The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.
The null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): The population variance is equal to 14.
Alternative Hypothesis (Ha): The population variance differs from 14.
To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.
For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.
In this case, n = 22, so the degrees of freedom is 21.
Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.
The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.
To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.
The chi-square test statistic is calculated as:
χ2 = (n - 1) ×(sample variance) / (population variance)
Plugging in the values, we have:
χ2 = (22 - 1) × 18 / 14
=27
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What additional information is needed to prove the triangles are congruent by the SAS Postulate?
The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.
We have, CB = CD
As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.
In triangle ACB and ACD
AC = AC (common)
CB= CD (given)
Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then
<ACB = <ACD
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In the right △ABC with m∠C=90°, m∠B=75°, and AB=12 cm. Find the area of △ABC.
Don't use trig to solve, don't know how to.
The area of the right triangle is 18.02 cm².
How to find area of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sum of angles in a triangle is 180 degrees.
Therefore, let's find the area of the right angle triangle as follows;
let's find the height and base of the triangle.
using trigonometric ratios,
cos 75 = adjacent / hypotenuse
cos 75 = base / 12
base = 3.10582854123
Therefore,
sin 75 = opposite / hypotenuse
sin 75 = h / 12
height = 11.5911099155
height = 11.59
Therefore,
area of the triangle = 1 / 2 × 3.11 × 11.59
area of the triangle = 36.0483518371 / 2
area of the triangle = 18.0241759186
area of the triangle = 18.02 cm²
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The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism? 3 4 4 5
The dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.
To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, let's consider the relationship between the two prisms.
A prism is a three-dimensional shape with two parallel, congruent bases connected by rectangular faces. Since the problem specifies that the dimensions of the smaller prism are being multiplied to obtain the dimensions of the larger prism, we can infer that the prisms are similar, meaning they have the same shape but possibly different sizes.
Let's denote the dimensions of the smaller prism as length, width, and height, and the corresponding dimensions of the larger prism as L, W, and H.
To find the factor by which the dimensions are multiplied, we need to compare the corresponding sides of the two prisms. Based on the information provided, we can establish the following relationships:
L = 3 × length
W = 4 × width
H = 4 × height
We can rewrite these relationships as:
length = L/3
width = W/4
height = H/4
Now, let's compare the ratios of corresponding sides:
length/L = (L/3)/L = 1/3
width/W = (W/4)/W = 1/4
height/H = (H/4)/H = 1/4
From these ratios, we can observe that each dimension of the smaller prism is one-third (1/3) the size of the corresponding dimension of the larger prism in terms of length, one-fourth (1/4) in terms of width, and one-fourth (1/4) in terms of height.
Therefore, the dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.
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Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
8 divided by the sum of a number and 4
Answer:
Step-by-step explanation: you are sped that is the answer black n
f(x)=x-4 Function Family: Parent Function: D: ; R: End Behavior: As x→∞, f(x)→ As x→→∞, f(x)- Increasing Interval: Decreasing Interval:
X-4<5 graph the solution of
The graph of the solution of the inequality is attached
How to graph the solution of the inequalityFrom the question, we have the following parameters that can be used in our computation:
x - 4 < 5
Add 4 to both sides of the inequality
So, we have
x - 4 + 4 < 5 + 4
Evaluate the like terms
So, we have
x < 9
This means that the solution of the inequality is x < 9
See attachment for the graph
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This figure represents the net of a square pyramid.
2 m
76
6 m
2 m
The total surface area of the square pyramid is 28 m²
What is an equation?An equation is an expression that is used to show how numbers and variables are related using mathematical operators
Given the square pyramid net:
Area of square base = 2 m * 2 m = 4 m²
Area of each triangle face = (1/2) * 2 m * 6 m = 6 m²
Area of the four triangle face = 4 * 6 m² = 24 m²
Total surface area = 24 m² + 4 m² = 28 m²
The total surface area is 28 m²
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If every floor is 5.079 meters tall how many floors are in the burj Khalifa (please help I need this before 12)
Answer:
147 floors
Explanation:
To determine the number of floors in the Burj Khalifa, we can use the information provided. We know that Andre stood 1000 meters away from the building and looked up at a 39.62-degree angle using a laser rangefinder. Let's calculate the height of the Burj Khalifa using basic trigonometry.
First, we can find the height of the building using the tangent function:
tan(angle) = height / distance
tan(39.62 degrees) = height / 1000 meters
height = tan(39.62 degrees) * 1000 meters
height ≈ 747.97 meters
Now, let's calculate the number of floors in the Burj Khalifa. We are given that each floor is 5.079 meters tall.
Number of floors = height / height of each floor
Number of floors = 747.97 meters / 5.079 meters
Number of floors ≈ 147.23 floors
Since we cannot have fractional floors, we can round the number down to the nearest whole number.
Therefore, there are approximately 147 floors in the Burj Khalifa.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Based on the information given about the geometry, the value of CF will b A. 6cm.
How to calculate the valueSince OE and OF are both 4 cm, then OEF is an equilateral triangle. This means that EOF is 60 degrees.
Since AB is 12 cm, then AB is twice the length of OE. This means that ABE is a 30-60-90 triangle.
In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30 degree angle. This means that CF is 6 cm.
In conclusion, the correct option is A.
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What is the volume of the prism?
A prism has hexagon bases with each side 12 centimeters. From the side of the base to the center of the base is 10 centimeters. The height of the prism is 9 centimeters.
Answer: 1080
Step-by-step explanation:
12x10x9=1080
Hoped this helped?!
Need assistance with #8, #9, #10, and #11
Any help will be graetly apprciated. Studying for final exam
Below are the right probabilities for each scenario;
8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]
9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]
10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].
11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex]; P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]
How do we solve the probability questions?For the compounded probability, we can solve them the following way;
8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32
b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16
c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4
9. There are 28 total students and 6 total outcomes on a standard die.
P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14
10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.
P(both flights delayed) = 6/14 × 8/12 = 2/7
11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.
a) P(nickel, then quarter) = (6/25) × (5/24) = 1/20
b) P(penny, then not a dime) = (4/25) × (15/24) = 1/10
c) P(both dimes) = (10/25) × (9/24) = 3/20
d) P(both nickels) = (6/25) × (5/24) = 1/20
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What is the y-intercept?
Answer:
-4
Step-by-step explanation:
i jus did this question
The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers. The data are normally distributed and s=9.904 weeks. Construct and interpret a 90% confidence interval for the population standard deviation of the age (in weeks) at which babies first crawl. 31 39 36 38 51 48 55 Click the icon to view the table of critical values of the chi-square distribution. choice.
Select the correct choice below and fill in the answer boxes to complete your
(Use ascending order. Round to three decimal places as needed.) O
A. If repeated samples are taken, 90% of them will have the sample standard deviation between ___ and___
B. There is a 90% probability that the true population standard deviation is between ___ and ___
C. There is 90% confidence that the population standard deviation is between and___ and ___
There is 90% confidence that the population standard deviation is between 5.094 weeks and 19.803 weeks.
The correct option is C.
What is the confidence interval or the population standard deviation?To construct a confidence interval for the population standard deviation, we can use the chi-square distribution.
Given data:
Sample size (n) = 12
Sample standard deviation (s) = 9.904 weeks
The chi-square distribution is right-tailed and at 90% confidence level, the significance level is 0.1 on each tail.
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 12 - 1
Degrees of freedom (df) = 11
From the chi-square distribution table, the critical values for a 90% confidence level with 11 degrees of freedom are 3.816 and 22.362.
Therefore, the 90% confidence interval for the population standard deviation is:
Lower bound = √(n-1) * s² / χ² upper)
Lower bound = √(11 * 9.904²) / 22.362)
Lower bound = 5.094
Upper bound = √(n-1) * s² / χ² lower)
Upper bound = √(11 * 9.904²) / 3.816)
Upper bound = 19.803
Therefore, there is 90% confidence that the population standard deviation of the age at which babies first crawl is between approximately 5.094 weeks and 19.803 weeks.
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Determine the length of side x.
NO SPAM OR I WILL REPORT YOU AND BAN YOU IMMEDIATELY
Answer:
x=12.124
simplified would be x=12
Step-by-step explanation:
As the degrees of freedom increase, the Chi-square distribution
Select one:
a.
becomes more right-skewed.
b.
becomes more left-skewed.
c.
becomes less skewed.
d.
does not change shape.
As the degrees of freedom increase, the Chi-square distribution becomes less skewed.
Option C is the correct answer.
We have,
The Chi-square distribution is a probability distribution that is commonly used in statistics.
It is often used in hypothesis testing and in constructing confidence intervals for population variances.
The shape of the Chi-square distribution depends on the degrees of freedom (df). The degrees of freedom represent the number of independent pieces of information used to estimate a parameter or make an inference.
When the degrees of freedom are small, such as 1 or 2, the Chi-square distribution is highly skewed to the right.
This means that the distribution has a long tail on the right side and is concentrated toward the lower values.
However, as the degrees of freedom increase, the Chi-square distribution becomes less skewed.
The distribution becomes more symmetrical and approaches a bell shape, similar to the shape of a normal distribution. This means that the values are more evenly spread out and there is less concentration towards the lower values.
Therefore,
As the degrees of freedom increase, the Chi-square distribution becomes less skewed.
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what 2 reports could be used to verify that retirement contributions were accurately remitted for the most recent payroll period
Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are the Payroll Summary Report and the Retirement Contribution Report.
Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are:
Payroll Summary Report: This report provides a summary of the payroll transactions for the period, including details of employee wages, deductions, and employer contributions.
It should include a specific section or breakdown for retirement contributions, showing the individual employee contributions and the corresponding employer contributions.
By reviewing this report, one can ensure that the retirement contributions have been accurately calculated and remitted.
Retirement Contribution Report: This report specifically focuses on the retirement contributions made by both employees and the employer.
It should provide a detailed breakdown of the contributions for each employee, including the employee's contribution amount, the employer's matching or non-elective contribution amount, and any additional details related to the retirement plan.
This report allows for a comprehensive review of the retirement contributions to verify if they match the expected amounts based on employee records and plan guidelines.
By comparing the information in these reports with the employees' individual contribution records and the retirement plan requirements, it is possible to verify that the retirement contributions were accurately remitted for the most recent payroll period.
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6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answer:
65/100 that is the answer to this question
A population data set produced the following information N-250 Σx=9880, Σy=1456. Σxy-85080 Σx²=485870, Σy² = 135675 Find the value of oe and p²
The value of p² is approximately 0.999999528.
To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.
The formula for the standard error of estimate (oe) is:
oe = √((Σy² - (Σy)² / N) / (N - 2))
Substituting the given values, we have:
oe = √((135675 - (1456)² / 250) / (250 - 2))
oe = √((135675 - 2124736 / 250) / 248)
oe = √(541.96)
oe ≈ 23.27
Therefore, the value of oe is approximately 23.27.
The coefficient of determination (p²) can be calculated using the formula:
p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))
Substituting the given values:
p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))
p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))
p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)
p² = 1 - (27647.68) / (59022875580.02)
p² ≈ 0.999999528
Therefore, the value of p² is approximately 0.999999528.
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What is the area of a trapezoid with bases that are 7 meters and 10 meters in length and a height of 12 meters? 42 m2 60 m2 102 m2 204 m2
The circle has center O. Its radius is 4 ft, and the central angle a measures 110°. What is the area of the shaded region?
Give the exact answer in terms of it, and be sure to include the correct unit in your answer.
The area of the shaded region is (133π/9) square feet.
Given that the radius (r) is 4 ft, the area of the entire circle is:
A = π(4)² = 16π ft²
To find the area of the sector, we need to calculate the fraction of the circle that the central angle represents.
The fraction is determined by dividing the measure of the central angle (110°) by the total angle in a circle (360°).
Fraction of the circle represented by the sector = 110° / 360° = 11/36
To find the area of the sector, we multiply the fraction by the area of the entire circle:
Area of the sector = (11/36) × (16π)
= (11π/9) ft²
Finally, to find the area of the shaded region, we subtract the area of the sector from the area of the entire circle:
Area of shaded region = Area of entire circle - Area of sector
Area of shaded region = 16π - (11π/9)
= (144π - 11π)/9
= (133π/9) ft²
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When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 40 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 4000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability of accepting the whole shipment is 0.9093. Therefore, almost all such shipments will be accepted.
What is the probability that this whole shipment will be accepted?The probability that the whole shipment will be accepted is calculated as follows;
First, we calculate the probability of having at most 3 batteries that do not meet specifications out of the 40 randomly tested batteries.
Assuming:
p = probability that a single battery does not meet specifications = 0.03q = probability that a single battery meets specifications = 1 - p = 0.97n = number of batteries tested = 40k = number of batteries that do not meet specifications (at most) = 3We can use the binomial probability formula to calculate the probability:
[tex]P(X \leq k) = \sum (from\: i = 0 \:to\: k) [(nCi) * p^{i} * q^{(n-i)}][/tex]
P(X ≤ 3) = [(⁴⁰C₀) * (0.03⁰) * (0.97⁴⁰] + [(⁴⁰C₁) * (0.03¹) * (0.97³⁹)] + [(⁴⁰C₂) * (0.03²) * (0.97³⁸)] + [(⁴⁰C₃) * (0.03³) * (0.97³)]
P(X ≤ 3) = 0.9093.
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PLEASE ANSWER ASAP!!
Answer:
-8 and 4
Step-by-step explanation:
P= -2
-2+6 = 4
-2-8= -8
Trapezoid TUVW is shown on the coordinate plane below:
Trapezoid TUVW on the coordinate plane with ordered pairs at T negative 5, 5, at U negative 2, 5, at V negative 2, 2, at W negative 7, 2.
If trapezoid T'U'V'W' represents trapezoid TUVW reflected over the y-axis, the ordered pair of W' is ___________.
The ordered pair of W' in trapezoid T'U'V'W' is (7, 2).To reflect a point over the y-axis, we need to change the sign of its x-coordinate while keeping the y-coordinate the same.
In trapezoid TUVW, the ordered pair of W is (-7, 2).
To find the ordered pair of W' in trapezoid T'U'V'W', we need to reflect the x-coordinate of W over the y-axis. Therefore, the x-coordinate of W' will be the opposite of the x-coordinate of W, while the y-coordinate remains the same.
Given that the coordinates of point W are (-7, 2), reflecting it over the y-axis means changing the sign of the x-coordinate, while keeping the y-coordinate the same.
So, when we reflect point W(-7, 2) over the y-axis, the x-coordinate becomes positive and the y-coordinate remains the same. Therefore, the ordered pair of W' is (7, 2).
The x-coordinate of W' will be -(-7) = 7, and the y-coordinate remains 2.
So, the ordered pair of W' is (7, 2).
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3. Solve for x.
X
37°
11
Answer:
13.77 units-----------------------
In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.
Missing is the length of hypotenuse, x.
Use cosine function:
cosine = adjacent leg / hypotenusePlug in known values and solve for x:
cos 37° = 11/xx = 11/cos 37°x = 13.77 (rounded)24. Find the area of the parallelogram that has a base of 23 cm and a height of 17 cm.
Answer 80 cm² 40 cm² 195.5 cm² 391 cm²
Answer:
391 cm²
Step-by-step explanation:
area of the parallelogram,
A = base * height
= 23 * 17
= 391 cm²
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: C-Cylinder
Step-by-step explanation:
In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.
Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.
I hope this helps!
Answer:
The correct answer is (C), cylinder.
Explanation:
When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.
The volume of the loading space on a moving truck is 432 cubic feet. The length of the truck is (x+6) feet. The width of the truck is x feet, and
the height is 6 feet. What is the actual length and width of the truck?
Answer:
length=12ft
width=6ft
Step-by-step explanation:
The volume formula is V=lwh.
Plug the values into the equation like this: 432=(x+6)(x)(6)
Divide both sides of the equation by 6: 72=(x+6)(x)
Distribute the x: [tex]72=x^{2} +6x[/tex]
Subtract the 72: [tex]0=x^{2} +6x-72[/tex]
Factor: 0=(x+12)(x-6)
x=-12
x=6
Now, plug in x into the original length and width equations.
length: (6+6)
length=12
width=6
Find f(x)/g(x)
F(x)= x3+6x2+x1/2
The solution of f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1
option C is correct.
Here, we have,
given that,
the functions are:
f(x) = x^3+6x^2+x^1/2
g(x) = x^1/2
so, we have,
f(x)/g(x)
= x^3+6x^2+x^1/2 / x^1/2
= x^3/ x^1/2 +6x^2/ x^1/2 +x^1/2/ x^1/2
=x ^5/2 + 6x^3/2 + 1
Hence, The solution of f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1
option C is correct.
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Lorri had a gross income of $3256.15 during each pay period in 2010. If she got paid monthly, how much of her pay was deducted for FICA in 2010?
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Here is your answer!
Answer:
[tex](x - 5)^2 + (y + 2)^2 = 5[/tex]
Step-by-step explanation:
The equation of a circle with a center at (h, k) and radius r is given by:
[tex]\bold{(x - h)^2 + (y - k)^2 = r^2}[/tex]
In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).
The distance between the center and the point is:
[tex]\sqrt{(5 - 4)^2 + ((-2) - 0)^2} = \sqrt{1 + 4} = \sqrt{5}[/tex]
Therefore, the equation of the circle is:
[tex](x - 5)^2 + (y + 2)^2 = \sqrt{5}^2[/tex]
Simplifying the equation, we get:
[tex]\bold{(x - 5)^2 + (y + 2)^2 = 5}[/tex] is a required equation