The concern of a study by Beynnon et al. (A-4) were nine subjects with chronic anterior cruciate ligamenttears. One of the variables of interest was the laxity of the anteroposterior, where higher values indicate more knee instability. The researchers found that among subjects with ACL-deficient knees, the mean laxity value was 17.4mm with a standard deviation of 4.3mm.
(a) What is the estimated standard error of the mean?
(b) Construct the 99 percent confidence interval for the mean of the population from which the nine subjects may be presumed to be a random sample.
(c) What is the precision of the estimate?
(d) What assumptions are necessary for the validity of the conidence interval you constructed?

Answer

its -1

Step-by-step explanation:

ED 2020 boiiiii

The residual value of the line of the best fit when x = 2 is -1

The equation of the line is given as:

y = 0.5x + 1

When x = 2, we have:

y = 0.5 * 2 + 1

Evaluate

y = 2

The residual is the difference between the actual value and the predicted value.

From the complete graph, the actual value is 1.

So, we have:

Residual = 1 - 2

Evaluate

Residual = -1

Hence, the residual value when x = 2 is -1

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Answer:

0.637

Step-by-step explanation:

The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out

Answer:

21

Step-by-step explanation:

1/5 of 30 is 6

10% of 30 is 3

3+6=9

30-9=21

which is 7/10

Answer:

Simon has 7/10 of the cakes left.

Answer:

Triangular Prism

volume 748

Answer:

n=N-1

Step-by-step explanation:

You can start by imagining this scenario on a small scale, say 5 squares.

Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!

The smallest value of n is N-1.

Square is a quadrilateral of equal length of sides and each angle of 90°.

Here given that there are 1×N squares i.e. N numbers of squares in one row.

The grasshopper can jump either one square or two squares to land on the next square.

Let's assume the scenario of 5 squares present in a row.

Let the grasshopper starts from the first square,

so the grasshopper can cover the full 5 squares in 2 methods;

one method is that it will jump one square at a time and reach at last square.

another method is it will jump all the squares to the finish and then backtrace.

If the grasshopper jumps one square at a time, it will take 4 jumps to cover all 5 squares.

Similarly, If a grasshopper jumps two squares at a time and then backtrace, it will take 2 jumps to reach the 5th square and then it will jump 1 square and then 2 squares to cover the 2 squares it missed, for which the number jump is also 4.

From the above it is clear that the number of jumps will always be one less than the total number of squares if the grasshopper begins from the first square and touch every square exactly once.

Therefore, the smallest value of n is N-1.

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Answer: there are 4 solutions

x = -2

x = -1/2 = -0.500

x =(3-√5)/2= 0.382

x =(3+√5)/2= 2.618

Step-by-step explanation:

Answer:

14.4 units

Step-by-step explanation:

In Trigonometry

[tex]\cos \theta =\frac{Adjacent}{Hypotenuse}\\[/tex]

In Triangle DEF,

[tex]\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).[/tex]

Answer:

48

Step-by-step explanation:

L = D + 28

⅓L = ⅘D

Solve the system of equations using elimination or substitution.  Using substitution:

⅓L = ⅘(L − 28)

Multiply both sides by 15:

5L = 12(L − 28)

Distribute:

5L = 12L − 336

Combine like terms:

336 = 7L

Divide:

L = 48

Answer: Working together, they can complete the task in 7 hours and 12 minutes.

Step-by-step explanation:

Ok, Briana needs 12 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/12hours = 1/12 task per hour.

This means that she can complete 1/12 of the task per hour.

Henry needs 18 hours to complete the task, then his ratio is:

1 task/18 hours = 1/18 task per hour.

This means that he can complete 1/18 of the task in one hour.

If they work together, then the ratios can be added:

R = 1/12 + 1/18 = 18/(12*18) + 12/(18*12) = 30/216

we can reduce it to:

R = 15/108 = 5/36

So, working together, in one hour they can complete 5/36 of the task, now we can find the number of hours needed to complete the task as:

(5/36)*x = 1 task

x = 36/5 hours = 7.2 hours

knowing that an hour is 60 minutes, then 0.2 of an hour is 60*0.2 = 12 minutes.

then x = 7 hours and 12 minutes.

Answer:

The rental of each chair is $2.75

The rental of each table is $8.5

Step-by-step explanation:

Let's name the unknowns "c" for the cost of each chair rental, and "t" for the cost of each table rental.

Now we can create the equations that represent the statements:

a) "The total cost to rent 2 chairs and 3 tables is $31."

2 c + 3 t = 31

b) "The total cost to rent 6 chairs and 5 tables is $59."

6 c + 5 t = 59

now we have a system of two equations and two unknowns that we proceed to solve via the elimination method by multiplying the first equation we got by "-3" so by adding it term by term to the second equation, we eliminate the variable "c" and solve for "t":

(-3) 2 c + (-3) 3 t = (-3)  31

-6 c - 9 t = -93

6 c + 5 t = 59

both these equations added give:

0 - 4 t = -34

t = 34/4 = 8.5

So each table rental is $8.5

now we find the rental price of a chair by using any of the equations:

2 c + 3 t = 31

2 c + 3 (8.5) = 31

2 c + 25.5 = 31

2 c = 5.5

c = 5.5/2

c = $2.75

Answer:

a)0.2275   b)95/105=19/21    c)10/105= 2/21

Step-by-step explanation:

a) The case "The test result is positive" consists in 2 parts.

The 1st one is "The person has the desease (15%=0.15)  and the test's  result is positive (95%=0.95)

The probability of that is P(desease, positive) = 0.15*0.95=0.1425

The 2nd one is "The person has no the desease (100%-15%=85%=0.85). However the test result is positive (10%=0.1)

The probability of that is P(not desease, positive)=0.85*0.1=0.085

The total probability that test is positive is the sum of 1st and 2-nd parts of the case: P(pos) = 0.1425+0.085=0.2275

b) As it has been shown in a) The test result can be positive in case that the person is really has the desease (95%) and in case the person has no the desease (10%).  This actually means that 95 persons from 105  having positive test result are really has the desease.

So the probability that the test result is positive and person has the desease is P (desease/positive)= 95/105

c) It's clearly seen that the sum of  probabilities of b) and c)  equal 1.

Both events make full group of events.

If the test result is positive the person can have the desease or can have not the desease. So ( no desease/positive)= 1-95/105=10/105

Answer:

[tex](\frac{-1}{2} , \frac{-\sqrt{3} }{2} )[/tex]

Step-by-step explanation:

Memorize your unit circle.

Step 1: Subtract 360 from 600 degrees to find rotation

600° - 360° = 240°

Step 2: Either find coordinates from unit circle or convert to radians

240° = 4π/3

Step 3: Find coordinates

Answer:

Option 2) Sin 35 = [tex]\frac{5}{x}[/tex]

Step-by-step explanation:

Sin 35 = [tex]\frac{opposite }{hypotenuse}[/tex]

Where opposite = 5' and hypotenuse = x(unknown)

=> Sin 35 = [tex]\frac{5}{x}[/tex]

Answer:

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

Step-by-step explanation:

To verify how dispersed a distribution is, we find it's coefficient of variation.

Coefficient of variation:

Mean of [tex]\mu[/tex], standard deviation of [tex]\sigma[/tex]. The coefficient is:

[tex]CV = \frac{\sigma}{\mu}[/tex]

Which year's GMAT scores show a more dispersed distribution

Whichever year has the highest coefficient.

2009:

Mean of 500, standard deviation of 90. So

[tex]CV = \frac{90}{500} = 0.18[/tex]

2010:

Mean of 570, standard deviation of 85.5. So

[tex]CV = \frac{85.5}{570} = 0.15[/tex]

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

2009's GMAT scores show a more dispersed distribution.

Given that in 2009: Mean = 500 and standard deviation = 90.

In 2010: Mean = 570 and standard deviation = 85.5.

If the standard deviation is higher then the scores will be more dispersed.

Note that: 90 > 85.5. And 90 corresponds to 2009.

So, 2009's GMAT scores show a more dispersed distribution.

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Answer:

d = 234.6 m

Step-by-step explanation:

You can consider a system of coordinates with its origin at the beginning of the walk of the student.

When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:

[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]

she is at the coordinates (52.97 , 28.16)m.

Next, when she walks 180m to the east, her coordinates are:

(52.97+180 , 28.16)m = (232.97 , 28.16)m

To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:

[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]

The displacement of the student on her complete trajectory was of 234.6m

Answer:

2.4 hours

Step-by-step explanation:

If Mary is running 26 miles at a pace of 7.5 miles per hour, it will take her 3.47 hours to run the full course.

26/7.5 = 3.466666...

If she has run 8 miles, 1.07 hours have passed.

8/7.5 = 1.06666666...

Subtract the total time from the time that has already passed to find the time left.

3.47 - 1.07 = 2.4

Mary has 2.4 hours left.

Answer:

Step-by-step explanation:

                              Y

p(x,y)            0          1            2

           0      0.10     0.04     0.02

x          1       0.08     0.2     0.06

            2       0.0      0.14     0.30

a) What is P(X = 1 and = 1)

From the table above we have

P(1,1) = 0.2

b)  Compute P(X ≤ 1 and Y ≤ 1).

[tex]=p(0,0)+p(0,1)+p(1,0)+p(1,1)\\\\=0.1+0.04+0.08+0.2\\\\=0.42[/tex]

C)

Let A ={X ≠ 0 and Y ≠ 0}

p{X ≠ 0 , Y ≠ 0}

= p(1,1) + p(1,2) + p(2,1) + p(2,2)

= 0.20 + 0.06 + 0.14 + 0.30

=0.7

d) The possible X values are in the figure 0,1,2

[tex]p_x(0)=p(0,0)+p(0,1)+p(0,2)\\\\=0.1+0.04+0.02\\\\=0.16\\\\p_x(1)=p(1,0)+p(1,1)+p(1,2)\\\\=0.08+0.2+0.06\\\\=0.34\\\\p_x(2)=p(2,0)+p(2,1)+p(2,2)\\\\=0.06+0.14+0.3\\\\=0.5[/tex]

The possible Y values are in the figure 0,1,2

[tex]p_y(0)=p(0,0)+p(1,0)+p(2,0)\\\\=0.1+0.08+0.06\\\\=0.24\\\\p_y(1)=p(0,1)+p(1,1)+p(2,1)\\\\=0.04+0.2+0.14\\\\=0.38\\\\p_y(2)=p(0,2)+p(1,2)+p(2,2)\\\\=0.02+0.06+0.3\\\\=0.38[/tex]

So the probability of x ≤ 1 is

[tex]p(x\leq 1)=p_x(0)+p_x(1)\\\\=0.34+0.16\\\\=0.50[/tex]

e) From the table

[tex]p_x(x=1,y=1)=p(1,1)\\\\=0.2\\\\p_x(1)=0.34\\\\p_y(1)=0.38[/tex]

we multiply both together

0.34  x 0.38

=0.1292

Therefore p(1,1) is not equal px(1), py(1)

Hence x and y are not independent it is not equal

Answer:

The type of observational study describer here is retrospective study.

Step-by-step explanation:

The complete question is:

Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Determine what type of observational study is described. Explain.

Solution:

In retrospective study design, the concerned outcome has previously taken place in each participant by the phase he or she is signed up for the study, and the information are gathered either from past data or by requesting the participants to recall exposures.

It is also known as a historic cohort study.

A retrospective study is completed as posterior experiment, using data on events that have already taken place in the history. In most cases some or most of the data has already been collected and stowed in the archive.

In the provided scenario, the researcher collect the past data for the exposure to sunshine over the previous twenty years for 250 women. And estimated the  total number of hours that each woman had been exposed to sunshine in the previous twenty years.

Then the researcher compares the amount of exposure to sunshine for the two groups.

Thus, the type of observational study describer here is retrospective study.

Answer:

its 2pi/3

Step-by-step explanation:

because the full radian measure of a circle is 2pi radians, the smaller circle is a third of the size of the larger one. Multiply straight across for (2pi/1)(1/3)  

The circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (radius)[/tex]

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (OB)[/tex]

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (x)[/tex]

Circumference of the Larger circle = 3 x Circumference of the smaller circle

[tex]2\times \pi \times x = 3\times Circumference\ of\ the\ smaller\ circle\\\\3\times Circumference\ of\ the\ smaller\ circle = 2\times \pi \times x \\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi \times x }{3}\\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi}{3}( x )\ units[/tex]

Hence, the circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].

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Answer:

It is only (5,24).

Step-by-step explanation:

You are correct.

Sometimes, check all options means there could be just one option.

Answer:

670 Cans of fruit will be left

Step-by-step explanation:

First you multiply 155 by the 6 weeks.

That equals 930 and then you subtract 930 from 1,600 and that gives you 670.

There are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week.

First term a = 1600

Common difference d = -155

After 6 weeks means on week 7.

n = 7

a(7) = 1600 + (7-1)(-155)

a(7) = 1600 - 930

a(7) = 670

Thus, there are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.

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Answer: 38 23/24

Step-by-step explanation:

Turn the mixed numbers into improper fractions

5 * 3 = 15

15 + 2 = 17

17/3

————————

6 * 8 = 48

48 + 7 = 55

55/8

————————

Now multiply the improper fractions

17/3 * 55/8

17 * 55 = 935

3 * 8 = 24

Divide 935 by 24 to get the answer as a mixed number.

935 / 24 = 38.95833

0.95833/1 = 23/24

935/24 as a mixed number is 38 23/24

Answer: 119 / 4

Step-by-step explanation:

5 2/3 x 6 7/8

= 17/3 x 6 x 7/8

= 17 x 2 x 7/8

= 17 x 2 x 7/8

= 17 x 7/4

= 119 / 4

Answer:

it it the highest or lowest point of a parabola

Answer:

[tex]-4x+28[/tex]

Step-by-step explanation:

[tex]18-2(x+x-5)[/tex]

[tex]18+(-2)(x)+(-2)(x)+(-2)(-5)[/tex]

[tex]18+-2x+-2x+10[/tex]

[tex]-2x-2x+10+18[/tex]

[tex]=-4x+28[/tex]

Answer:

1.36364

Step-by-step explanation:

I calculated the solution on a calculator

So the answer to 1 d.p is 1.4

Answer:

ge

Step-by-step explanation:

ge

Answer:

x<16

Step-by-step explanation:

number n

eight less than four times a number ... 4 x n - 8

is less than 56 ... < 56

4 x n - 8 < 56

4 x n < 56 + 8

4 x n < 64/4

n < 64 / 4

n < 16

Answer:

Step-by-step explanation:

Let the number be x

Four times the number :  4x

Eight less than four times a number: 4x - 8

4x - 8 < 56

Now add 8 to both sides,

4x < 56+8

4x < 64

Divide both sides by 4,

x < 64/4

x < 16

Possible values of number = Value less than 16

Answer:

-3

Step-by-step explanation:

a-2+3=-2

-3 -3

a-2=-5

+2 +2

a=-3

// have a great day //

Answer:

a = -3

Step-by-step explanation:

a - 2 + 3 = -2

Add like terms.

a + 1 = -2

Subtract 1 on both sides.

a = -2 - 1

a = -3

The value of a in the equation is -3.

Answer:

63 points

Step-by-step explanation:

63 points is the lowest score having 6 as "leaf" and 3 as "stem"

Answer:

63 points

Step-by-step explanation:

The lowest score is 63 with a stem of 6 and leaf of 3.