The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.
To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.
Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.
Given f(x) = 2x^2 + 3x and g(x) = 5x^2 - 2x - 6
What is (f+g)(x)?
A. -3x^2 + 5x + 6
B. 10x^2 + x + 6
C. 7x^2 + x - 6
D. 3x^2 - 5x - 6
Answer:
C. 7x^2 + x - 6
Step-by-step explanation:
f(x) = 2x^2 + 3x and g(x) = 5x^2 - 2x - 6
(f+g)(x) = 2x^2 + 3x + 5x^2 - 2x - 6
(f+g)(x) = 7x^2 + x - 6
1. Collin noticed that various combinations of nickels and dimes could add up to $0.65.
Let x equal the number of nickels
Let y equal the number of dimes
What is the domain where y is a function of x and the total value is $0.65?
A. (0,1,2,3,4,5,6,7,8,9,10,11,12,13)
B. (1,2,3,4,5,6,7,8,9,10,11,12,13)
C. (0,1,3,5,7,9,11,13)
D. (1,3,5,7,9,11,13)
Answer:
Step-by-step explanation:
dimes only cannot give total ending in 5 cents
so theres at least 1 nickel
n by the same reason, no.of nickels must be odd no.
most nickels is 0.65/0.05=13
combining the above, ans is D. (1,3,5,7,9,11,13)
Answer:
The Answer Is D (1,3,5,7,9,11,13)
Step-by-step explanation:
given sec theta=-4/3 and 90°
Answer:
Option A.
Step-by-step explanation:
It is given secθ = - [tex]\frac{4}{3}[/tex]
then cosθ = -[tex]\frac{3}{4}[/tex]
Now we know the identity
sinθ = [tex]\sqrt{1-cos^{2}\theta }[/tex]
= [tex]\sqrt{1-(-\frac{3}{4} )^{2}}[/tex]
= [tex]\frac{\sqrt{7} }{4}[/tex]
Now sin2θ = 2sinθcosθ
Now we put the values of cosine and sine in the formula
sin2θ = 2×(-[tex]\frac{3}{4}[/tex])([tex]\frac{\sqrt{7}}{4}[/tex])
= -[tex]\frac{3\sqrt{7}}{8}[/tex]
Therefore, option A. is the answer.
According to the Substitution Property of Equality: If y = -5 and 7x + y = 11, then _______ . Question 9 options: 7(-5) + y = 11 7x - 5 = 11 7x + 5 = 11 -5 + y = 11
Answer:
7x - 5 = 11
Step-by-step explanation:
To solve for x, substitute y = -5 into the equation 7x + y = 11.
This becomes 7x + (-5) = 11 or 7x - 5 = 11.
18-3n+2=n+20-4n which is the solution 0 (0) or all reals
Answer:
that is a true statment.
20 - 3n = -3n + 20
Step-by-step explanation:
add the numbers, collect the like terms.
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with mean 371 minutes and standard deviation 65 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 528 minutes and standard deviation 108 minutes. A researcher records the minutes of activity for an SRS of 6 mildly obese people and an SRS of 6 lean people.Use z-scores rounded to two decimal places to answer the following:What is the probability (Image for It appears that people who are mildly obese are less active than leaner people. One study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? What is the probability (Image for It appears that people who are mildly obese are less active than leaner people. One study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?
Answer:
0.0322; 0.9929
Step-by-step explanation:
Since the data is normally distributed, we use z scores for these probabilities.
The formula for a z score of a sample mean is
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
For the sample of mildly obese people, the mean, μ, is 371; the standard deviation, σ, is 65; and the sample size, n, is 6.
Using 420 for X,
z = (420-371)/(65÷√6) = 49/(65÷2.4495) = 49/26.5360 ≈ 1.85
Using a z table, we see that the area under the curve to the left of this is 0.9678. However, we want the area to the right, so we subtract from 1:
1-0.9678 = 0.0322
For the sample of lean people, the mean, μ, is 528; the standard deviation, σ, is 108; the sample size, n, is 6.
Using 420 for X, we have
z = (420-528)/(108÷√6) = -108/(108÷2.4495) = -108/44.0906 ≈ -2.45
Using a z table, we see that the area under the curve to the left of this is 0.0071. We want the area under the curve to the right, so we subtract from 1:
1-0.0071 = 0.9929
The probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 3.2%. For the 6 lean people, this probability is approximately 0.7%.
Explanation:For this type of problems, we use the concept of z-scores in statistics. The z-score is a measure of how many standard deviations a data point is from the mean. In this case, we will first calculate the standard error by dividing the standard deviation by the square root of sample size and then find the z-score by dividing the value of interest (420 minutes) minus mean by the standard error.
For mildly obese people, mean = 371 min, standard deviation = 65 min, sample size = 6. So, standard error = 65/sqrt(6) ≈26.51. The z-score for 420 min = (420-371)/ 26.51 ≈1.85. This indicates 420 minutes is 1.85 standard deviations above the mean. The probability that z-score exceeds 1.85 (assuming a one-tailed test since we are looking for the mean to be more than 420 minutes) is 0.032 (approximately). Hence, the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 0.032 or 3.2%.
For lean people, mean = 528 min, standard deviation = 108 min, sample size = 6. Using the same approach, standard error = 44.11. The z-score for 420 min = (420-528)/44.11 ≈-2.45. This indicates 420 minutes is 2.45 standard deviations below the mean. The probability that z-score is less than -2.45 (assuming a one-tailed test for under 420 minutes) will be more than 99%. The probability that z-score exceeds -2.45 (420 min or more time) is about 1 - 0.993 = 0.007. Hence, the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes is about 0.007 or 0.7%.
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Identify the range of the function shown in the graph.
Answer:
C
Step-by-step explanation:
The range is the set of ALLOWED y-values of the function (graph). Also, the range is the y-values for which the function is defined.
Looking at the graph, we see that the graph is defined between y = 1 and y = 7. So the range is 1 ≤ y ≤ 7
the correct answer is C
Which of the following statements is true according to the measurements in the diagram?
A carnival charges a $5 admission fee plus $1 per ride. What does it cost to ride 6 rides, including the admission fee?
Answer:
the answer is 11 dollars
Step-by-step explanation:
Answer:
11 dollars
Step-by-step explanation:
A number from 8 to 15 is drawn at random. What is the probability that the number is an even number?
Answer:
The probability that the answer is an even number is 50%.
Step-by-step explanation:
There are 8 terms: 8, 9, 10, 11, 12, 13, 14, 15. Even numbers: 8, 10, 12, 14. So, 4 out of the 8 terms are even, which is equivalent to 50%.
The probability that the number is an even number is 1/2.
What is the probability?The probability is defined as the ratio of number of favourable outcomes and the the total number of possible outcome.
A number from 8 to 15 is drawn at random.
The number between 8 to 15 are 8, 9, 10, 11, 12, 13, 14, 15 = 8
Total even number = 8, 10, 12, 14 = 4
The probability that the number is an even number is;
[tex]\rm Probability =\dfrac{Total \ even \ number}{Total \ number}\\\\Probability =\dfrac{4}{8}\\\\Probability =\dfrac{1}{2}[/tex]
Hence, the probability that the number is an even number is 1/2.
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Please answer this multiple choice question!
Answer:
C. 48
Step-by-step explanation:
If you cut the circle in half through the points M and C it splits 96 in half which is 48 which is the same size as M
Answer:
c. 48°Step-by-step explanation:
Look at the pictures.
(the picture 1)
Inscribed angle and central angle.
(the picture 2)
In a circle, central angle is two times larger than inscribed angle that intercept the same arc.
We have the central angle C. m∠C = 96°.
The inscribed angle M: m∠M = 96° : 2 = 48°
Solve for y.
xy + p = 5
The value of y for the equation [tex]xy + p = 5[/tex].
What is equation?An equation is a statement of equality between two mathematical expressions containing one or more variables.
According to the given question.
We have a equation
[tex]xy + p = 5[/tex]
Solve the above the equation for y
[tex]xy +p - p = 5 -p[/tex] ( subtracting p both the sides)
[tex]\implies xy = 5-p[/tex]
[tex]\implies \frac{xy}{x} = \frac{5-p}{x}[/tex] (dividing both the sides by x)
[tex]\implies y = \frac{5-p}{x}[/tex]
Therefore, the value of y for the equation [tex]xy + p = 5[/tex].
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-2(bx-5) = 16 the value of x in terms of b is the value of x when b is 3 is ????
Answer:
x = -3/bx = -1 when b=3Step-by-step explanation:
Eliminating parentheses, you get ...
-2bx +10 = 16
Subtract 10 and divide by -2b:
x = 6/(-2b)
x = -3/b
__
When b=3, you have ...
x = -3/3
x = -1
the graph shows that lisa's earnings are proportional to the number of hours that she works.This relationship can be represented by an equation in the form y = kx. what is the value of k in the equation?
c. 25 because she gets $25 per hour
A survey found that women's heights are normally distributed with mean 63.9 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 69.7 in. and standard deviation 3.6 in. Consider an executive jet that seats six with a doorway height of 55.9 in. Complete parts (a) through (c) below. a. What percentage of adult men can fit through the door without bending? The percentage of men who can fit without bending is 0.02%. (Round to two decimal places as needed.) b. Does the door design with a height of 55.9 in. appear to be adequate? Why didn't the engineers design a larger door?
Using the normal distribution, it is found that:
a) The percentage of men who can fit without bending is 0.02%.
b) A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
Men have mean of 69.7 in, thus [tex]\mu = 69.7[/tex]Standard deviation of 3.6 in, thus [tex]\sigma = 3.6[/tex]The proportion is the p-value of Z when X = 55.9, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.9 - 69.7}{3.6}[/tex]
[tex]Z = -3.83[/tex]
[tex]Z = -3.8[/tex] has a p-value of 0.0002.
0.0002 x 100% = 0.02%
The percentage of men who can fit without bending is 0.02%.
Item b:
A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
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Evaluate 3^2+(6-2)•4-6/3
Answer:
23
Step-by-step explanation:
3^2+(6-2)•4-6/3
Order of operations:
= 9 + (4)•4 - 6/3
= 9 + 16 - 2
= 25 -2
= 23
32+(6−2)(4)− 6/3
your answer is =23
32+(6−2)(4)− 6/3
=9+(6−2)(4)− 6/3
=9+(4)(4)− 6/3
=9+16− 6/3
=25− 6/3
=25−2
=23
Help a need ma grade up
To answer this we must know BIDMAS
Brackets) Let's do 8-6 as (2*3 is 6 as we substitute X with 3) and that gives us 2
Indices) Let's do 2 square which gives 4
Addition) Then finally add 4 to 4 giving us 8
The answer is 8
PLsss help 15 points!
In the figure below, △ABC ~ △PQR. If the Area of △ABC is 40 cm2, what is the area of △PQR? show your work.
Answer:
90 square cm.
Step-by-step explanation:
For similar figures, the length of corresponding sides are proportional.
So we can write 4k = 6 where k is the proportionality constant.
Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y
Solving 4k = 6, we see that k = 6/4 or 3/2
We need area, so we multiply area of ABC by k^2 to get area of PQR.
[tex]40(\frac{3}{2})^2\\=40(\frac{9}{4})\\=90[/tex]
Area of PQR = 90 cm^2
Answer:
The area of △PQR is [tex]90\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
so
Let
z-----> the scale factor
x---> the corresponding side triangle PQR
y---> the corresponding side triangle ABC
[tex]z=\frac{x}{y}[/tex]
substitute the values
[tex]z=\frac{6}{4}=1.5[/tex]
step 2
Find the area of triangle PQR
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z-----> the scale factor
x---> the area of triangle PQR
y---> the area of triangle ABC
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]z=1.5[/tex]
[tex]y=40\ cm^{2}[/tex]
substitute the values
[tex]1.5^{2} =\frac{x}{40}[/tex]
[tex]x=40(1.5^{2})=90\ cm^{2}[/tex]
There is a 70% chance that your car will get stuck in the snow during the next big snow fall. Given that you are already stuck in the snow with your car, the chance that you will require a tow truck to pull you out is 90%. What is the chance that you will get stuck in the snow with your car AND require a tow truck to pull you out?
Hint: P(A|B)= P(A∩B) / P(B)
66%
63%
78%
29%
Answer:
63%
Step-by-step explanation:
This is a problem of conditional probability.
The two events that are given are:
Car stuck in the snow - Let it be event S. P(S) = 70% = 0.70Require a tow truck - Let it be event T.We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)
We are also given the conditional probability, which is P(T | S) = 90% = 0.90
Using the given formula for our case we can modify the formula as:
[tex]P(T|S)=\frac{P(S \cap T)}{P(S)}[/tex]
[tex]0.90=\frac{P(S \cap T)}{0.70}\\\\ P(S \cap T)=0.90 \times 0.70\\\\ P(S \cap T)=0.63[/tex]
Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out
The probability of getting stuck in the snow and requiring a tow truck is found by multiplying the individual probabilities, resulting in a 63% chance.
The question asks for the probability that you will get stuck in the snow with your car AND require a tow truck to pull you out. To calculate this combined probability (P(A AND B)), we use the rule of multiplication for dependent events, which states P(A AND B) =[tex]P(B|A) imes P(A).[/tex] Here, P(A) is the probability of getting stuck in the snow, and P(B|A) is the probability of requiring a tow truck given that you are stuck.
In numbers, this becomes P(A AND B) = [tex]0.90 imes 0.70 = 0.63 or 63%[/tex]. Therefore, the chance that you will get stuck in the snow and require a tow truck to pull you out is 63%.
Which graph has the most appropriate scales and units for this situation ?
Answer:
your answer is A HOPE THIS HELPS!!!
Step-by-step explanation:
Answer:
The graph B is the most appropriated
Step-by-step explanation:
Due to we need to know the charging of the company as a function of miles, it is practical to enter into the graph with the miles into the horizontal axis and obtain the charge over the vertical axis. In fact, the common usage, it is by entering the unknown quantity (independent variable) into the x-axis (horizontal axis) and looking function calculated value into the y-axis (vertical axis).
Taking the previous into account, we chose the graph from option B.
Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?
f(x) = 2(x + 7)(x + 5)(x – 2)
f(x) = 2(x – 7)(x – 5)(x + 2)
f(x) = (x + 7)(x + 5)(x + 5)(x – 2)
f(x) = (x – 7)(x – 5)(x – 5)(x + 2)
ANSWER
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
EXPLANATION
If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.
If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.
If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.
The fully factored form of the polynomial is
[tex]f(x) =a (x + 2)(x - 7) {(x - 5)}^{2} [/tex]
It was given that the polynomial has a leading coefficient of 1.
Hence a=1.
This implies that,
[tex]f(x) =(x + 2)(x - 7) {(x - 5)}^{2}[/tex]
Or
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
Answer:
f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D
Step-by-step explanation:
Estimate the circumference of the circle with the given radius or diameter. Use 3.14 for ?. Round to the nearest unit. (Half. 24in written inside the circle) 1. 27in. 2. 79in. 3. 1,809in. 4. 152in. Mathematics, Connexus. Rectangular prisms and volume Part 1, Math 6B, Unit 3: Geometry and Measurement.
Answer:
The perimeter of a circle can be found by using the followinfg expression
P = 2*π*r
where
π = 3.14
r = radius of the circle = half the diameter of the circle
In this case, if we are given the radius, we use
P = 2*π*r
If we are given the diameter, we use
P = 2*π*(D/2) = π*D
1) 27in
radius = 27in
P = 2*(3.14)*(27 in) = 169.56 in
diameter = 27 in
P = (3.14)*(27 in) = 84.78 in
2) 79 in
radius = 79 in
P = 2*(3.14)*(79 in) = 496.12 in
diameter = 79 in
P = (3.14)*(79 in) = 248.06 in
3) 1809 in
radius = 1809 in
P = 2*(3.14)*(1809 in) = 11360.52 in
diameter = 1809 in
P = (3.14)*(1809 in) = 5680.26 in
4) 152 in
radius = 152 in
P = 2*(3.14)*(152 in) = 954.56 in
diameter = 152 in
P = (3.14)*(152 in) = 477.28 in
Answer:
no
Step-by-step explanation:
A man who is 6 feet tall casts a shadow thaty is 11 feet long at the same time a tree casts a shadow that is 33 feet long what is the height of the tree
Answer:
The height of the tree is 18 feet tall
Step-by-step explanation:
Set up a proportion:
6 feet over 11 feet long equals x feet over 33 feet long
6/11 = x/33
198 = 11x
x = 18
The height of the tree is 18 feet tall
Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour. Victoria's daughter made cookies using 340 grams of butter for every 400 grams of flour. What will Victoria think of her daughter's cookies?
Victoria's daughter's cookies will have more butter. Victoria uses 0.68g of butter per gram of flour, whereas her daughter uses 0.85g of butter per gram of flour.
Answer:
Daughter is using 0.17 gram more butter for each gram flour.
Step-by-step explanation:
Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour = [tex]\frac{170}{250}[/tex] = 0.68
Therefore, this recipe needs 0.68 grams of butter for every gram flour.
Her daughter made cookies using 340 grams of butter for every 400 grams of flour = [tex]\frac{340}{400}[/tex] = 0.85
She is using 0.85 grams of butter for every gram flour.
Victoria's daughter is using 0.17 gram of butter more on every gram flour.
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 4x + 1, [0, 2] Yes, it does not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on double-struck R. No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiable on (0, 2). There is not enough information to verify if this function satifies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE). c =
[tex]f(x)=3x^2-4x+1[/tex] is a polynomial and thus continuous everywhere and differentiable on any open interval. (second option)
The MVT then guarantees the existence of [tex]c\in(0,2)[/tex] such that
[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{5-1}2=2[/tex]
We have
[tex]f'(x)=6x-4[/tex]
so
[tex]6c-4=2\implies6c=6\implies c=1[/tex]
The true statement is: (b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable
Mean value theorem states that:
If [tex]\mathbf{f(x)\ is\ continuous}[/tex] [a,b] and
[tex]\mathbf{f(x)\ is\ differentiable}[/tex] on (a,b),
Then there is a point c in (a,b), such that: [tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
The function is given as:
[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]
And the interval is: [tex]\mathbf{[0,2]}[/tex]
We have
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
This becomes
[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2 - 0}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2}}[/tex]
Calculate f(2) and f(0)
[tex]\mathbf{f(2) = 3\times 2^2 - 4\times 2 + 1 = 5}[/tex]
[tex]\mathbf{f(0) = 3\times 0^2 - 4\times 0 + 1 = 1}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{5-1}{2}}[/tex]
[tex]\mathbf{f'(c) = \frac{4}{2}}[/tex]
[tex]\mathbf{f'(c) = 2}[/tex]
Recall that:
[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]
Differentiate
[tex]\mathbf{f'(x)= 6x - 4}[/tex]
Substitute c for x
[tex]\mathbf{f'(c)= 6c - 4}[/tex]
Substitute 2 for f'(c)
[tex]\mathbf{ 6c - 4 = 2}[/tex]
Collect like terms
[tex]\mathbf{ 6c = 4 + 2}[/tex]
[tex]\mathbf{ 6c = 6}[/tex]
Divide both sides by 6
[tex]\mathbf{c = 1}[/tex]
The interval is given as: [0,2]
The value of c is true for interval (0,2).
Hence, the true statement is:
(b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable
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n article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 15 of 19 repairs were successful while for shorter tears, 21 of 29 repairs were successful. (a) Is there evidence that the success rate is greater for longer tears? Use . What is the -value? (b) Calculate a one-sided 95% confidence bound on the difference in proportions that can be used to answer the question in part (a). (a) There evidence that the success rate is greater for longer tears. The -value is Round your answer to four decimal places (e.g. 98.7654). (b) The one-sided 95% confidence bound is . Round your answer to three decimal places (e.g. 98.765).
To answer the question, a statistical hypothesis test comparing the proportions of successful repair attempts is needed. This involves calculating a Z-score and referencing Z-tables or statistical software for the p-value. Also, a one-sided 95% confidence interval needs to be calculated for the proportion differences using the Z-test.
Explanation:To answer this question, we need to perform a statistical hypothesis test which involves the comparison of proportions. Let's denote p1 as the proportion of successful repairs for tears greater than 25 mm (15 successful out of 19 trials), and let p2 for tears shorter (21 successful out of 29 trials).
To find the p-value, we need to implement a Z-test using the formula Z = (p1 - p2) - 0 / sqr((p(1-p)(1/n1 + 1/n2)) where p = (x1 + x2) / (n1 + n2). By substituting the values in the formula we get our z-score, which is used to find the p-value from the Z-tables or by using statistical software.
As for the 95% confidence interval, we will also use the Z-test formula, but this time the Z-value for the 95% one-sided confidence level which is approximately 1.645. Substituting the values in we can calculate our confidence bound. Please remember that to make accurate calculations you need to use calculated Z-score and confidence interval in the Z distribution method.
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(a) The p-value is 0.1814, and we do not have evidence that the success rate is significantly greater for longer tears.
(b) The one-sided 95% confidence bound on the difference in proportions is 0.184.
To answer your question regarding the success rates of arthroscopic meniscal repair for varying tear lengths, let's break it down into two parts: (a) the p-value and the evidence regarding the success rates, and (b) calculating a one-sided 95% confidence bound on the difference in proportions.
Part (a): Evidence and p-value Calculation:-
Define Success Rates:
For tears greater than 25 mm:
Number of successful repairs (x1) = 15Total repairs (n1) = 19Success rate (p1) = x1/n1 = 15/19 ≈ 0.7895For shorter tears:
Number of successful repairs (x2) = 21Total repairs (n2) = 29Success rate (p2) = x2/n2 = 21/29 ≈ 0.7241Hypotheses:
Null Hypothesis (H0): There is no difference in success rates, i.e., p1 ≤ p2.Alternative Hypothesis (H1): The success rate for longer tears is greater, i.e., p1 > p2.Calculate the z-statistic:
The formula for the z-statistic comparing two proportions is:
[tex]z = \frac{p_1 - p_2}{\sqrt{p(1 - p)(\frac{1}{n_1} + \frac{1}{n_2})}}[/tex]
where [tex]p = \frac{x_1 + x_2}{n_1 + n_2}[/tex] is the combined proportion.
Combined proportion (p):
[tex]p = \frac{15 + 21}{19 + 29} = \frac{36}{48} = 0.75[/tex]
Z-statistic calculation:
[tex]z = \frac{0.7895 - 0.7241}{\sqrt{0.75 \times (1 - 0.75) \times \left(\frac{1}{19} + \frac{1}{29}\right)}}[/tex]
Upon performing the necessary computations:
Using values,Find the p-value:
This represents the probability of observing a value as extreme (or more extreme) than the z-statistic under the null hypothesis. Using z-tables or a calculator for a right-tailed test:
Decision:
If we use an alpha (α) level of 0.05, since the p-value (0.1814) is greater than α, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the success rate is greater for longer tears.Part (b): One-sided 95% Confidence Bound:-
Confidence Interval for the Difference in Proportions:
The formula for the confidence interval is given by:
[tex](p_1 - p_2) \pm z_{\alpha} \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Differences in proportions:
[tex]p_1 - p_2 = 0.7895 - 0.7241 = 0.0654[/tex]
Calculate the margin of error:
[tex]ME = z_{\alpha} \times \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Confidence Bound:
The one-sided confidence bound:Result:
The one-sided 95% confidence bound on the difference in proportions is approximately 0.184.Which expression is equivalent to the fraction below?
5/8
A. 8 5
B. 8 • 8
C. 8 - 5
D. 8 + 5
E. 5 8
F. 5 • 5
5/8=expression is equivalent to
5 8
my mom tell me this its E oksy
The complement of an angle is one-fourth the measure of the supplement of the angle. What is the measure of the angle to the nearest whole degree?
Answer:
the answer is 60
Step-by-step explanation:
A store is having a sale where everything is discounted 30%. Find the discount and the sales price if a customer buys an item they normally sells for $365
Answer:
$255.50
Step-by-step explanation:
✯Hello✯
↪ Alright so the item is originally 365 dollars
↪ you have to work out 30% of this which is 109.50
↪ then do 365- 109.50
↪ thats $255.50
❤Gianna❤
I REALLY NEED HELP!
What is the future value of the 10% savings from earnings of $1,470 if it earns 3.5% annual interest,
compounded monthly for 25 years?
Use the compound interest formula to estimate the future value.
A = P (1+r/n)^nt
A.
$295.72
B.
$352.19
C.
$419.43
D.
$523.89
What is the future value of the 10% savings from earnings of $36,000 if it earns 6.25% annual interest, compounded quarterly for 15 years?
Use the compound interest formula to estimate the future value.
A = P (1+r/n)^nt
A.
$912.65
B.
$9,126.53
C.
$1,825.31
D.
$18,253.31
Justin contributes $208 each month to a savings account that earns 5% annual interest. Calculate his annuity savings over the course of 25 years.
Use
S = P ((1+r^n)-1/r)
A.
$9.927.23
B.
$65,520.00
C.
$62,660.00
D.
$123,866.02
Answer:
B
Step-by-step explanation:
The compound interest formula is [tex]A = P (1+r/n)^nt[/tex] where:
P is the starting amount called the principler is the rat written as a decimaln is the number of times compounded in a yeart is the number of yearsSubstitute a value into each variable to solve.
P = $147 since 10% of 1,470 is being invested which makes P = 0.10(1470) = 147.The rate is 3.5% or r = 0.035.n = 12 because it is compounded monthly meaning 12 times a year.t = 25 since it will earn for 25 years.[tex]A = P (1+r/n)^{nt}\\A = 147(1 + \frac{0.035}{12})^{12*25}\\A = 147 ( 1 + 0.002916)^{300}\\A = 147(1.002916)^{300}\\A = 352.19[/tex]
Repeat this process for each formula.
Answer:
B. $352.12
B. $9,126.53
D. $123,866.02
Step-by-step explanation:
Hope this helps! Have an awesome day/night!