a) The bigger the value, each box plot is spread out. The ages of the top 50% of customers are more varied than 50% of lower consumers. Hence, each plot is slanted to the right.
b) The BMW 3 series is likely to have an outlier. It has the longest whisker.
c) When comparing median age, younger people are likely to purchase the BMW 3 series and while older people are more likely to purchase the BMW 7 series. However, because each data set is so dissimilar, this is not a rule.
d) The spread is the smallest in the second quarter of the box. The difference between the first quartile and the median seems to be barely three years.
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The complete question is:
A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.
a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.
b. Which group is most likely to have an outlier? Explain how you determined that.
c. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?
d. Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.If the perimeter is less than 78cm and x is an interger.Find the largest value of x
The largest value of x is 13.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.
The perimeter is less than 78 cm and x is an integer.
The perimeter of the pentagon = the sum of all the sides.
x + x+1 + x+3 + x-2 + 6 < 78
4x + 10 - 2 < 78
4x < 70
x < 14
The largest value of x is 13.
Therefore, the largest value of x is 13.
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In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 
ANSWER FAST PLEASE
WILL GIVE BRAINLIEST
There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.
It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.
There may be a correlation, but there is no direct link.
How does correlation work?Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.
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4. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)?
166158 is the break-even point for the manual process
What is Expression?An expression is combination of variables, numbers and operators.
Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.
Let the number of bags will be x
36234+2.14x..(1)
The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.
84420+1.85x..(2)
From equation 1 and 2
36234+2.14x=84420+1.85x
2.14x-1.85x=84420-36234
0.29x=48186
Divide both sides by 0.29
x=166158
Hence, 166158 is the break-even point for the manual process
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Hassan's history class is taking a field trip to the state capitol building. The capitol building is
50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to
view a local monument. The bus driver plans to drive at an average speed of 40 miles per
hour.
Which equation can you use to find how many hours, x, the second part of the trip will take?
The equation that can be used to find how many hours, x, the second part of the trip will take is:
distance = rate x time
Which equation can you use to find how many hours?Where distance is the remaining distance from the capitol building to the school, rate is the average speed of the bus, and time is the time it takes to travel that distance.So, if we know that the distance is 50 miles and the rate is 40 miles/hour, we can find the time it takes to travel the remaining distance by plugging these values into the equation and solving for x:50 miles = 40 miles/hour x xthen by dividing both sides by 40 miles/hourx = 50/40 = 1.25 hours The equation to use to find how many hours, x, the second part of the trip will take is:distance = rate x timeIn this case, the distance is the remaining distance from the capitol building to the school, which is 50 miles - (40 miles/hour x 0.75 hours) = 35 miles. The rate is the average speed of the bus, which is 40 miles/hour. Therefore, the equation to find the time, x, of the second part of the trip is:35 miles = 40 miles/hour x xTo solve for x, divide both sides of the equation by 40 miles/hour:x = 35 miles / 40 miles/hour = 0.875 hours, or 52.5 minutes.To learn more about capitol building refer to;
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division problem can be described using this model
The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
What is division?
Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.
When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
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Use the formula F =9 over 5 C + 32 to answer the following
Maha checked the outside temperature at noon one day and found it was 26° C. At 10 PM when she checked, the outside temperature was 18° C. How much, in degrees Fahrenheit, did the temperature drop between noon and 10 PM? Round your answer to the nearest tenth.
The temperature drop between noon and 10 PM is 14.4° F.
What is the conversion of Celsius to Fahrenheit?Celsius to Fahrenheit is the conversion of temperature from Celsius unit to Fahrenheit unit. Temperature scales provide a way of measuring how hot or cold a body is. Fahrenheit and Celsius are temperature scales.
The formula to convert Celsius to Fahrenheit is given by: °F = °C × (9/5) + 32.
Given that, Maha checked the outside temperature at noon one day and found it was 26° C.
So, the temperature in Fahrenheit is °F =26° ×(9/5)+32
= 46.8+32
= 78.8° F
At 10 PM when she checked, the outside temperature was 18° C.
So, the temperature in Fahrenheit is °F =18° ×(9/5)+32
= 32.4+32
= 64.4° F
Difference in temperature =78.8-64.4
= 14.4° F
Therefore, the temperature drop between noon and 10 PM is 14.4° F.
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in trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the [ select ] , the value of the hypotenuse is [ select ] , and is the angle adjacent to the [ select ] .
In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.
So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.
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The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)
a) The function is P = 500e^0.4t
b) The count after 10 hours is 27299
c) it would reach 80000 in 13 hours
What is the function?We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;
P = Poe^rt
P = population at time t
Po = Initial population
r = Population growth rate
t = Time taken
Then we have;
P = 500e^0.4t
After ten hours;
P= 500e^0.4 * 10
P = 27299
The count would reach 80000 when;
80000 = 500e^0.4 t
80000/500 = e^0.4 t
160 = e^0.4 t
ln160 = e^0.4 t
ln160 = 0.4t
t = ln160/0.4
t = 13 hours
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show me prymind with base length: 8 feet side length: 6.56 feet (calculated using the pythagorean theorem) height: 12 feet rmid
A diagram of a pyramid with the given measurements is not possible to generate.
But we can calculate he base length, side length and height of a pyramid using the Pythagorean theorem.
In a pyramid, the slant height (rmid) can be found using the Pythagorean theorem. If the base length (b) and the height (h) of the pyramid are known, the slant height (rmid) can be calculated using the formula:
rmid = sqrt(b^2 + h^2)
In this case,
rmid = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.4
You can also use this information to find the side length of the pyramid, which is the length of one of the triangular faces. Using the Pythagorean theorem again:
side length = sqrt(rmid^2 - (b/2)^2)
In this case,
side length = sqrt(14.4^2 - (8/2)^2) = sqrt(207.36 - 16) = sqrt(191.36) = 6.56
So, based on the information provided, the base length of the pyramid is 8 feet, the side length is 6.56 feet and the height is 12 feet and the slant height is 14.4 feet.
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for 14-21 write two equivalent fractions for each
The fractions with different numerators and denominators but the same value are said to be equivalent fractions.
What is an equivalent fraction about?For instance, since 2/4 and 3/6 both equal the 1/2, they are equivalent fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
A rule that says the result of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.
Equivalent fractions are those that, despite their visual differences, represent the same value. For instance, if you have a cake and cut it into two equal pieces, you will have consumed half of the cake.
In this case, it should be noted 1/2 is the same as 3/6.
Note that an overview was given as your information is incomplete.
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Let ABCD be a parallelogram. Let M be the midpoint of line AB and N be the midpoint of line AD. Diagonal BD intersects line CM and line CN at P and Q, respectively. Find PQ/BD.
The value of PQ / BD of given parallelogram where Diagonal BD intersects line CM and line CN at P and Q, respectively = 1/3
Let's consider the two triangles BMP and DCP.
Here,
∠DPC = ∠BPM (because they are vertically opposite angles)
∠DCP = ∠BMP (because they are alternate interior angles of transversal CM with DC // BM)
∴△BMP∼△DCP (By AA theorem)
Thus,
ABCD is a parallelogram. Therefore AB = DC and AD = BC.
It is given that M is the midpoint of AB
BD = DQ + BQ BD = BP + PD
BD = 2BQ + BQ BD = 2PD + PD
BD = 3BQ BD = 3PD
therefore
BQ = PD And
Since DQ = 2BQ then DQ = 2PD and
PD + PQ = 2PD subtract PD from each side
PQ = PD
so BQ = PD = PQ
BD = PD + PQ + BQ
BD = PQ + PQ + PQ
BD = 3PQ
Therefore the value of PQ / BD of given parallelogram is PQ / BD = 1/3.
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Homework 3x-5; x-5; an al 2x-14;.:. arithmetic sequence. Calculate the Value of x Find the Which term the First three are in Determine the general term of the Sequence Soth term the sequence is equal to -62 terms of
The value of x is found to be 3 and the arithmetic sequence is found to be 4, -2, -8, ... .
What is arithmetic sequence?
The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.
The arithmetic sequence is 3x - 5, x - 5, 2x - 14, ....
If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term.
(x - 5) - (3x - 5) = (2x - 14) - (x - 5)
x - 5 - 3x + 5 = 2x - 14 - x + 5
-2x = x - 9
-2x - x = -9
-3x = -9
x = 3
The first three terms can be obtained by substituting the value of x in the terms -
The first term - 3(3) - 5 = 4
The second term - 3 - 5 = -2
The third term = 2(3) - 14 = -8
Therefore, the arithmetic sequence is 4, -2, -8, .....
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At a given point 67.7ft at ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees find the height of the roof worker and the distance of the ø if someone is observing below.
The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.
The base will be calculated as:-
tan(38.6) = P / B
tan(38.6) = 67.7 / B
B = 67.7 / tan(38.6)
B = 54.8 ft
The height will be calculated as:-
Cos(42.4) = B / H
H = 84.8 / Cos(42.4)
H = 114.83 ft
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Answer the questions in image!
(The answers are already there, just figure out which go where.)
50 points!
As a town gets smaller the population of its high school decreases by 4% each year the senior class has 160 students now. In how many years will it have about 100 students? write an equation. then solve the equation without graphing.
The number of years that it will it have about 100 students is 11 years.
How to calculate the number of tears?Final population = Initial population * (1-0.04)^years
Where 0.04 is the percentage decrease (4%) converted to decimal form, and "years" is the number of years in the future.
We can use this formula to find the number of years it will take for the senior class to have about 100 students:
Final population = 100
Initial population = 160
100 = 160 * (1-0.04)^years
We can solve for "years" by taking the natural logarithm of both sides:
ln(100) = ln(160 * (1-0.04)^years)
ln(100) = ln(160) + ln((1-0.04)^years)
and then we can solve for the power of (1-0.04)
ln(100) - ln(160) = ln((1-0.04)^years)
now we can get the value of years
years = (ln(100) - ln(160)) / ln(1-0.04)
which is around 10.72 , so it would take about 11 years for the senior class to have about 100 students.
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a manufacturer buys a new machine costing $180000 dollars. it is estimated that the machine has a useful lifetime of ten years and a salvage value of 6000 dollars at that time. assume the value of the machine varies linearly during this time. do not include dollar signs in your answers.
A manufacturer buys a new machine costing $180000 dollars. The value of the machine at the end of 10 years is $6000.
Calculate the annual depreciation of the machine.
Depreciation = (Purchase Price - Salvage Value) / Useful Life
Depreciation = (180000 - 6000) / 10
Depreciation = 174000 / 10
Depreciation = $17400 per year
Calculate the value of the machine at the end of each year.
Year 1: 180000 - 17400 = $162600
Year 2: 162600 - 17400 = $1452000
Year 3: 1452000 - 17400 = $1277600
Year 4: 1277600 - 17400 = $1103200
Year 5: 1103200 - 17400 = $928800
Year 6: 928800 - 17400 = $754400
Year 7: 754400 - 17400 = $580000
Year 8: 580000 - 17400 = $405600
Year 9: 405600 - 17400 = $231200
Year 10: 231200 - 17400 = $6000
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an ordinary annuity pays 1000 quarterly for two years. how many payments are there?
The number of payments for the ordinary annuity that pays $1,000 quarterly for two years is 8.
What is an ordinary annuity?An ordinary annuity's cash flows or payments occur at the end of the period, unlike an annuity due.
For quarterly payments, in a year, payments are made 4 times, that is, every three months.
For two years, the payments will be made 8 times (4 x 2).
Thus, we expect the ordinary annuity to pay $8,000 ($1,000 x 2 x 4).
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if we take a sample of reee's pieces has 1000 pieces. the manufacturer says that exactyl 40% of the candies are organe. if we select a sample of 50 pieces, how many will be oragne. let x
If we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.
The manufacturer says that exactly 40% of the candies are orange. We can use this information to find the expected value of the number of orange candies in a sample of 50 candies.
Expected value is found by multiplying the number of trials (in this case, 50) by the probability of success (in this case, 40% or 0.40)
x = (50)(0.40) = 20 candies.
So, if we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.
It's worth noting that this is an expectation, the actual number of orange candies in the sample of 50 candies may be different from the expected value.
The correct question of the following problem is:
If a sample of 1000 Reese's Pieces contains 40% orange candies, and a random sample of 50 Reese's Pieces is selected, how many orange candies can be expected to be in the sample of 50 Reese's Pieces? Let x be the number of orange candies in the sample of 50 Reese's Pieces.
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The t-test takes into account the _____ and _____ of the data, and the p-value tells us _____.
The p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.
We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.
You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.
Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.
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Expand a^2= (b-x)^2 +h^2
The expanded value of the given equation is a²+2bx = b² + x ²+ h² .
Expansion - what is it?Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.
Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.
Given : a^2= (b-x)^2 +h^2
a² = (b-x)² + h²
we know that (c-d)² = c²+d² + 2cd
So, a² = b² + x² -2bx + h²
a²+2bx = b² + x ²+ h²
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In a garden 5/6 of the area is filled with native plants. The native plants take up to 107/4 m2 . Let g represent the total area of the garden. chooses 2 answers. pleas help me :(
The total area of the garden is given as follows:
32.1 m².
How to obtain the total area of the garden?The total area of the garden is obtained applying the proportions in the context of this problem.
The area of native plants is given as follows:
107/4 = 26.75 m².
This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:
5g/6 = 26.75.
g = 26.75 x 6/5
g = 32.1 m².
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The figure below is dilated by a factor of centered at the origin. Plot the resulting image.
A graph of the resulting image after a dilation by a factor of 1/4 centered at the origin is shown in the image attached below.
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair T (8, 8) → Ordered pair T' (8 × 1/4, 8 × 1/4) = Ordered pair T' (2, 2).
Ordered pair R (-8, -4) → Ordered pair R' (-8 × 1/4, -4 × 1/4) = Ordered pair R' (-2, -1).
Ordered pair S (4, -8) → Ordered pair S' (4 × 1/4, -8 × 1/4) = Ordered pair S' (1, -2).
Lastly, we would use an online graphing calculator to plot the resulting data points.
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A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 25%
The best grade that can be earned is given as 0.8575
How to solve for the gradeIf he is able to get the sum of 100 percent in the final exam, trhis would count as 25 percent of the total grade that he has
100 - 25 = 75%
Then we would have
0.75 * 81 + 25 / 100
= 85.75 / 100
= 0.8575
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Question
A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 15% of the course grade.
What is the best course grade your friend can earn?
What is the sum of the geometric sequence −2, −6, −18, … if there are seven terms?
Group of answer choices
−728
−128
−1,458
−2,186
The sum of the first seven terms is given by -2186
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...
The geometric sequence is given here by -2,-6,-18...
We can observe that the common ratio is r=3
thus the sequence of upto 7 terms is given by
-2,-6,-18,-54,-162,-486.-1458
Thus the sum of all seven terms is given by
S=-2-6-18-54-162-486-1458
=-2186
Hence, The sum of the first seven terms is given by -2186
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Solve the equation on the
interval [0, 2π).
3 sin x = sin x + 1
The solution to the equation on the interval is x = π/6 + 2πn, where n is any non-negative integer less than 2.
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
3 sin x = sin x + 1
Interval = [0, 2π).
To solve the equation 3sin(x) = sin(x) + 1, we first subtract sin(x) from both sides to get 2sin(x) = 1.
So, we have
2sin(x) = 1
Then, we divide both sides by 2
sin(x) = 1/2.
Therefore, x = arcsin(1/2) + 2πn, where n is any integer.
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Barbara ran
after lunch.
3
of a mile before lunch and of a mile
8
12
How far did she run in all?
Answer:
Step-by-step explanation:
1/2 is your answer
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 79.
The linear regression equation for this data is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is given as follows:
73.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
The points from this data-set are given as follows:
(70, 55), (89, 92), (79, 81), (84, 74), (84, 77), (70, 65) and (64, 68).
Inserting these points into a calculator, the regression equation is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is obtained as follows:
y = 79 - 6
y = 73.
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The distribution of values taken by a statistic in all possible samples of the same size from the same population is None of the above The population parameter The sampling distribution of the statistic The probability that the statistic is obtained The variance of the values
The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.
The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.
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Answer:
Step-by-step explanation:
The slope's simplest form is 1/2.
An experiment subject only to random fluctuation within a normal distribution collects the following set of unitless numerical values: 15.8, 17.8, 19.5, 20.0, 14.7, 16.6, 16.8, 19.4, 18.3
A number of hypotheses are put forward for the theoretical value of what is measured here. Select all of the theoretical values given below that can be ruled out by our usual 1-sigma uncertainty criterion. A. 15.6 B. 15.9 C. 19.5 D. 19.7 E. None of these theoretical values is confirmed by this data.
A one-sigma uncertainty criterion means that if a theoretical value falls within one standard deviation of the measured data, it is considered consistent with the data.
Using this criterion, we can rule out theoretical value D. 19.7, since it is outside the range of measured values.
The other theoretical values A. 15.6, B. 15.9, and C. 19.5 fall within one standard deviation of the measured data, so they cannot be ruled out by this criterion.
Therefore, the only theoretical value that can be ruled out by our usual 1-sigma uncertainty criterion is D. 19.7
It's worth noting that this method just gives a rough idea of the consistency of a theoretical value with the data.
Other methods, such as the chi-squared test, or Bayesian analysis could be used to find the best-fit theoretical value and its uncertainty, and confirm or rule out other theoretical values.
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