ANSWER
[tex]2v + u = \binom{5}{15}[/tex]
EXPLANATION
It was given that:
[tex]u = \binom{1}{3} [/tex]
and
[tex]v = \binom{2}{6} [/tex]
[tex]2v + u =2 \binom{2}{6} + \binom{1}{3} [/tex]
Perform the scalar multiplication to obtain:
[tex]2v + u = \binom{4}{12} + \binom{1}{3} [/tex]
We add the corresponding components to get;
[tex]2v + u = \binom{4 + 1}{12 + 3}[/tex]
[tex]2v + u = \binom{5}{15}[/tex]
The first choice is correct.
Answer:
A
Step-by-step explanation:
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.Suppose x is any positive number. Circle 1 has a center at (−2, 7) and a radius of 8x. Circle 2 has a center at (−3, 0) and a radius of 5x. Why is Circle 1 similar to Circle 2?Circle 1 and Circle 2 have the same area, and Circle 1 has a radius 0.625 times longer than Circle 2.Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6.Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 0.625.Circle 1 and Circle 2 have the same circumference, and Circle 1 has a radius 1.6 times the length of Circle 2's radius.
Answer:
The correct answer is "Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6"
Step-by-step explanation:
We can tell this because first they identify the movement properly. When going from (-3, 0) to (-2, 7), we move to the right one and up 7.
Also, we know there is a scale factor of 1.6, because when we look at the radius of each circle, we can divide and find that factor.
8x/5x = 1.6
Victoria can make 8 necklaces in four days. How long does it take to make one necklace?
it takes her half a day to make one necklace
Answer:
1/2 day
Step-by-step explanation:
4/8=1/2
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°
The length of the side of square a is twice the length of the side of square b. What is the ratio of the area of square a to the area of square b
➷ As you can tell, the ratio of the lengths is 2 : 1 (the length of a is twice the length of b)
The ratio for area would be the squared version of the length ratio
2^2 = 4
1^1 = 1
The ratio for area is 4 : 1
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In circle O, the measure of ∠ROW is 110°. What is the measure of arc RAW?
Answer:
250°
Step-by-step explanation:
We know that a circle has a total of 360°.
Now we know that ∠ROW is 110° and that Arc RAW has the same End points as ∠ROW.
We can safely assume that arc RAW will be the difference of ∠ROW and 360°.
So we then get:
360° - 110° = 250°
This means that Arc RAW will be 250°
Can you help me answer this question?
Answer:
674.2 lb
Step-by-step explanation:
(5 ft)·(8 ft)·(1.2 in)·(12 in/ft)²·(2.54 cm/in)³·(2.7 g/cm³)/(453.592 g/lb) ≈ 674.2 lb
_____
Comment on units conversion
Units conversion is easily done using conversion factors that have a value of 1. That is, the value of the numerator is equal to the value of the denominator. (12 in = 1 ft, for example). The numerator units are chosen to match units you want, while the denominator units are chosen to match units you want to cancel.
Here, we convert in³ to cm³ to lb using conversion factors given and ones we know.
Which of the following statements is true according to the measurements in the diagram?
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
On average, how long does it take for each person to throw away 100 pounds of garbage?
Answer: About 22.73 days.
Step-by-step explanation: Each person throws away about 4.4 pounds of trash daily. So the way to calculate this is to divide 100 pounds by 4.4 to find out how many days it would take for a person to throw away 10 pounds of trash.
If the apy of a saving account is 2.8% and if the principal in the savings account is $2600 for an entire year, what will be the balance of the savings account after all the interest is paid for the year
Answer:
[tex]\$2,672.80[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P=\$2,600\\r=0.028[/tex]
substitute in the formula above
[tex]A=\$2,600(1+0.028*1)=\$2,672.80[/tex]
HELP PLEASE!
Find the exact values of cos and sin for the angle measure. 180 degrees
Answer:
[tex]\large\boxed{\sin180^o=0\ and\ \cos180^o=-1}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\sin(2\theta)=2\sin\theta\cos\theta\\\\\cos(2\theta)=\cos^2\theta-\sin^2\theta\\\\180^o=2(90^o)\\\\\sin90^o=1\\\\\cos90^o=0\\===================\\\\\sin180^o=\sin(2\cdot90^o)=2\sin90^o\cos90^o=2(1)(0)=0\\\\\cos180^o=\cos(2\cdot90^o)=\cos^290^o-\sin^290^o=0^2-1^2=-1[/tex]
let f(x)=x+3 and g(x)=x^2. find (gf)(5)
Answer:
[tex]g(f(5))=64[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x+3[/tex]
[tex]g(x)=x^{2}[/tex]
we know that
[tex]g(f(x))=(x+3)^{2}[/tex]
so
[tex]g(f(5))=(5+3)^{2}=64[/tex]
Please help. I think I know the answer but I am not 100 percent sure.
Answer: 105°
Step-by-step explanation:
∠U and ∠S are supplementary angles, so
∠U + ∠S = 180°
x + 75° = 180°
x = 105°
Answer:
x = 105 degrees.
Step-by-step explanation:
RS is parallel to TU so x + 75 = 180
x = 105 degrees.
As its is isosceles y is also = 105 degrees.
In last year, San Diego basketball team won 32 games, and lost 8 games. What percent of the games were won?
Answer:
80%
Step-by-step explanation:
The total amount of games last year was 40.
32 + 8 = 40
question says the percent of games were won which means 32/40
In percentage, it means 80%
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.
Which expression can you use to find the slope of the line containing the points -3, 2 and 7 , -1
Use the formula y1-y2/ x1-x2. 2+1/-3-7= 3/-10
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.
A plane veered off its course at an angle of 11 degrees. If the plane ended up 170 miles due west of its planned destination, how far did it fly? Estimate your answer to two decimal places.
Answer:
890.99
Step-by-step explanation:
170/x=sin11
Find the percent increase from 9.56 to 9.65
Round your answer to the nearest tenth of a percent
Can someone explain how to do this? ive tried to look online but it doesnt get the correct answer i guess.
Answer:
Step-by-step explanation:
9.65-9.56=0.09
0.09/9.56=0.009414
0.009414*100=0.94%
9.56 increased by 0.94% to 9.65
Before she went on a diet, Jenna's waist measured 32.45 inches.After the diet, it measured 26.97 inches.How many inches did Jenna lose?
Answer:
5.48
Step-by-step explanation:
32.45 - 26.97 = 5.48
Answer:
Jenna lost 5,48
Step-by-step explanation:
Before the diet Jenna's waist measured 32.45 inches.
After the diet Jenna's waist measured 26.97 inches.
To get the difference between the two measures, we have to discount the new measure from the previous one.
So, difference is 26.97 inches-32.45 inches= -5,48. It is negative because she lost inches.
How do you do this problem? SImple and concise answer please! PLEASE HELPPPPPPPPP
Answer:
b^(6c) = 3a is the only answer
Step-by-step explanation:
There is only one answer that works, and you put a check by it.
b is the base
When it is raised to the 6c power, you get 3a.
b^(6c) = 3a is the only answer
=========================
The only other possible answer would be
a = (1/3) b^(6c) which isn't there.
Please help if possible.............
Answer:
y = 16
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, hence
10y - 29 = 7y + 19 ( subtract 7y from both sides )
3y - 29 = 19 ( add 29 to both sides )
3y = 48 ( divide both sides by 3 )
y = 16
Which type of graph would be best for displaying the frequencies of ages of runners in a race, according to five-year age groups?
a bar graph
a circle graph
a histogram
a line graph
A Histogram would be best
In the same circle, chord AB determines a 115° arc and chord
AC determines a 43° arc. Find m∠BAC.
Answer:
101 degrees
Step-by-step explanation:
- A circle with two chords
- The two cords have common start point A on the circle
- The chord AB subtended arc AB with measure 115°
- The chord AC subtended arc AC with measure 43°
- The measure of any circle is 360°
* These two cords divide the circumference of the circle into
three arcs, arc AB , arc AC and arc BC
∵ The measure of arc AB = 115°
∵ The measure of arc AC = 43°
∵ The measure of the circle is 360°
∴ The measure of arc BC = 360 - (115 + 43) = 360 - 158 = 202°
- In the circle, the angle whose vertex is on the circle is
called inscribed angle and subtended by the opposite arc,
its measure is half the measure of the subtended arc
∵ ∠BAC is an inscribed angle subtended by arc BC
∴ m∠BAC = 1/2 measure of arc BC
∵ The measure of arc BC = 202°
∴ m∠BAC = 202 ÷ 2 = 101°
We have 7 sandwiches. Everyone ate 1/4 sandwich for a snack. How many people had sandwiches
By dividing the 7 sandwiches into quarters, 28 quarters are available, allowing for 28 people to have 1/4 sandwich each.
The student has asked: "We have 7 sandwiches.
Everyone ate 1/4 sandwich for a snack.
To find out how many people can have sandwiches, we first need to understand how much of a sandwich each person gets.
Since each person ate 1/4 of a sandwich, we can take the total number of sandwiches (7) and divide them into quarters, giving us [tex]7 * 4 = 28[/tex] quarters of sandwiches.
Since each person eats one quarter, 28 people can have sandwiches.
The function below has been transformed from f(x) = x2. Describe the transformation. h(x) = 4x2 + 12
Answer:
vertically expanded by a factor of 4then, translated upward 12 unitsStep-by-step explanation:
If f(x) = x² and g(x) = 4x² = 4f(x), the function g(x) represents a vertical expansion of f(x) by a factor of 4.
If h(x) = g(x) +12, the function h(x) represents a translation of g(x) by 12 units upward.
Together, these transformations on f(x) are ...
vertical expansion by a factor of 4translation upward by 12 units_____
Please be aware that there are alternate transformations that will do the same thing:
h(x) = 4(f(x) +3) . . . . is a translation upward by 3, then a vertical expansion by a factor of 4
h(x) = f(2x) +12 . . . . is horizontal compression of f(x) by a factor of 2, then a translation upward by 12.
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
Mr. Fox took 3,648 pieces of candy and divided it into treat bags of 14 pieces of candy each. How many treat bags was he able to make with the candy?
3 /(6x4 x7x7 x1(6 would be 11 because the power of 3x11 would be 33 leaving it to the power of 11
In the chinese symbol for yin and yang, the dash shows two semicircles formed by the curve seperating yin(dark) and yang(light). Is the circumference of the entire yin and yang symbol, less than, greater than, or equal to the perimeter of the yin?
The perimeter of the yin is bigger than the circumference of the full yin and yang symbol. This is due to the fact that the yin and yang symbol is made up of two semicircles which extend beyond the boundaries of the separate yin and yang halves.
What is Yin and yang Symbol?The Yin and Yang symbol is a Chinese symbol that represents complementary characteristics found in all things, such as light and dark, hot and cold, good and evil, and so on. A circle is divided into two sections, one black and one white, containing a smaller circle of the opposing color in each section.
Yin is represented by the black portion, which is connected with feminine traits, passivity, darkness, or coldness. Yang is represented by the white part, which is connected with masculine attributes such as activity, brightness, and warmth. The symbol is intended to reflect the harmony and balance of both of these opposing energies.
Therefore, the perimeter of the yin is bigger than the circumference of the full yin and yang symbol.
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Final answer:
The circumference of the entire yin and yang symbol is greater than the perimeter of the yin semicircle, as the full symbol represents a complete circle while the semicircle includes only half the circumference plus its diameter.
Explanation:
The question about the Chinese symbol for yin and yang essentially asks about the relationship between the circumferences of two geometric shapes. If we consider the yin and yang symbol as a whole to be a circle, and the yang (or yin, since they are symmetrical) as a semicircle, then we can infer the following regarding circumferences and perimeters:
The circumference of a circle is 2πr, where r is the radius of the circle. The perimeter of a semicircle (half of the full circle and including the diameter) is πr + 2r. If we take the full yin and yang symbol to have a circumference of 2πr (since the full symbol is also circular), then the perimeter of the yang semicircle (which includes the straight edge boundary of the yin) would be less than the circumference of the full symbol, as it lacks the other semicircle's curved edge. In mathematical terms, πr + 2r is less than 2πr for any positive value of r.