Both the given expression are equivalent expression as 5m + 4.
Given that,
to determine whether the two given expressions are equivalent ot each other,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4
Thus, Both the given expression are equivalent expression as 5m + 4.
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suppose a jar contains 15 red marbles and 14 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.
If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.
Probability
Total marbles:
Total marbles=15+14
Total marbles = 29
Chance that a red will be pulled=2/29
Chance that the second marble will be red =1/28
Hence,
Probability :
Probability = 2/29*1/28
Probability = 0.00246
Therefore If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812
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Math Question Attached
The slope of the straight line is 4/5
Slope of a LineThe slope of a line is a measure of the ratio between the rise and run of that line. The slope of a line is an integral quantity used to calculate the equation of a line
In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.
The slope of a line basically the change in y-coordinate with respect to change in x-coordinate.
This is easily done with a formula given as
m = y₂ - y₁ / x₂ - x₁
Taking data points from the graph attached;
A = (5, 2)B = (0, -2)Substituting the values into the slope equation;
m = -2 - 2 / 0 - 5
m = -4 / - 5
m = 4/5
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solve 3^x-6^ =3^4
[tex]3^x^-^6=3^4[/tex]
a)-2
b)4
c)6
d)10
Step-by-step explanation:
[tex] {3}^{10 - 6} [/tex]
[tex] = {3}^{4} [/tex]
The Rodriguez family ate One-third of a pan of brownies, and they plan to divide the remaining brownies into two equal parts. They will take one part to their block party and the other part to share with co-workers. How much of the whole pan of brownies will each place get?
A model has 2 shaded parts and 1 unshaded part.
Answer:
1
Step-by-step explanation:
The equation to represent this would be (1 - (1 / 3)) / 2
1 - (1 / 3) = 2 / 3
2 / 3 / 2 = 1 / 3
two poles are connected by a wire that is also connected to the ground. the first pole is 20 ft tall and the second pole is 10 ft tall. there is a distance of 30 ft between the two poles. where should the wire be anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed?
The wire should be anchored to the ground to minimize the amount of wire needed 20 ft from the left pole.
What is the quadratic equation?
ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x.
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _{l} = 20^{2} + x^{2} = x^{2} + 400[/tex]
Similarly for the 2nd part of the wire
[tex]L^{2} _{t} = 10^{2} + (30 - x^{2})[/tex]
= 100 + 900 - 60x + x²
= x²+ 1000 - 60x
We want to minimize the length of the wires, or [tex]L^{2} _{l} + L^{2} _{r}[/tex]
[tex]\frac{x}{\sqrt{{x}^2 + 400} } + \frac{x - 30}{\sqrt{{x}^2 + 400}} = 0[/tex]
we can take the first derivative of this and set it to 0
x = 20
Hence, the wire should be anchored to the ground to minimize the amount of wire needed 20ft.
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Exponential Growth
Graph: y = 2*
20
-1
O
X
1
2
y
Growth
b>1
Answer:
it's 20 if u look closely
Which expression is equivalent to ? Assume . m=0 n=0
7m-(7n-18m) is an expression which is equivalent to (2mn)^4/6m^-3 n^-2 Assume m=0 n=0
What is a expression in maths?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)
for example 4m +5 where 4 is the coefficient of m and 5 is the constant term in other word 4m and 5 are the term of the expression and m is the variable in the expression and addition is the operator.
m=0, n=0.
8m^7n^6/3 10m^7n^6/3 8m^16n^12/3 m^4n^6/3
-7m-(3n-(8m-4n-10m)
-7m-(3n-(8m-4n+10m))
-7m-(3n-(18m-4n))
-7m-(3n-18m+4n)
-7m-(7n-18m)
complete question is
Which expression is equivalent to (2mn)^4/6m^-3 n^-2? Assume m=0 n=0
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Un tren de juguete eléctrico viaja alrededor del árbol de Navidad en círculos. La vía del tren mide 6 pies de diámetro. ¿Cuál es la distancia que recorre el tren?
Answer:
i need points
Step-by-step explanation:
In the diagram below of triangle EFGEFG, HH is the midpoint of \overline{EG}
EG
and II is the midpoint of \overline{FG}
FG
. If m\angle GFE=87-7x∠GFE=87−7x, and m\angle GIH=51+2x∠GIH=51+2x, what is the measure of \angle GIH∠GIH?
Applying the definition of midpoint, the measure of angle GIH in the triangle shown is: 59°.
What are the Corresponding Angles of Similar Triangles?The corresponding angles of two similar triangles are always congruent to each other.
Given that H is the midpoint of Eg and I is the midpoint of FG, two similar triangles are created, where angles GFE and GIH are corresponding angles.
Given:
m∠GFE = 87 - 7x
m∠GIH = 51 + 2x
m∠GFE = m∠GIH [corresponding angles are congruent]
Substitute
87 - 7x = 51 + 2x
Solve for x
-2x - 7x = 51 - 87
-9x = -36
Divide both sides by -9:
-9x/-9 = -36/-9
x = 4
m∠GIH = 51 + 2x = 51 + 2(4)
m∠GIH = 59°
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if you were trying to store a list of single digit numbers in your short-term memory, about how many should you be able to store on average? group of answer choices 10 2 15 7
If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.
What is short-term memory?
Short-term memory is a concept in psychology that defines the capacity for holding a small amount of information in mind for a short interval. The concept of short-term memory is given by Atkinson-Shiffrin. The information of short-term memory can be transformed into long-term memory through rehearsal.
According to several studies, short-term memory has a space limit of 7 ± 2 chunks of information. The fact is written by a cognitive psychologist of Harvard University named George A. Miller and was published in 1956 in psychological reviews.
Hence, If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.
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sonia can paint a room in 12 hours. roman can paint the same room in 15 hours. how long does it take for both sonia and roman to paint the room it they are working together
It will take 7 hours to paint a room when Sonia and Roman works together.
Given,
Time taken by Sonia to paint a room = 12 hours
Time taken by Roma to paint the same room = 15 hours
We have to find the time taken by both of them to paint the room if they work together.
Here,
Sonia takes 12 hours
Roman takes 15 hours
LCM of 12 and 15 = 60
12 × 5 = 60
15 × 4 = 60
Total number of works is 60
Now,
Number of works done by Sonia = 5 in an hour
Number of works done by Roman = 4 in an hour
So,
5 + 4 = 9 work can be done by them together in an hour
Then,
Time taken to complete 60 works;
60/9 = 6.66 ≈ 7 hours
That is,
In 7 hours Sonia and Roman paint a room together.
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2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). (1
01
02
4/3
Answer:
4/3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-3 - 1)/(-2 - 1)
slope = -4/(-3)
slope = 4/3
a woman decides to purchase a $23,800 car and makes a down payment of $3,500. she arranges to borrow the remainder from a bank that will charge her 4.5% interest. she will make monthly payments for 4 years. a. find her monthly payment amount.
The monthly payment amount a woman has to pay for the car is $462.91.
Here we have to find the monthly payment amount.
The cost of car = $23,800
Down payment = $3,500
Rate(r) = 4.5%
time(t) = 4 years
Periodic interest(i) = 0.045/12
Formula to calculate monthly payment:
A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1
Loan amount = 23800 - 3500
= $ 20300
A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1
= 20300× 0.004488 / 0.196814
= 462.91
Therefore the monthly payment is $462.91.
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Bicycle Parade There was a parade of bicycles and tricycles. Jackie counted the number of wheels; there were 23 wheels. Tony counted the riders; 10 children were riding. How many bicycles were there and how many tricycles?
why would a manager be interested in analyzing risk? a. to determine a distribution of outcomes. b. to determine a confidence interval on the most likely outcomes. c. to determine a range of outcomes. d. to determine a most likely outcome. g
A manager be interested in analyzing risk to determine a range of outcomes.
What are the reasons to analyze risk?Project managers and their teams undertake risk analysis, such as calculating the likelihood of various undesirable outcomes affecting a project, to avoid or minimize their impacts. The process can help reduce exposure, time, and budget overruns and keep businesses in compliance.
Analyzing risk can help to uncover threats to the success of the projects or business operations, such as: vulnerabilities in security; potential litigations, penalties and non-compliance issues; and, mistakes in budget or scheduling.
In general, there are 4 accepted ways to respond to risks, those are: avoidance, mitigation, acceptance, and transfer.
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Pam, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering 748 points for signing up, plus 86 points for every night Pam books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 734 points, plus 87 points per night. If Pam books a certain number of nights, the points she earns with either hotel will be the same. How many nights will that be? How many points will she have?
Answer:
Step-by-step explanation: x is the number of days she is booked.
List an equation
748+86x=734+87x
x=14
14 nights and plugging x into the equation 1952 points
Barbara ell iced tea for $1. 49 per bottle and water for $1. 25 per bottle. She wrote an equation to find the number of bottle he need to ell to earn $100
The equation representing the number of bottle Barbara need to sell to earn $100 is; 1.49x + 1.25y = 100.
Define the term arithmetic equation?In order to find the next item in the pattern, a specific number is added to each item in the series. The number added, also known as the common difference, must be exactly the same for every phrase in the series.For the given question-
Price of each iced tea bottle = $1.49.Price of each water bottle = $1.25.Let the number of iced tea bottle be 'x'.
Let the number of water bottle be 'y'.
Total price = 100
Thus, the equation for the total cost becomes-
1.49x + 1.25y = 100.
Therefore, the equation representing the number of bottle Barbara need to sell to earn $100 is; 1.49x + 1.25y = 100.
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Which of the following Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?statements is true about the graphs of f(x)=x and g(x)=f(x+7)?
A statement which is true about the graphs of f(x) = x and g(x) = f(x + 7) is: C. g(x) is the graph of f(x) translated 7 units to the left.
What is a translation?In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) or g(x) = f(x + 7) simply means shifting a graph 7 units to the left as illustrated by the graph shown in the image attached below.
In this context, we can reasonably infer and logically deduce that the parent function f(x) = x was shifted by 7 units to the left.
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Complete Question:
Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?
A. g(x) is the graph of f(x) translated 7 units down.
B g(x) and f(x) have the same y-intercept.
C g(x) is the graph of f(x) translated 7 units to the left.
D g(x) is the graph of f(x) translated 7 units to the right.
Find the magnitude of the vector v = <-2, 5>.
Convert these unlike fractions to equivalent like fractions and add them. You must use the lcd to get the answer correct. If possible, reduce the final sum. 14512.
Unlike fraction 1/7 is converted to equivalent like fraction 2/14 and the sum of 2/14 + 3/14 = 5/14.
As given in the question,
Given fraction is equal to:
1/7=? + 3/14=?
Here there are two fractions
1/7 and 3/14
LCD( least common denominator) of 7 and 14 is equal to 14.
Now make them like fractions
1/7 is equivalent to
( 1/7) × ( 2/2) = 2/ 14
Now 2/14 and 3/14 are like fractions
Sum of like fractions is:
2/14 + 3/14
= ( 2+ 3) / 14
= 5/ 14
Therefore, the conversion of unlike fraction 1/7 to like fraction is 2/14. And sum of 2/14 + 3/14 = 5/14.
The complete question is:
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum. 1/7=? + 3/14=?
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based on a sample of size 41, a 95% confidence interval for the mean score of all students, μ, on an aptitude test is from 60 to 66. find the margin of error.
To find the margin of error we have to use the formula,
Margin of error = Z * ơ / √n ,
Where
z = critical factor
ơ = population standard deviation
n = sample size
Now we have to find confidence interval
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-ME
Where margin of error ME = zr/√n
Given that;
Mean = ц
Standard deviation r = 25
Number of samples n = 41
Confidence interval = 95%
z(at 95% confidence) = 1.96
Xbar = 60.............(1)
Xbar + E = 66.........(2)
from equating both the equations we get
E= 6
and for finding the value of margin of error we know that its the half of the E
Margin of error = E/2
=6/2
=3
Therefore , the Margin of error is 3
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A school staff meeting had 60 teachers in attendance, 30% of whom were first-year teachers. How many first-year teachers were in the meeting?
Why do we take the square root of the mean squared error to calculate the root mean squared error?.
The square in RMSE is utilized because it consistently provides a positive number for error, preventing errors from canceling one another out, and grants higher weight to values further from the target function, emphasizing locations for which the estimator is unreliable. To reverse the results of squaring, use the square root.
What is RMSE?
The difference between values (sample or population values) predicted by a model or estimator and the values observed is typically measured using the root-mean-square deviation (RMSD) or root-mean-square error (RMSE).
The RMSD is the quadratic mean of the square root of the second sample moment of the discrepancies between expected values and observed values.
When computations are made outside of the data sample that was used for estimation, the deviations are referred to as errors (or prediction errors) instead of residuals.
The RMSD is used to combine the sizes of predictions' mistakes for different data points into a single indicator of predictive power. .
RMSD is a metric for accuracy that is used to compare the predicting mistakes of various models.
Hence, The square in RMSE is utilized because it consistently provides a positive number for error, preventing errors from canceling one another out, and grants higher weight to values further from the target function, emphasizing locations for which the estimator is unreliable. To reverse the results of squaring, use the square root.
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The longest side of a triangle is a cm. The second side is b cm shorter than the first side. The third side is half as long as the second side.
Write an expression, in its simplest form, for the perimeter of the triangle.
Answer:
2.5a - 1.5 b or
5/2a - 3/2b
Step-by-step explanation:
a + (a - b) + 0.5(a - b) =
a + a - b + 0.5a - 0.5b =
2a - b + 0.5a - 0.5b =
2a - 1.5 b + 0.5a =
2.5a - 1.5 b
assuming the population standated deviation is known, which of the following statements is true about the standard deviation of the sample mean x
Assuming the population standard deviation is known and the standard deviation of the sample mean x : option (b) is correct : the standard error of the sample mean decreases.
Central Limit theory:In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.
Standard deviation:Standard deviation is a calculation of the dispersion or variation in a set of numbers. If the standard deviation is a small number, it means the data points are close to their average value. If the deviation is large, it means the numbers are spread out, further from the mean or average.
There are different ways to write out the steps of the population standard deviation calculation into an equation. A common equation is:
σ = ([Σ(x - u)2]/N)1/2
Where:
σ is the population standard deviation
Σ represents the sum or total from 1 to N
x is an individual value
u is the average of the population
N is the total number of the population
Sample Mean:A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.
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Cara throw the ame dice three time. Find the probability that Cara doe not throw a ix until her third throw
Cara has a 25/216 chance of waiting until her third throw before throwing a six.
Define the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset among possible experiment results. Depending on the experiment, a sample area could contain a variety of results.for the stated question-
Total times the dice is thrown = 3.
Total number of sample space = 6 x 6 x 6 = 216.
The probability of coming six = 1/6
The probability of not coming six = 1 - 1/6 = 5/6.
Probability of getting 6 in third throw = 5/6 x 5/6 x 1/6
Probability of getting 6 in third throw = 25/216
Thus, Cara has a 25/216 chance of waiting until her third throw before throwing a six.
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The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between 30,000 and 60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,545 . Assume that the standard deviation is $2,160. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean for each of the following sample sizes: 30, 50, 100 and 400? Round your answers to four decimals.
n= 30
n= 50
n= 100
n= 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.
The probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within +-210 of U ranges from BLANK for a sample of size 30 to BLANK for a sample of size 400 .
Expert Answer
0.4056 0.5082 0.6690 0.9482 A large sample the probabili…View the full answer
a) The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean is 0.9482.
b) When trying to estimate the population mean, a greater sample size offers the benefit of improving the estimation's accuracy.
a. The z-score is calculated as follows:
z = (x - μ) ÷ (σ ÷ √n)
Where the sample size is n, the sample mean is x, the population mean is y, and the population standard deviation is z.
By entering the specified values, we obtain:
n = 30: z = (x - 17,545) ÷ (2,160 ÷ √30) = (x - 17,545) ÷ 216
n = 50: z = (x - 17,545) ÷ (2,160 ÷ √50) = (x - 17,545) ÷ 174
n = 100: z = (x - 17,545) ÷ (2,160 ÷ √100) = (x - 17,545) ÷ 132
n = 400: z = (x - 17,545) ÷ (2,160 ÷ √400) = (x - 17,545) ÷ 53
To find the odds that a sampling distribution could be within $210 of both population mean and the z-score, we must first figure out the likelihood that now the z-score would be within 1.96 standard deviations of the mean. This is because the 95th percentile, or the number under which 95% of the data lies, is represented by the z-score of 1.96, which is the value in this case.
To ascertain the likelihood, we must attempt searching up the z-scores in a z-table and get the pertinent probabilities. A z-table is a table that lists the probability associated with various z-scores.
Using the z-scores we used to develop the concept, we could look up the alternatives in a z-table and find the following probability:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
For each of the aforementioned sample sizes, the likelihood that a sampling of taxpayers from this income category who itemized deductions will exhibit a sample mean that is within $210 of the population mean is:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
b. The likelihood that the sample means will closely match the true population mean is thereby increased.
The standard deviation averages commonly fall as the sample size rises. In other words, as the sample mean becomes less likely to depart from the actual population mean, the likelihood that the random variable will be close to the population mean increases.
For instance, in the aforementioned case, the likelihood that they would give it a shot would be within 210 of a population mean would rise from 0.4056 for a random sample of just 30 to 0.9482 for a random sample of 400.
This means that the likelihood that they give it a chance will fall within the allowed range of the sample % likewise increases as the sample size increases.
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PLS HELP!!! QUICK PLS! I'LL MAKE BRAINLIEST
Write an equation for the graph of each quadratic and compare to each other. Be sure to discuss the similarities and differences.
Using the table the quadratic equation is y = x² - 2
from the curve the quadratic equation is y = x² + 1
How to write the equation of the quadratic graphQuadratic equation is written of the form
y = a(x - h)² + k
from the table the vertex is
v(h, k) = v(0, -2)
substituting the values to the formula
y = a(x - 0)² - 2
y = ax² - 2
Using the point (2, 2) from the table
y = ax² - 2
2 = a * 2² - 2
2 = 4a - 2
4a = 2 + 2
4a = 4
a = 1
The equation of the curve is
y = x² - 2
from the graph the vertex is
v(h, k) = v(0, 1)
substituting the values to the formula
y = a(x - 0)² + 1
y = ax² + 1
Assuming a unit on the graph is a unit we take point (1, 2) where the curve passed
y = ax² + 1
2 = a * 1² + 1
2 = a + 1
a = 2 - 1
a = 1
The equation of the curve is
y = x² + 1
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HELLPPPPP ITS maTHhHhHh
Answer:
7
Step-by-step explanation:
if he gets $35 in 5 hours then he gets $7 an hour, and 7*7=49.
Answer: 7 hours
Step-by-step explanation:
$35/5 hours=$7 an hour
$49/$7 an hour=7 hours of mowing
for the given scenario, determine the type of error that was made, if any. (hint: begin by determining the null and alternative hypotheses.) an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck. one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis. assume that in reality, the mean temperature inside its delivery truck is 32 degrees. was an error made? if so, what type?
There is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
Given, an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck.
one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis.
The mean temperature inside its delivery truck is 32 degrees.
As, the temperature inside the delivery truck should be 30 degrees and should not be greater than 30 degrees then, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
So, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
Hence, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
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