a) The Physical Therapist would need to get a sample size of 304 for males and 267 for females, respectively, to estimate the difference in the proportion of men and women using estimates of 21.7% male and 18.1% female from the previous year. b) The Physical Therapist would need to get a sample size of 386 to estimate the difference in the proportion of men and women.
a) In order to find out the difference in the proportion of men and women who participate in regular sustained physical activity, if a Physical Therapist wishes to estimate within five percentage points with 90% confidence and uses the estimates of 21.7 % male and 18.1% female from a previous year, the sample size should be calculated as follows: For male:
Sample size = [z-score(α/2) /E]² × P (1 - P)
Where, z-score(α/2) = 1.645 (for 90% confidence interval)
E = 0.05 (5 percentage points)
P = 0.217 (21.7 % in proportion)
Therefore,Sample size = [1.645/0.05]² × 0.217 × (1 - 0.217)= 303.86≈ 304
For female:
Sample size = [z-score(α/2) /E]² × P (1 - P)
Where, z-score(α/2) = 1.645 (for 90% confidence interval)
E = 0.05 (5 percentage points)
P = 0.181 (18.1 % in proportion)
Therefore, Sample size = [1.645/0.05]² × 0.181 × (1 - 0.181)= 267.07≈ 267
b) If the Physical Therapist does not use any prior estimates, then the worst-case scenario should be considered. The proportion for the worst-case scenario will be 0.5 (50%) because it represents maximum variability. In this case, the sample size will be calculated as follows:
Sample size = [z-score(α/2) /E]² × P (1 - P)
Where, z-score(α/2) = 1.645 (for 90% confidence interval)
E = 0.05 (5 percentage points)
P = 0.5 (50% in proportion)
Therefore, Sample size = [1.645/0.05]² × 0.5 × (1 - 0.5)= 385.6≈ 386
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Please help I will give brainliest!
Answer:
Step-by-step explanation:
Distributive Property
commutative property of addition.
assosciative property of addition
Answer:
distrubutive property
Step-by-step explanation:
solve the integral given below for suitable using the Beta function 1 (₁-t²g x dt = ?
The solution to the given integral is: frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
Given integral: int_0^1 (1-t^2)g(x) dt
To solve the given integral, we will make use of Beta function.
The Beta function is defined as follows:
B(p,q) = int_0^1 t^{p-1}(1-t)^{q-1} dt
Using substitution, t = sin theta, we get:
int_0^1 (1-t^2)g(x) dt = int_0^{frac{pi}{2}} (1-sin^2 theta)g(x) cos theta dtheta
= int_0^{frac{\pi}{2}} cos^2 theta g(x) d\theta
= frac{1}{2}\int_0^{\frac{\pi}{2}} (1+\cos 2\theta) g(x) d\theta
= frac{1}{2} \left(\int_0^{\frac{\pi}{2}} g(x) dtheta + int_0^{frac{pi}{2}} g(x) cos 2theta dtheta right)
Using B(p,q)$ for the second integral, we get:
int_0^1 (1-t^2)g(x) dt = frac{1}{2}left(frac{pi}{2}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x) right)
= frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
Hence, the value of the given integral int_0^1 (1-t^2)g(x) dt is frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
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Complete the statement. Round to the nearest hundredth if necessary.
6 lb =
oz
Answer: 96 oz
Step-by-step explanation:
Can someone plzzz helpppp!!!!
Answer:
[tex] m\angle SXW =113\degree [/tex]
Step-by-step explanation:
In circle with center X, VS is diameter.
So [tex] \widehat {SWV} [/tex] is a semicircular arc.
[tex] \therefore m\widehat{SWV} = 180\degree [/tex]
[tex] \therefore (12x+7)\degree + (21x +8)\degree = 180\degree [/tex]
[tex] \therefore (33x+15)\degree = 180\degree [/tex]
[tex] \therefore 33x+15 = 180 [/tex]
[tex] \therefore 33x = 180-15 [/tex]
[tex] \therefore 33x = 165 [/tex]
[tex] \therefore x =\frac{165}{33} [/tex]
[tex] \therefore x =5 [/tex]
[tex] m\angle SXW =m\widehat{SW} [/tex]
(Measure of central angle is equal to the measure of its corresponding minor arc)
[tex] m\angle SXW =(21x + 8)\degree [/tex]
[tex] m\angle SXW =(21\times 5+ 8)\degree [/tex]
[tex] m\angle SXW =(105+ 8)\degree [/tex]
[tex] m\angle SXW =113\degree [/tex]
Help meeeeeeeeeeeeeee pls
Answer:
-3.5
all u have to do is get the 2 and the 7 and just subtract and the 8 and 10
on the graph of f(x)=sinx and the interval [0,2π), for what value of x does f(x) achieve a maximum? choose all answers that apply.
On the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
The function f(x) = sin(x) is a periodic function with a period of 2π. Within one period, the function oscillates between the values of -1 and 1. The maximum value of sin(x) is 1, and it occurs when the angle x is π/2.
In the given interval [0, 2π), the function f(x) = sin(x) completes one full period. Starting from x = 0, the function increases and reaches its maximum value of 1 at x = π/2. After that, it starts decreasing and goes through one complete cycle by the time it reaches x = 2π.
Therefore, on the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
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A booster club sells raffle tickets • Before tickets go on sale to the public, 120 tickets are sold to student athletes. • After tickets go on sale to the public, the tickets sell at a constant rate for a total of 8 hours spread over I days. • At the end of this time, all tickets have been sold. If represents the hours since tickets go on sale to the public and represents the number of raffle tickets sold, which graph best represents the scenario?
Answer:
The top graph.
Step by step:
Before the tickets go on sale, 120 tickets were already sold.
After that, the tickets sell at a constant rate for a total of 8 hours.
At the end of this time, all the tickets were sold (we have 0 tickets left)
If x (horizontal axis) represents the hours since tickets go on sale, and y (vertical axis) represents the number of raffle tickets sold.
Then, at x = 0, we should already see y = 120
Because we start with 120 tickets sold.
Then, as x increases, the number of tickets sold also should increase, until we get x = 8 hours, where y stops increasing because all tickets are already sold.
Then we should have an increasing line that stops increasing at x = 8 hours.
Then the correct option is the above graph, where we have:
An increasing line.
y = 120 in the vertical axis (y = 120 when x = 0)
Determine in each case for the linear system X′ = AX whether the
equilibrium point is a sink, a source, a saddle, or a nodal source
(centre), and draw the respective phase diagram.
Equilibrium point is a sink, a source, a saddle, or a nodal source (centre).
The equilibrium point is a sink in a phase diagram. A sink is a point towards which any system that begins near it will converge. This is a stable point that attracts nearby systems towards it. When the system comes close to the sink, it will slow down as it approaches, then stop at the sink. A sink is a stable equilibrium point. This is also known as an attractor that attracts nearby points. The phase diagram is a visual representation of the equilibrium point's behavior in the system. The arrows that come into or go out of the sink are pointing towards it, and they represent the direction of the flow of the system. Thus, the sink's shape is inward, indicating that any system near it will converge towards it.
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Please Help!!! Unit 8: Right Triangles & Trigonometry Homework 6: Trigonometry Review
The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Triangles and AnglesFrom the given diagram, we have the following
Adjacent = 14Hypotenuse = 13The required angle is x
Using the SOH CAH TOA identity
[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]
Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
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What’s the answer????
Answer:
I believe its 10 but forgive me if I'm wrong
18 x 1/6 simplify if can thank u
Answer:
3
Step-by-step explanation:
[tex]18*\frac{1}{6} \\\\3[/tex]
Answer:
=3x
Step-by-step explanation:
18x^1 / 6
=3x
The slope of the line containing the points (6, 4) and (-5, 3) is:
1
-1
1/11
Answer:
1/11
Step-by-step explanation:
(6, 4) and (-5, 3)
Slope:
m=(y2-y1)/(x2-x1)
m=(3-4)/(-5-6)
m= (-1)/(-11)
m = 1/11
A. 37
B. 53
C. 127
D. 217
The following set of data is from a sample of n = 6. 4 9 10 4 3 12 a, Compute the mean, median, and mode. b. Compute the range, variance, and standard deviation. a. Compute the mean, median, and mode. Mean=(Type an integer or decimal rounded to four decimal places as needed.) Compute the median Median-(Type an integer or a decimal. Do not round.) What is the mode? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The mode(s) is/are (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode for this data set 5. Compute the range, Range-(Type an integer or a decimal. Do not round.) ompute the variance.
a. The mean of the data set is 6.3333, the median is 4.5, and there is no mode. b. The range of the data set is 9, and the variance is 11.8667.
a. To compute the mean, we sum up all the values in the data set and divide it by the number of data points. In this case, the sum is 4 + 9 + 10 + 4 + 3 + 12 = 42. Dividing this by 6 (the number of data points), we get a mean of 42/6 = 6.3333.
To compute the median, we arrange the data set in ascending order: 3, 4, 4, 9, 10, 12. Since the number of data points is even, we take the average of the middle two values, which are 4 and 9. The median is (4 + 9) / 2 = 4.5.
The mode is the value(s) that appear most frequently in the data set. In this case, none of the values are repeated, so there is no mode.
b. The range is the difference between the largest and smallest values in the data set. In this case, the largest value is 12 and the smallest value is 3, so the range is 12 - 3 = 9.
The variance measures the variability of the data set. It is calculated by taking the average of the squared differences between each data point and the mean. Using the formula for sample variance, the calculations are as follows:
[tex](4 - 6.3333)^2 + (9 - 6.3333)^2 + (10 - 6.3333)^2 + (4 - 6.3333)^2 + (3 - 6.3333)^2 + (12 - 6.3333)^2 = 71.2[/tex]
Dividing this sum by n-1 (where n is the number of data points) gives us the sample variance: 71.2 / 5 = 14.24.
Therefore, the variance is 14.24.
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An object is acted upon by the forces F1=(10,6,3), and F2=(0,4,9). Find forces F3 that must act on the object so that the sum of the forces is zero.
The forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
To find the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero, we need to find a vector [tex]F_3[/tex] that satisfies the equation
[tex]F_1 + F_2 + F_3 = 0.[/tex]
Given the forces:
[tex]F_1[/tex] = (10, 6, 3)
[tex]F_2[/tex] = (0, 4, 9)
We can rearrange the equation to solve for [tex]F_3[/tex]:
[tex]F_3 = -F_1 - F_2[/tex]
Now, let's calculate [tex]F_3[/tex]:
[tex]F_3[/tex] = -(10, 6, 3) - (0, 4, 9)
= (-10, -6, -3) - (0, 4, 9)
= (-10-0, -6-4, -3-9)
= (-10, -10, -12)
Therefore, the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
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identify the values of coefficient a,b,and c in the quadrant equation
5x² = 4x + 7
a =
b =
C=
Answer:
a = 5, b = -4, c = - 7-----------------------
Standard form of a quadratic equation:
ax² + bx + c = 0Convert the given into standard form:
5x² = 4x + 7 5x² - 4x - 7 = 0Compare the equations to find coefficients
a = 5, b = -4, c = - 7thanks for the help! i dont really understand numbers with letters easily : )
Answer: x=6
Step-by-step explanation: Hope this help :D
Can someone help me please?
Answer:
81
Step-by-step explanation:
81
Answer:
6+3=9x9=81 final answer 81.
Step-by-step explanation:
NEED HELP ASAP!!!!
A rectangular billboard for a high school is 10 feet high and 20 feet long. In a scale model of the school, the billboard is 3.5 inches long. How many inches tall is the scale model?
-i got 1.75
Answer:
I got 1.75 too
Step-by-step explanation:
20/3.5 is 5.7
10/5.7 is 1.75
The rectangular billboard is 1.75 inches tall in the scale model.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the ratio between the dimensions of the new and old shapes.
Given that, a rectangular billboard for a high school is 10 feet high and 20 feet long.
In a scale model of the school, the billboard is 3.5 inches long.
So, the scale factor = 3.5/20
= 0.175 inches
Thus, the height is 10×0.175
= 1.75 inches
Therefore, the rectangular billboard is 1.75 inches tall in the scale model.
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help plzzzzzzzzzzzzz
Answer:
Building new bike paths.
Step-by-step explanation:
The reason I choose this answer was because the other ones would all use more gas when bike paths would limit the amount of driving and add to the amount of biking done.
PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
SHOW YOUR WORK!!!
Calculate the volume of the following three-dimensional object
Answer:
2305.33π square inches
Step-by-step explanation:
The volume of a sphere is V = (4/3) πr ^ 3
Because the diameter is 24, the radius is 12.
Substituting 12 for r in the above equation:
V = (4/3) π (12 ^ 3) = (4/3) (1728) π = 2305.33π square inches, or 7238.23 square inches.
Answer:
Measure the length, width and height of the square or rectangle prism or object in inches. Record each of these on paper. Multiply the three measurements together to find the volume using either paper and pencil or a calculator. This is the equation: Volume = length x width x height.
I think that is:
24/2 = 12² = 144 x 3.14 = 452.16.
¯\_(ツ)_/¯
a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3.
What is the measure of the other acute angle ?
PLEASE SHOW YOUR WORK!!! WILL MARK BRAINLIEST!!!
On a youth soccer team 3 out of 12 team members have played in previous years. Based on this information, if 180 kids are in the youth soccer league, then how many could be expected to have played the year before?
Answer:
45
Step-by-step explanation:
3 out of 12 is 1/4, or 0.25, so if you divide 180 by 4, then using the same logic, you can expect 45 kids to have played last year.
3 = 1/4 OR .25 of 12, 12 divided by 4 = 3
180 divided by 4 = 45
Answer:
yes its 45 i did the test and i got an 100
Step-by-step explanation:
heres proof
PLEASE MARK BRAINLIEST!!!!!!can someone check my answer make sure it's right, if it's wrong can you please explain thanks ❤️❤️
Answer:
it is wrong
Step-by-step explanation:
the reason it is wrong is because I said so
Answer:
I am going to say no BECAUSE there are two y values, on the same point. For it to be linear it should only have one point per value. I think... good luck.
I need this done today please help!
Answer:
1.
2. 4:7
3.
4.10:4
5.
id k the rest sorry :/
4.
Which properties of equality justify steps c and f?
A. Multiplication Property of Equality; Division Property of Equality
B. Addition Property of Equality; Division Property of Equality
C. Subtraction Property of Equality; Multiplication Property of Equality
D. Addition Property of Equality; Subtraction Property of Equality
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
The answer is D, because in step c. you add to both sides to get rid of the on the right hand, so you use the fact that you can add the same number to both sides of an equation.
Likewise, in step f. you divided both sides by to get rid of the coefficient, so you use the fact that you can divide both sides of an equation by the same number.
...............................................................................................................................................
Answer:
Option C and B
Step-by-step explanation:
In the question step C is 23 + 11 = -11 +(-4x) + 11
which is in the form of a + b = c + a
In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.
property which signifies this step is
Addition property of equality :
In step 'f' expression is
In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.
In this step division property of equality has been applied.
Therefore Option C and B are the correct options.
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
hope it helps...
What is the range of the function f : [0,[infinity]) → R, defined by the rule f(t) = e^-2x ? (a) (0,1] (b) R (c) ([0,1] (d) (0,[infinity]).
The range of the function f is (0, [infinity]). The correct option is d.
The range of the function f : [0, [infinity]) → R, defined by the rule f(t) = e^(-2x), can be determined by analyzing the behavior of the exponential function.
As x approaches infinity, e^(-2x) approaches 0, but it never reaches 0. This means that the function f(t) will approach 0 as t approaches infinity, but it will never actually reach 0.
On the other hand, as x approaches negative infinity, e^(-2x) approaches positive infinity. Therefore, the function f(t) will approach positive infinity as t approaches 0.
Based on this analysis, we can conclude that the range of the function f is (0, [infinity]), which means option (d) is the correct answer.
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Consider the seriesn+1
(-1)
(n +1)
7t
ns1
Reviewing the Alternating Series Test to determine which of the following statements is true for the given series. Assume you can only use the Alternate Series Test. Do not go beyond it.
a) The series converges
b) Sincelim anメ0, the series diverges
c) Sincean+i S ancannot be shown to be true for all n, the series diverges
d)Sincean+i S ancannot be shown to be true for all n, the Alternating Series Test cannot be applied
e)Sincelim anメ0, the Alternating Series Test cannot be applied
The correct option is (a). The other options are incorrect because the given series satisfies all the conditions of the alternating series test, and thus, the test is applicable.
The given series is as follows: n+1
(-1)
(n +1)
7t
ns1
An alternating series test is a significant tool for determining whether or not a given series converges. A series is said to be convergent if the sequence of partial sums converges to a finite limit, and divergent otherwise. For the alternating series test to apply to a series, there must be the following three conditions: The series must have alternating terms, meaning that every other term is negative. The sequence of absolute values of the terms of the series must be monotonically decreasing, meaning that the absolute values of each successive term must be smaller than the preceding term's absolute value. The sequence of absolute values must approach zero in the limit. Thus, it can be observed that for the given series, the first two conditions are met. Now, to check the third condition, we must calculate the limit of the terms.
Let us take an=1/(n+1)7tnSince lim an=0, the series passes the third test as well.
Thus, we can apply the alternating series test to the given series. By the alternating series test, we have that the series converges. Thus, the correct option is (a). The other options are incorrect because the given series satisfies all the conditions of the alternating series test, and thus, the test is applicable. Thus, we can safely conclude that option (a) is correct.
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Confidence intervals based on pivotal quantities. Let Y1, Y2, . . . , Yn follow an Exponential distribution with parameter β. Note that βYn ∼ Gamma(n, n) and 2nβYn ∼ χ 2 df=2n are both pivotal quantities. (a) Explain why both statistics are indeed pivotal quantities. (b) Construct a 95% confidence interval for β using each pivot and provide interpretations. (c) Compare both intervals. Which one would you recommend using? Explain why
In the context of the Exponential distribution with parameter β, the statistics βYn and 2nβYn are both pivotal quantities. They can be used to construct confidence intervals for β.
A pivotal quantity is a function of the data and a parameter that has a known distribution regardless of the parameter's true value. In this case, both βYn and 2nβYn are pivotal quantities because their distributions (Gamma and chi-squared, respectively) do not depend on the unknown parameter β.
To construct a 95% confidence interval for β using the first pivot, βYn, we can utilize the properties of the Gamma distribution. The interval will be of the form [a, b], where a and b are the lower and upper bounds determined based on the cumulative distribution function of the Gamma distribution. This interval represents a range of plausible values for the parameter β.
Similarly, to construct a 95% confidence interval using the second pivot, 2nβYn, we can employ the chi-squared distribution. The interval will have the form [c, d], where c and d are the lower and upper bounds determined based on the cumulative distribution function of the chi-squared distribution. This interval also represents a range of plausible values for β.
When comparing both intervals, considerations such as width, interpretability, and efficiency are important. The recommended interval would be the one that is narrower (smaller width) and easier to interpret. Additionally, the efficiency of the estimators used in constructing the intervals should be taken into account.
In conclusion, both pivotal quantities, βYn and 2nβYn, can be used to construct 95% confidence intervals for β. The choice between them depends on factors such as width, interpretability, and efficiency. A comprehensive analysis considering these factors will determine the most suitable interval to use.
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