A linear clear variation is represented by the equation y = kx, in which k is the area under the curve y = mx + b and b is the zero-valued y-intercept.
Y KX Y is what kind of variation?The polynomial y = mx (commonly stylized y = kx), which seems referred to as a direct variation, can be obtained from the theory y = mx + b if m is a sufficiently small factor and b = 0. In other words, you may claim that y directly depends on x or that y is proportionate to x.
K in Y KX: What does it mean?The standard format for presenting a direct variation is y=kx. The letters "y" and "x" are variables, and the letter "k" is a constant. Making a table will allow you to identify those ordered pairs that statisfy the example of y=2x.
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How are the ordered pairs (,) and (,−) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
Answer: no exact answer
Step-by-step explanation:
There are 21 pieces of $2 notes and $10 notes in an envelope. If the total value of all the notes is less than
$110, find the minimum number of $2 notes in the envelope.
Answer:
Let the number of $2 notes be x, while that of $10 notes be y.
Set two equations
x + y = 21 y = 21 - x ------- 1
2x + 10y < 110 ------ 2
Sub 1 into 2
2x + 10(21-x) < 110
2x + 210 - 10x < 110
-8x < -100
x > 12.5
Minimum number of $2 notes in the envelope = 13
Karen likes to make lemonade using the lemons from her grandmother's
trees. There is a proportional relationship between the number of pitchers of
lemonade Karen wants to make, x, and the number of lemons she needs, y.
4) The equation that models this relationship is y = 5x.
4) How many pitchers of lemonade can Karen make with 15 lemons?
Answer: If there is a proportional relationship between the number of pitchers of lemonade Karen wants to make, x, and the number of lemons she needs, y, and the equation modeling this relationship is y = 5x, then we can find the number of pitchers Karen can make with 15 lemons by solving for x:
15 = 5x
Dividing both sides by 5:
3 = x
So Karen can make 3 pitchers of lemonade with 15 lemons.
Step-by-step explanation:
AB and BC form a right angle at point B. If A = (-3-1) and B = (4,4) what is the equation of Bc
Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.
The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:
m = (4 - (-1)) / (4 - (-3)) = 5 / 7
So the slope of the line BC is 5/7.
One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:
b = y - mx
where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:
b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7
So the equation of line BC in the slope-intercept form is:
y = (5/7)x - 16/7
Step-by-step explanation:
the sun is shining and a spherical snowball of volume 260 ft3 is melting at a rate of 11 cubic feet per hour. as it melts, it remains spherical. at what rate is the radius changing after 6.5 hours?
If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h .
A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.
We have to find the rate at which the radius is changing after 6.5 hours.
So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.
Volume Of Sphere is V = (4/3)πr³ and dV/dt = -11 ft³/h ;
So, dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt) ;
derivative of volume formula with respect to "r", we get:
⇒ dV/dr = 4πr² ;
Substituting the given values in chain rule equation, we get:
⇒ -11 = (4/3)πr² × dr/dt ;
⇒ dr/dt = -11/((4/3)πr²)
For rate of change of the radius when t = 6.5 hours, we find the radius at that time.
The initial volume of the snowball = 260 ft³.
After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be: V = 260 - (11 × 6.5) = 188.5 ft³ ;
So , V = (4/3)πr³
⇒ 188.5 = (4/3)πr³
⇒ r³ = (188.5 × 3 / (4π)) ;
≈ 3.55ft
Now we substitute r = 3.55 feet
⇒ dr/dt = -11/[(4/3)π(3.55)²] ;
⇒ dr/dt ≈ -0.208 ft/h ;
Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing .
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Select all the measures of variability that can be used to compare two data sets.
A. Mean
B. Interquartile Range
C. Median
D. Mode
E. Range
Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.
Variability is most generally measured proving the following descriptive data:area:
Difference between highest and lowest values.
Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:
Sort all the values in the dataset from lowest to highest.
Subtract the lowest value from the highest value. Interquartile range:
area of the middle half of the distribution
standard deviation:
mean distance from mean
Standard deviation is a useful measure of the variance of a normal distribution.
A normal distribution distributes data symmetrically without skew. Most of the values are clustered around the central region, with values tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.
deviation:
mean squared distance from mean
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10 cm
8 cm
12 cm
5 cm
6.4 cm
The perimeter of the rectangle is 36 cm.
What is a rectangle?A rectangle is a two-dimensional figure with length and width.
The area of a rectangle is Length x width.
We have,
Length = 10 cm
Width = 8 cm
Now,
The perimeter of the rectangle.
= 2 (length + width)
= 2 (10 + 8)
= 2 x 18
= 36 cm
Thus,
The perimeter of the rectangle is 36 cm.
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The complete question.
The length ad width of a rectangle is 10 cm and 8 cm.
Find the perimeter of the rectangle.
a) 28
b) 12
c) 6.4
d) 36
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)"+1
n=1
Answer:
The expression is a summation, or the sum of a sequence of terms. Each term is equal to 900 * (1.04)^n+1, where n starts at 1 and goes up to infinity.
To calculate this sum, we would need to find the limit of the sequence as n approaches infinity. However, finding the exact value of this sum is not possible and would require the use of mathematical tools like mathematical analysis.
To estimate the value, we can use a calculator or spreadsheet to calculate the sum for a finite number of terms and then see how the sum changes as we increase the number of terms. For example, if we calculate the sum for n = 1 to 100, we would get an estimate of the value. If we then calculate the sum for n = 1 to 200, we would get a closer estimate.
In this case, we can round the expression to the nearest integer, which would be 53.
Step-by-step explanation:
Belle has a collection of trading cards. The table shows how many of each type of card she has. A card will be randomly drawn from her collection and replaced 60 times
Type: Number:
Baseball 13
Football. 8
Basketball. 5
Soccer. 9
What is a reasonable prediction for the number of times a basketball or soccer card will be drawn?
Find the slope of the line graphed below.
Answer:
the slope is -6/-5
What is the common ratio of the geometric sequence shown? -2,4,-8,16,. . .
Answer:
-2,-4,-8,-16
common ratio of geometric sequence shown is -2
this sequence is in the decreasing form.
the next number in this sequence is -32
I hope that helps.
eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. find the work required to stretch the spring an additional 3 inches.
The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:
[tex]F = kx[/tex]
where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).
Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:
[tex]W = (1/2) k x^2[/tex]
Solving for k, we get:
[tex]k = (2W) / x^2[/tex]
Plugging in the values for W and x, we get:
[tex]k = (2 * 18) / (4^2) = 2.25[/tex]
So the spring constant is 2.25 pounds per inch.
Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:
[tex]F = kx[/tex]
= [tex]2.25 * 3[/tex]
= 6.75 pounds
Finally, we can find the work required to stretch the spring an additional 3 inches:
[tex]W = (1/2) k x^2[/tex]
= [tex](1/2) * 2.25 * 3^2[/tex]
= 10.125 foot-pounds
Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
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If P is the centroid, and GP=2.2, find the indicated
lengths.
A
PC =
GC =
ttt
B
++
H
type your answer...
type your answer...
C
The length of PC and GC is 4.4 and 6.6 respectively.
What is centroid of a triangle?
A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1
Given ABC is the triangle.
In which G, H, J are the midpoints on AB, BC, AC sides respectively.
Then, AH, CG, BJ are the medians and they are intersect at the point P.
P is the centroid of the triangle.
Given, GP =2.2 we have to find the PC and GC.
We know that the centroid divided the median in 2:1 ratios.
i.e., AP:PH = CP:PG = BP:PJ = 2:1
We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]
⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.
Hence, the length of PC and GC is 4.4 and 6.6 respectively.
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Can someone explain and help me through this?
a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.
b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes.
Information from the Warm Up:
According to the Travel Almanac, the world’s fastest land animal is the cheetah. It can travel at up to 70 mph. Think of this scenario: A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.
Can we say that this cheetah’s average rate was 55 mph?
That’s one of the things you’ll determine as you work to complete this task. Make a conjecture. What do you think the answer will be?
well, let's get the info first.
so going forth the Cheetah goes 70mph and going back it modestly does 40mph.
can we say that on average it did 55mph?
well, what's that? on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.
well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.
A)
since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say
[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]
[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]
B)
[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]
Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State the sampling method Charlie used.
Charlie could have used quota sampling instead of non-random sampling.
What are sampling methods?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 studentsGiven is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.
Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.
Therefore, Charlie could have used quota sampling instead of non-random sampling.
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{COMPLETE QUESTION IS -
Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}
Hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2. If the surface area of hexagonal prism B is 172 cm^2, find the surface area of hexagonal prism A, the preimage.
Hexagonal prism A has a surface area of 43 cm2.
What is the surface area equation?A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).
The surface area of a hexagonal prism is given by the formula:
SA = 2B + PH
where B is the base's surface area, P is its perimeter, and H is the prism's height.
Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:
SA_B = 4×SA_A
where SA_B is the surface area of prism B and SA_A is the surface area of prism A
We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:
172 = 4×SA_A
SA_A = 43 cm²
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What is 2x times 2x in algebra
Answer: 4x2
Step-by-step explanation:
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]
Equation 1: 2x - 5y = -8
Equation 2: 4x + 5y = 14
Emily solved the system of equation above using the Elimination Method. She
multiplied equation 1 by a number, then added the resulting equations
together to eliminate the variable . What number did Emily multiply equation
1 by so that she could eliminate the x terms?
To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.
Elimination Method:In mathematics, the Elimination method is about deleting one of the words containing any of the variables to make the calculations easier.
To solve the equations, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same.
The term is then eliminated or removed from the result by adding or subtracting from both equations.
Here we have
Equation 1: 2x - 5y = -8
Equation 2: 4x + 5y = 14
We can multiply given equations as follows
To eliminate 'x' terms multiply the multiply equation 1 with -2
-2 × Equation 1 => - 4x + 10y = 16 ---- (Equation 3)
Now add Equation (2) and Equation (3)
=> 4x + 5y - 4x + 10y = 14 + 16
=> 15y = 30
=> y = 2
Now substitute y = 2 in equation (2)
=> 2x - 5(2) = -8
=> 2x - 10 = -8
=> 2x = 2
=> x = 1
Therefore,
To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.
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A large rectangular movie screen in an IMAX theater has an area of 11,224 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide
With an area of 11,224 square feet and the dimensions of the screen if it is 30 feet longer than it is wide, the width of the screen is 91.5 feet, and the length of the screen is 121.5 feet.
Let's call the width of the screen "w". Then, the length of the screen would be "w + 30". The area of the screen is 11,224 square feet, so we can set up an equation:
w * (w + 30) = 11,224
Expanding the right side of the equation, we get:
w^2 + 30w - 11,224 = 0
We can use the quadratic formula to solve for w:
w = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = 30, and c = -11,224.
Plugging in the values, we get:
w = (-30 ± √(30^2 - 4 * 1 * -11,224)) / 2 * 1
= (-30 ± √(900 + 44,896)) / 2
= (-30 ± √(45,796)) / 2
= (-30 ± 213) / 2
Taking the positive solution, we get:
w = (183 / 2) = 91.5 feet
So the width of the screen is 91.5 feet, and the length of the screen is 91.5 + 30 = 121.5 feet.
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W X
Y
Z
List the sample space for the experiment.
Os = {X, Y, Z}
Os = {W, Z, Z}
Os = {W.Y.Y. Z}
Os = {W, X, Y, Z}
Answer:
Os = {W, X, Y, Z}
Step-by-step explanation:
The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.
Answer:
the answer is the last one
Step-by-step explanation:
os= {w, x, y, z}
Write tan theta in terms of a and b.
Answer:ab
Step-by-step explanation:
because..........
What the least common denominator of the 2, 3/7, 3,4 ?
The least common denominator of the number 2, 3, 4, 7 is found to be 42.
Here, the least common denominator of the following numbers is asked,
2, 3, 4, 7
Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).
We can find the value which will be a multiple of all those numbers,
4 is multiple of 2 but 3 and 7 are not.
6 is a multiple of 2 and 3 but 7 is not.
42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.
So, the least common denominator of 2, 3, 4, 7 is 42.
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Complete question - What is the least common denominator of 2, 3, 7, 4.
Lisa's average score on 4 tests is 82. What does she need to score on her fifth test to have an average final score of 85?
Answer:
Lisa would need to score 97 on her 5th test.
Step-by-step explanation:
If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.
If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).
To determine what she needs to get on her 5th test we need to subtract 328 from 425.
425 - 328 = 97
question 7
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
16.5 cm²
Step-by-step explanation:
the measure of an exterior angle (32°) is found by dividing the difference between the measures of the intercepted arcs (54° and arc abject BF) by two.
32 = (BF - 54)/2
64 = BF - 54
arc angle BF = 64 + 54 = 118°
the area of that sector is
pi×r² × 118/360 = pi×4² × 118/360 = pi×16 × 118/360 =
= pi×2 × 118/45 =
= 16.47590814... ≈ 16.5 cm²
The length of a cell phone is 1.41.4 inches and the width is 2.82.8 inches. The company making the cell phone wants to make a new version whose length will be 1.611.61 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:
Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:
(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)
We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:
(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)
Cross multiplying, we get:
(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)
Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.
the angle of depression from the top of a cliff to a nearby town is 23 degrees. if the top of the cliff is 360 feet above the town, how far is the town from the base of the cliff? do not round until you reach your answer, and then round your answer to the nearest tenth of a foot.
The length of town from the base of the cliff is 848.25 feet
Concept of height and distance
You can use trigonometry formulas to find height and distance from anything. If you know the distance from the Qutub Minar to your current location and the angle at which you can see the top of the Minar, you can find the altitude of the Qutub Minar. Use trigonometry to find the elevation. This is because the ground, minaret elevation, and contour lines all combine to form a 90 degree right triangle between the minaret and the ground.
The distance is usually the "base" of the right triangle formed by the minar's elevation and line of sight. The length of the horizontal plane also forms the base of a triangle parallel to the ground at a given height, so we know the distance. The line of sight forms the "hypotenuse" of a right triangle. Lines perpendicular to the ground form the "height" of the triangle.
To calculate elevation or depression you can use the following formulas:
sinθ = hypotenuse /height.
cosθ = hypotenuse /base,
tanθ = base /height
where θ is the elevation or depression angle.
and in this question the angle of depression is 23 degree and height is 360 feet and we have to calculate the base
tan 23 degree = 360/base
base = 360/tan 23
=360/0.4244
= 848.25 feet.
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What is A ‘ C please help
Answer: 11.7 in.
Step-by-step explanation:
I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.
Pls help thank you will mark the Brainliest
The exponential equation is given by the function y = 30.5(0.7)ˣ
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The standard form of an exponential equation is:
y = abˣ
where b is the rate of change and a is the initial value.
Let y represent the number of games sold x years since 2015.
From the graph, at point (0, 30.5):
30.5 = ab⁰
a = 30.5
Also, at point (1, 21.35):
21.35 = ab¹; but a = 30.5, hence:
21.35 = 30.5b
b = 0.7
The equation is y = 30.5(0.7)ˣ
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imagine math - item 92070
I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?
one reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a popu- lation mean is that (a) z can be used only for large samples. (b) z requires that you know the population standard deviation s. (c) z requires that you can regard your data as an srs from the population. (d) z requires that the sample size is at most 10% of the population size. (e) a z critical value will lead to
One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.
The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.
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