The consumer surplus at the equilibrium quantity is 84,375.
To find the equilibrium quantity, we need to set the demand function equal to the supply function and solve for x.
Demand function: d(x) = 300 - 0.3x
Supply function: s(x) = 0.5x
Setting them equal to each other:
300 - 0.3x = 0.5x
Now, let's solve for x:
300 = 0.5x + 0.3x
300 = 0.8x
x = 300 / 0.8
x = 375
The equilibrium quantity is 375.
To find the consumer surplus at the equilibrium quantity, we need to calculate the area between the demand curve and the price line at the equilibrium quantity.
Consumer Surplus = ∫[0 to x](d(x) - s(x)) dx
Plugging in the values of the demand and supply functions:
Consumer Surplus = ∫[0 to 375]((300 - 0.3x) - (0.5x)) dx
Simplifying:
Consumer Surplus = ∫[0 to 375](300 - 0.3x - 0.5x) dx
Consumer Surplus = ∫[0 to 375](300 - 0.8x) dx
Integrating:
Consumer Surplus = [300x - 0.4x^2/2] evaluated from 0 to 375
Consumer Surplus = [300x - 0.2x^2] evaluated from 0 to 375
Consumer Surplus = (300 * 375 - 0.2 * 375^2) - (300 * 0 - 0.2 * 0^2)
Consumer Surplus = (112500 - 0.2 * 140625) - (0 - 0)
Consumer Surplus = 112500 - 28125
Consumer Surplus = 84375
The consumer surplus at the equilibrium quantity is 84,375.
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Eddie's Tea Shop has caffeinated tea and decaffeinated tea. During the lunchtime rush, the tea shop served 32 teas in all, 25% of which were caffeinated. How many caffeinated teas did the tea shop serve?
Answer: 8 teas were caffeinated
Step-by-step explanation:
To solve is to turn 25% into a decimal:
This is 25/100 turned into 0.25
*Multiply this by 32
This gives the number 8
*To do this, multiply without the decimal: 25 x 32 = 800
Then place the decimal back 2 places to the left of the last number:
8.00
Is segment PQ a perpendicular bisector of segment RS?
No, segment PQ is not a perpendicular bisector of segment RS. A perpendicular bisector is a line that passes through the midpoint of a segment and is perpendicular to it.
To determine if a line is a perpendicular bisector, we can use the equation (x1 + x2)/2 = xmid and (y1 + y2)/2 = ymid to find the midpoint of the segment and then use the equation y = mx + b to find the equation of the line. If the slope of the line is the negative reciprocal of the slope of the segment, then the line is a perpendicular bisector. In this example, if the coordinates of the endpoints of segment RS are (x1,y1) and (x2,y2), then the midpoint of the segment is (xmid, ymid) where xmid = (x1 + x2)/2 and ymid = (y1 + y2)/2. The equation of the line PQ can be written as y = mx + b. To determine if PQ is a perpendicular bisector, we must calculate the slope of the segment RS and the slope of the line PQ and then compare the two slopes. If the slope of the line PQ is the negative reciprocal of the slope of the segment RS, then PQ is a perpendicular bisector. Otherwise, PQ is not a perpendicular bisector.
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For what value of x is △PQR ∼ △TUV?
The value of x that makes △PQR ∼ △TUV is 27.
What is the similarity of triangles?
The similarity of triangles refers to the relationship between two or more triangles in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.
Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion.
If △PQR ∼ △TUV, then we can write:
PQ/UV = QR/UT = RP/VT = k (the proportionality constant)
If we know the value of two of the sides in one triangle and the corresponding two sides in the other, we can find the value of k.
we know that,
PQ = 27, TU = 18, QR = 36, and UV = x.
We can find the value of k by using the proportionality constant:
k = PQ/UV = 27/x
Then we can use k to find the value of RP:
RP/VT = k, so RP = k * VT
We can find the value of VT by using the similar triangles:
QR/UV = RP/VT,
QR/UV = k, ............(RP/VT = k)
so,
(36/18) = (27/x) * VT
VT = (2/1) * (x/27)
Finally, we can find the value of x by solving this equation:
1/x = (2/1) * (1/(27*VT))
1/x = 2/(27*VT)
1/x = (2/1) * (1/(27*((2/1) * (x/27))))
1/x = (2/1) * (1/(27*(2/1) * (x/27)
1/x = (2) * (1/(27*2) * (x/27)
1/x² = 1/729
x = 27
Hence, the value of x that makes △PQR ∼ △TUV is 27.
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4) Lola gets to have 60 minutes of screen time today. So far, she has spent 22 minutes playing games on her phone. She has also spent 26 minutes watching videos online. How many minutes does Lola have left?
Answer: 12
Step-by-step explanation: 22+26=48
60-48=12. SO she 12 minutes left
Determine if the triangles are similar
1. yes SSS
2. yes SAS
3. yes AA
4. No, not similar
Answer: 4. No, not Similar
Step-by-step explanation:
<QSR = 62
because of vertical angles
we have 3 different angles and no sides
What is the rate of change of the function?
The price of strawberries at Fine Foods is shown in the graph. At best Market, the price y for x pounds of strawberries is given by y=2.90x. Which store sells strawberries at a cheaper unit price?
Best Market sells strawberries at a cheaper unit price.
What is unit?The definition of a unit of measurement is a particular magnitude of a quantity that has been established and accepted by law or convention and is used as a standard for measuring other quantities of the same kind. Any other quantity of that type can be expressed as a multiple of the unit of measurement.
For instance, a length is a physical quantity. The metre is a unit of length that corresponds to a particular, predetermined length (symbol m). For instance, "10 metres" (or 10 m) is 10 times the fixed, predetermined length known as "metre."
In best Market, the price y for x pounds of strawberries is given by
y = 2.90x
Lets find the slope of Fine Foods strawberries
y - y₁ = m(x - x₁)
From the graph take two points, lets say (3, 6) and (5, 10)
Put the points in the formula
10 - 6 = m(5 - 3)
4 = 2m
m = 4/2 = 2
The slope is 2
Now, lets convert it to slope intercept form
y - 10 = 2(x - 5)
y = 2x - 10 + 10
y = 2x - 10 + 10
y = 2x
For a certain same price Fine Foods provides 2x pounds of strawberries while Best Market provides 2.90x pounds of strawberries.
Thus, Best Market sells strawberries at a cheaper unit price.
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Lesly bought 4 bags of pretzels and 2 boxes of granola bars for $17.55. What is the cost for one bag of pretzels? What is the cost for a box of granola bars?
The cost of one bag of pretzel is $ 1.80
The cost of one bag of granola bars is $ 3.15
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of one pretzel be represented as x
Let the cost of one granola bar be represented as y
Now , the equation will be
4 bags of pretzels and 2 boxes of granola bars for $13.50
Substituting the values in the equation , we get
4x + 2y = 13.50 be equation (1)
And , 1 bag of pretzels and 5 boxes of granola bars for $17.55
Substituting the values in the equation , we get
x + 5y = 17.55 be equation (2)
Multiply equation (2) by 4 , we get
4x + 20y = 70.2 be equation (3)
Subtracting equation (1) from equation (2) , we get
18y = 56.70
Divide by 18 on both sides of the equation , we get
y = $ 3.15
So , the cost of one granola bar is $ 3.15
Substituting the value of y in equation (1) , we get
4x + 2 ( 3.15 ) = 13.50
4x + 6.30 = 13.50
Subtracting 6.30 on both sides of the equation , we get
4x = 7.20
Divide by 4 on both sides of the equation , we get
x = $ 1.80
So , the cost of one pretzel is $ 1.80
Hence , the equations are solved
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You pick a card at random. Without putting the first card back, you pick a second card at random. 1 2 3 4 What is the probability of picking a 2 and then picking a factor of 12?
The the probability of picking a 2 and then picking a factor of 12 is 1/6.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Sample space = {1, 2, 3, 4}
The probability of just picking up a 1 is 1/4.
Now, the remaining cards = 3
So, the probability of getting a factor of 12 (i.e., 3 and 4} is
= 2/3
Thus, the combined probability is
= 1/4 x 2/3
= 2/12
= 1/6
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use the distributive property to write an equvialent expression 6(g +h)
Answer:
6g+6h
Step-by-step explanation:
This is one way to re-write using the distributive property
Answer:
6g+6h
Step-by-step explanation:
The distributive property tells us how to solve expressions in the form of a(b + c). So, one simple way of rewriting the equation would just be 6g + 6h.
Using percent like this question:125000 times 20?
Tanisha left her house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then she stopped and went into the store for 3 minutes. From there, she drove in the same direction at a speed of 3 blocks per minute until she got to the bank, which is 12 blocks away from the store. She stopped at the bank for 7 minutes. Then she drove home at a speed of 5 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Tanisha is xx minutes after she leaves her house, until she gets back home.
This prompt is about being able to represent time and distance on a graph called Distance-Time Graph. See the graph attached.
What is a Distance-Time Graph and why is it important?
A Distance-Time Graph is a sort of graph that depicts the relationship between distance and time for a moving object.
It is a handy tool for studying an object's motion since it allows one to simply ascertain the object's speed and acceleration. It is also significant because it gives a visual depiction of an object or subject's motion, making the underlying physical ideas easier to grasp.
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Full Question:
Tanisha left her house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then she stopped and went into the store for 3 minutes. From there, she drove in the same direction at a speed of 3 blocks per minute until she got to the bank, which is 12 blocks away from the store. She stopped at the bank for 7 minutes. Then she drove home at a speed of 5 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Tanisha is xx minutes after she leaves her house, until she gets back home.
Make a graph of showing the number of blocks away from home that Tanisha is x minutes after she leaves her house, until she gets back home.
What are the 7 types of system?
The 7 types of system are-
Physical or abstract systems, open and closed systems, larger system, permanent and temporary, Natural systems, Man-made system.
Define the term system and its types?Physical or abstract systems:
Physical or abstract systems can be static or dynamic in nature. Physical systems are tangible objects. A conceptual or nonphysical abstract system. Conceptualizing actual circumstances is what is meant by the abstract.open and closed systems:
Both open and closed systems interact with their surroundings on a regular basis. The outside is where it gets input from and where it gets output from. A closed system is protected from the effects of the outside world.larger system:
Each system is a component of a larger system, which is divided into subsystems and supersystems. When the emphasis is on production, goal distribution, and sources of profit and income, the business firm is viewed as the system or total system.Permanent and temporary:
A system that is permanent lasts for a period of time that is lengthy in comparison to human activity. A temporary system is one that has a limited lifespan.Natural systems:
Natural systems and systems made by humans. Natural systems are ones created by nature and found in the environment.Deterministic and probabilistic systems: In a deterministic system, every event's outcome can be predicted with absolute certainty.Man-made system:
It's generally accepted that knowing more about a situation or event makes it less uncertain.To know more about the system, here
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What is DE? Max amount of points.
Proportionality can be used to find the length of side DE in the triangle by multiplying both sides by EB and dividing both sides by FC. This yields the equation DE = (FC * DF) / EB. Simplifying this equation yields DE = 31.72.
What is meant by parallel lines?EF is parallel to BC and DF, EB, FC are given.
We can use the theorem that states:
Parallel lines have corresponding angles congruent and corresponding sides proportional.
We may use proportionality to get the length of the triangle's side DE. When two ratios are equal, this is referred to as proportionality. In this scenario, we will use the ratios of side DE to side FC and side EB to side DF. Given that side DE is proportional to side FC and side EB is proportionate to side DF, we can construct an equation stating that the ratio of side DE to side FC equals the ratio of side EB to side DF. This equation is written as DE/FC = DF/EB.
We can then solve this equation for side DE by multiplying both sides by EB and dividing both sides by FC.
This yields the equation DE = (FC * DF) / EB.
We can then plug in the given values for FC, DF, and EB to find the length of side DE.
When we do this, we get that DE = (15.4 * 20.6) / 19.3.
Simplifying this equation yields DE = 31.72.
Rounding to the nearest tenth, DE = 31.7. This is the length of side DE in the triangle.
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Databae A contain 40 data item and i made up with equal number value of 0 and 100 and ha a mean of 50. Databae B alo ha a 40 entrie made up equally of value 49 and 51 and alo ha a mean of 50. Which databae will have the maller value for it tandard devation?
For the given mean and the number of items, the database B has smaller value of the standard deviation compare to database A.
As given in the question,
For data base A:
Number of items = 40
Mean of database A = 50
Values of database A spread between 0 to 100
For data base B:
Number of items = 40
Mean of database B = 50
Values of database B spread between 49 to 51
Standard deviation of data base
= √ (1/40)[ (x₁ - 50)² + (x₂- 50)² + (x₃ - 50)² + ......+ (xₙ - 50)² ]
Here mean and number of items of both the data base is same.
Data base B spread between 49 to 50 only.Data base spread between 0 to 100.Standard deviation of B is smaller than the standard deviation of A.Therefore, the standard deviation of data base B is having smaller value compare to data base A.
The above question is incomplete , the complete question is :
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
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Please help
WILL MARK BRAINLIEST
Answer:
4
Step-by-step explanation:
(8x-2)+15x+90=180
Combine like terms
23x+88=180
-88 -88
23x=92
÷23 ÷23
X=4
What is the additive inverse of _7 11?
The additive inverse of 7 11 is -7 11, which is the same number but with the opposite (or negative) sign. This means that when added together the two numbers will total zero.
Additive inverse of 7 11 = -7 + 11 = -7 11
The additive inverse of a number is the same number with the opposite sign, which can be helpful when solving equations. For example, if we have the number 7 11, the additive inverse would be -7 11. To find the inverse, we simply switch the sign from positive to negative (or vice versa). This means that when the two numbers are added together, the total sum will be zero. For example, 7 11 + (-7 11) = 0. The inverse of a number can also be helpful when we are looking for an unknown variable in an equation. For example, if we have the equation 3x + 7 11 = 4, we can find the value of x by subtracting 7 11 from both sides:
3x + 7 11 = 4 --> 3x
= -7 11 + 4 --> 3x
= -3 11 --> x = -1 11.
This means that x = -1 11.
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How do you solve a 3 step equation using substitution?
To solve the 3 step equation, we have to solve the one equation in two variable. Then substituting the value in other equation and further solving according to the given rule.
In the substitution approach, we will examine the two equations and choose which variable is the most straightforward to solve for in order to transform one of the equations into x =, y =, or z =. The other equation's x, y, or z will then be appropriately replaced. The outcome will be an equation we can solve that has just one unknown. A variable whose coefficient is 1 or -1 should be isolated.
Use the steps below to solve systems using substitution:
(1) Choose an equation and determine the value of one of its variables.
(2) Substitute the variable you just solved in the other equation.
(3) Address the fresh equation.
(4) Enter the discovered value into any equation that calls for both variables, then get the value for the other one.
(5) Verify the answers to the two initial equations.
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There is a proportional relationship between the weight and total cost of a bag of lemons. One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94.
Describe how you would graph the proportional relationship.
The required function here is C(x) =2.2x
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94.
One bag weighs 2.4 pounds and costs $5.28.
and therefore 1 pound weighing bag will cost = 5.28/2.4
=$2.2
Thus we can construct an equation if there are x pounds then the cost function C(x) =2.2x
Hence, the required function is C(x) =2.2x
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Kerry invited 23 friends to his pool party. They played a game where everyone had to separate into groups. Each group had the same number of children. The game could not be played with all 24 children in one group, and each group had to have more than 2 children.
Which of the following are ways that they could divide into groups?
Answer:
abeStep-by-step explanation:
yeah hope its was helpful
Answer:
A,C,E
Step-by-step explanation:
group:children
4x6=24 good
12x2=24 but has to have more than 2 children in each group
8x3=24 good
4x9=36 36>24
2x12=24 good
What are the two main forms of factor analysis Mcq?
The two different types of factor analysis are confirmatory and exploratory.
A technique for simulating observed variables and their covariance structure in terms of unseen variables is component analysis (i.e., factors). The two different types of factor analysis are confirmatory and exploratory.
A key phase in the scale building process is exploratory factor analysis (EFA), which is a technique to examine the underlying structure of a group of observed variables. Factor extraction is EFA's first stage. We will talk about how principal components analysis and common factor analysis approach variance partitioning differently.
Confirmatory factor analysis (CFA), a technique for confirming a factor structure that has already been developed, will be covered in the seminar's last section. Identification, model fit, and degrees of freedom will be discussed in relation to the three-item, two-item, eight-item, one-factor, and two-factor CFAs. For the EFA and CFA portions of the seminar, respectively, SPSS and R (lavaan) will be used.
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Selected all answers that apply to the table
Please help
$30 is the price for 12 tickets and A further ticket costs $2.50.Simply expressed, a single unit value is extracted from a specified multiple .
what is unitary method ?The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and opposite are comparable. (Linear Algebra, Academic Analysis, Mathematics of Matrix or Operators)
given
0 - 00
4 - $ 16
$30 is the price for 12 tickets.
A further ticket costs $2.50 as it traverses the source,
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The complete question is :- The costs of movie tickets are shown in the table.
Type of Ticket Cost per Ticket
Child $6.50
Adult $8.50
Senior $5.50
Which equations represent the total cost, c, to buy 2 of each type of ticket? Choose all that apply.
c = $6.50 + $8.50 + $5.50
c = (2 × $6.50) + (2 × $8.50) + (2 × $5.50)
c = ($6.50 + $8.50 + $5.50) ÷ 3 × 2
c = 2 × $6.50 × $8.50 × $5.50
c = ($6.50 + $8.50 + $5.50) × 2
Bert found =of an apple pie in the refrigerator. He shared " of the pie with
his friends. How much of the apple pie was left?
Bert incorrectly calculated how much of the apple pie was left. Which step contains the first error?
The amount of the apple pie that was left will be 3/4.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends.
The amount of the apple pie that was left will be:
= 2 1/2 - 1 3/4
= 3/4
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Complete question
Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends. How much of the apple pie was left?
ApplyA typical television newscast has three cameras. The center cameradirectly faces the news anchor's desk. The other two cameras are both angled45° away from the center camera. Suppose each camera has a field of 60°.What is the total angle covered by the three cameras? Explain your reasoning.
The center camera and the two angled cameras cover a total of 60° + 60° + 60° = 180°.
The total angle covered by the three cameras is 180°. The center camera has a field of 60° and the other two cameras, which are angled 45° away from the center camera, each has a field of 60°.
Therefore, together, the center camera and the two angled cameras cover a total of 60° + 60° + 60° = 180°.
When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol "°" stands for the angle. The Latin word "Angulus" is where the word "angle" originated.
Typically, an angle is measured with a protractor and expressed in degrees. Angles of 30°, 45°, 60°, 90°, and 180° are shown here. The many types of angles are determined by the angles' degrees values.
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Two lines in the same plane that never touch are:
a) perpendicular
b) collinear
c) skew
d) parallel
Answer:
d. parallel
I wish you luck in your assignments.
Which is the correct similarity statement?
Using similar triangle theorem, the similarity statement will be "ΔGJL ≈ Δ HLK".
What are similar trianglesSimilar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and sides that are proportional to each other.
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.
In this problem, we can see that both triangles are similar and have the same angle.
The correct similarity statement will be "ΔGJL ≈ Δ HLK"
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16 is what percent of 35.7?
When base is 24 cm & height is 15 cm then area of a triangle is equal to?
The area of triangle with the base 24 centimetres and height 15 centimetres is 180 cm².
The area of triangle is calculated by the formula -
Area of triangle = 1/2 × b × h, where b represents base of the triangle and h represents height of the triangle.
Keep the values in formula to find the area of triangle.
Area of triangle = 1/2 × 24 × 15
Performing division on Right Hand Side of the equation
Area of triangle = 12 × 15
Performing multiplication on Right Hand Side of the equation
Area of triangle = 180 cm²
Thus, the area of triangle is 180 cm².
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Books weigh about 12 ounces and we are putting 15 pounds in each box
How many boxes will be needed to pack 1200 picture books
please help it’s on a math question statistics
Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.
A test statistic is what?A test statistic in a research study is the figure that is applied to decide whether to confirm or refute hypothesis. This statistic compares the results of a study or sample to what the null hypothesis would predict.
A conjecture is a proposal that makes sense in light of the available information but has neither been confirmed nor refuted. A assertion on which hypotheses will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).
Here,
given:
=> 60= μ
=> 15.9 = σ
=> n=40
=>x' = 63
utilized formula is
=> Z = (x' - μ) / σ/(√n)
=> Z = (63 -60) / 15.9 / √40
=> Z = 3 / 15.9/√40
=> Z = 3 / 2.5140
=> Z = 1.19
Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.
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