A function has y-intercept of 4 and a slope of 1/3. Which equation below describes the function? A. y = 1/3x2 + 4 B. y = 1/3x + 4 C. y = 1/3 + x + 4 D. y = 4x + 1/3

Answers

Answer 1

Answer:

B. y = 1/3x + 4

Explanation:

Given a function whose:

• Slope, m = 1/3

,

• y-interept, b = 4

To find the equation that describes the function, substitute the given values into the slope-intercept form of a line.

\(y=mx+b\)

This gives:

\(y=\frac{1}{3}x+4\)

The correct equation is option B.


Related Questions

1. You want to gather descriptive statistics to predict results of a general election in which there is evidence that people in different demographic groups (i.e., by gender, political party, and socioeconomic status) will vote differently. How do you sample registered voters

Answers

To sample registered voters for gathering descriptive statistics, use random sampling techniques such as simple random sampling or stratified sampling to ensure representative and unbiased data.

We have,

When sampling registered voters to gather descriptive statistics for predicting election results, it is important to employ a sampling method that ensures representative and unbiased data.

Here are some approaches to consider:

Random Sampling:

Use a random sampling technique, such as simple random sampling or stratified random sampling. Randomly select registered voters from the voter registration list, ensuring that each voter has an equal chance of being selected.

Stratified Sampling:

Divide the registered voters into relevant demographic groups (e.g., gender, political party, socioeconomic status). Within each group, use random sampling to select an appropriate number of voters proportional to their representation in the population. This helps ensure that each demographic group is adequately represented in the sample.

Cluster Sampling:

Divide the population into clusters, such as geographic regions or voting precincts. Randomly select a few clusters, and then randomly sample registered voters within those selected clusters. This approach can be useful when it is logistically challenging to access the entire population.

Oversampling:

If certain demographic groups are of particular interest due to their potential impact on the election, you may choose to oversample those groups. This involves intentionally selecting more individuals from those groups to ensure sufficient representation in the sample.

Thus,

To sample registered voters for gathering descriptive statistics, use random sampling techniques such as simple random sampling or stratified sampling to ensure representative and unbiased data.

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Find the slope of the line with the following points:
(9,3) & (-2,6)

Answers

Answer:

m=-0.2727272727

Step-by-step explanation:

Use the formula m=(y *2 - y *1) / (x *2 - x *1)

So it will be (6-3) / ((-2)-9)

Which results in 3/-11 = -0.272727272727272

Please answer each part in almost 500 words.

a. Suppose Jet Airways wants to ascertain the image it has in the minds of its patrons. Construct a seven-item and semantic differential scale to measure the perceived image of the airlines. Make sure that the seven under each format correspond to the same seven dimensions.

b) Find a technical and business report from your library or on the internet and examine the contents of the reports against what has been discussed in the chapter. What deviations did you find from the stated structure? What you think could have been the reason for this?

Answers

a) Part A: The perceived image of Jet Airways

Jet Airways is one of the well-known airlines in India. It is headquartered in Mumbai and operates both domestic and international flights. The perceived image of Jet Airways in the minds of its customers is important to the success of the airline. Perceived image refers to what the customers think about the airline, and this is important for customer loyalty and retention.

Constructing a seven-item and semantic differential scale to measure the perceived image of Jet Airways would be as follows:

1. Reliability: how reliable is Jet Airways on a scale of 1 to 7 (with 1 being extremely unreliable and 7 being extremely reliable)

2. Responsiveness: how responsive is Jet Airways to the needs of its customers on a scale of 1 to 7 (with 1 being extremely unresponsive and 7 being extremely responsive)

3. Empathy: how empathetic is Jet Airways to the concerns of its customers on a scale of 1 to 7 (with 1 being extremely unempathetic and 7 being extremely empathetic)

4. Assurance: how assured do you feel when you travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely unassured and 7 being extremely assured)

5. Tangibles: how do you rate the physical appearance of Jet Airways on a scale of 1 to 7 (with 1 being extremely poor and 7 being extremely good)

6. Price: how do you rate the price of Jet Airways on a scale of 1 to 7 (with 1 being extremely expensive and 7 being extremely affordable)

7. Convenience: how convenient is it to travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely inconvenient and 7 being extremely convenient)

The above semantic differential scale helps in measuring the perceived image of Jet Airways. The seven-item and semantic differential scale ensure that the seven under each format correspond to the same seven dimensions.

By answering each question, the customers can rate Jet Airways on various factors, and the airline can use this feedback to improve its service and overall image.

b) Part B:

Examination of a technical and business report

The structure of a technical and business report includes a title page, abstract, table of contents, introduction, main body, conclusion, and references. An examination of a technical and business report from the internet reveals some deviations from the stated structure. One of the significant deviations is the absence of the abstract section. The abstract provides a brief summary of the report, including the purpose, methodology, and findings. The report from the internet did not have an abstract section, and this deviation could be due to the report being a short summary of a more extensive study.

The report from the internet did not have a separate conclusion section. The conclusion is important as it summarizes the findings of the study and provides recommendations for further research. The report from the internet integrated the findings and recommendations into the main body of the report, and this deviation could be due to the length of the report.

Another deviation is the lack of a reference section. The reference section is essential as it provides the sources used in the study. The report from the internet did not have a reference section, and this deviation could be due to the type of report and the fact that it was not a formal research report.

In conclusion, technical and business reports should follow a specific structure to ensure that they are clear, concise, and easily understood. Deviations from the stated structure can affect the quality and accuracy of the report. The deviations in the report from the internet could be due to the length, type, and purpose of the report.

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Bao i the oldet of four ibling whoe age are conecutive even integer. If the um of their age i 60, find Bao' age

Answers

Thus, Bao age is 27.

What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

acc to our question-

Let the ages of the four siblings be;x , x + 1 , x + 2, x + 3(Ashley's age)If the sum of their ages is 100We have;x + x + 1 + x + 2 + x + 3 = 100collect like terms4x + 6 = 1004x = 100 - 64x = 96Make 'x' the subjectx = 96/ 4x = 24But Bao age is x + 3 = 24 + 3 = 27Thus,Bao's age is 27

hence,Thus, Bao age is 27.

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Find f'(x). f(x) = 4 In (8 + 9x) f'(x)=0

Answers

The derivative of f(x) = 4 ln(8 + 9x) is f'(x) = 36/(8 + 9x).

To find the derivative of f(x), we use the chain rule and the derivative of ln(u) = 1/u. Let u = 8 + 9x, then f(x) = 4 ln(u). Using the chain rule, we have:

f'(x) = (d/dx)(4 ln(u)) = 4 (d/dx)ln(u) = 4(1/u) (du/dx)

To find du/dx, we take the derivative of u with respect to x, which is simply 9. Therefore:

f'(x) = 4(1/u) (du/dx) = 4(1/(8 + 9x)) (9) = 36/(8 + 9x)

Therefore, the derivative of f(x) is f'(x) = 36/(8 + 9x).

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Question This figure is made up of two rectangular prisms. What is the volume of the figure?

Question This figure is made up of two rectangular prisms. What is the volume of the figure?

Answers

Answer:

1586 cm³

Step-by-step explanation:

bottom big one v= wlh = 22* 13 * 5 =1430

top little one v= wlh= 6*2*13 =156

total = 1586

When Jake volunteers at the animal shelter, he divides 2/3 cup of cat food equally between 2 cats. How much food does he give each cat?Use the area model

When Jake volunteers at the animal shelter, he divides 2/3 cup of cat food equally between 2 cats. How

Answers

1/3

each cat gets 1/3 of the food because 2/3 ÷ 2/1 = 1/3.

A vehicle accessory shop is considering buying a new style of wheels for $155.00 and selling them at $240.00 for each wheel. Fixed costs related to this new style of 1020.00. It is estimated that 16 wheels per month could be sold.(a) How many wheels must they sell to break even?(b) How much profit will the accessory shop make each month

Answers

(a) The accessory shop needs to sell 9 wheels to break even.

(b) The accessory shop will make a profit of $1320.00 each month.

(a) To determine the number of wheels the accessory shop must sell to break even, we need to calculate the break-even point. The break-even point is reached when the revenue equals the total cost. The total cost is the sum of the fixed costs and the variable costs per unit.

Fixed costs: $1020.00

Variable costs per wheel: $155.00 (purchase cost)

Break-even point = Total fixed costs / (Selling price per wheel - Variable cost per wheel)

Break-even point = $1020.00 / ($240.00 - $155.00)

Break-even point ≈ 8.83

Since we cannot sell a fraction of a wheel, the accessory shop must sell at least 9 wheels to break even.

(b) To calculate the monthly profit, we need to subtract the total cost from the total revenue.

Profit per wheel = Selling price per wheel - Variable cost per wheel

Profit per wheel = $240.00 - $155.00 = $85.00

Total profit = Profit per wheel x Number of wheels sold

Total profit = $85.00 x 16 = $1360.00

However, we need to deduct the fixed costs from the total profit to obtain the net profit.

Net profit = Total profit - Fixed costs

Net profit = $1360.00 - $1020.00 = $340.00

Therefore, the accessory shop will make a profit of $340.00 each month.

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Roberto' employer offer a liding paid vacation. When he tarted work, he wa given three paid day of vacation. For each ix-month period he tay at the job, hi vacation i increaed by two day. Let x repreent the number of 6-month period worked and y repreent the total number of paid vacation day. Write an equation that mode the relationhip between thee two variable

Answers

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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which value of X is in the solution set of the inequality -2X + 5 > 17

A) -8
B) -4
C)-6
D)12

Answers

Answer: B

Step-by-step explanation:

First you must get the X term on its own. To do that, you must remove the +5 because it is on the same side of the > symbol as the x term. When removing a term we must to the opposite to what the equation states so, as the equation say +5 we must -5 from BOTH sides of the > sign instead. This leaves is with -2x>12. To find the value of X, we divide both sides by -2 (since currently the x is multiplied by -2 and we need to do the opposite) and we get x<-6. Remember when dividing by a negative number we flip the sign. The value of x must be lower than -6 and the only value lower than -6 from the given solutions is -4, so the answer is B.

Find the hcf by using long division method (219,1321,2320,8526)

Answers

Step-by-step explanation:

I have attached the working

Find the hcf by using long division method (219,1321,2320,8526)

In AABC, m2A = 15° and mZB= 120°.
Select the triangle that is similar to AABC.
OA. ADEF, in which mZD= 15° and
m2F = 40°
OB. AJKL, in which mZJ= 15° and
mZL=45°
OC. APQR, in which mZP= 45° and
m/R = 105°
D. AMNP, in which mZM= 15° and
mZN=135°

Answers

The triangle that is similar to the triangle ΔABC is the triangle ΔJKL, the correct option is therefore;

B. ΔJKL, in which m∠J = 15° and m∠L = 45°

What are similar triangles?

Triangles are similar if they have the same measure of two of their interior angles, and therefore, have the same shape, but they may have different size.

The specified known angles of the triangle indicates that the known angles are;

m∠A = 15°, m∠B = 120°

Therefore, the third angle of the triangle is; 180 - (15 + 120) = 45

The third angle of the is 45 degrees

Therefore, the triangle that is similar to the specified triangle has an angle interior angle of either; 15°, or 120°, or 45°

The correct option is therefore option B. ΔJKL, in which m∠J = 15 and m∠L = 45°, which indicates that m∠K = 180° - (15° + 45°) = 120°

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If 9 avocados cost $5, how much do 18 avocados cost? (find unit rate then multiply by 18)

Answers

Answer:

For this problem, you could just multiply $5 by 2 OR you could divide $5 by nine to find your Unit Rate and then multiply that number by 18.

a statistics professor asked students in a class their ages. based on this information, the professor states that the average age of students in the university is 21 years. this is an example of .

Answers

The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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How do you find the angles of a 5/12/13 triangle?

Answers

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

What is Law of cosines formula?

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

a² = b²+ c²– 2bc cos αb²= a² + c²– 2ac cos βc²= b² + a² – 2ba cos γ

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

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How do you find the angles of a 5/12/13 triangle?

Please Help Asap...! :)

Please Help Asap...! :)

Answers

A) The time in minutes that it would reach 40% charge is; 48 minutes

B) The percent at 1 hr 48 minutes is; 90%

How to solve Linear Equation Word problems?

The general form of the equation of a line in  slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given parameters, we can find the slope from the formula;

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

m = (30 - 10)/(36 - 12)

m = 20/24

m = 5/6

Thus, for a 40% charge, we have;

5/6 = (40 - 30)/(t - 36)

Cross multiply to get;

5(t - 36) = 60

t - 36 = 12

t = 48 minutes

B) After 1 hr 48 minutes or 108 minutes, it means that;

Percentage = 5/6 * 108

= 90%

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A woman walks 5 rounds along the border of a square field of area 49². Find the total distance she walks in m.​

Answers

You need to estimate the square root of 200 ft². Rewrite 200 as 2 x 100, then square root of (2*100) is:

10*sqrt(2). The sqrt(2) = 1.414, so the length of each side of the square will be 10*1.414 = 14.14 ft or about 14 ft.

Answer:

140m

Step-by-step explanation:

perimeter of a square with area 49 is 7×4=28, 28 × 5 rounds = 140m

what are the answers to this?? please help!!!

what are the answers to this?? please help!!!

Answers

its a and c maybe. cuz im smart

Answer is b and c

Reason

a = 35 + 210s + 325t ❌

b = 35 + 30s - 45t ✅

c= 35 + 30s -45t ✅

d= 35 + 30s -45 ❌

e = -35 + 30s - 45t ❌

URGENT PICTURE INCUDED

URGENT PICTURE INCUDED

Answers

Answer:

C and F

Step-by-step explanation:

any - h value is to the right and any - k value is down

A three-centimeter cube has been painted red on all sides. it is cut into one centimeter cubes. how many cubes will be there with only one side painted red?

Answers

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)

Answers

The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

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please help and thank u can u answer another question after this one?

please help and thank u can u answer another question after this one?

Answers

Answer:

y = x^2

Explanation:

Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 14 to 30, in increments of 1. A left whisker extends from 16 to 18. The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22. The right whisker extends from 26 to 28. All values estimated.

Answers

Answer:

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

We use a box plot to present the 5-Number summary of a set of data.

The values contained in the 5-Number summary are:

Minimum ValueFirst QuartileMedian Third Quartile,Maximum Value

In the box plot, the following rules apply:

The whisker starts from the minimum value and ends at the first quartile.The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median.The end whisker starts at the third quartile and ends at the maximum value.

Using these, we interpret the given box plot

A left whisker extends from 16 to 18, therefore:

Minimum Value=16First Quartile =18

The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22.

Median=22Thrid Quartile=26

The right whisker extends from 26 to 28.

Maximum Value =28

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Box plot has boxes with some lines ( called whiskers ).

Box plot on the graphical level tells about 5 points:

   Minimum (Q0 or 0th percentile),    Maximum (Q4 or 100th percentile),    Median (Q2 or 50th percentile),    First quartile (Q1 or 25th percentile),    Third quartile (Q3 or 75th percentile).

There is starting whisker or left whisker denoting point minimum (Q0) and extends from there the line to Q1 ( first quartile).

Then the box starts which starts from Q1 and touched Q3. In the middle it passes through Q2 ( The median of the data ), and thus has a line in it.

At last, there is end whisker or right whisker denoting end quantile or Q4 (the maximum point).

Given data:

Left whisker extends from 16 to 18.

     Thus Q0 = 16

              Q1 = 18

Box plot starts from 18 and extends to 26, and is split by a vertical line segment at 22.

    Thus Q2 = 22

             Q3 = 26

The right whisker or end whisker extends from 26 to 28

    Thus Q4 = 28.

Thus the description of data is given as:

\(Q_0 = Minimum = 16\\Q_1 = First\: quartile = 18\\Q_2 = Second \:quartile = Median= 22\\Q_3 = Third\: quartile = 26\\Q_4 = Maximum = 28\\\)

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List two pairs of adjacent angles.

Answers

Answer:

A Linear Pair is two adjacent angles whose non-common sides form opposite rays. ∠1 and ∠2 form a linear pair. The line through points A, B and C is a straight line.

Hope this helps

Answer:

Two adjacent angles can be supplementary or complementary.

Step-by-step explanation:

IF they are supplementary then they are a linear pair.

Revise the MeanMedian2 class from Chapter 9 Exercise 2A so that the user can enter any number of values up to 20. If the list has an even number of values, the median is the numeric average of the values in the two middle positions. Allow the user to enter 9999 to quit entering numbers.

Answers

The revised MeanMedian2 class allows the user to input up to 20 values, with the option to stop entering numbers by inputting 9999. It calculates both the mean and median of the provided values.

To implement this functionality, the MeanMedian2 class can prompt the user to enter values in a loop until either 20 values are entered or the user inputs 9999. The entered values can be stored in a list. Once the user is done entering values, the class can compute the mean and median. For the mean, it can sum all the values in the list and divide by the number of values. For the median, it needs to handle two scenarios: an odd number of values and an even number of values. If the list has an odd number of values, the median can be obtained by simply finding the middle value. However, if there is an even number of values, the two middle values can be averaged to get the median.

With this revised class, users can easily input any number of values, up to 20, and get accurate mean and median calculations. Additionally, the option to quit by entering 9999 provides a convenient way for users to stop entering values whenever they want. This updated implementation improves the flexibility and usability of the MeanMedian2 class.

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solve: -12=24+6y y=2 y=-2

Answers

Answer:

this problem is false -12=2

Step-by-step explanation:

the sides are not equal

Last Thursday was costume day at Terrence's school. 50% of the 272 students wore a costume. How many students wore a costume?

Answers

Answer:

136

Step-by-step explanation:

272÷2=126

A set of midterm exam scores has a median that is much larger than the mean. Which of the following statements is most consistent with this information?
a. A stem plot of the data would be symmetric
b. A stem plot of the data would be skewed left
c. A stem plot of the data would be skewed right
d. The data set must be so large that it would be better to draw a histogram rather than a stem plot

Answers

The correct answer is option c A stem plot of the data would be skewed right.

A median that is larger than the mean in a set of exam scores suggests that the data is skewed to the right (or positively skewed), meaning that there are more scores at the high end of the distribution. This results in a longer tail on the right side of the distribution, which is often seen in data that contains outliers or extreme values. In this case, a stem plot of the data would be skewed to the right, showing a long tail on the right side of the plot.

Option a (a stem plot of the data would be symmetric) is incorrect because a symmetric distribution would have a median and mean that are equal, which is not the case here.

Option b (a stem plot of the data would be skewed left) is incorrect because a skewed left distribution would have a median that is smaller than the mean, which is not the case here.

Option d (the data set must be so large that it would be better to draw a histogram rather than a stem plot) is incorrect because the size of the data set does not affect the skewness of the data or the choice of a plot to use.

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the price of a widget was $704. over eight years, the price dropped to $336. assume a linear trend. (a) find a linear model p

Answers

When a widget of price $704 dropped to $336 over eight years, the linear trend of price can be expressed as y = -46x + 704, where y is the price of the widget and x is the number of years passed.

Therefore, the answer is y = -46x + 704

A linear trend implies the trend can be represented by a linear equation. The highest power of variable in a linear equation is 1.

Let us say the trend is expressed as y = mx + c, where y is the price of the widget and x is the number of years passed.

Initially, that is when x = 0 the price is $704. Substituting this

704 = m × 0 + c

Therefore, c = 704.

Over 8 years, that is when x = 8 the price is $336. Substituting this

336 = m × 8 + 704

m = - (704 - 336)/ 8

m = -46

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Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5

Answers

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

For similar question on vertex.

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