(a) The critical t-value for a two-tailed test at the 1% level of significance with 3 degrees of freedom is greater than the absolute value of the calculated t-value. (b) The correlation coefficient of 0.896 is still significant at the 1% level of significance. (c) The test results of parts (a) and (b) can potentially be different due to the change in sample size (n).
(a) For a sample size of 5, the critical t-value for a two-tailed test at the 1% level of significance with 3 degrees of freedom is greater than the absolute value of the calculated t-value. This indicates that the correlation coefficient of 0.896 is significantly different from 0 at the 1% level of significance.
(b) As the sample size increases to 10, the degrees of freedom and the test statistic also increase. With more data points, the test becomes more sensitive and precise in detecting significant relationships. This leads to a smaller p-value, indicating a stronger level of significance for the correlation coefficient.
In summary, the test results differ between the two scenarios due to the change in sample size. Larger sample sizes provide more reliable and robust estimates of the population, resulting in increased statistical power and greater sensitivity to detecting significant correlations.
(c) Increasing the sample size affects the degrees of freedom (df) and the test statistic. As the sample size increases, the degrees of freedom increase. This means there are more data points available to estimate the population parameters, resulting in a larger sample.
With more data, the test statistic becomes more precise and provides a more accurate assessment of the true correlation in the population.
Additionally, as the degrees of freedom increase, the critical t-value decreases. This is because a larger sample size allows for greater precision and narrower confidence intervals. As a result, it becomes harder to reject the null hypothesis and find a significant correlation.
Therefore, as n increases, the degrees of freedom and the test statistic increase, leading to a smaller p-value and a higher likelihood of finding a significant correlation.
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What is the surface area of a right circular cylindrical oil can, if the radius of its base is 4 inches and its height is 11 inches?
a. 85 pi in.2
b. 100 pi in.2
c. 120 pi in.2
d. 225 pi in.2
Answer:
c
Step-by-step explanation:
Use a unit circle and 30°-60°-90° triangles to find the degree measures of the angle.
angles whose sine is
[tex] \frac{ \sqrt{3} }{2} [/tex]
Options:
30° + n × 360° and 330° + n × 360°
60° + n × 360° and 120° + n × 360°
240° + n × 360° and 300° + n × 360°
150° + n × 360° and 210° + n × 360°
Answer:
its B
Step-by-step explanation: Cause I have big brain. >:)
What is the area of a circle whose diameter is 102
Answer:
area = 8167.14 units ²
Step-by-step explanation:
area = πr²
r = 102/2 = 51
area = (3.14)(51²) = 8167.14 units ²
eight more than the quotient of a number and four
Answer:
hi
Step-by-step explanation:
Given the points a(0, 0), B(e, f), c(0, e) and D(f, o), determine if line segments AB and CD are parallel, perpendicular or
neither
Find the metal solution to the linear system of differential equations 937 (b) (2 points) Give a physical description of what the solution curves to this linear system look like. What happens to the solution curves as to 12?
The solution to the system of equations is[tex]X(t) = c_1 * e^{6t} * [37 \ \ -3] + c_2 * e^{-3t} * [-37\ \ 12][/tex]. The solution curves exhibit a combination of exponential growth and decay, and as t approaches infinity, they converge towards the eigenvector associated with the negative eigenvalue.
To find the general solution to the linear system of differential equations:
[tex]X' = \left[\begin{array}{ccc}9&37\\-1&-3\end{array}\right] X[/tex]
We need to find the eigenvalues and eigenvectors of the coefficient matrix [[9 37] [-1 -3]].
Let A be the coefficient matrix.
The characteristic equation is given by:
det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
The coefficient matrix A - λI is:
[tex]X' = \left[\begin{array}{ccc}9-\lambda&37\\-1&-3-\lambda\end{array}\right] X[/tex]
Setting the determinant equal to zero:
[tex]det (\left[\begin{array}{ccc}9-\lambda&37\\-1&-3-\lambda\end{array}\right] )[/tex]
Expanding the determinant, we get:
[tex](9-\lambda)(-3-\lambda) - (-1)(37) = 0[/tex]
Simplifying the equation, we have:
[tex](\lambda-6)(\lambda+3) = 0[/tex]
Solving for λ, we find two eigenvalues:
[tex]\lambda_1 = 6\\\lambda_2 = -3[/tex]
Next, we find the eigenvectors corresponding to each eigenvalue.
For [tex]\lambda_1 = 6[/tex]:
[tex](A - \lambda_1I)v_1 = 0[/tex]
Substituting the values, we have:
[tex]\left[\begin{array}{ccc}3&37\\-1&-9\end{array}\right] v_1 = 0[/tex]
Solving the system of equations, we find v1 = [37 -3].
For [tex]\lambda_2 = -3[/tex]:
[tex](A - \lambda_2I)v_2 = 0[/tex]
Substituting the values, we have:
[tex]\left[\begin{array}{ccc}12&37\\-1&0\end{array}\right] v_2 = 0[/tex]
Solving the system of equations, we find [tex]v_2[/tex] = [-37 12].
Therefore, the general solution to the linear system of differential equations is:
[tex]X(t) = c_1 * e^{6t} * [37 \ \ -3] + c_2 * e^{-3t} * [-37\ \ 12][/tex]
where [tex]c_1\ and\ c_2[/tex] are constants.
b) The solution curves to this linear system represent trajectories in the state space. The behavior of the solution curves depends on the eigenvalues.
Since we have [tex]\lambda_1 = 6[/tex] and [tex]\lambda_2 = -3[/tex], the system has one positive eigenvalue and one negative eigenvalue. This indicates that the solution curves will exhibit a combination of exponential growth and decay.
As t approaches infinity, the exponential term with [tex]e^{-3t}[/tex] will dominate, and the solution curves will converge towards the eigenvector associated with the negative eigenvalue, [-37 12].
On the other hand, as t approaches negative infinity, the exponential term with [tex]e^{6t}[/tex] will dominate, and the solution curves will diverge away from the origin in the direction of the eigenvector associated with the positive eigenvalue, [37 -3].
In summary, the solution curves will either converge or diverge depending on the initial conditions, and as t approaches infinity, they will converge towards the eigenvector associated with the negative eigenvalue.
Complete Question:
a) Find the metal solution to the linear system of differential equations
[tex]X' = \left[\begin{array}{ccc}9&37\\-1&-3\end{array}\right] X[/tex]
b) Give a physical description of what the solution curves to this linear system look like. What happens to the solution curves as to 12?
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A fcompany has a constant 306200 shares during the fiscal year. At the beginning of the year it has an equity of $4699902 in their balance sheet, and during the year, as indicated by the income statement, it has a net income $399786 and pays out $297789 in dividends. What will be its book value per share at the end of the fiscal year? Answer to two places.
The book value per share at the end of the fiscal year will be approximately $15.35.
To calculate the book value per share, we need to divide the equity at the end of the fiscal year by the number of shares outstanding. Let's break down the calculation:
The number of shares outstanding: The company has a constant 306,200 shares during the fiscal year.
Equity at the beginning of the year: The balance sheet shows an equity of $4,699,902 at the beginning of the year.
Net income: The income statement indicates a net income of $399,786.
Dividends paid: The company pays out $297,789 in dividends.
To find the equity at the end of the fiscal year, we need to add the net income and subtract the dividends paid from the equity at the beginning of the year:
Equity at the end of the fiscal year = Equity at the beginning of the year + Net income - Dividends paid
= $4,699,902 + $399,786 - $297,789
= $4,801,899
Finally, to calculate the book value per share, we divide the equity at the end of the fiscal year by the number of shares outstanding:
Book value per share = Equity at the end of the fiscal year / Number of shares outstanding
= $4,801,899 / 306,200
≈ $15.65 (rounded to two decimal places)
Therefore, the book value per share at the end of the fiscal year will be approximately $15.35.
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What is the area?
____ Square millimeters
Answer: 210 mm²
Step-by-step explanation:
A = 1/2(long base + short base) x height
A = 1/2(18 + 10)(15)
A = 1/2(28)(15)
A = 210 mm²
An airplane is flying in a direction of 75° north of east at a constant flight speed of 300 miles per hour. The wind is blowing due west at a speed of 25 miles per hour. What is the actual direction of the airplane? Round your answer to the nearest tenth. Show your work. PLS PLS PLSPLS HELP URGANT
Answer:
79.7°
Step-by-step explanation:
We resolve the speed of the plane into horizontal and vertical components respectively as 300cos75° and 300sin75° respectively. Since the wind blows due west at a speed of 25 miles per hour, its direction is horizontal and is given by 25cos180° = -25 mph. We now add both horizontal components to get the resultant horizontal component of the airplane's speed.
So 300cos75° mph + (-25 mph) = 77.646 - 25 = 52.646 mph.
The vertical component of its speed is 300sin75° since that's the only horizontal motion of the airplane. So the resultant vertical component of the airplane's speed is 300sin75° = 289.778 mph
The direction of the plane, Ф = tan⁻¹(vertical component of speed/horizontal component of speed)
Ф = tan⁻¹(289.778 mph/52.646 mph)
Ф = tan⁻¹(5.5043)
Ф = 79.7°
hypotheses are always statements about which of the following? question content area bottom part 1 choose the correct answer below. sample statistics sample size estimators population parameters
Hypotheses are always statements about the d. population parameters
Hypotheses are assertions or claims concerning population characteristics stated in statistics. An attribute or value of a population, such the population mean or percentage, is referred to as a population parameter. Based on sample data, hypothese are developed to draw conclusions or inferences about these population attributes.
The hypothesis can be expressed as comparisons of population metrics or as statements of equality or inequality. They serve as a basis for statistical studies and are used to examine certain assertions or research hypotheses. Finding pertinent solutions to the scientific inquiry is the main goal of the hypothesis. It is supported by a few evidences, and experimental methods are used to test the whole statement of the hypothesis.
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Complete Question:
Hypotheses are always statements about which of the following? choose the correct answer below.
a. sample statistics
b. sample size
c. estimators
d. population parameters
Find the optimum solution and draw the graph
Maximise Z= x + y, subject to x - y S-1, -x + y = 0, x,
The optimum solution for the maximization problem is Z = 0 at the point (0, 0). The graph of the feasible region consists of the line y = x and the shaded region above the line y = x - 1.
To compute the optimum solution and draw the graph for the maximization problem:
Maximize Z = x + y
Subject to the constraints:
x - y ≤ 1
-x + y = 0
x, y ≥ 0
First, let's plot the feasible region by graphing the constraints on a coordinate plane.
For the constraint x - y ≤ 1, we can rewrite it as y ≥ x - 1. This represents a boundary line with a slope of 1 and a y-intercept of -1. Shade the region above this line to satisfy the constraint.
For the constraint -x + y = 0, rewrite it as y = x. This represents a line passing through the origin with a slope of 1. Plot this line.
Next, plot the x and y axes and shade the feasible region that satisfies both constraints.
To compute the optimum solution, we need to evaluate the objective function Z = x + y at the corner points (vertices) of the feasible region.
The corner points can be identified by the intersection of the lines and the feasible region boundaries. In this case, there is only one corner point, which is the intersection of the lines y = x and y = x - 1. Solving these equations simultaneously gives x = 0 and y = 0.
Thus, the optimum solution occurs at the corner point (0, 0), where Z = 0 + 0 = 0.
Therefore, the optimum solution is Z = 0 at the point (0, 0).
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Mark is going to an awards dinner and wants to dress appropriately. He has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of Mark's possible outfits are listed below.
Ir we take outfits 1, 2, 5, and 6 as a subset of the sample space, which of the statements below describe this subset?
Choose all answers that apply:
(Choice A)
The subset consists of all the outfits that do not have a white shirt.
(Choice B)
The subset consists of all the outfits that have either a blue shirt or a black shirt.
(Choice C)
The subset consists of all the outfits that have a black shirt.
(Choice D)
The subset consists of all the outfits that have a white shirt.
Solution:
Outfit Shirt Slacks Tie
Outfit 1 Blue Black Red
Outfit 2 Blue Grey Red
Outfit 3 White Black Red
Outfit 4 White Grey Red
Outfit 5 Black Black Red
Outfit 6 Black Grey Red
We take the outfits 1, 2 , 5 and 6 as a subset of the sample space.
So these 1, 2, 5 and 6 consists either a blue shirt or a black shirt.
The subset consists of all the outfits that do not have a white shirt.
So the correct options are :
1. (Choice A)
The subset consists of all the outfits that do not have a white shirt.
2. (Choice C)
The subset consists of all the outfits that have a black shirt.
picture is shown !
Complete the remainder of the
table for the given function rule:
y = -2x + 9
please help
Answer: 17; 13; 9; 5; 1
Step-by-step explanation:
y = -2x + 9
When x = -4, y = 17
When x = -2 , y = -2x + 9 = -2(-2) + 9 = 13
When x = 0 , y = -2x + 9 = -2(0) + 9 = 9
When x = 2 , y = -2x + 9 = -2(2) + 9 = 5
When x = 4 , y = -2x + 9 = -2(4) + 9 = 1
Determine whether the polygons to the right are similar. If so, write a similarity statement and give the scale factor. If not, explain.
Answer:
(a) Similar polygons; scale factor is 2
(b) Similar polygons; scale factor is 1.5
Step-by-step explanation:
Given
See attachment for polygons
Required
Determine if they are similar or not
Solving (a): The triangle
The angles in both triangles show that the triangles are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
[tex]k = \frac{DF}{BA} = \frac{FE}{AC} = \frac{DE}{BC}[/tex]
[tex]k = \frac{6}{3} = \frac{8}{4} = \frac{10}{5}[/tex]
[tex]k = 2=2=2[/tex]
[tex]k = 2[/tex]
The scale factor is 2
Solving (b): The trapezium
The angles in both trapeziums show that the trapeziums are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
[tex]k = \frac{KN}{GJ}[/tex]
[tex]k = \frac{6}{4}[/tex]
[tex]k = 1.5[/tex]
The scale factor is 1.5
Plz help me, correct answers will get brainliest <3
Answer:
∠ B = 48°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180° for ∠ B
∠ B = 180° - (90 + 42)° = 180° - 132° = 48°
(50 POINTS) Express each sum using summation notation.
14. 3 + 3^2/2 + 3^3/3 ... + 3^n/n
15. 1 + 3 + 5 + 7 +... [2(12) - 1]
14: a
1
=
39
/2 0.25 313% 16%
15: 54
utilizando as propriedades dos radicais calcule ⁵√32⁵
[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \red{ \boxed{ \boxed{ \tt{ \huge{{ \: 32 \: }}}}}}[/tex]
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is
2.6
π
2.6π2, point, 6, pi meters long.
What is the radius
r
rr of the circle that the python forms?
Answer: 1.3
Step-by-step explanation:
The radius of the circle that python forms is 1.3 meters.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given that,
Length of python = 2.6π meters
The length of the python forms the circumference of the circle after curling.
Circumference of a circle = 2π r, where r is the radius.
2π r = 2.6π
2r = 2.6
r = 2.6 / 2
r = 1.3
Hence 1.3 meters is the radius of the circle.
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It a math study guide plz help me
the answer is 12.57
Step-by-step explanation:
The formula to find circumference is 2×pi×r. Two is the radius. So when you plug it into the formula you get 12.57.
Somebody pls help
Solve the problems. What are the equations of the trend line shown here?
Answer:
1) y = -7/10x + 21
Step-by-step explanation:
1)
Points (5, 7) and (15, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-7)/(15-5)
m=(-7)/10
m= -7/10
Slope-intercept:
y - y1 = m(x - x1)
y - 7 = -7/10(x - 5)
y - 7 = -7/10x + 14
y = -7/10x + 21
Find the distance between the points (4,10) and (4, -7)
Answer:
17
Step-by-step explanation:
Hello There!
Once again we are going to use the distance formula to find the answer
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This time we need to find the distance between the points (4,10) and (4,-7)
*we plug in the values into the formula)
[tex]d=\sqrt{(4-4)^2+(-7-10)^2} \\4-4=0\\-7-10=17\\d=\sqrt{0^2+(-17)^2} \\0^2=0\\-17^2=289\\\sqrt{289} =17[/tex]
so we can conclude that the distance between the points (4,10) and (4,-7) is 17 units
Use R for this question. Use the package faraway teengamb data (data(teengamb, package="faraway") ) for this question. a. Make a plot of gamble on income using a different plotting symbol depending on the sex (Hint: refer to page 66 in the textbook for similar code).
The code creates a scatter plot of the "gamble" variable on the "income" variable, with different plotting symbols based on sex, using the "faraway" package in R.
Here's the code to make a plot of the "gamble" variable on the "income" variable using different plotting symbols based on the sex in R:
# Load the required package and data
library(faraway)
data(teengamb)
# Create a plot of a gamble on income with different symbols for each sex
plot(income ~ gamble, data = teengamb, pch = ifelse(sex == "M", 16, 17),
xlab = "Gamble", ylab = "Income", main = "Gamble on Income by Sex")
legend("topleft", legend = c("Female", "Male"), pch = c(17, 16), bty = "n")
This code will create a scatter plot where the "income" variable is plotted against the "gamble" variable. The plotting symbols used will be different depending on the "sex" variable.
Females will be represented by an open circle (pch = 17), and males will be represented by a closed circle (pch = 16). The legend will indicate the corresponding symbols for each sex.
Make sure to have the "faraway" package installed in R and load it using 'library'(faraway) before running this code.
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three line segments have measures of 4 units, 6 units, and 8 units. Will the segments form a triangle?
Given:
Three line segments have measures of 4 units, 6 units, and 8 units.
To find:
Will the segments form a triangle?
Solution:
We know that three line segments can form a triangle if the sum of two smaller sides is greater than the largest side.
Three line segments have measures of 4 units, 6 units, and 8 units. Here, the measure of the largest sides is 8 units.
The sum of two smaller sides is
[tex]4+6=10[/tex]
[tex]4+6>8[/tex]
Since the sum of two smaller sides is greater than the largest side, therefore the segments will form a triangle.
Which gives the line of best fit?
Answer:
B
Step-by-step explanation:
Michelle ordered 200 T-shirts to sell at the school carnival. She paid $2.80 per shirt, plus 5% of the total
order for shipping. When she sells each T-shirt at the carnival, she adds a 150% markup to the total price
she paid for the shirt (including the cost of shipping).
For what price does she sell each T-shirt?
Answer:
$7.35
Step-by-step explanation:
We have 200 shirts
Cost $2.80 each
plus a 5% charge for shipping.
Selling price
150% markup
Recall when we use percentages, we need to express them as decimals.
Michelle's cost for each shirt was
2.80 (1.05) = 2.94
The markup is
2.94 (1.50) = 4.41
The markup is added to the cost to get the final selling price.
2.94 + 4.41 = $7.35
Michelle will sell each shirt for $7.35
Evaluate each expression using the values m = 7, r = 8, and t = 2.
1. 5m – 6
2. 4m + t
3. r/t
4. mt
5. 5t + 2m
6. rm
7. 3m – 5t
8. mr/t
PEEEEASSSSEEEE HELP!!!! :(
So I'll walk through the first 2. Then please try the other ones and let me know if you run into more problems.
5m-6
If m is equal to 7, then replace m with 7.
5(7)-6
5x7=35 so the expression is now 35-6. Solve.
35-6=29
So that was the first one.
4m+t
We just do what we do with the first problem.
4(7)+(2)
4x7=28 so the expression is 28+2.
28+2=28
---
hope it helps
p.s. When there is subtraction, add. When there is division, multiply to cancel that out. When there is multiplication, divide to cancel. etc.
Answer:
1,5(7)-6=29
2,4(7)+2=30
3,8/2=4
4,7*2=14
5,5(2)+2(7)=24
6,8*7=56
7,3(7)-5(2)=11
8,7*8/2=28
Write the repeating rational number 0.828282… as a fraction.
Answer:
Step-by-step explanation:0.828282 = 0.828282/1 = 8.28282/10 = 82.8282/100 = 828.282/1000 = 8282.82/10000 = 82828.2/100000 = 828282/1000000
And finally we have:
0.828282 as a fraction equals 828282/1000000
Factoring Perfect Square Trinomials
a^2- 2ab + 4b
Step-by-step explanation:
[tex]i \: \: think \: \: it \: \: is \: \\ \\ {a}^{2} - 2ab + {b}^{2} \\ \\ that \: is \: for \: \: {(a - b)}^{2} [/tex]
I hope that is useful for you :)
GIVING BRAINIEST!!
Which equation represents: "72% of what number is 64"
64 = 0.72 (x)
x = 7.2 (64)
64 = 7.2 (x)
x = .72 (64)
Answer:
64 = 0.72 (x)
Step-by-step explanation:
Answer: 64 = 0.72 (x)
Step-by-step explanation:
Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore?