The equation of line that passes through the point (8,6) and has a slope of 0 is y = 6.
Define the equation of the line?The set of points that make up a line in a coordinates system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line with in coordinate axis as a set of variables, x, and y.As the sated question-
The passing point; (x1, y1) = (8,6)
slope m = 0
Thus, equation lo line by slope intercept form is-
y - y1 = m(x - x1)
y - 6 = 0(x - 8)
y = 6
Thus, the equation of the line that passes through the point (8,6) and has a slope of 0 is y = 6.
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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:
Is this function linear or nonlinear? y=1x responses linear linear nonlinear
Answer: Nonlinear.
Step-by-step explanation:
how many ways are there to deal hands from a standard playing deck to four players if: (a) each player gets exactly 13 cards. (b) each player gets seven cards and the rest of the cards remain in the deck?
Th number of possible ways for
a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
In this question, we have been given that there are four players. the select cards from the standard deck of 52 cards.
We need to find the number of possible ways for given situations.
(a) each player gets exactly 13 cards.
Using combination, we get an expression,
^{52}C_13 * ^{39}C_13 * ^{26}C_13 * ^{13}C_13
= 52! / (13! 13! 13! 13!)
= 53644737765488792839237440000
(b) each player gets seven cards and the rest of the cards remain in the deck
Using combination, we get an expression,
^{52}C_7 * ^{45}C_7 * ^{38}C_7 * ^{31}C_7 * ^{24}C_24
= 52! / (7! 7! 7! 7! 24!)
Therefore, a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
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PLEASE HELP!!!!
Suppose you are developing an Excel spreadsheet that finds the unit
price of any object. You plan to put the number of units in cell E2, and
the price of the object in cell D2.
What formula should you write in cell C2 to find the unit price?
The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
What is the unit price?
The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.
To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.
Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).
To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00
So, Object= Number of units in cell = C2
Price of Object = B2
Unit Price Formula = D2
Therefore, by considering the above example.,
Object = C2 = 50
Price = B2 = 8.00
D2 Formula= Price of Object/ Number of Units
Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
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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
ANSWER PLSSSSSS
This scatter plot shows the number of magazines checked out and the number of books checked out.
Choose the statement that is best supported by the data in the scatter plot.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
1The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
2The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
3The data shows a non-linear association between the number of magazines checked out and the number of books checked out.
4The data shows no apparent association between the number of magazines checked out and the number of books checked out.
The correct statement regarding the scatter plot is given as follows:
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
What is the scatter plot?The scatter plot, as shown by the image given at the end of the answer, is a series of points of the data-set in the following format:
(Number of books checked out, Number of magazines checked out).
From the graph, the points are given as follows:
(2,4), (3,6), (4,0), (4,2), (5,7), (6,5), (7,2), (9,1).
Inserting these points into a linear regression calculator, the line of best fit is given as follows:
y = -0.36x + 5.18
Which has a negative slope, meaning that it is a negative linear relationship and the first option is correct.
Missing InformationThe scatter plot is given by the image shown at the end of the answer.
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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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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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On 2 May 2000, a man borrowed a sum of money from a bank at 6.5% p.a. simple interest and on 2 September 2000, the interest amounted to $137.50. Calculate the amount of money he borrowed.
The amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
Explain the term simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.The formula for calculating simple interest;
SI = P R T/100,
where
P stands for principal, R for rate of interest, and T for time period. Here, the rate (r%) is expressed as r/100, where r% is the percentage rate.In the case of simple interest, the principal is the amount of money that does not change over the course of a year.
Time = 4/12 year
For the given values-
137.50 = P × 6.5 × 4 /1200
P = 137.50 × 1200 / 6.5 × 4
P = $6346.15
Thus, the amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
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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...
compare continuous functions f, g, and h, and match the statements with the function they best describe. drag each description to the correct location on the table. this function has the highest y-intercept.this function is increasing over the longest interval.this function is decreasing over the longest interval.this function has the lowest y-intercept.
From the given properties of the functions,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)Functions given in the picture are 'f', 'g' and 'h'.
From the graph given for function 'f',
y - intercept = 1
Increasing in the interval → (-∞, -0.8] and (0.6, ∞)
Decreasing in the interval → [-0.8, 0.6]
From the table given for the function 'g',
Decreasing in the interval → [-2, 2]
y-intercept = -1
For function 'h',
h(x) = 4x³ + 3
Table of the input-output values for function will be,
x h(x)
-2 -29
-1 -1
0 3
1 7
2 35
Therefore, function 'h' will increase in the interval → (-∞, ∞)
y-intercept → y = 3
Therefore, from these properties of the functions we conclude,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)To know more about Function check the below link:
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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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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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1/2(x-8)+1=2(1/8x-1)
Answer:4
Step-by-step explanation:
distribute 1/2 into x-8 and distribute 2 into 1/8x-1 on other side
1/2x-4+1=1/4x-2
combine like terms
1/4x=1
multiply both sides by 4 to solve x
x=4
f a circle has an area that is 225 pi square feet or more, what are the possible diameters d for the circle?
The diameter of the circle is 30 feet.
What is diameter?
The center of the circle is the midpoint of a line segment that connects two points on the circle's perimeter, and this line segment is indicated by the diameter of a circle.
The diameter of a circle is precisely equal to twice the radius' length.
Let us suppose the diameter of a circle is D then, the area is computed according to the formula
[tex]A = \frac{\pi D^2}{4}[/tex]
where
A is the area and D is the diameter.
Plug A = 225 pi in the above equation,
[tex]225 \pi =\frac{\pi D^2}{4} \\225 = \frac{D^2}{4} \\D^2 = 900\\D = 30[/tex]
Hence, the diameter of the circle is 30 feet.
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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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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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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%
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:
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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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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 !!!!!
Pls help
, I really need an answer for this rn
Answer: 34.00 and 2.10
Step-by-step explanation:
Write an inequality that represents the graph below. Please help
Answer: x≥3
Step-by-step explanation:
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
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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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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(a) residents of a city have monthly incomes (in dollars) that are distributed around an unknown mean, with a standard deviation of 500 dollars. the incomes are recorded for a random sample of 36 residents. an average value of 1500 dollars is obtained. what is the 90%-confidence interval for the population mean estimate?
The 90% confidence interval for the population mean estimate is (1362.9167,1637.0833).
Given that,
n=36 residents
Standard deviation = 500 dollars
Mean u = 1500 dollars
X = 1500 dollars
(1-α)% = 90%
(1-α)= 0.9
α = 0.10
α/2 = 0.05
Z α/2 = Z 0.05
Z α/2 = 1.645
90%-confidence interval for the population mean estimate is
=X ± Z α/2 (σ/√n)
= 1500 ± (1.645)(500/√36)
=(1362.9167,1637.0833)
Therefore, the 90%-confidence interval for the population mean estimate is (1362.9167,1637.0833).
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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.
Using the factor theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?.
The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.
What is Factor Theorem?A factor theorem is a tool used in mathematics to thoroughly factor polynomials.
It is a theorem that connects the polynomial's zeros and factors.
The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.
So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).
A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.
The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.
Tests of each option reveal that only option A is accurate:
f(x) = x³ – 2x² – 3x + 6
Testing each of the three results in:
[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]
Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.
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Complete question:
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?
a. f(x) = x3 – 2x2 – 3x + 6
b. f(x)= x3 – 2x2 + 3x + 6
c. f(x) = x3 + 2x2 – 3x + 6
d. f(x) = x3 + 2x2 – 3x – 6
b. suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm?
The average waist size of the population is 85 cm, and the standard deviation is 15 cm. then A sample mean waist size of at least 86.3 cm has a 0.931 probability of occurring.
We can use the Z-score formula to find the probability.
Z = (86.3 - 85) / (15 / sqrt(277))
Z = 0.2 / 0.106
Z = 1.89
The probability of a sample mean waist size of at least 86.3 cm is 0.931.
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