There is enough evidence to conclude that the mean fasting cholesterol of teenage boys whose fathers had a heart attack is significantly higher than expected with a significance level of α = 0.05.
Given that the mean fasting cholesterol of teenage boys in the United States is 175 mg/dL.
An SRS of 49 boys whose fathers had a heart attack reveals the mean cholesterol of 195 mg/dL with a standard deviation of 45 mg/dL.
We are to perform a test to determine if the sample mean is significantly higher than expected, and show all hypothesis testing steps.
Hypotheses: H0: μ = 175Ha: μ > 175
Level of Significance: α = 0.05
Assumptions: Random Sample Independence of the sample mean and the sample standard deviation.
Normality of the data:
Since the sample size is large (n ≥ 30), we can safely assume normality using the Central Limit Theorem.
Standard Deviation can be used in place of the population standard deviation.
To perform the test, we need the test statistic:
z = (195 - 175) / (45 / √49)
= 20 / (45/7)
= 3.11
Rejection Region:
Critical Value: Since this is a right-tailed test, the critical value will be obtained from the z-distribution table. At α = 0.05, the critical value is 1.645.
Rejection Region: z > 1.645.
Test Statistic: z = 3.11
Decision Rule: Reject the null hypothesis if the test statistic is greater than the critical value. Otherwise, fail to reject the null hypothesis.
Conclusion: Since the test statistic (z = 3.11) falls in the rejection region
(z > 1.645), we reject the null hypothesis.
There is enough evidence to conclude that the mean fasting cholesterol of teenage boys whose fathers had a heart attack is significantly higher than expected with a significance level of α = 0.05.
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what is the distance between (6,-7) (3,-5)
Answer:
4,684 km
Step-by-step explanation:
What is 3b to the second power if b is 4
Pedro said, "On summer vacation, I spent 3 1/2 weeks with my uncle and two weeks more with my friend than with my uncle." How many weeks did he spend with his uncle and his friend? Use fraction strips or number lines to find the sum.
Answer:
Pedro spent 9 weeks with his uncle and his friend.
Step-by-step explanation:
First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:
[tex]3\frac{1}{2}[/tex] 2
___________________
1 2 3 4 5 6 7 8 9 10
[tex]3\frac{1}{2}+2=5\frac{1}{2}[/tex]
Now, you can find the and answer by adding up the number of weeks he spent with his uncle plus the weeks he spent with his friend:
[tex]3\frac{1}{2}[/tex] [tex]5\frac{1}{2}[/tex]
__________________________________
1 2 3 4 5 6 7 8 9 10
[tex]3\frac{1}{2} + 5\frac{1}{2}=9[/tex]
According to this, the answer is that Pedro spent 9 weeks with his uncle and his friend.
What is a brief description of a radian?
simply saying its circular measure
Please help me. I don’t know
Step-by-step explanation:
Area of square = Length x Length =
[tex] {length}^{2} [/tex]
Given Area of square =
[tex]256 {ft}^{2} [/tex]
[tex] {length}^{2} = 256 \\ length = \sqrt{256} \\ = 16ft[/tex]
Consider the system of linear equations 2- y = kx - y = k (a) Reduce the augmented matrix for this system to row-echelon (or upper-triangular) form. (You do not need to make the leading nonzero entries 1.) (b) Find the values of k (if any) when the system has (a) no solutions, (b) exactly one solution (if this is possible, find the solution in terms of k), (e) infinitely many solutions (if this is possible, find the solutions).
The system of linear equations has no solutions for any value of k except when k = 2, where it has infinitely many solutions.
(a) To reduce the augmented matrix for the system of linear equations to row-echelon form, we can write the system of equations as:
2 - y = kx
-y = k
To eliminate y in the first equation, we can multiply the second equation by (-1) and add it to the first equation:
(2 - y) - (-y) = kx - k
2 = kx - k
This gives us a new system of equations:
2 = kx - k
Now, we can represent this system in augmented matrix form:
[1 -k | 2]
(b) To find the values of k, we can examine the augmented matrix.
If the system has no solutions, it means that the rows of the augmented matrix result in an inconsistent equation, where the last row has a leading nonzero entry. In this case, for the system to have no solutions, the augmented matrix should have a row of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix [1 -k | 2] doesn't have this form, so there are no values of k that lead to no solutions.
If the system has exactly one solution, the augmented matrix should be in row-echelon form, with each row having at most one leading nonzero entry. In this case, the augmented matrix should not have any rows of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix can be reduced to row-echelon form as follows:
[1 -k | 2]
From this form, we can see that there are no restrictions on the value of k. For any value of k, the system will have exactly one solution.
If the system has infinitely many solutions, the augmented matrix should have at least one row of the form [0 0 | 0]. In our case, the augmented matrix can be reduced to:
[1 -k | 2]
From this form, we can see that if k = 2, the last row becomes [0 0 | 0]. Therefore, for k = 2, the system will have infinitely many solutions.
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convert the force in parts b from newtons to pounds. (1 lb = 4.45n). what are the chances the driver will be able to stop the child?
Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).
To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.
Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.
However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.
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Using the Proportion to Find a Missing Measure
Try it
5
www
Use the proportion to solve for the unknown base measure of the enlarged trapezoid.
2 .
1 Set up the proportion
3.25 6.5
2.Use cross products
2(6.5) = 3.25()
3. Simplify
13 = 3.25x
4 Divide both sides by 3.25
The missing base measure of the enlarged trapezoid is
cm
Answer:
4 cm
Step-by-step explanation:
Solve the inequality.
- 5x > 25
Answer and Step-by-step explanation:
Divide -5 from both sides of the inequality.
x < -5 is the answer.
Here's Why:
If you were to add 5x to both sides, it results in this:
0 > 25 + 5x
Now, we subtract 25 from both sides.
-25 > 5x
When we divide 5 from both sides, we see that it results in -5 > x, which is the same as x < -5.
#teamtrees #PAW (Plant And Water)
Pls help ASAP. SHOW WORK
The new figure after the revolution is a cylinder of radius 5 and length 8
The volume is 200π
How to determin the new figure after the revolutionFrom the question, we have the following parameters that can be used in our computation:
The graph
The shape on the graph is a rectangle with
length = 5
width = 8
When revolved across the x-axis, we have the shape to be
A cylinder of radius 5 and length 8 (option a)
This is calculated as
V = πr²h
substitute the known values in the above equation, so, we have the following representation
V = π * 5² * 8
Evaluate
V = 200π
Hence, the volume is 200π
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Assume that the differences are normally distributed. Complete parts (a) through (d) below.
Observations 1, 2, 3, 4, 5, 6, 7, 8
хi 45.4 45.5 45.5 42.9 45.2 47.4 51.4 43.1
Yi 46.5 46.6 49.7 47.5 48.1 50.3 52.2 45.5
(a) Determine di = Xi - Yi for each pair of data.
Observations 1 2 3 4 5 6 7 8
di = _______________
The differences di = Xi - Yi for each pair of data are:
-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.
To determine the differences di = Xi - Yi for each pair of data, we subtract the corresponding values of Xi and Yi:
Observations: 1 2 3 4 5 6 7 8
Xi: 45.4 45.5 45.5 42.9 45.2 47.4 51.4 43.1
Yi: 46.5 46.6 49.7 47.5 48.1 50.3 52.2 45.5
di = Xi - Yi: -1.1 -1.1 -4.2 -4.6 -2.9 -2.9 -0.8 -2.4
Therefore, the differences di = Xi - Yi for each pair of data are:
-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.
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let f(x) = x 4 and g(x) = x – 3. if g is a vertical translation of f, how many units and in what direction is f translated to form g?
The number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x) is -2 units. Since the value of d is negative, the direction of the translation is downwards. Thus, we can say that f(x) is translated 2 units downwards to form g(x).
f(x) = x⁴ and g(x) = x – 3, Since g is a vertical translation of f, we know that the graph of g(x) can be obtained by translating the graph of f(x) vertically up or down by some units, d. Thus, we can express g(x) as follows:g(x) = f(x) + d
Here, d represents the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x). Now, f(x) = x⁴, which means that the graph of f(x) is a standard cubic graph that has not undergone any transformation. We can represent this graph by the equation y = x⁴.
When g(x) is a vertical translation of f(x), we can write g(x) = y + d where d is the number of units by which f(x) is translated vertically to obtain g(x). Thus, we can rewrite g(x) as:
g(x) = f(x) + d
Substituting the values of f(x) and g(x), we get: x – 3 = x⁴ + d
Rearranging the equation, we have:x⁴ = x – 3 – d
Now, the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x), we need the value of d. To do this, we can use the fact that the graphs of f(x) and g(x) intersect at some point. At this point, the value of f(x) is equal to the value of g(x). Thus, we can write x⁴ = x – 3 – d
Solving this equation, we get x⁴ = x – (3 + d), the value of d by comparing the coefficients of x on both sides of the equation. On the left-hand side of the equation, the coefficient of x is 0, while on the right-hand side of the equation, the coefficient of x is 1. Thus, we can write:
0 = 1 – (3 + d)
Simplifying this equation, we get: d = -2
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The percent of Tom winning a game is 20%, he played 30 games. How mang games did he lose?
Answer:
He won 6 games and lost 24 games.
Work out the surface area of this cylinder. Give your answer in terms of π.
Please help.
Don’t comment a random link or I will report you!!
Answer:
2010.62cm²
Step-by-step explanation:
The equation for the surface area of cylinder is:
A = 2πrh + 2πr²
Hope it was helpful
PLEASE HELP! WILL GIVE BRAINLIEST ANSWER!!
Distance run by each member of the Chicago Race Club.
In which interval is the median distance?
A. 0-5
B. 5-10
C. 10-15
D. 15-20
Answer:
I wanna say that it is 10-15
Step-by-step explanation:
Answer:
10-15
Step-by-step explanation:
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Answer this question please
Let's assume you are conducting an experiment to determine the effect of a new drug on the incidence of epileptic seizures. You select 20 epileptics from the 150 epileptics being treated at a nearby hospital and administer the drug to them. You record the number of seizures in each of the 20 subjects for one month. The 20 subjects constitute _________.
Answer:
The 20 subjects constitutes the sample
Step-by-step explanation:
Given
[tex]Total = 150[/tex]
[tex]Selected = 20[/tex]
Required
What does 20 represent?
The 150 patients being treated is the population of the study. When a certain amount is selected from a population, the selected is referred to as a sample.
So, this means that, 20 represents sample of the study.
or your retirement you want to have enough funds in your RRSPs to provide an income stream of $25,000 for 30 years. How much money would you need to have accumulated if your RRSPs averaged a real return of four percent per year? (Round to the nearest thousand) a. $441,000 O b. $432,000 C. $384,000 O d. $1,402,000
Money needed to have accumulated if the RRSPs averaged a real return of four percent per year is $432,000
Amount of income stream = $25,000
Time = 30 years
According to the 4% rule, a retiree can risk not having enough money for at least 30 years by comfortably withdrawing 4% of their assets in their first year of retirement and adjusting that amount for inflation each year after that.
Calculating the present value -
[tex]PV = FV / (1 + r)^n[/tex]
Substituting the values -
[tex]PV = $25,000 / (1 + 0.04)^30[/tex]
[tex]PV = $25,000 / (1.04)^30[/tex]
= 432,309
Rounded the nearest thousand the return amount comes to $432,000
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i’m stuck i really need help on this, thanks!
Answer:
A.) 0.25
B.) 0.125 (maybe don't trust me)
Step-by-step explanation:
what is the set of all solutions to the equation 2 = − x 2 =−xsquare root of, x, plus, 2, end square root, equals, minus, x ?
The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.
To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.
Starting with the given equation, we can simplify it step by step:
2 = -x√(x + 2) - x
Adding x to both sides:
2 + x = -x√(x + 2)
Squaring both sides to eliminate the square root:
(2 + x)^2 = (-x√(x + 2))^2
Expanding and simplifying:
4 + 4x + x^2 = x^2(x + 2)
Simplifying further:
4 + 4x = x^3 + 2x^2
Rearranging terms:
x^3 + 2x^2 - 4x - 4 = 0
Factoring the equation:
(x + 1)(x^2 + x - 4) = 0
Setting each factor to zero:
x + 1 = 0 or x^2 + x - 4 = 0
Solving the first equation, we find x = -1.
For the second equation, we can use the quadratic formula:
x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))
x = (-1 ± √(1 + 16)) / 2
x = (-1 ± √17) / 2
However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.
Hence, the set of all solutions to the equation is {x = -1}.
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A Correlation Coefficient Of −0.8 Indicates Strong Indirect Relationship. TRUE/FALSE
The given statement “A correlation coefficient of −0.8 indicates strong indirect relationship” is true because it indicates a strong inverse or negative relationship between the variables.
What is the correlation coefficient?A correlation coefficient is a statistical measure of the degree to which variables are related to one another. It is a numerical value that ranges from -1 to 1 and represents the strength and direction of the relationship between two variables.
If the correlation coefficient is -1, the relationship is strong and negative (inverse). On the other hand, if the correlation coefficient is 1, the relationship is strong and positive (direct).
When the correlation coefficient is zero, it indicates no relationship between the variables. When the correlation coefficient is near zero, it indicates a weak relationship between the variables.
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Write an equation of the line that passes through the point (4, 14) and is parallel to the line whose equation is y=3x-7.
Answer:
y = 3x + 2
Step-by-step explanation:
If the line is parallel, then the slope remains the same.
To find the y-intercept, just plug the coordinates into the equation
y = 3x + b
14 = 3(4) + b
14 = 12 + b
2 = b
The equation is y = 3x + 2
Answer:
Slope intercept form
y=3x^2−19x+42
or
Point slope form
y−14=(3x−7)⋅(x−4)
Step-by-step explanation:
:)
Tell whether the angles are complementary, supplementary, or neither.
Answer:
supplementary (add together to = 180°)
Step-by-step explanation:
Step-by-step explanation:
Supplementary angles add up to 180
complementary angles add up to 90
75+105=180
so the angles are supplementary
Hope that helps :)
Which expression is represented on the number line?
Answer:
b
Step-by-step explanation:
if the probability of winning $10 on a bet is 50% and the probability of winning nothing is 50%, what is the expected value of the bet?
The expected value of the bet is $5.
The expected value of the bet is calculated by multiplying each possible outcome by its corresponding probability and summing them up. In this case, there are two possible outcomes: winning $10 with a probability of 50% (0.5) and winning nothing with a probability of 50% (0.5).
To find the expected value, we multiply the value of each outcome by its probability:
Expected Value = ($10 * 0.5) + ($0 * 0.5) = $5 + $0 = $5.
Therefore, the expected value of the bet is $5. This means that, on average, for each bet placed, we can expect to win $5. It represents the long-term average outcome and is useful in assessing the overall value or profitability of the bet.
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K divided by 5 = 12.4
Answer:
k=62
Step-by-step explanation:
K divided by 5 = 12.4
Multiply both sides by 5
5k/5=12.4×5
Simplify;
k=62
Hope this helped!!
Answer:
k = 62
Step-by-step explanation:
To solve we need to get k on one side alone.
To do this we can multiply buth sides by 5
[tex]\frac{k}{5} =12.4[/tex] ---> =12.4*5
This gives us x=62
You can check this by putting 62 in for k and solving the problem.
euler's formula, v − e f = 2, relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron. solve euler's formula for e.
The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.
Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.
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Which statement is true? pls help :)
Answer:
The First Choice
Step-by-step explanation:
1/4 is equal to .25
.25 x 4= 1.00
25 x 4= 100
Need help! much appreciated
Answer:
C-D = 6
A-B = 3.25
D = 118
Step-by-step explanation:
C-D = 6 because the line is the same as B-C
A-B = 3.25 because the line is the same as A-D
D = 118 because the angle of B is vertically opposite to D
10x+11=51 solve for x
Answer:
x=4
Step-by-step explanation: