total pressure but the static pressure remains the same.

The "K" factor (i.e. loss factor) for a sudden contraction and a rapid expansion in fully developed turbulent flow are 0.50 and 1.0.

A single pipe of known diameter, surface roughness and length joins two reservoirs and the free water surface between them is 57m.

We have to first guess the Reynolds number as the flow rate is unknown, then calculate a value for f and iterate to get the answer.

The effect of rounding a pipe inlet (where the fluid flows from a reservoir into the pipe) on the loss coefficient K will not change the coefficient. To minimize pressure losses in a venturi meter, the shape change from the inlet to the outlet must be fast change in, slow change out.Viscosity always causes losses in a piping system due to which there is a drop in total pressure.

The “K” factor for sudden contraction and rapid expansion is 0.50 and 1.0 respectively. The flow rate of a single pipe can be calculated by first guessing the Reynolds number, then calculating a value for f, and iterating to get the answer. Rounding a pipe inlet does not change the coefficient of loss.

To minimize pressure losses in a venturi meter, the shape change from the inlet to the outlet must be fast change in, slow change out.

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Step-by-step explanation:

making a the subject of the eqaution am=n+p we will have to divide both terms of the equation by m

\( \frac{am}{m} = \frac{n}{m} + \frac{p}{m} \\ a = \frac{n}{m} + \frac{p}{m} \)

The endpoints of the latus rectum of the parabola are \((\dfrac{1}{2} , \dfrac{1}{2} )\) and \((\dfrac{-1}{2} , \dfrac{1}{2} )\).

The latus rectum of a parabola is a line segment that passes through the focus and is perpendicular to the axis of symmetry.

Given: equation of the parabola is \(\(y = \frac{1}{2}x^2\)\).

For a parabola with equation \(\(y = \frac{1}{2}x^2\)\), the standard form is

    \(\(y = ax^2\)\)

and, the vertex of the parabola is at the origin (0, 0).

Now, the focus of the parabola is located at a distance of a units above the vertex, \(\(a = \dfrac{1}{2}\)\).

So, the focus is at \((0, \(a\))\) = \((0, \frac{1}{2} )\).

Since the axis of symmetry is the y-axis, the latus rectum will be a horizontal line.

The endpoints of the latus rectum will be equidistant from the focus and lie on a line parallel to the x-axis.

The distance from the focus to each endpoint of the latus rectum is twice the focal length, i.e., 2a = 1.

The endpoints of the latus rectum will be at a distance of 1 unit from the focus in the positive and negative x-directions.

So, the endpoints of the latus rectum are \((\dfrac{1}{2} , \dfrac{1}{2} )\) and \((\dfrac{-1}{2} , \dfrac{1}{2} )\).

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The question is incorrect format, the correct format is

Find the endpoints of the latus rectum of the parabola below.\(\(y = \frac{1}{2}x^2\)\)enter the endpoints as ordered pairs (x,y).

Answer:

155,588

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = growth rate

N = number of years 2021 - 2014 = 7

130,000(1.026)^7 = 155,587.6

rounding off to the nearest whole  number is 155,588

To round off to the nearest whole number, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

Answer:

Step-by-step explanation:

\(x^{3}-2x^{2}-x+2\\ =x(x^{2}-2x-1)+2\\\)

We can clearly see here that x = 1 is one of the solution where this expression becomes zero

= x( (x-1)^2-2 ) + 2

Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer: 4 19/36 inches

Step-by-step explanation:
To add the two measurements together, you need to find a common denominator. In this instance, it will be 36.

2 * 4 = 8, 9 * 4 = 36, which means our first measurement turns into 10 8/36

1 * 9 = 9, 4 * 9 = 36, which means our second measurement turns into 5 9/36

Adding these together we get 15 17/36.

Subtract this from 20.

The amount of string that is left is 4 19/36 inches.

Hope this helped!

Answer:

1/4

Step-by-step explanation:

Use the slope formula to find the slope.

slope = (y2-y1)/(x2-x1)

slope = -1 - -2 / -2- -6

= 1/4

The 104 adults and 105 youth admissions were purchased if the admission fee is $8.00 for an adult and $4.50 for a youth.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

At the local fair, the admission fee is $8.00 for an adult and $4.50 for a youth.

Let's suppose the number of admission of adults is x and for youth is y, then,

x + y = 209 ...(1)

8x + 4.50y = 1304.5 ...(2)

After solving the above two linear equation, we get:

x = 104

y = 105

Thus, the 104 adults and 105 youth admissions were purchased if the admission fee is $8.00 for an adult and $4.50 for a youth.

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