If there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces, then we have to use one sample t test (option b).
In this case, we have a sample of 22 cartons and we want to determine if the mean amount of milk in the cartons is less than 32 ounces. Since we are only dealing with one sample and comparing its mean to a known population mean of 32 ounces, we can use a one sample t test. This test will help us determine if the sample mean is significantly different from 32 ounces.
To perform a one sample t test, we need to calculate the sample mean and sample standard deviation of the amount of milk in the 22 quart cartons. We can then use these values, along with the known population mean of 32 ounces, to calculate the t statistic. This t statistic will tell us how many standard errors the sample mean is away from the hypothesized population mean of 32 ounces.
We can then calculate the p-value, which is the probability of getting a t statistic as extreme as the one we calculated, assuming the null hypothesis is true.
If the p-value is less than our chosen significance level (usually 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the mean amount of milk in the cartons is less than 32 ounces.
Hence the correct option s (b).
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Solver for x.
-2cosx+2cos2x =0
To solve for x in the equation -2cosx+2cos2x=0, we can use the trigonometric identity cos2x = 2cos^2x - 1 to rewrite the equation as:
-2cosx + 4cos^2x - 2 = 0
Next, we can rearrange the terms and factor out a 2 to obtain:
2cos^2x - cosx - 1 = 0
This is now a quadratic equation in terms of cosx. We can solve for cosx using the quadratic formula:
cosx = [1 ± sqrt(1 - 4(2)(-1))] / (2(2))
cosx = [1 ± sqrt(9)] / 4
cosx = (1/2) or (-1/2)
Now, we need to find the values of x that correspond to these values of cosx. We can use inverse trigonometric functions to do this:
cosx = 1/2 => x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.
cosx = -1/2 => x = 2π/3 + 2πn or x = 4π/3 + 2πn, where n is an integer.
Therefore, the solutions for x are:
x = π/3 + 2πn, x = 2π/3 + 2πn, x = 4π/3 + 2πn, x = 5π/3 + 2πn, where n is an integer.
Last year there were 500 cell phone users in a city. The number of cell phones users doubled every 10 years. This model represents: a linear function. an exponential function.
The model having number of cell phone users in the city doubled every 10 years is an exponential function not a linear function.
Because it represents the growth rate exponentially.
Last year number of users of the cell phone in a city = 500
Number of cell phones users doubled every 10 years.
The model that represents the number of cell phone users in the city is an exponential function, not a linear function.
This is because the number of cell phone users is doubling every 10 years.
Which means that the rate of growth is increasing exponentially.
In an exponential function, the variable in the exponent increases or decreases at a constant rate.
It is the case here as the number of cell phone users is doubling at a constant rate of every 10 years.
The exponential function that represents the number of cell phone users in the city can be written as,
f(x) = 500 × [tex]2^{x/10}[/tex]
where x is the number of years since the initial count of 500 cell phone users.
This function gives the number of cell phone users after x years,
And the exponent x/10 represents the doubling of the number of cell phone users every 10 years.
Therefore, the model represents the exponential function.
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Mínimo común múltiplo y máximo divisor ejemplos
The number of bottles a machine fills is proportional to the number of minutes the machine operates. The machine fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, the machine fills in x minutes.
How do i do this if the minutes only go up to 9 and the y axis is only 125???
Answer:
Since the machine fills 250 bottles every 20 minutes, we can write the proportion:
250 bottles / 20 minutes = y bottles / x minutes
Simplifying this proportion, we get:
y = (x/20) * 250
This equation represents a linear relationship between the number of bottles (y) and the number of minutes (x), where the slope is 250/20 = 12.5 bottles per minute.
To create a graph, you can plot the points (0, 0) and (9, 112.5) since the y-axis only goes up to 125. This will give you a straight line that starts at the origin and goes up to about 112.5 on the y-axis at x = 9.
Step-by-step explanation:
PLS HELPP 20 POINTS
A box contains hair clips of 3 diff sizes. -15 small hair clips -12 medium hair clips -6 large hair clips
If one hair clip is randomly selected from the box,what is the probability that the hair clip will be either small or medium?
A)9/11
B)3/7
C)2/9
D)1/6
Answer: 17/33
Step-by-step explanation:
Or means add the 2 probabilities
There are a total of 33 outcomes.
getting a small clip is 15/33
getting a medium clip is 12/33
add the two probabilities 15/33 +12/33 = 17/33
I'm sure of my numbers. I think the question is off or answers
an angle measures 26 more than it's supplementary angles what is the meaure of both angles
The measure of the angles which are supplementary to each are 103 and 77 degrees.
What is the meaure of both angles?Supplementary angles sum up to 180 degrees.
Let the measure of the angle we're trying to find "x".
We know that this angle is 26 degrees more than its supplementary angle, which we can call "y".
So we can write:
x = y + 26
Since x and y are supplementary, their measures add up to 180 degrees:
x + y = 180
Now we can substitute the first equation into the second equation to eliminate "y":
(y + 26) + y = 180
2y + 26 = 180
Subtracting 26 from both sides:
2y = 154
Dividing both sides by 2:
y = 77
To find the other angle, we can use the first equation we wrote:
x = y + 26
Plug in y = 77
x = 77 + 26
x = 103
Therefore, the angles are 103 and 77 degrees.
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A cylinder has a radius of 16 inches. Its volume is 13,665. 28 cubic inches. What is the height of the cylinder?
Use ≈ 3. 14 and round your answer to the nearest hundredth
The height of the cylinder is 17.00 inches, under the given condition that radius of the cylinder is 16 inches, volume is 13,665. 28 cubic inches and have to round the answer to the nearest hundred.
Therefore, the volume of a cylinder is given by V = πr²h
Here,
V= volume of the cylinder,
r= radius of the cylinder
h= height
Given that the radius of the cylinder is 16 inches and its volume is 13,665.28 cubic inches, then we can proceed to evaluate the height of the cylinder
V = πr²h
h = V / (πr²)
h = 13665.28 / (π(16)²)
h = 13665.28/ 3.14 x (256)
h = 13665.28/ 803.8
h = 17.00 inches
Then, the height of the cylinder is approximately 17.00 inches.
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in a lottery daily game, a player picks three numbers from 0 to 9 (without repetition). how many different choices does the player have
In a lottery daily game, a player picks three numbers from 0 to 9 (without repetition) there are 120 ways of choices that can be calculated with combinations.
A player picks three numbers from 0 to 9 in a lottery daily game without any repetition of digits). There is no specification of order.
Since we are not specified that there will be some order in selection of digits (we can assume that there is no such order). Hence .
Therefore, we apply the formula of combinations as the order of items does not matter in case of combinations.
By applying the formula of combinations with no repetition we get,
Number of choices the player has in a lottery game is = nCr = n! /{( n - r)! r!}
where, n is the total number of digits, that is n = 10
and r is the number of required digits, r = 3
Number of choices the player has in a lottery game is = 10 ! /{ ( 10-3)! 3!}
= 120
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11-4 skills practice areas of regular polygons and composite figures answers
The 11-4 skills practice areas of regular polygons and composite figures involve finding the areas of different geometric shapes using specific formulas and methods.
To find the area of regular polygons, you can use the formula (1/2) x apothem x perimeter.
For composite figures, you can break the shape into smaller, more manageable shapes like rectangles, triangles, or circles, and then calculate the area of each component before adding them together.
Hence, The 11-4 skills practice areas of regular polygons and composite figures teach you to find areas using the appropriate formulas and methods, improving your geometry understanding and problem-solving abilities.
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A scientist who studies fossils is known as a paleontologist. If a paleontologist finds a fossil of animal remains with 88.5% as much Carbon-14 as the animal would have contained if the animal were alive today, how long ago did the animal live?
Use the formula for Carbon-14: y=ae (exponent) -0.00012t
The time for which the animal lived based on the given parameters is: 1018 years
How to solve exponential decay functions?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y = a(1 - b)ˣ
where:
y is the final amount
a is the original amount
b is the decay factor
x is the amount of time that has passed.
We are told that a paleontologist finds a fossil of animal remains with 88.5% as much Carbon-14 as the animal would have contained if the animal were alive today. Thus:
y/a = 88.5% = 0.885
Thus:
0.885 = e^(−0.00012t)
In 0.885 = -0.00012t
t = 1018 years
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Find the value of x and y
The value of x and y are 12.4 and 7.4
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then asinA=bsinB=csinC.
To calculate the value of y;
y/sin60° = 5/sin36
ysin36 = 5 × sin60
0.588y = 4.33
divide both sides by 0.588
y = 4.33/0.588
y = 7.4 ( 1 d.p)
The value of x can be found by using Pythagoras theorem.
x² = 12² + 3²
x² = 144+ 9
x² = 153
x = √153
x = 12.4( 1 d.p)
therefore the value of x and y are 12.4 and 7.4
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One link in a chain was made from a cylinder that has a radius of 2 cm and a height of 20
cm. How much plastic coating would be needed to coat the surface of the chain link?
Use 3.14 for л.
O
Drive-Up Banking Arrivals. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at ran-dom, with an arrival rate of 24 customers per hour or 0. 4 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process
There is a 67.03% probability that no customers will arrive at the drive-up teller window in one minute.
The Poisson distribution formula can be used to calculate the probability of a specific number of customer arrivals in a given time interval. For example, if we want to calculate the probability of two customers arriving at the drive-up teller window in one minute, we can use the following formula:
P(X=2) = (e⁻⁰°⁴)*(0.4²)/2!
where P(X=2) is the probability of two customer arrivals, e is the base of the natural logarithm, and 2! is the factorial of 2.
Using this formula, we can calculate the probability of any number of customer arrivals in one minute. For instance, the probability of no customers arriving in one minute is:
P(X=0) = e⁻⁰°⁴ = 0.6703
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Which one of the following sets of data does not determine a unique triangle?
Choose the correct answer below.
O A. A=50°, b=21, a=19
OB. A=45°, b= 10, a = 12
OC. A=30°, b=8, a=4
O D. A=130°, b=4, a = 7
By angle sum property of triangle, the correct option is Option D: A=130°, b=4, a=7.
What is triangle?A triangle is a three-sided polygon, which is a closed figure with three straight sides and three interior angles.
According to the given information:
The correct answer is Option D: A=130°, b=4, a=7.
In a triangle, the sum of the measures of the interior angles is always 180 degrees. Therefore, if one angle of a triangle is given, the other two angles can be determined by subtracting the given angle from 180 degrees.
In Options A, B, and C, the given angle A is less than 90 degrees, which means that the triangle would be acute, and there is a unique triangle that can be formed using the given data. The given sides b and a are also of appropriate lengths to form a triangle based on the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
However, in Option D, the given angle A is 130 degrees, which is greater than 90 degrees. This would result in an obtuse triangle, where one angle of the triangle is greater than 90 degrees. In this case, the given sides b=4 and a=7 may not be of appropriate lengths to form a triangle, as they may not satisfy the triangle inequality theorem. Therefore, Option D does not determine a unique triangle, as the given data may not be able to form a valid triangle.
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Forty-five people were asked about how many miles they walked in one week. The results are shown in the graph. What is the mean number of miles walked by the girls?
5 4/11 miles
5 6/25 miles
5 1/2 miles
5 miles
5 1/8 miles
The average distance walked is 5 + 4/11 miles.
What is the mean number of miles walked by the girls?By using the graph we can see that:
5 girls walked 4 miles.9 girls walked 5 miles3 girls walked 6 miles.5 girls walked 7 milesSo there are a total of:
5 + 9 + 3 + 5 = 22 girls.
And the average distance walked is:
A = (5*4 + 9*5 + 3*6 + 5*7)/22
A = 118/22 = 110/22 + 8/22 = 5 + 8/22 = 5 + 4/11
So the correct option is the first one.
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5x2 - 27 ÷ y - (9 + 13)
What is the value of the expression when x = 10 and y = 9?
The value of [tex]5x^{2} - 27[/tex] ÷ y - (9 + 13) when x = 10 and y = 9 is 2501
What is BODMAS?BODMAS is an acronym and it standsB = BracketO = OrderD = DivisionM = MultiplicationA = AdditionS = Subtraction
How to determine this
[tex]5x^2 - 27 /y - (9 + 13)[/tex]
Where x = 10y = 9By substituting the values
[tex]5(10)^2 - 27 / y - (9 + 13)[/tex]
By removing bracket [tex]50^2 - 27 / 9 - 9 + 13[/tex]
Order, by finding the square root of 502500
- 27 / 9 - 9 + 13
By dividing
2500 - 27/9 - 9 + 132500 - 3 - 9 + 13
By addition
2500 + 13 - 3 - 92513 - 3 - 9
By subtraction
2513 - 12= 2501
Therefore, the value of the expression is 2501
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Answer:
Step-by-step explanation:
If 124n = 232five, find n.
Answer:
18.75 or 1.87
Step-by-step explanation:
If its 124n=2325, n is 18.75
If its 124n=232, n is 1.87
john measured a line to be 1.7 inches long. if the actual length of the line is 2.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Therefore, the percent error is approximately 19.0% (rounded to the nearest tenth of a percent).
The percent error is a measure of the accuracy of a measurement or calculation. It is calculated by taking the absolute value of the difference between the measured or calculated value and the actual or accepted value, dividing that difference by the actual or accepted value, and then multiplying by 100 to express the result as a percentage.
The formula for percent error is:
% error = |(measured or calculated value - actual or accepted value) / actual or accepted value| x 100
The formula for percent error is:
(percent error) = [(|measured value - actual value|) / actual value] x 100%
Substituting the given values:
(percent error) = [(|1.7 - 2.1|) / 2.1] x 100%
(percent error) = [0.4 / 2.1] x 100%
(percent error) = 0.190476 x 100%
(percent error) = 19.0%
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Gertrude is saving money to buy a bicycle that costs $346. Gertrude
has $16 and will save $22 each week. How many weeks will it take
Gertrude to save enough money to buy the bicycle?
Answer: it will take her 15 weeks.
Step-by-step explanation: first, you subtract 16 from 346, which you get 330. next, you divide 330 by 22 because gertrude saves $22 per week. in total, 330 / 22 is 15.
liquid polymer is supplied to a water treatment plant as an 8% solution. how many gallons of liquid polymer should be used to make 55 gallons of a 0.5% polymer solution?
The amount of 8% liquid polymer to make 55 gallons of a 0.5% polymer solution is around 3.4 gallons.
The relationship between concentration and volume will be used to find the volume of liquid polymer. The formula to be used is -
[tex] C_{i}[/tex] [tex] V_{i}[/tex] = [tex] C_{o}[/tex] [tex] V_{o}[/tex], where [tex] C_{i}[/tex] and [tex] C_{o}[/tex] are initial and final concentration and [tex] V_{i}[/tex] and [tex] V_{o}[/tex] are initial and final volume.
Keep the values in formula -
[tex] C_{i}[/tex] × 8% = 55 × 0.5%
Rearranging the equation
[tex] C_{i}[/tex] = 55 × 0.5%/0.8%
Performing multiplication and division on Right Hand Side of the equation
[tex] C_{i}[/tex] = 3.4375 gallons
Hence, the volume of liquid polymer is around 3.4 gallons.
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Use the Pythagorean Theorem to find x.
Answer:
11
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, [tex]a^2+b^2 = c^2[/tex] , where c is the hypotenuse, and a and b are the legs. So to use the Pythagorean theorem, we let [tex]a=x-3,b=x+4[/tex] and [tex]c=x+6[/tex]. Expanding everything gives [tex]2x^2+2x+25=x^2+12x+36[/tex]
Moving everything to one side tells us
[tex]x^2-10x-11=0[/tex]
So
[tex](x-11)(x+1)=0[/tex]
This means that either x = 11 or x = -1. But looking back at our equation, x = -1 is a false solution, because sides of a triangle could not be negative in length, and x-3 = -4 when x =-1. Therefore x = 11.
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The 8 s the solution of equation StartFraction x Over 8 EndFraction = 1 i.e., x/8 = 1. So, the correct option is D).
To determine for which equations 8 is a solution, we can simply substitute 8 for x in each equation and see if the equation holds true.
Substituting x = 8 in the given equations, we get
x + 6 = 8 + 6 = 14 (not equal to 8)
x + 2 = 8 + 2 = 10 (not equal to 8)
x - 4 = 8 - 4 = 4 (not equal to 8)
x - 2 = 8 - 2 = 6 (not equal to 8)
2x = 2(8) = 16 (not equal to 8)
3x = 3(8) = 24 (not equal to 8)
x/2 = 8/2 = 4 (not equal to 8)
x/8 = 8/8 = 1 (equal to 8)
Therefore, only one equation x/8 = 1 has 8 as a solution.
Mathematically, we can evaluate this equation as follows
x/8 = 1
Multiplying both sides by 8
x = 8 * 1
x = 8
Since we have substituted x=8 and obtained the same value on both sides of the equation, the equation holds true for x=8. So, the correct answer is D).
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Rafael has a spinner equally divided into 4 sections of different colors: red, blue, yellow, and green. He also has a fair 6-sided die. Find the probability the spinner lands on blue and he rolls an even number.
Answer:
Step-by-step explanation:
The probability of the spinner landing on blue is 1/4, since there are 4 equally likely outcomes.
The probability of rolling an even number on a fair 6-sided die is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.
To find the probability of both events happening together (landing on blue and rolling an even number), we multiply their probabilities:
P(blue and even) = P(blue) x P(even)
= 1/4 x 1/2
= 1/8
Therefore, the probability of the spinner landing on blue and rolling an even number is 1/8.
suppose we have five coins, and each coin has a different probability of showingheads when flipped. the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5. assume we toss all five coins at the same time. what is theexpected value of the number of heads?
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
Then the expected value of the number of heads can be evaluated by multiplying each probability with its corresponding number of heads and suming them.
For the given case, we possess five coins with different probabilities of getting heads when flipped.
Therefore, getting heads for each coin in context of probability are 0.1, 0.2, 0.3, 0.4 and 0.5
Now, the expected value of the number of heads is
Expected value = [tex](0.1 * 1) + (0.2 * 1) + (0.3 * 1) + (0.4 * 1) + (0.5 * 1)[/tex]
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5
=1.5
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
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Golf Tournament In a golf tournament, the top 6 men's scores are 65, 68, 70, 72, 73, 75. The top women's scores are 69, 71, 73, 74, 77, 80. Compare the spread of the data for the two sets of scores using (a) the range and (b) the mean absolute deviation.
The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.
The MAD indicates that the men's score spread is marginally less than the women's score spread.
How to explain the rangeThe difference between a dataset's largest and lowest values is known as the range.
The range for the men's scores is: 75 - 65 = 10.
The range for the women's scores is 80 - 69 = 11.
The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.
The average distance between each data point and the dataset's mean is measured by the mean absolute deviation (MAD).
Find the mean first before calculating the MAD for the men's scores:
(65 + 68 + 70 + 72 + 73 + 75) / 6 = 70.5
The MAD indicates that the men's score spread is marginally less than the women's score spread.
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please help :)
Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the vertices are integers.
Which statement is true about the slope of HK and the slope of PK?
The slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.
Hence the correct option is (G).
Here in the given graph we can see that H, P, K are on the same line that is the points H, P, K are collinear.
We know that in Cartesian Coordinate Plane, the slope of one line is unique.
Slope = (Change in y coordinate)/(Change in x coordinate)
We can see that the coordinates are:
H = (-12, 10)
K = (-4, 5)
P = (4, 0)
So the slope of HK = (10 - 5)/(-12 - (-4)) = 5/(-8) = -5/8
Slope of PK = (5 - 0)/(-4 - 4) = 5/(-8) = -5/8
Hence the slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.
So the correct option will be (G).
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The question is incomplete. The complete question will be -
Is this proof valid? Why or why not? Do a thorough job of your explaining your reasoning.
Suppose that: a+b=c
This can be written as: 4a-3a+4b-3b-4c-3c
This can be reorganized to: 4a+4b-4c=3a+3b-3c
This can be factored: 4(a+b-c) = 3(a+b-c)
Dividing both sides by (a+b-c) 4=3
...So 4=3
The proof is not valid, nor does it prove that 4 is equal to 3
Deductions from the proofThis evidence is not true.
The error occurs in the step involving factoring, where both sides of the equation are divided by (a + b - c).
The problem is that if (a + b - c) equals zero, it is not permissible to divide both sides of the equation by (a + b - c) because it is not defined to be divided by zero
Moreover, even if (a + b - c) is not equal to zero, dividing both sides by (a + b - c) does not result in an equation
In this particular case, the fact that 4(a + b - c) = 3(a + b - c) implies that (a + b - c) = 0 or 4 = 3. One valid conclusion only if 4 = 3 is false.
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which of the following is true of structural equation models? group of answer choices they allow researchers to compare two competing models. they help in eliminating the third-variable problem in nonexperimental research. they can only be represented in a histogram. they allow researchers to easily calculate the variance of a set of scores.
a) 'they allow researchers to compare two competing models' is true of structural equation models.
a) They allow researchers to compare two competing models.
Structural equation modeling (SEM) is a statistical method used to analyze the relationships between multiple variables. It allows researchers to test and compare different models, including models with latent variables that are not directly observable. SEM can be used for both confirmatory and exploratory purposes, and it is a popular method in many fields, including social sciences, psychology, and business. Therefore, option (a) is true of structural equation models.
Option (b) is incorrect because SEM does not eliminate the third-variable problem in nonexperimental research. Rather, SEM allows researchers to control for and account for the effects of other variables in the model.
Option (c) is incorrect because structural equation models are not represented in a histogram. SEM involves constructing and testing a series of equations that represent the hypothesized relationships between variables.
Option (d) is also incorrect because SEM does not allow researchers to easily calculate the variance of a set of scores. SEM is used to test theoretical models and examine the relationships between variables, but it does not provide a direct measure of variance.
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-6
What is the line's slope?
-2
6
N
-2
-4
-6
2
4
Step-by-step explanation:
To find the slope of the line, we need to select any two points on the line and then use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the points (-2, 6) and (2, -6) on the line. Then, we can calculate the slope as:
slope = (-6 - 6) / (2 - (-2))
slope = -12 / 4
slope = -3
Therefore, the slope of the line is -3.
solve for x
x+3 > 70
x+3< 70
Using inequalities we know that x=68 and x=66 respectively.
What are inequalities?A mathematical phrase in which the sides are not equal is referred to as being unequal.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
So, solve the inequalities as follows:
x+3>70
x>70-3
x>67
Then, it will be x = 68.
Then,
x+3<70
x<70-3
x<67
Then, it will be s = 66.
Therefore, using inequalities we know that x=68 and x=66 respectively.
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