Which of these relations is a function?
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The length of the line segment PR from the given parameters is: 8x - 8

The line segment addition postulate is a postulate that states that if we are given two points on a line segment, X and Z, a third point Y lies on the line segment XZ if and only if the distances between the points meet the requirements of the equation XY + YZ = XZ

We are given the parameters:

PQ = 3x - 2

QR = 5x + 6

Thus:

PR = PQ + QR

PR = 3x - 2 + 5x - 6

PR = 8x - 8

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We shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.

Ratiοs are a way οf cοmparing twο οr mοre quantities by expressing their relative sizes οr amοunts. They can be written in the fοrm a:b οr a/b, where a and b are the quantities being cοmpared. Ratiοs are οften used in mathematics and everyday life tο express prοpοrtiοns, rates, and οther relatiοnships between quantities.

Tο make the same cοlοr as the sample, we need tο maintain the same ratiο οf blue tο yellοw paint.

The ratiο οf blue tο yellοw paint in the sample is 3:8, which simplifies tο 3/8.

If we have 24 οunces οf blue paint, we can use this ratiο tο find the amοunt οf yellοw paint needed:

(3/8) * 24 = 9 οunces

Therefοre, we shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.

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Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):

P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)

From the table, we have:

P(male) = 1110/3538 ≈ 0.314

P(nursing major) = 1016/3538 ≈ 0.287

P(male and nursing major) = 94/3538 ≈ 0.027

Therefore:

P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574

Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.

(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:

P(being female or not being a nursing major) = P(female) + P(not nursing major)

From the table, we have:

P(female) = 2428/3538 ≈ 0.686

P(not nursing major) = 1728/3538 ≈ 0.489

Therefore:

P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175

This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):

P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)

From the table, we have:

P(female and nursing major) = 700/3538 ≈ 0.198

Therefore:

P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977

Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.

(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:

P(not being female or being a nursing major) = 1 - P(being female or being nursing major)

From part (a), we have:

P(being male or being nursing major) ≈ 0.574

Therefore:

P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426

Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.

(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.

Step-by-step explanation:

Answerer Latoya got a better deal because she paid less than Herman by 25 cents

Step-by-step explanation:

Latoya 18 divided by 8= $2.25

Herman 15 divided by 6= $2.50

So Latoya saves $0.25 cents

Answer:

10

Step-by-step explanation:

5×6=20+y

30=20+y

30-20=y

10=y

therefore y=10

The best estimate of the probability of receiving a prize would be the ratio of the number of prizes awarded to the total number of people who played the game.

a) For 10 people, 2 prizes were awarded, so the estimate of the probability of receiving a prize is 2/10 or 0.2 (20%).

b) For 50 people, 6 prizes were awarded, so the estimate of the probability of receiving a prize is 6/50 or 0.12 (12%).

c) For 100 people, 18 prizes were awarded, so the estimate of the probability of receiving a prize is 18/100 or 0.18 (18%).

Therefore, the best estimate of the probability of receiving a prize would be c) 100 people and 18 prizes awarded, which gives an estimate of 0.18 or 18%.

Check the picture below.

The perimeter of triangle N is 72 inches.

Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.

Here given the triangles M and N are similar, the ratio of sides N:M is 4:3

We can say that M and N with constant term x is, (by ratio proportion rule)

M = 3x and N = 4x and

Given the lengths of triangle M are 12 inches, 18 inches and 24 inches

for triangle M = 3x, (Using above ratio proportion rule)

3x = 12 inches                    3x = 18 inches                    3x = 24 inches

x = 4                                    x = 6                                    x = 8

Similarly, for similar triangle N = 4x, (Using above ratio proportion rule) put all values of x = 4, 6, 8

for x =4                                for x =6                                for x =8

4x = 4×4                               4x = 4×6                              4x = 4×8  

16 inches                             24 inches                            32 inches

Length of triangle N is 16 inches, 24 inches and 32 inches

Perimeter of triangle N = 16+24+32 = 72 inches

Therefore, the Perimeter of triangle N is 72 inches.

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Step-by-step explanation:

4/25=0.16

6%=0.06

0.1=10%

0.875=7/8

The equations of the other two sides are AD: y = -3x + 3 and DC: y = 1/2x - 1/2.

What is point-slope form?

The point-slope form is a way to write the equation of a straight line in algebra. It is used when you know the coordinates of a point on the line and the slope of the line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.

Since AB and BC are two sides of a parallelogram, they are parallel to each other. Thus, we can use the slope formula to find the slopes of these sides.

Slope of AB:

m = (y₂ - y₁)/(x₂ - x₁)

= (6 - 3)/(6 - 0)

= 3/6

= 1/2

Slope of BC:

m = (y₂ - y₁)/(x₂ - x₁)

= (3 - 6)/(7 - 6)

= -3/1

= -3

Now that we know the slopes of AB and BC, we can use the point-slope form to find the equations of the other two sides.

Equation of AD:

We know that AD is parallel to BC and passes through point A. So, we can use the point-slope form with the slope of BC and point A.

y - y₁ = m(x - x₁)

y - 3 = -3(x - 0)

y - 3 = -3x

y = -3x + 3

Equation of DC:

We know that DC is parallel to AB and passes through point C. So, we can use the point-slope form with the slope of AB and point C.

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 7)

y - 3 = 1/2x - 7/2

y = 1/2x - 1/2

Therefore, the equations of the other two sides are:

AD: y = -3x + 3

DC: y = 1/2x - 1/2

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This is the explicit fοrmula fοr this sequence.

An arithmetic series is a set οf integers that are οrdered and have a cοmmοn difference between each fοllοwing wοrd. The cοmmοn difference, fοr instance, between the mathematical series 3, 9, 15, 21, and 27 is 6. An alternative term fοr an arithmetic sequence is an arithmetic prοgressiοn.

The first term is 21 and the cοmmοn difference is -4 (the amοunt added οr subtracted tο get frοm οne term tο the next).

The explicit fοrmula fοr an arithmetic sequence is a n = a + (n - 1)d2, where a is the first term, d is the cοmmοn difference, and n is the term number.

Substituting 21 fοr a and -4 fοr d, we get:

a n = 21 + (n - 1)(-4)

Simplifying, we get:

a n = 21 - 4n + 4

a n = 25 - 4n

This is the explicit fοrmula fοr this sequence.

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Answer:

9000000 Milligrams

Step-by-step explanation:

We know that,

1 kilogram = 10^6 Miligram

So, 9  Kilpgrams = 9×10^6 = 9000000 Milligrams

Option C. To translate the triangle downward by 3 units, we need to subtract 3 from the y-coordinate of each vertex. This will shift the entire triangle down by 3 units.

The original triangle has vertices (1, 4), (2, 7), and (5, 3):

   (1,4)

     / \

    /   \

(2,7)----- (5,3)

To translate the triangle downward by 3 units, we subtract 3 from the y-coordinate of each vertex:

(1, 4) -> (1, 1)

(2, 7) -> (2, 4)

(5, 3) -> (5, 0)

The new triangle has vertices (1, 1), (2, 4), and (5, 0):

   (1,1)

     / \

    /   \

(2,4)----- (5,0)

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A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?

A. (4, 4), (6, 7), (7, 3)

B. (1, 7), (2, 10), (5, 6)

C. (1, 1), (2, 4), (5, 0)

D. (-2, 4), (-1, 7), (2, 3)

Based on the information given in the histogram, option B. The distribution of the data is asymmetrical, so the mean and the median are likely outside the "1,000-1,099 photocopies" category is the correct statement.

What is histogram?

The histogram shows that the distribution of the data is asymmetrical, with a longer tail towards the right. This means that there are more schools that made a higher number of photocopies than those that made a lower number of photocopies. Therefore, the mean and median are likely to be higher than the midpoint of the "1,000-1,099 photocopies" category, which has the highest frequency.

In a skewed distribution, the mean is typically affected by the outliers, while the median is a better measure of central tendency. Therefore, the median is more likely to be within the "1,000-1,099 photocopies" category, while the mean is likely to be higher.

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Answer:

Step-by-step explanation:

The two given points are (8, 0) and (8, -8).

Using the distance formula, the distance between the two points can be calculated as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where x1 = 8, y1 = 0, x2 = 8, and y2 = -8

d = sqrt((8 - 8)^2 + (-8 - 0)^2)

d = sqrt(0 + 64)

d = sqrt(64)

d = 8

Therefore, the distance between the two points is 8 units.

Answer:

[tex]5(4+c)[/tex]

The rectangular form of the parametric equation is given as follows:

y = y = 2x² - 12x + 14, where x is in the interval [-1, 3].

The parametric equation in the context of this problem is defined as follows:

The interval for t is given as follows:

[-4,0].

Hence the bounds of the interval for x are given as follows:

From the first equation, we can write t as a function of x as follows:

t = x - 3.

Replacing into the second equation, the rectangular form of the equation is given as follows:

y = 2(x - 3)² - 4

y = 2(x² - 6x + 9) - 4

y = 2x² - 12x + 14.

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Answer: y = "2x^2 - 12x + 14", where x is on the interval ["-1, 3"].

Step-by-step explanation: I took the test.

Answer:

Nonexamples of base and exponent in math would be any mathematical expressions that do not involve raising a base to an exponent. For example, 2 + 3 or √4 do not involve base and exponent.

An example of coefficient and exponential form is 5x², where 5 is the coefficient and x² is the exponential form. A nonexample could be x²/5, which does not have a coefficient in front of the exponential form.

An example of expanded form is 5x + 2, where the expression is fully written out. The standard form of the same expression would be 2 + 5x. A nonexample of expanded form is 2(x + 3), where the expression is not fully written out.

Examples of exponent laws include the product rule (a^m * a^n = a^(m+n)), quotient rule (a^m / a^n = a^(m-n)), and power rule ((a^m)^n = a^(mn)). A nonexample of an exponent law could be the sum of powers rule, which does not exist in traditional exponent laws.

The solutions for all the parts are given below.

Exponentiation is one of the mathematics operations.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by 'a' times to itself.

So, a is the exponent of m.

1) Non-examples of a base and exponent in math would be: "2 + 3" or "5 - 7" as these are expressions and not a base raised to an exponent.

2) An example of a coefficient and exponential form would be "2x^3" where 2 is the coefficient and x^3 is the exponential form. A nonexample would be "3x + 2" as it is an expression and not in exponential form.

3) An example of an expanded form would be 235 = 2 x 100 + 3 x 10 + 5 x 1, where each digit is multiplied by its corresponding place value. An example of standard form would be 235 written as is, without being broken down into its place values. A nonexample of expanded form would be 235 written as 2 + 3 + 5, as this is not a multiplication of the digits with their place values.

4). Examples of exponent laws include:

Product law: aᵇ x aⁿ = a⁽ᵇ ⁺ⁿ⁾

Quotient law: [tex]a^m / a^n = a^{(m-n)}\\[/tex]

Power law: [tex](a^m)^n = a^{(m \times n)}[/tex]

Negative exponent law: [tex]a^{(-n)} = 1/a^n[/tex]

Zero exponent law: [tex]a^0 = 1[/tex].

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The closest option to the total distance driven is 270.

We kept an eye on them from afar. Compared to earlier, she perceives a distance between her and her brother. They had been close friends once, but now there was a great distance between them. He desires to disassociate himself from his old boss.

We must combine the distances for each hour in order to calculate the total distance travelled:

Distance total = 62 + 70 + 68 + 72

272 miles roundtrip.

Thus, option 270 comes the closest to the total mileage driven.

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Answer:

Bring a book and read until they call her.

Step-by-step explanation:

this is a productive and professional way to pass the time while waiting for an interview. It shows that she is prepared and focused on the task at hand. Checking social media or applying for other jobs on her phone may give the impression that she is not fully committed to the interview or is easily distracted. sitting and waiting is also an option, but bringing a book to read is a better use of her time.

hope this helps

D.Sit and wait patiently.

17.  Number of hours, h     10 + 2h    Total Cost

         1                             10 + 2 x 1          12

         2                            10 + 2 x 2         14

         3                            10 + 2 x 3         16

         4                             10 + 2 x 4        18

This is true because as shown in the first example, you have to sub in the number of hours into the "h" value, and multiply it times two. After that, you add ten.

Answer:

vertex = (- 4, 6 )

Step-by-step explanation:

the vertex is the turning point on the curve.

this is situated at (- 4, 6 )

Answer:

The coordinates of the vertex are:

[tex]\left(\;\boxed{-4}\;,\;\boxed{6}\;\right)[/tex]

Step-by-step explanation:

The graph shows a parabola that opens downwards.

The vertex of a parabola that opens downwards is its maximum point.

From inspection of the graph, the maximum point is (-4, 6).

Therefore, the coordinates of the vertex are (-4, 6).

Answer:

Step-by-step explanation:

We can use the two given data points to find the slope of the line that represents the population growth over time.

The population at time t=3 is 1285, which means that the population has increased by P1 = 1285 - P0, where P0 is the initial population at time t=0 (which is not given). Similarly, the population at time t=8 is 2460, which means that the population has increased by P2 = 2460 - P0.

The time elapsed between t=3 and t=8 is 8-3 = 5 years.

The slope of the line that represents the population growth over time is given by:

slope = (P2 - P1) / (t2 - t1)

where t1 and t2 are the corresponding times.

Substituting the given values, we get:

slope = (2460 - 1285) / (8 - 3)

slope = 235

This means that the population is increasing by 235 people per year.

To find the initial population at time t=0, we can use either of the two given data points. Let's use the population at time t=3:

P1 = 1285 - P0

235 * 3 = 705

1285 - 705 = 580

Therefore, the initial population at time t=0 (i.e., in the year 1990) was 580 people.

We can now use the slope to find the population at any given time t after 1990.

Let P(t) be the population at time t after 1990.

Then, P(t) = P0 + slope * (t - 0)

P(t) = 580 + 235t

For example, the population in the year 2000 (i.e., when t=10) would be:

P(10) = 580 + 235(10) = 3330

Therefore, the population in the year 2000 would be 3330 people.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53[/tex]

The quadratic equation for the height of the rock, h = -16·t² + 79·t + 50, indicates;

a. The times at which the rock will be 125 feet above the beach are about; 3.66 seconds and 1.28 seconds

b. The maximum height reached is about 147.5 feet and it will take about 2.5 seconds for the rock to reach maximum height

A quadratic equation is an equation of the form, f(x) = a·x² + b·x + c, where; a ≠ 0, and a, b, and c are numbers.

a. The function for the height of the rocket is presented as follows;

h(t) = -16·t² + 79·t + 50

The time at which the height is 125 feet can be found as follows;

h(t) = 125 feet

h(t) = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 125 - 125 = 0

-16·t² + 79·t - 75 = 0

The quadratic formula indicates that we get;

t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32

t = (79 ± √(1441))/32

t = (79 + √(1441))/32 ≈ 3.66

t = (79 - √(1441))/32 ≈ 1.28

b. The time at which the rock is at the maximum height can be obtained by using the formula for finding the input value at the maximum value of a quadratic function, which is; at the maximum height, x = -b/2·a

Therefore, at the maximum height, we get;

The time, t = -79/(2 × (-16)) = 2.46875

The time it takes the rock to reach the maximum height is 2.46875 seconds ≈ 2.5 seconds

The maximum height is therefore;

h(2.46875) = -16×2.46875² + 79×2.46875 + 50 = 147.515625 ≈ 147.5

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Answer:

1. One solution

2. No solution

3. Infinite solutions

4. Two solutions

5. Three solutions

Step-by-step explanation:

You're welcome  ♡

Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.

Stοcks, alsο knοwn as the shares οr equities, represent οwnership in  cοrpοratiοn. When yοu buy stοck, yοu are buying  small piece οf οwnership in  cοmpany. The value οf  stοck is determined by  supply and demand fοr  shares in  market, as well as by the cοmpany's financial perfοrmance, industry trends, and οther factοrs.

I can suggest sοme pοssible financial gοals that sοmeοne in a career related tο finance might have:

Saving fοr retirement: A financial prοfessiοnal might set a gοal οf saving a certain amοunt οf mοney each year fοr their retirement.

Investing in stοcks οr οther assets: A finance prοfessiοnal might set a gοal οf investing in stοcks οr οther assets in οrder tο grοw their wealth οver time.

Building an emergency fund: A finance prοfessiοnal might set a gοal οf building an emergency fund tο cοver unexpected expenses οr incοme disruptiοns.

Paying οff debt: A finance prοfessiοnal might set a gοal οf paying οff debt, such as student lοans οr credit card debt, in οrder tο imprοve their financial stability.

Saving fοr a dοwn payment οn a hοme: A finance prοfessiοnal might set a gοal οf saving fοr a dοwn payment οn a hοme in οrder tο purchase a prοperty and build equity.

Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.

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An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change and common ratio.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function is typically represented by the following mathematical expression:

f(x) = a(b)^x

Where:

Based on the given exponential function y = a(b)^x, we can logically deduce that the y-intercept is represented by a, b is the rate of change, and common ratio.

In conclusion, an asymptote is a line which the graph of a given function approaches, but it would neither touch nor cross.

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