The interval of convergence is given as: ⟹|x|<1
What is Maclaurin series?
Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.
We will utilize the common power series representation of the functions, such as sine and the logarithmic function, to find the first three non-zero terms of the Maclaurin series representation for the function. We shall multiply the terms of each expression to obtain the final expression.
[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]
[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]
The series representation shown above is only accurate when ⇒|x| < 1.
Given that;
f(x) = 4 sin(x) ln(1+x)
We are familiar with how functions are represented by power series:
[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]
[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]
The series representation shown above is only accurate when ⇒|x| < 1.
[tex]sin(x) ln(1+x) = [x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........][x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........][/tex]
[tex]sin(x) ln(1+x) = x^2 -\frac{x^3}{3}+\frac{x^4}{4} +\frac{x^5}{5} +........[/tex]
Finally, the function's power series representation is given as:
⇒ [tex]f(x) = 4 sin(x) ln(1+x) = 4 [x^2 - \frac{x^3}{2}+\frac{x^4}{6} +\frac{x^5}{6}+..... ][/tex]
The interval of convergence is given as: ⟹|x|<1.
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at the beginning of the day, the stock market goes up 30 1/2 points. At the end of the day, the stock market goes down 120 1/4 points. What is the total change in the stock market from the beginning of the day to the end of the day?
The total change in the stock market from the beginning of the day to the end of the day is 89.75
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
At the beginning of the day, the stock market goes up 30 1/2 points.
At the end of the day, the stock market goes down 120 1/4 points.
The total change in the stock market from the beginning of the day to the end of the day.
= 120(1/4) - 30(1/2)
= 481/4 - 61/2
= 120.25 - 30.5
= 89.75
Thus,
The total change in the stock market from the beginning of the day to the end of the day is 89.75
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If f(1)=160 and f(n+1)= -2f(n) what is f(4)
Answer:f(4)=−2f(3)=(−2)∗(+640)=−1280
Solve for x please help
The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
No cup of ketchup remains.
From the question ingredients for one batch of barbecue sauce are as follows:Brown Sugar =1/4 C
Cider Vinegar = 1/2 C
Ground Cumin = 1tsp
Ketchup = 2/3 C
Pepper = 1tsp
Total Quantity of Ketchup =9 cups
Calculating How much ketchup remaining:1 batch of barbecue sauce =2/3 Cup
x batch of barbecue sauce =9 Cups
cross multiplying and making x batch of barbecue sauce subject of the formula:x batch of barbecue sauce = 9 Cups *1 batch of barbecue sauce
2/3 Cup
x batch of barbecue sauce =13[tex]\frac{1}2}[/tex] batches
we know that;
1 batch of barbecue sauce =2/3 Cup
Therefore,
The total number of ketchup Cups used = Total batch of barbecue sauce *quantity for1 batch of barbecue sauce
= 13[tex]\frac{1}2}[/tex] batches * 2/3 Cup
The total number of ketchup Cups used = 9 Cups
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The function f(x) has a domain of [-5, 2] and a range of [-3, 6]. If f(x) is reflected over the y-axis, horizontally translated 3 units to the right and vertically stretched by a factor of 2, what will the domain and range of the transformed graph be? Group of answer choices
The domain and the range of the transformed graph are given as follows:
Domain: [1,8].Range: [-6,12].What are the domain and the range of a function?The definitions of the domain and of the range of a function are given as follows:
Domain: input values -> values of x.Range: output values -> values of y.After the reflection over the y-axis, the domain of the function is of:
[-2,5].
(as the reflection over the y-axis changes the signal of the x-values of the function).
After the translation of 3 units right, the domain of the function is of:
[1,8].
As the translation adds 3 to each value of x of the function.
After the vertical stretch by a factor of 2, the range of the function is of:
[-6,12].
As the stretch means that all the output values of the function are multiplied by 2.
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For what values of [tex]c[/tex] will [tex]A=\left[[tex]\begin{array}{cc}1 & 4 \\ c & c^2\end{array}\right][/tex] be invertible?[/tex]
For all [tex]c[/tex] such that [tex]c \neq[/tex]
(If there are multiple values, separate them by comma(s).)
Answer:
(1,-2),(6,21)
Step-by-step explanation:
Give me an example of how stewardship could be practiced by religious believers today
What is the value of the digit 4 in the number 3.04?
Choose the correct answer.
The value of the digit 4 in the number 3.04 is 0.04.
What is the Place Value of a digit ?
Place value is the value a digit in a number represents based on the number's place within the whole.
Here, The place value of the digit 4 is hundredths.
So, Value of digit 4 = 4/100 = 0.04.
Hence, Value of digit 4 in 3.04 is 0.04.
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Marta and her family landed in Hong Kong at 1405 hrs then caught another flight, which got them to Dubai at 2250 hrs. If it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai, how long did they have to wait for their second flight?
The had to wait for the second flight for 40 mins.
How long was the wait?We know that sometimes when a person is travelling there may be need to have a flight that connects a person from one place to another and at times you would have to wait for a connecting flight and this wait would add to the total time that is required for the journey.
Now we are told in the question that it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai and that they left Dubai at 2250 hrs but landed in Hong King at 1405 hrs. The time in between must be; 2250 hrs - 1405 hrs = 8: 45 hrs thus the time of waiting is 40 minutes.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
6115
Explanation:
[tex]70000(1-0.15)^{15} \approx 6115[/tex]
On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities.10.38 9.08 11.7 6.4 12.32 14.43 15.4610.02 14.4 16.08 17.5 19.08 17.88 12.7516.7 17.25 15.54 14.7 18.81 17.89 14.818.32 15.95 26.75 22.22 22.66 20.88 23.3518.95 23.6 19.16 23.65 27.7 26.95 27.0426.89 24.58 37.76 26.41 38.91 29.36 41.55(a)Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for ≠ as needed.)H0:Ha:(b)What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)(c)At α = 0.05, can your null hypothesis be rejected? What is your conclusion?Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.(d)Repeat the preceding hypothesis test using the critical value approach.State the null and alternative hypotheses. (Enter != for ≠ as needed.)H0:Ha:Find the value of the test statistic. (Round your answer to three decimal places.)State the critical values for the rejection rule. Useα = 0.05.(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistic≤test statistic≥State your conclusion.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .
The charge at which anything happens is referred to as the velocity at which it happens.
The required details for mean rate :
(a) H0: µ = 21.62
Ha: µ ≠ 21.62
(b) t = -1.231
p-value = 0.2253
(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.
(d) H0: µ = 21.62
Ha: µ ≠ 21.62
t = -1.231
check statistic ≥ 2.020
Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.
The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.
The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.
The crucial values for t at this level of significance are t=2.019.
Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
6115
Explanation:
[tex]70000(1-0.15)^{15} \approx 6115[/tex]
graph the line that represents this equation
[tex]3x-4y=8[/tex]
The graph of the line that represents the given equation, 3x - 4y = 8, is shown below
Graph of Linear equationsFrom the question, we are to graph the line that represents the given equation.
The given equation is
3x - 4y = 8
To graph the line, we will determine x-intercept and y intercept of the line.
The x-intercept in the point where y equals zero on the line
and
The y-intercept in the point where x equals zero on the line
Determining the x-intercept
3x - 4y = 8
Set y = 0
3x - 4(0) = 8
3x = 8
x = 8/3
The x-intercept is (8/3, 0)
Determining the y-intercept
3x - 4y = 8
Set x = 0
3(0) - 4y = 8
-4y = 8
y = 8/-4
y = -2
The y-intercept is (0, -2)
Using the x-intercept and y-intercept, the graph of the line is shown below
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Pointssssssssssssssssss
By solving a linear equation we will see that DE = 22.67 units.
How to find DE?For the given square we know that EC = 7x - 3 and AE = 4x + 8, notice that both EC and AE are half of a diagonal of the square, so these measures must be the same one, then we can write the linear equation:
7x - 3 = 4x + 8
solving for x:
7x - 4x = 8 + 3
3x = 11
x = 11/3
And DE is also half of the diagonal, so the measure of DE is the same than the measure of EC, then it is:
DE = 7x - 3 = 7*11/3- 3 = 22.67
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square pqrs has sides of length $4$, and $m$ is the midpoint of $\overline{rs}$. a circle centered at $m$ with radius $2$ intersects the circle centered at $p$ with radius $4$ at points $n$ and $s$. what is the distance from $n$ to $\overline{ps}$?
The distance between N and PS is 3.2.
What is the midpoint of the segment?
Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.
From the below figure,
N is the intersection of the red and blue circles.
I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).
Then the formula for the red circle is:
(x-2)² + (y-4)² = 4.
The formula for the blue circle is
x² + y²- 16 = 0.
Solving for x and y yields intersections
(0, 4) and (3.2, 2.4),
the first being S and the latter being N.
Hence, the distance between N and PS is 3.2.
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You have at most 7 hours to spend playing soccer and swimming. You
want to spend at least 2 hours playing soccer and more than 2 hours
swimming. Write and graph a system that represents the situation. Give
one example of the amount of time you can spend on each activity.
Answer:
Step-by-step explanation:
What is 17 x 5.8 SHOW YOUR WORK please send a photo of work by pressing
Answer:
98.6
Step-by-step explanation:
in photo!!
PLS HELP MEEEEEEEEEEEEEEEEEEEE
The area of the triangle in the image is 1/20 square centimeters.
How to find the area of the figure in the image?This is a rather trivial problem.
On the image, we can see a triangle where the height and the base are known quantities.
Remember that for a triangle of height H and base B, the area is given by the formula:
A = B*H/2
Here we can see that:
H = (1/6) cm
B = (3/5) cm
Then we can replace these two fractions on the area formula, we will get:
A = (1/6 cm)*(3/5 cm)/2
A = (3/5*6 cm²)/2
A = (3/30*2 cm²)
A = (3/60 cm²) = (1/20 cm²)
That is the area of the triangle in the image.
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What is the result when 3x + 7 is subtracted from -x + 2?
Subtracting the polynomials, 3x + 7 is subtracted from -x + 2, the result is: -4x - 5.
How to Subtract Polynomial Expressions?To find the difference of two polynomials, like terms should be combined and simplified together.
Subtracting 3x + 7 from -x + 2, we have the following:
(-x + 2) - (3x + 7)
Open the parentheses:
-x + 2 - 3x - 7
Combine like terms
-x - 3x + 2 - 7
= -4x - 5
Therefore, the result is -4x - 5.
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PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent. Which statement is used to prove that angle PTR is always equal to angle STQ? (1 point) Lines PQ and RS do not have a fixed length. Angle PTR and angle PTS are supplementary angles. Lines PQ and RS intersect at an angle less than a right angle. Angle PTR and angle PTS are complementary angles.
The statement that is used to prove the congruence of angles PTR and STQ is given by:
Lines PQ and RS intersect at an angle less than a right angle.
What are congruent angles?Congruent angles are angles that have the same measure.
One example of congruent angles is for vertical angles, as these angles are opposite by the same vertex in crossing segments, with an angle less than a right angle of 90º, and then these two angles will be congruent.
The common vertex in the segment given at the end of the answer is of:
T.
The vertical angles are both acute angles, that is, angle measures that are less than 90º, which is the reason for the correct statement.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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The producer of the Yummy Nibbles candy chews reports that their packages contain
10%
each brown and red candies, and
20%
each yellow, blue, and orange candies. The rest of the candies are green. Use this information to compute each of the probabilities requested in parts (a) \& (b). Sentence answers to these questions are not required. It pt (a) Suppose you randomly pick two Yummy Nibbles candies (without replacement), what is the probability that at least half of those candies you select are red? 14 pts! (b) Suppose instead you randomly pick two-hundred Yummy Nibbles candies (without replacement), what is the probability that at least half of those candies you select are red?
2/45 is the probability that the ball will be both red.
What is Probability?Probability is the measure of the possibility of an event to occur.
It basically ranges from 0 t0 1
10% of the candies are green
10% of the candies are red
20% of the candies are yellow
20% of the candies are blue
20% of the candies are orange.
Hence,
P ( brown ) = .1
P ( red ) = .1
P ( blue ) = .2
P ( yellow ) = .2
P ( orange ) = .2
P ( green ) = .2
The rest is brown. The percentage of brown candies is not important to this problem.
If you pick a candy at random, what is the probability that it is either red or yellow?
Probability of red = 0.1
Probability = (¹⁰C₁ × 0.1 + ¹⁰C₁ ×0.1) / ¹⁰C₂
= 2 / 45
2/45 probability that it is both red.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!
Answer:
the remaining mass is 7.3 g
Step-by-step explanation:
a=30g
t=200 years
h=98 years
f(98)=a([tex](\frac{1}{2})^ \frac{t}{h}[/tex]
f(98)=30([tex](\frac{1}{2})^ \frac{200}{98}[/tex]
f(98)=7.3
Please help!
Worth 20
the Area will be 280 inch².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The base of triangle = 20inch
The height of triangle = 14inch
Area is = (base * height) = (20*14)
Area = 280 inch²
Hence the Area will be 280inch²
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32) Jeff's car gets 144 miles with a full tank of gas. If his gas tank hold 16 gallons,
how many miles per gallon is his car getting?
9 miles per gallon of gas is used in his car.
What is gallons?The standard volume and capacity for measuring liquids is the gallon.The word gallon is shortened to gal.Currently, there is only one definition for the gallon in the imperial system and two that is dry and liquid in the US customary system.
Here the given information is as,
Car travels = 144 miles
Tank hold gas = 16 gallons
So, for miles per hour,
= 144 / 16
= 9 miles / gallon
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there are 4 different mathematics courses, 5 different science courses, and 2 different history courses. must take one of each how many different ways can this be done
A student can take one of each subject in 40 different ways as calculated using the properties of permutation and combination..
So there are four separate math classes, five different science courses, and two different history courses.
There are now 4 ways to complete a math course.
There are 5 different ways to take science courses.
There are two ways to take a history course.
Total ways are now calculated as the product of the potential ways for each course, which equals 4 × 5 x 2 or 40 ways.
As a result, there are 40 possible combinations for three subjects.
In mathematics, a permutation of a set is, if the set also has an ordered structure, the rearranging of its members into a sequence or linear order. The technique of altering an ordered set's linear order is known as permutation.
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A line with the slope of 10/17 passes through the point (17,3). Whats is its equation in slope intercept form?
Answer:
y = 10/17x - 7
Step-by-step explanation:
→ Write in standard form
y = 10/17x + c
→ Substitute in (17, 3)
3 = 10 + c
→ Solve for c
c = -7
→ Rewrite
y = 10/17x - 7
what is answers in 2 this items help me please
1) missing number is 7 (answer #2)
Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)
20 minus 10 minus 3 is 7, so that's the missing number.
2) missing number is 3 (answer #4)
This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)
10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!
Hopefully this helps!
A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.
The 95% confidence interval for the population mean SAT score is given as follows:
(1340, 1460).
How to calculate the confidence interval?The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.
The bounds are obtained according to the equation defined as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 1400, n = 64, s = 240[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.
Then the lower bound of the interval is of:
1400 - 1.998 x 240/sqrt(64) = 1340.
The upper bound of the interval is of:
1400 + 1.998 x 240/sqrt(64) = 1460.
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Match the correct volume formula with each described figure. (see picture below)
The volume formula for this problem are given as follows:
Cone: V = πx³/3.Prism: V = x³.Pyramid: V = x³/3.Cylinder: V = πx³.How to obtain the volumes?The volume of a cone with radius r and height h is given as follows:
V = πr²h/3.
The volume of a square prism of side length s is given by the multiplication of the side length squared by the height, as follows:
V = s²h.
For the square pyramid, we have that the height is one third of the prism, hence:
V = s²h/3.
The volume of the cylinder is three times the volume of the cone, hence:
V = πr²h.
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Graph the given sequence to help you answer the
questions.
19, 15, 11, 7, ...
Which point is found on the graph?
Is the sequence linear? Why?
What type of sequence is it?
Answer: the answer is A,B,E
Step-by-step explanation:
Answer: The answer is (four/seven)
Yes, because it forms a straight line.
Arithmetic; it's a linear function.
Step-by-step explanation:
2023 Edgen
Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean
How to know the use of t-test and z-score?T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.
The z-core formula is:
Z₁=[tex]\frac{x-m}{s}[/tex]
Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.
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Complete question:
Which of the following is a fundamental difference between the t statistic and a z-score?
A) The t statistic uses the sample mean in place of the population mean
B) All of the choices are differences between t and z.
C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.
D) The t statistic uses the sample variance in place of the population variance.
