Equation is C=25n + 2500 And The total cost to produce 3000 toys is $77,500 And With $32500, a total of 1200 toys can be produced
A linear equation is what, exactly?
An algebraic equation with only a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
A) Lets have linear equation y=mx+b,
C (total cost) = y and n (number of toys) =x.
The original development cost plus the production cost of each toy would equal the overall cost of creating n toys.
Because m is multiplied by n, the number of toys, the cost to produce a toy will equal m.
Due to the fact that b is a constant and its value is unaffected by the quantity of toys, it will always equal the development cost.
Therefore, C=25n + 2500
B) by above, equation put n=1750
C= 25(3000) + 2500
C= $77,500
C) Now, again by same equation, but C instead of n.
=> 32500= 25n +2500
=> 30000=25n
=> n = 1200
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jogger runs around a circular track of radius 70 ft. let (x,y) be her coordinates, where the origin is the center of the track. when the jogger's coordinates are (42, 56), her x-coordinate is changing at a rate of 18 ft/s. find dy/dt.
The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.
Given,
The radius of the circular track in which the jogger runs = 70 feet
The coordinates of the jogger = (42, 56)
The rate of change in x coordinate = 18 feet/sec
Let (x,y) be the coordinates
We have to find dy/dt;
Then we know x,y satisfies the equation of the circle as
x² + y² = 70²
Let us differentiate this implicit function with respect to t
2x dx/dt + 2y dy/dt = 0
At this point, dx/dt 18 and x = 42. y = 56
Substitute to have
2 × 42 × 18 + 2 × 56 dy/dt = 0
1512 + 112 dy/dt = 0
dy/dt = 1512/112
dy/dt = 13.5 feet
Therefore,
The derivative dy/dt here is 13.5 feet
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3) you roll a die 48 times with the following results. number 1 2 3 4 5 6 frequency 2 14 2 12 3 15 use a significance level of 0.05 to test the claim that the die is fair. use the p-value method. (a) set up the null hypothesis and alternative hypothesis and indicate the claim. (b) calculate the test statistic. be sure to set up the equation. round to three decimal places.
The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75
What do you understand by Hypothesis testing?A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.
How to solve?
If the die is fair, the probability of getting any of the six numbers is equal (1/6).
The test statistic (TS) is given as:
TS=∑(Oi−Ei)2Ei∼χ2n−1
TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8
TS=21.75
In conclusion, the die is unfair.
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I don’t understand need help asap please. Complete the square to determine the minimum or maximum value of the function defined by the expression a^2-2a-8 show work
Answer:
(a-1)^2-9
Step-by-step explanation:
First you divide the coefficient of a by 2, which is 1. Now, do this: [tex](a-1)^2-8[/tex] where the -1 is half the coefficient of a. What this does is get the first two terms: a^2 and 2a, but we have an extra + 1(expanding this out gives [tex]a^2 -2a + 1[/tex]. So we have to subtract 1 to cancel it out. This gives [tex](a-1)^2-9[/tex], because -8-1=9. We can check this by expanding it out, and seeing if it equals our previous equation. Expanding this out gives [tex]a^2-2a+1-9[/tex], which is equal to our originial equation.
Yesterday, Ralph took a math test and a history test. The sum of his scores was 170. He scored
10 points higher on his math test than on his history test. What score did Ralph receive on
his math and history tests?
Answer:ralph got an 90 on his math test and a 80 on his history test
Step-by-step explanation:
so i divided 170 and that = to 85 so i took the two 5 from the two 80 and added it to the 80 for math
a farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). the farmer has 47 meters of fence and wants the garden to have an area of 266 sq-meters. what should the dimensions of the garden be?
The dimensions of the garden would be length = 28 meters and width = 9.5 meters
A database of research funds called Dimensions connects funding to articles, clinical trials, and patents as well as other outcomes. Dimensions is a division of the technology firm Digital Science, which has its global headquarters in London, United Kingdom.
Let the width be = w
Let the length be = L
enclose three side ( 2w+L) = 47 meter
L = 47-2w
Area of field = w*L
Area = w(47 - 2w)
266 = 47w - 2w²
2w² - 47w + 266 = 0
Solving this, we get
w = 14 or w = 9.5
The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)
= 47 - 19
= 28 meters.
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Help me please I’m begging and crying
Answer:
x=-12
Step-by-step explanation:
it would be -2=-x-14 then solve as normal algebraic equation
add 14 to each side 12=-x
then divide by -1 on each side so you get x=-12 for the final answer hope this helps
A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required for the frame is represented by the function W(x), and the amount of glass is represented by the function G(x). The frames have lengths represented by the function f(x) and widths represented by g(x). Which statement describes the combined functions W(x) and G(x)? The amount of glass required has a constant rate of change, but the amount of wood does not. The amount of wood required has a constant rate of change, but the amount of glass does not. Both the amount of wood required and the amount of glass required have a constant rate of change. Neither the amount of wood required nor the amount of glass required has a constant rate of change.
The correct statement regarding the rate of change of the functions is given as follows:
The amount of wood required has a constant rate of change, but the amount of glass does not.
How to obtain the rate of change of the functions?The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.
For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.
For the glass function, we have that:
When x increases by one from 2 to 3, the output G(x) increases by 21.When x increases by one from 3 to 4, the output G(x) increases by 33.Hence the rate of change is not constant, and then the second statement is the correct statement.
Missing InformationThe table is given by the image shown at the end of the answer.
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the perpendicular bisector of side AB of triangle ABC intersects side AB at point D and BC at point E. If angle CAB = 82 degrees and angle C = 68 degrees, what is angle CAE
After finding the value of the angle CAE will be equal to 22°.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the information provided in the question,
The perpendicular bisector of side AB of ABC intersects side AB at point D and BC at point E in the ABC equation. Also, m∠CAB = 82° and m∠C = 68°.
Join A and E.
In Δ ABC
∠A+∠B+∠C = 180° (Angle sum property of triangle.)
82°+∠B+68° = 180°
∠B = 180°-150°
∠B =30°
In Δ ADE and Δ BDE
AD=B D(DE shown is a perpendicular bisector.)
∠ADE =∠BDE = 90°
DE is common.
Δ ADE ≅ Δ EDB (By using the property SAS)
∠DEB=∠D A E [By using the property CPCT] (1)
In Δ DBE
∠EDB + ∠DBE+∠BED = 180°
90° +30°+∠BED = 180°
∠BED = 180°-120°
∠BED = 60°
So, ∠BAE=∠BED=60° (By using equation 1)
∠CAE=∠CAB - ∠BAE
∠CAE = 82°-60°
∠CAE = 22°.
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a researcher designs a study where participants are randomly assigned to one of the two groups--one is run at night and one is run during the day. each participant in each group is then measured twice, under two different conditions, red and blue. this is best described as a(n) design.
The correct answer is Independent groups design.
Given that,
Participants in a study are randomly allocated to one of two groups; one group is run at night, while the other is run during the day. Then, each member of each group is measured twice under the red and blue conditions, respectively.
Independent groups design.
Independent measures style, conjointly called between groups is an experimental style wherever completely different participants are employed in every condition of the experimental variable. This suggests that every condition of the experiment includes a distinct cluster of participants.
Therefore, the correct answer is Independent groups design.
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This is a Linear equation.
Based on the slope (-8) of the linear equation, the amount Austin pays each week, which is $8.
What is a Linear Equation?A linear equation can be defined as y = mx + b, which shows the relationship between variable x and variable y, where we have the following:
Slope value = m = change in y / change in x [this is also the unit rate]
Y-intercept of initial value = b.
Given that the table represents a linear equation, find the slope or unit rate of the linear equation, which represents the amount Austin pays every week.
Slope (m) = change in L / change in t
Using two pairs of values from the table, (2, 24) and (4, 8):
Slope (m) = change in L / change in t = (24 - 8) / (2 - 4) = 16/-2
Slope (m) = -8
This implies that, Austin pays $8 every week.
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the combined average weight of an okapi and a llama is 450450450 kilograms. the average weight of 333 llamas is 190190190 kilograms more than the average weight of one okapi. on average, how much does an okapi weigh, and how much does a llama weigh? on average, an okapi weighs kilograms and a llama weighs kilograms.
Answer:
Okapi weighs 290, and llama weighs 160.
the weights of a certain dog breed are approximately normally distributed with a mean of 53 pounds, and a standard deviation of 6.2 pounds. use your graphing calculator to answer the following questions. write your answers in percent form. round your answers to the nearest tenth of a percent. a) find the percentage of dogs of this breed that weigh less than 53 pounds. % b) find the percentage of dogs of this breed that weigh less than 46 pounds. % c) find the percentage of dogs of this breed that weigh more than 46 pounds. %
(i) The percentage of dogs of this breed that weigh less than 53 pounds P(X<53) = 50.0%
(ii) The percentage of dogs of this breed that weigh less than 46 pounds P(X<46) = 15.2%
(iii) The percentage of dogs of this breed that weigh more than 46 pounds P(X>46) = 84.8%
What is Standard Deviation?
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.
Solution:
Mean weight (μ) = 53 pounds
Standard deviation (σ) = 6.2 pounds
The z-score for any given weight, 'X', is given by the following expression;
z = (X - μ)/σ
(i) P(X<53)
Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.
P(X<53) = 50.0%
(ii) P(X<46)
z = (46-53)/6.2
z = -1.12
this is equivalent to 15.2 percentile
P(X<46) = 15.2%
(iii) P(X>46)
P(X>46) = 100% - P(X<46) = 100% - 15.2%
P(X>46) = 84.8%
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5 parts!!! 100 pionts I WILL GIVE BRANLIST
part 1 Using the table provided above, list the average gas price for 2010.
part 2 Find the linear regression equation that models the data above. Round to the nearest thousandth if needed.
part 3 List the domain of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 4 List the range of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 5 Use the linear regression equation to predict how much you expect gas to cost in 2025?
1. The average gas price for 2010 is of: $2.22.
2. The linear regression equation is given as follows: y = 0.176x + 0.5.
3. The domain is: [0,∞).
4. The range is: [0.5,∞).
5. Gas is expected to cost $4.55 in 2025.
How to obtain the linear regression equation?The linear regression is obtained inserting the points of the table into a linear regression calculator.
The variables of the problem are given as follows:
Input x: number of years after 2002.Output y: cost of gas.Hence the points are given as follows:
(0, 0.7), (1,1.04), (2, 1.15), (3, 1.38), (4, 1.86), (5, 1.70), (6, 2.55), (7, 1.29), (8, 2.22), (9, 2.56).
Inserting these points into a calculator, the equation is given as follows:
y = 0.176x + 0.5.
The estimate for 2025 is the numeric value when x = 23, as 2025 is 23 years after 2002, hence:
y = 0.176(23) + 0.5 = $4.55.
The domain and the range are given as follows:
Domain: values of 0 and greater, representing the number of years after 2002.Range: values of 0.5 and greater, representing the costs.More can be learned about linear regression at https://brainly.com/question/29613968
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Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
Month Time (minutes)
1 47
2 43
3 39
4 36
5 35
6 33
What is the equation for the line of best fit where x represents the month and y represents the time?
y = −2.78x + 33.6
y = −2.78x + 48.5
y = 2.78x + 33.6
y = 2.78x + 48.5
The required regression equation is y = -2.78x + 48.5 for the line of best fit where x represents the month and y represents the time.
The table is given in the question.
As per the given table, the required solution would be as:
Let x represents the month and y represents the time
[tex]\bar{x}[/tex] = (1+2+3+4+5+6)/6 = 21/6 = 3.5
[tex]\bar{y}[/tex] = (47+43+39+36+35+33)/6 = 233/6 = 38.83
Sum of x = 21
Sum of y = 233
Mean x = 3.5
Mean y = 38.8333
Sum of squares (SSX) = 17.5
Sum of products (SP) = -48.5
Regression Equation = y = bx + a
b = SP/SSX = -48.5/17.5 = -2.77143
a = MY - bMX = 38.83 - (-2.77×3.5) = 48.53333
y = -2.78x + 48.5
Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.
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Answer:
y = -2.78x + 48.5
Step-by-step explanation:
I just took the test like 2 seconds ago...
Determine the value of "z" in the equation
z + (14 - 5i) = 9 + 2i
Answer:
z = − 5 + 7i
Step-by-step explanation:
z + 14 - 5i = 9 + 2i
Subtract 14 from both sides.
z - 5i = 9 + 2i -14
Subtract 14 from 9 to get -5.
z - 5i = -5 +2i
Add 5i to both sides.
z = -5 + 2i + 5i
Combine real and imaginary parts.
z = -5 + (2+5)i
Add 2 to 5.
z = -5 + 7i
Hope this helps!
Answer:
7i - 5
Step-by-step explanation:
z + (14 - 5i) = 9 + 2i
=> z + 14 - 5i = 9 + 2i
=> z = 9 + 2i + 5i - 14
=> z = 7i - 5
what is the additive inverse of -4x - 8
The additive inverse of (-4x - 8) is 4x+8.
What is Additive Inverse?
Additive inverse refers to any number that when added to the original number gives the result as zero. For instance, the additive inverse of 8 is -8 as 8 + (-8) = 0. It is possible to get the additive inverse of negative numbers too. For example, the additive inverse of -10 will be 10 as -10 + 10 = 0.
The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign. For example, the additive inverse of 8 is -8, whereas the additive inverse of -6 is 6.
The addition of a number and its additive inverse is equal to the additive identity.
we know that (-4x - 8) + (4x+8) = 0 .
Hence, The additive inverse of (-4x - 8) is 4x+8.
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college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected students must be surveyed in order to be 9898% confident that the sample percentage has a margin of error of 1.51.5 percentage points? (a) assume that there is no available information that could be used as an estimate of p^p^.
3206 students are randomly chosen since there is no knowledge of the sample fraction.
Explain the term Margin of Error?When determining the confidence interval, the margin of error is crucial. The critical z value,the sample size, and proportion can all be used to determine the margin of error in the case of proportion.The following can be used to represent the formula for calculating the margin of error for a single proportion:
ME = z√p(1 - p)/n
In order to be 91% certain that the sampling percentage seems to have an error margin of 1.5 percentage points, the number of randomly chosen students that must be surveyed is equal to;
0.015 = 1.6954×√0.5(1 - 0.5)/n
0.015/1.6954 = √0.5(0.5)/n
On further solving,
n = 3205.128
n ≈ 3206
As a result, 3206 students are randomly chosen since there is no knowledge of the sample fraction.
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The correct question is-
College officials want to estimate the percentage of students who carry a gun, knife, or other such weapons. How many randomly selected students must be surveyed in order to be 91% confident that the sample percentage has a margin of error of 1.5 percentage points?
a) Assume that there is no available information that could be used as an estimate of p.
There are two buildings beside each other that are 47 feet and 31 feet high. The buildings are 12 feet apart. What is the distance between the rooftops of the buildings?.
By using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
So, draw a figure of the 2 buildings as follows:
(Refer to the image attached below)
Now, we know that we can get the distance between the rooftops using the Pythagorean theorem.
Pythagorean theorem: c² = a² + b²
Now, insert the values and calculate as follows:
c² = a² + b²
c² = 12² + 16²
c² = 144 + 256
c² = 400
c = √400
c = 20ft
Therefore, by using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.
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Which is the equation of the line, in point-slope form, with a slope of 5 that passes through (1, −3)?
A. y = 5x − 3
B. y = −5x + 1
C. y + 3 = 5(x − 1)
D. y − 3 = 5(x + 1)
Answer: The correct answer is C. y + 3 = 5(x − 1)
Step-by-step explanation:
Change the equation into slope-intercept form
y + 3 = 5(x − 1)
y = 5x - 8
Using the slope-intercept form of y = mx + b, m = slope, and b = the y-intercept.
Therefore, y = 5x - 8 has a slope of 5 and a y-intercept of -8
When we graph the slope from y = -8, it passes through (1, -3)
if you repeated the experiment with a glass of water that had 5 teaspoons of salt and another glass that had 10 teaspoons, what do you think would happen?
This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
1. When salt is dissolved in water, the chemical bond between the salt atoms is broken by the water molecule.
2. When a teaspoon of salt is added to water, the salt molecules fill any open places in the water. Since water is a fluid with atoms that may move around freely, when salt is dissolved in it, these open spaces are filled, making salt particles invisible.
3. The resulting solution becomes denser. The mass of the solution increases when salt is added to water. As a result, the solution's density rises.
4. This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
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Which best describes the location of A', the image of A
after a dilation by a factor of 1/2 with center at C?
c²
A' will be closer to A than to C
O A' will be half way between C and A
O A' will be closer to C than to A
C will be the midpoint of the line
connecting A and A'
'A
Answer:
1/c2
Step-by-step explanation:
PLEASE HELP!!!! HURRY!!!!
I think it might be all them but the third one, if I'm wrong sorry.
hello everyone one last time, I just want to say I've been here before and thank you all for support :3 and to finish out with a question...what is the liklihood of pulling a red marble out of a bag of 8 blue marbles and 3 red marbles.
Answer: 27.3 %
Step-by-step explanation:
There are 8 blue and 3 red marbles in the bad so total is 11 marbles
We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%
Is this function linear or nonlinear? y=1x responses linear linear nonlinear
Answer: Nonlinear.
Step-by-step explanation:
A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. Compute the appropriate test for the data provided below.
Education Business/Management Behavioral/Social Science Fine Arts
62 72 42 80
81 49 52 57
75 63 31 87
58 68 80 64
67 39 22 28
48 79 71 29
26 40 68 62
36 15 76 45
Source SS df MS F
Between 63.25 3 21.0833333333 .04
Within 12298.25 28 439.2232143 Total 12361.5 31 What is your computed answer? F = .04 (3,28), not significant
What would be the null hypothesis in this study? There will be no difference in history test scores between students with different academic major.
What would be the alternate hypothesis? There will be a difference somewhere in history scores between the four groups with different academic major.
What probability level did you choose and why? p = .05 There is little risk involved if either a Type I or a Type II major is made.
What were your degrees of freedom? 3, 28
Is there a significant difference between the four testing conditions? No significant differences were found between the four groups in terms of performance on a U.S. history exam.
Interpret your answer. Students regardless of academic major performed equally (in this case poorly) on a high school senior standardized U.S. history exam.
If you have made an error, would it be a Type I or a Type II error? Explain your answer. If I have made an error, it would be a Type II error. There really is a difference in history knowledge between academic major but somehow I failed to demonstrate that with this study.
On solving the provided question, significant difference between the four testing conditions is α = 0.10
What does the term "alternative hypothesis" mean?An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.
Null hypothesis: : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major
Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.
Determine the significance level. α = 0.10
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Pls help
, I really need an answer for this rn
Answer: 34.00 and 2.10
Step-by-step explanation:
PLEASE FAST 20 POINTS
An octagon has 8 sides. One angle of a regular octagon measures (9w + 8)°. Determine the value of w. Round to the nearest whole number.
w = 19
w = 16
w = 14
w = 135
For the octagon whose measure of angle is (9w + 8)°, the value of w is 14.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Angle of regular octagon = 9w + 8
Since, angle of an octagon is 135°
Equate 9w + 8 to 135,
9w + 8 = 135
9w = 127
w = 14.11
w = 14
The required value of w is 14.
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Answer:
he octagon whose measure of angle is (9w + 8)°, the value of w is 14.
Step-by-step explanation:
What is angle?
An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Angle of regular octagon = 9w + 8
Since, angle of an octagon is 135°
Equate 9w + 8 to 135,
9w + 8 = 135
9w = 127
w = 14.11
w = 14
The required value of w is 14.
i hope this helps !!!!!
8 baskets ?
16 movies = ————
?
How many movies will fit into 24
baskets?
Answer:
48 movies
Step-by-step explanation:
8/16=1/2
24/48=1/2
Write an inequality that represents the graph below. Please help
Answer: x≥3
Step-by-step explanation:
why should we use non-parametric tests? choose the one false answer. group of answer choices because they are more powerful than parametric tests because when you have quantitative data but assumptions of normality are not met because when you are only using ordered data because when there is no linearity
Option B. Because when you have quantitative data, but assumptions of normality are not met. This is because, unlike parametric tests, non-parametric tests do not make assumptions about the data's underlying distribution.
Why should we use non-parametric tests? Option B. Because when you have quantitative data, but assumptions of normality are not met.Non-parametric tests are often used when dealing with data that is not normally distributed, as they allow for a more accurate analysis of such data. They can also be used when a linearity of the data cannot be assumed and when dealing with ordinal data. Non-parametric tests are more powerful than parametric tests, which makes them a good choice when a more precise analysis is needed.
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