Please answer the question below
Jump to level 1 Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 6 inches. The heights of 8 randomly selected students
Answers
The required probability that the mean height of the sample is within 2 inches of the population mean is approximately 0.649.
Suppose the mean height in inches of all 9th-grade students at one high school is estimated. The population standard deviation is 6 inches. The heights of eight randomly selected students are taken. Let X be the mean height of the eight randomly selected students.
Then, X follows a normal distribution with mean μX and standard deviation σX, given by:
μX = μ = Population mean = Mean height of 9th-grade students = UnknownσX = σ/√n = 6/√8 = 2.12 inches.
Here, n = 8 is the sample size.
We need to find the probability that the mean height of the sample is within 2 inches of the population mean i.e.\(P(μ - 2 ≤ X ≤ μ + 2) = P((μ - μX)/σX ≤ (2 - μ + μX)/σX) - P((μ - μX)/σX ≤ (-2 - μ + μX)/σX)P(-0.94 ≤ Z ≤ 0.94) - P(Z ≤ -2.94) ≈ 0.651 - 0.002 = 0.649\)
Note: Here, we have used the standard normal distribution table to calculate the probability of Z-score.
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Related Questions
May I please get help with this math problem I have tried several times but still couldn’t find the right answer
Answers
According to the Triangle Inequality Theorem, the sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.
In this case, you know the lengths of two sides of the triangle, and you also know that "x" represents the length of the third side. Then, you can set up the following:
\(13+19>x\)Solving the inequality, you get:
\(\begin{gathered} 32>x \\ \end{gathered}\)You can rewrite it as:
\(x<32\)Hence, the answer is:
\(x<32\)full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class. true or false: full-time high school students spend more time per week on their courses than full-time college students.
Answers
Answer:
The answer to your question would be true.
The given statement 'full-time high school students spend more time per week on their courses than full-time college students' is true because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
Full-time high school students spend more time per week on their courses than full-time college students. It is because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
College courses usually last for one hour per day, whereas high school students attend classes for 5-6 hours per day. Hence, college students spend around 15-18 hours per week attending classes, while high school students spend around 30 hours per week in the classroom.
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This linear function has the domain (-2, -1, 0, 1, 2). find the range or output of. h(x)=2x+3
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The linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.
To find the range, we substitute each value of the domain for x, in the linear function h(x) = 2x + 3, as follows:
For the domain value, x = -2:
h(-2) = 2(-2) + 3,
or, h(-2) = -4 + 3,
or, h(-2) = -1.
Therefore, for the domain value, x = -2, the range value h(-2) is -1.
For the domain value, x = -1:
h(-1) = 2(-1) + 3,
or, h(-1) = -2 + 3,
or, h(-1) = 1.
Therefore, for the domain value, x = -1, the range value h(-1) is 1.
For the domain value, x = 0:
h(0) = 2(0) + 3,
or, h(0) = 0 + 3,
or, h(0) = 3.
Therefore, for the domain value, x = 0, the range value h(0) is 3.
For the domain value, x = 1:
h(1) = 2(1) + 3,
or, h(1) = 2 + 3,
or, h(1) = 5.
Therefore, for the domain value, x = 1, the range value h(1) is 5.
For the domain value, x = 2:
h(2) = 2(2) + 3,
or, h(2) = 4 + 3,
or, h(2) = 7.
Therefore, for the domain value, x = 2, the range value h(2) is 7.
Therefore, the linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.
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Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models (this is the product mix). The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.’s sales product mix for a week is?
Answers
Each model should be produced on a weekly basis to maximize net profit is $75,900.
What is Net profit?
In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.
As given,
Number of products sold:
T ≥ 1.5G
Maximize Profit Z = 150T + 130G
Labor Constraint:
Labor hours Available:
Production Department:
Number of labor hours available per day = 58 × 7 = 406
Number of days in a week = 5
Number of lobor ours available per week = 406 × 5 = 2030
Assembly Department:
Number of labor hours available per day = 25 × 7 = 175
Number of days in a week = 5
Number of labor hours available per week = 175 × 5 = 875.
Labor hours Required:
Labor hours required for G1 model:
Labor hours required at Production department = 3.5G
Labor hours required at assembly department = 2G
Labor hours required for T1 model:
Labor hours required at Production department = 4T
Labor hours required at Assembly department = 1.5T
Total labor hours required at Production department = 3.5G + 4T
Total labor hours required at Assembly department = 2G + 1.5T.
Constraint:
Labor hours required ≤ Labor hours Available.
Production department Labor constraint
3.5G + 4T ≤ 2030
Assembly department Labor constraint:
2G + 1.5T ≤ 875
The function:
Maximum Profit Z = 150T +130G
Constraint:
3.5G +4T ≤ 2030
2G + 1.5T ≤ 875
T ≥ 1.5G
Suppose that for example:
10.5G +12T = 6090
16G + 12T = 7000
Solve both equations simultaneously,
5.5G = 7000 - 6090
5.5G = 910
G = 910/5.5
G = 363
Since, T > G
Hence,
T = 363,
G = 165
Calculate Profit:
150T + 130G = 150 × 363 + 130 × 165
= 54450 + 21450
= 75900
Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.
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“The product of r and s is more than 4”
Answers
Answer: rs>4
Step-by-step explanation: The product of r and s just means rs. Then, when it says more than, you know its going to be a greater than sign: >. So your inequality would be rs>4
One-Step Equations 20 points if you solve them
Answers
Answer:
All answers below in explanation!
Step-by-step explanation:
1. x / 3 = 15 - 5
2. 2x = 11 + 6
3. x = -12
4. 400 - 20x = 60
Somebody please help me
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a fair coin is tossed four times. what is the probability that heads (h) will appear at least twice?
Answers
Answer: 11/16
Step-by-step: Whenever dealing with a problem like this. Times how many times its being tossed: 4x2 Then times that by two again: 4x2x2.
The probability of getting heads at least twice when tossing a fair coin four times is 6/16 or 0.375, and this can be calculated using either the counting method or the binomial probability formula.
The probability of getting heads or tails on a single coin toss is always 1/2 or 0.5. In order to determine the probability of getting heads at least twice when tossing a fair coin four times, we need to consider all the possible outcomes.
There are a total of 16 possible outcomes when tossing a fair coin four times, as each coin toss can result in either heads (H) or tails (T). These outcomes are:
HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT
Out of these 16 possible outcomes, there are 6 outcomes in which heads appear at least twice:
HHHH
HHHT
HHTH
HHTT
HTHH
THHH
Therefore, the probability of getting heads at least twice when tossing a fair coin four times is 6/16 or 0.375.
Another way to calculate this probability is by using the binomial probability formula:
P(X≥2) = 1 - P(X<2)
P(X<2) = P(X=0) + P(X=1)
Where X is the number of heads that appear in four coin tosses.
P(X=0) = (1/2)^4 = 1/16
P(X=1) = 4(1/2)^4 = 4/16
Therefore, P(X<2) = 1/16 + 4/16 = 5/16
And P(X≥2) = 1 - 5/16 = 11/16 or 0.375.
In conclusion, the probability of getting heads at least twice when tossing a fair coin four times is 6/16 or 0.375, and this can be calculated using either the counting method or the binomial probability formula.
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solve each pair of simultaneous epuations by additions methood
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A company has to decide whether to invest money in the development of a microbiological product. The company's research director has that there is a 60% chance that a successful development could be achieved in 2 years. However, if the product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present-value terms of $ 3 million. (Present value is designed to take the company's time preference for money into account. The concept is explained in Chapter 8) In the event of a successful development, a decision would have to be made on the scale of production. The returns generated would depend on the level of sales which could be achieved over the period of the product's life. For simplicity, these have been catorized as either high or low. If the company opted for large-volume production and high sales were achieved, then net returns with a present-value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million.In contrast, if the company decided to invest only small-scale production facilities then high sales would generate net returns with a present value if facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of $2 million. The company's marketing manager estimates that there is a 75% chance that high sales could be achieved.(a) Construct a decision tree to represent the company's decision problem. (b) Assuming that the companys objective is to maximize its expected returns, determine the policy that it should adopt. (c) There is some debate in the company about the probability that was estimated by the research diretor. Assuming that allo other elements if the problem remain the same, determine how low this probility would have ti be before the option of not developing the product should be chosen. (d) before the final decision us nade the company us taken iver by a bew owner, who has the utilities shown below for the sums of money involved in the decision. (The owner has no ointerest in other attributes which may be associated with the decision, such as developing a prestige product or maintaining employment.) What implications does this have for the policy that you iidentified in (b) and why?Present value of net returns New owner's utility-$3m, $0m, $1m, $2m, $4m, $6m 0, 0.6, 0.75, 0.85, 0.95, 1.0
Answers
The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
The initial node represents the decision whether to invest in the development of the microbiological product.
The two possible outcomes are a successful development or failure after 2 years.
(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.
Starting from the end nodes and working backwards, we have:
For large-scale production with high sales:
Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m
For large-scale production with low sales:
Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m
For small-scale production with high sales:
Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m
For small-scale production with low sales:
Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m
At the 2-year node, the expected value for a successful development is:
For large-scale production:
Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m
For small-scale production:
Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m
Finally, at the initial node, the expected value for investing in the development is:
Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m
Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.
(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:
Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp
Setting this equal to zero and solving for p, we get:
p = 1
Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.
(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.
The utilities are increasing and concave, indicating diminishing marginal utility of money.
This means that the new owner is risk-averse.
The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.
To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.
If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.
If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.
If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.
If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.
If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.
Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
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The common ratio of AP is 3,given that the 5th is greater than the first term by 400,the 5th term of the gp
Answers
The 5th term of the geometric progression is a₅ = 405
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the 5th term of the geometric progression be a₅
Now , the common ratio of the GP is r = 3
And , a₅ = a + 400 be equation (1)
On simplifying the equation , we get
a₅ = ar⁴
Substituting the value of a₅ in the equation , we get
ar⁴ = a + 400
when r = 3
a ( 3 )⁴ = a + 400
81a = a + 400
Subtracting a on both sides of the equation , we get
80a = 400
Divide by 80 on both sides of the equation , we get
a = 5
Now , the 5th term of the GP is a₅ = ar⁴
On simplifying the equation , we get
a₅ = 5 ( 3 )⁴
a₅ = 5 x 81
a₅ = 405
Hence , the 5th term of the GP is 405
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solve for x
2x×7÷2=8
Answers
Answer:
x=8/7
2x times 7 divided by 2 = 8
solve for x
Step-by-step explanation:
2x ×7/2 =8
2x =8×2/7
x=8×2/2×7
x=8/7 or 1⅐.
hope this helps you.
13/19 as a decimal rounded to the nearest tenth.
Answers
Answer:
0.7
Step-by-step explanation:
13/19 as a decimal rounded to the nearest tenth.
13/19 = 0.68421...
rounded:
= 0.7
Answer:
0.684
Step-by-step explanation:
13/19
= 13 ÷ 19
= 0.68421052631579
=0.684
Find the sum of (8a +2b - 4 ) and ( 3b - 5)
Answers
The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.
To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.
So we have:
(8a + 2b - 4) + (3b - 5)
= 8a + 2b + 3b - 4 - 5 (grouping like terms)
= 8a + 5b - 9
Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).
We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.
In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.
Using the distributive property, we can add the terms with the same variable together:
(8a + 2b - 4) + (3b - 5)
= 8a + (2b + 3b) - (4 + 5)
= 8a + 5b - 9
Thus, we obtain the same result.
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4. John is packing books into boxes. Each box can hold either 15 small books or 8
large books. He needs to pack at least 35 boxes and at least 350 books, Write a
system of linear inequalities to represent the situation
Answers
Answer:
Your system of inequalities is:
x + y ≥ 35
15x + 8y ≥ 350
Step-by-step explanation:
Let x = number of boxes of small books and let y = number of boxes of large books.
Since John needs to pack at least 35 boxes:
(number of boxes of small books) + (number of boxes of large books) (is at least) 35
x + y ≥ 35
Since John needs to pack at least 350 books:
(number of small books packed) + (number of large books packed) (is at least) 350
(number of small books per box)(number of boxes of small books) + (number of large books per box)(number of boxes of small books) ≥ 350
15x + 8y ≥ 350
Zaboca Printing Limited (ZPL) has only one working printer. Eight (8) customers submitted their orders today Monday 6th June 2022. The schedule of delivery of these orders are as follows:
Jobs (in order of arrival) Processing Time (Days) Date Due
A 4 Monday 13th June 2022
B 10 Monday 20th June 2022
C 7 Friday 17th June 2022
D 2 Friday 10th June 2022
E 5 Wednesday 15th June 2022
F 3 Tuesday 14th June 2022
G 8 Thursday 16th June 2022
H 9 Saturday 18th June 2022
All jobs require the use of the only printer available; You must decide on the processing sequence for the eight (8) orders. The evaluation criterion is minimum flow time.
i. FCFS
ii. SOT
iii. EDD
iv. CR
v. From the list (i to iv above) recommend the best rule to sequence the jobs
Answers
The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.
The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.
In this case, applying the EDD rule, the sequence of jobs would be as follows:
D (Due on Friday 10th June)
F (Due on Tuesday 14th June)
E (Due on Wednesday 15th June)
C (Due on Friday 17th June)
G (Due on Thursday 16th June)
H (Due on Saturday 18th June)
A (Due on Monday 13th June)
B (Due on Monday 20th June)
By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.
Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.
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Determinar la pendiente, la ordenada en el origen de la siguiente ecuacion
8\3x + 1\4y = 4
Answers
The slope of the equation 8/3x + 1/4y = 4 is -32/3 and the y-intercept is 16.
To determine the slope and y-intercept of the equation 8/3x + 1/4y = 4, we need to convert it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To do this, we'll isolate y on one side of the equation by subtracting 8/3x from both sides:
8/3x + 1/4y = 4
1/4y = -8/3x + 4
y = -32/3x + 16
Now we have the equation in slope-intercept form y = mx + b, where m = -32/3 and b = 16. Therefore, the slope of the equation is -32/3 and the y-intercept is 16.
The slope of a line is the ratio of the change in the vertical coordinate (rise) to the change in the horizontal coordinate (run) between any two points on the line. It tells us how steep the line is. A negative slope means that the line is decreasing from left to right, while a positive slope means that the line is increasing from left to right.
The y-intercept is the point where the line crosses the y-axis. It tells us the value of y when x is equal to zero. If the y-intercept is positive, the line intersects the y-axis above the origin, while if the y-intercept is negative, the line intersects the y-axis below the origin.
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help. i can't find the answer anywhere and i hate doing slope
Answers
Answer:
put one point at (2, -4) and the other at (0, -1)
you can find the second point using the slope -3/2
help me please The total number of students who could attend a field trip is represented by the variablet. The number of students in Group A is less than the number in Group B. Group A has 6 students more than the total number of students, while Group B has 3 less than the total number of students. Which inequality represents this situation?
O ¼t + 6 < t – 3
O (¼ + 6)t < t – 3
O ¼t + 6 < 3 – t
O 6t + ¼ < t – 3
Answers
Answer:
1/4 +6<t-3
Step-by-step explanation:
the answer is tahta
Answer: I think it is the first answer
Step-by-step explanation:
Group A = < Group B
Group A has 6 more than total so 1/4t+6
Group B has 3 less than total so t-3
Graph the inverse of the line provided on the graph.
Drawing Tools
Click on a tool to begin drawing.
Answers
What is the importance and advantage of using graph representation when organizing your data?
Answers
The importance and advantage of using graph representation when organizing your data are that it makes data presentable, summarizing, better way of comparison of data.
An organized diagram or pictorial representation of the relationship between values or data is referred to as a graph. it is a a diagram that depicts a variable's variation in comparison to that of one or more other variables, such as a series of points, lines, line segments, curves, or areas.
The following are the three advantages of graphs:
It makes data look good and makes it easy to understand.It helps to concisely summarize the data.Better data comparison is made possible by it.Know more about graphs here: https://brainly.com/question/17267403
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Been here for hours which one is it
Answers
Answer:
3 I do belive
Step-by-step explanation:
Answer:
-1/4 slope and 50 y intercept
Step-by-step explanation:
from,
m= (y-y1)/(x-x1)
just decide what values of x and y will be your y,x and y1 ,x1
y=50, y1=25,x=0,x1=100
m is the slope.
y intercept is the value of y
Given the quadrilateral ABCD, what is the length of diagonal AC?
A 16/2
B 8/2
C 13
D 4/2
Square roots by the way
Answers
Answer: a
Step-by-step explanation:
Guys pls help me?!!!!!! With a.
Answers
Answer: I do not comprehend
Step-by-step explanation:
Answer:
I think it is 5.50 not sure but I hope this helps.
Step-by-step explanation:
PLEASE HELP ME
#6 Choose the graph of the solution to this inequality. *
Answers
Answer:
D
Step-by-step explanation:
An open line is < and >
A filled line is > and equal, and < and equal
when you plug -3.5 into -6 you get 21 but when you go right, ex -3x-6 you get 18 which is less than 21
Answer:
I think it is c
Step-by-step explanation:
hope it help
Find the value of N such that x + N = 71/10 and x/N 1/70 are equivalent equations
Answers
Answer: N =
Step-by-step explanation:
- So, we're trying to find a value of N, so we can use one of the equations, isolate x, and create a new equation to find a value that N can equal.
- It's up to you which one to choose, but I suggest isolating the fraction. X is equal to 1/70N. Now, plug that into the first equation, which should be 1/70N + N = 71/10.
N can also be written as 70/70N, because that's equal to 1 N, our current value of N.
71/70N = 71/10
. Find a value of N that makes the statement equivalent. In this case, N = 7 works.
13=8-5d
I need to solve for the given variable
Answers
Answer:
d= (-1)
Step-by-step explanation:
13=8-5d
13-8=-5d
5=-5d
1=-d
-1=d
thats it
How many paralellograms are there in the picture?
Answers
Correct option is D)
We shall label the figure as shown below:
The simplest parallelograms are ABML, BCNM, COON, DEFO, OFGH, NOHl, MNIJ and LMJK i.e. 8 in number.
The parallelograms composed of two components each are ACNL, BDOM, CEFN, LNIK, MOHJ, NFGI, ABJK, BCLJ, CDHI and DEGH i.e. 10 in number.
The parallelograms composed of three components each are ADOL, BEFM, LOHK and MFGJ i.e. 4 in number.
The parallelograms composed of four components each are AEFL, LFGK, ACIK, BOHJ and CEGI i.e. 5 in number.
The parallelograms composed of six components each are ADHK and BEGJ i.e. 2 in number. AEGK is the only parallelograms composed of eight components.
Total number of parallelograms in the figure =8+10+4+5+2+1=30
Hence, the answer is (D).
Answer:
Option D is correct
Step-by-step explanation:
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the rationale for avoiding the pooled two sampled t procdues for interferences is that
Answers
There are several rationales for avoiding the pooled two-sampled t procedures for inferences. Here are a few:In certain cases, the assumption of equal population variances may be wrong, causing the pooled t procedures to yield unreliable results.
In case the assumption of equal population variances is violated, Welch's t-test is more powerful than the pooled t-test.If the sample sizes of the two groups being compared are significantly unequal, the pooled t-test can produce misleading results, and Welch's t-test should be used instead.Therefore, the rationale for avoiding the pooled two-sampled t procedures for inferences is that the assumption of equal population variances might be inaccurate, causing unreliable and less efficient results.When comparing two population means, a two-sample t-test is commonly used. The pooled two-sample t-test is one of the most widely utilized methods for comparing means. It assumes that the two populations have equal variance, and it has been shown to be quite reliable when this assumption is valid.However, if the populations have unequal variances, this assumption can be incorrect, and the pooled t-test can yield unreliable results. If the population variances are not equal, the Welch's t-test is often used. It does not assume equal variances and is more powerful when this assumption is not met. When comparing two groups with different sample sizes, the t-test may produce misleading results if the variances are unequal. In this situation, Welch's t-test is used because it is more accurate and effective in these circumstances.
Thus, if we don't know if the variances of the populations are equal, we should avoid using the pooled t-test and instead use Welch's t-test, which is more powerful and does not require the equal variance assumption.
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another financial analyst, who also works for the online trading platform, claims their clients have a lower proportion of stock portfolios that contain high-risk stocks. this financial analyst would like to carry out a hypothesis test and test the claim that the proportion of stock portfolios that contain high-risk stocks is lower than 0.10. why is their hypothesis test left-tailed?
Answers
The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.
In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.
By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.
Therefore, a left-tailed hypothesis test is appropriate in this scenario.
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