-11 <= 2x + 5 < 15
This means that 2x+5 is less than 15 and greater than or equal to -11
The last answer choice is correct.
5a) Determine the measure of each unknown angle
Answer:
Step-by-step explanation:
25, i think
What is the numbers of π
Answer:
3.141592653589793238462643383279502884197169399375105820974944592307816406286
Step-by-step explanation:
Point H is on line segment GI. Given GI = 3x, HI = 2, and
GH = 5x - 6, determine the numerical length of GH
Answer:
GH = 4
Step-by-step explanation:
given H is on the line GI , then
GH + HI = GI , that is
5x - 6 + 2 = 3x ( subtract 3x from both sides )
2x - 4 = 0 ( add 4 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Then
GH = 5x - 6 = 5(2) - 6 = 10 - 6 = 4
halfway through the baseball season, a player has stolen 33 bases out of 42 tries. how many consecutive bases must the player successfully steal in order to raise his steal percentage to 85%?
For the player to increase his base-steal percentage to 85%, he must successfully steal 18 consecutive bases.
The player must successfully steal x successive bases, which we'll represent as a number. Then, we can construct the following equation and solve it for x:
(33 + x) / (42 + x) = 0.85
The player must reach a new steal percentage of 85%, which is represented by this equation. By adding (42 + x) to both sides, we can get a solution for x:
33 + x = 0.85(42 + x)
By enlarging the right side, we obtain:
33 + x = 35.7 + 0.85x
When we take 0.85x out on both sides, we get:
0.15x = 2.7
When we multiply both sides by 0.15, we get:
x = 18
Hence, for the player to increase his base-steal percentage to 85%, he must successfully steal 18 consecutive bases.
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I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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Help!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
\(Slope (m) = -\frac{2}{3}\)
Step-by-step explanation:
To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.
Thus, on the line, let's pick 2 points as our coordinate pairs at:
When x = -6, y = 5 => (-6, 5), and
When x = 3, y = -1 => (3, -1)
Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)
\( Slope (m) = \frac{y2 - y1}{x2 - x1} \)
\( Slope (m) = \frac{-1 - 5}{3 - (-6)} \)
\( Slope (m) = \frac{-1 - 5}{3 + 6} \)
\( Slope (m) = \frac{-6}{9} \)
\(Slope (m) = -\frac{2}{3}\)
HELP ME WITH LINEAR RELATIONSHIPS MATH PLEASE, THANK YOUUU !!
Answer:
find the area
Step-by-step explanation:
25+10=35 so the answer to the other side is i think you devide 35 by 5 which is 7 i think the answer is 7
Answer:
2
Step-by-step explanation:
just set it up like a fraction and equal them to each other with 5 over x and 25 over 10. then solve for x
What is y? make sure to show all your work for full points
PLEASE ANSWER THIS QUESTION FAST MY TEST IS GOING I WILL MARK YOU THE BRAINLIEST PLEASE ANSWER FAST ITS URGENT....
Answer:
I think C 130 probably wrong
Answer:
130 degrees
Step-by-step explanation:
Since there are vertical angles 2x and 3x-50 are the same. So you would do 2x=3x-50. The picture below shows how I got x=50. SO now you know x=50, it's important to remember that line AC equals 180 degrees. So what you nees to do is 180-50 to get what y equals. y should equal 130 degrees.
Can you use a right triangle to represent the distance between any two points on the coordinate plane?.
Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.
We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:
( 3, 4 ) and ( − 2, 1 )
We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.
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2. A parallelogram must be a rhombus when its (2 pts)
(1) diagonals are perpendicular
(2) diagonals are congruent
(3) opposite sides are parallel
(4) opposite sides are congruent
A parallelogram must be a rhombus when its diagonals are perpendicular.
What is a rhombus?A rhombus is a quadrilateral that has all its four sides equal in length. The diagonals of the rhombus bisect each other at a right angle. Also, the opposite angles of a rhombus are equal in measure and opposite sides are parallel to each other.
Given that, a parallelogram is a rhombus,
According to the definition of a rhombus, we know that, The diagonals of the rhombus bisect each other at a right angle.
Hence, the true statement is A parallelogram must be a rhombus when its diagonals are perpendicular.
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Solve the formula a(m+r) -t=s for a.
9514 1404 393
Answer:
a = (s +t)/(m +r)
Step-by-step explanation:
Add t, then divide by the coefficient of 'a'.
\(a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}\)
Function A is represented by the equation y = 2x+5.
Function B is a linear function that goes through the points shown in the
table.
X 1 3 4 6
y -1 3 5 9
Which statement correctly compares the rates of change of the two
functions?
A. The rate of change of function A is 5.
The rate of change of function B is 4.
B. The rate of change of function A is 2.
The rate of change of function B is 2.
C. The rate of change of function A is 2.
The rate of change of function B is 4.
D. The rate of change of function A is 5.
The rate of change of function B is 2.
Answer:
B
Step-by-step explanation:
rate of function A: 2 (coefficient for x)
rate of function B: 2, because an increment of 1 in x (e.g. 3 to 4) yields increment of 2 in y (3 to 5)
anyone please appreciate yall x
Answer:
h = 2.5 cm
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = Ah ( A is the area of the triangular end, h is the length of prism )
Here V = 35 and h = 7, thus
7A = 35 ( divide both sides by 7 )
A = 5 cm²
Thus
A = \(\frac{1}{2}\) × 4 × h = 5
2h = 5 ( divide both sides by 2 )
h = 2.5 cm
an led light bulb is 40% efficient, compared to an incandescent, which is 5% efficient. what exactly do these numbers mean?
An LED light bulb is 40% efficient, compared to an incandescent, which is 5% efficient which means that an LED light bulb will convert 40% of the energy used into visible light, while an incandescent light bulb will only convert 5% of the energy used into visible light.
The other 95% of the energy used by an incandescent bulb is lost as heat, making it less efficient. LEDs are much more energy efficient than incandescent bulbs. LEDs are able to produce the same amount of light as an incandescent bulb with only a fraction of the energy. This is because LEDs emit light in a narrow spectrum which reduces energy loss due to the amount of light that is not visible to the human eye. In addition, LEDs do not contain filaments that require power to heat up, meaning that much less energy is wasted as heat.
LEDs also have a longer lifespan than incandescent bulbs. This is due to the fact that LEDs have no filament to burn out, meaning they can last up to 50,000 hours or more. On the other hand, an incandescent bulb typically has a lifespan of around 1,000 hours. This means that an LED light bulb can potentially last up to 50 times longer than an incandescent bulb.
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: Question 2 Candy Chemical Berhad is a manufacturer of a chemical solution for industrial purposes. The product is called Oxychemical. The following information relates to the operation of Candy Chemical Berhad 0 Budgeted production and sales units are 120,000 can of Oxychemical per annum () A standard can of an Oxychemical consists of the following costs Direct material Direct labour Variable overhead Fixed overhead 12 litres at RM15 per tre 4 hours at RM12 per hour 4 hours at RM16 per hour RM10 per hour () All overheads are absorbed based on direct labour hours. (iv) The standard selling price per can for Oxychemical is RM450. (v) Actual results for the manufacture and sales of Oxychemical for the month of December 2021 were as follows: Sales 12,000 cans at RM430 per can 13,000 cans Production Direct material 160,000 litres at RM14 per litre Direct labour worked and 55,000 hours at RM12.50 per hour paid Variable overhead RM828,000 Fixed overhead RM440,000 (vi) There were no opening inventories of finished goods Required to calculate the following variances, indicating whether each is favourable (F) or unfavourable (UF) (a) Direct material price. (3 marks) (b) Direct material usage. (3 marks) (c) Direct labour rate. (3 marks) (d) Direct labour efficiency (3 marks) (0) (3 marks) (1) Fixed overhead efficiency (3 marks) (9) Fixed overhead expenditure. (3 marks) (h) Briefly explain ONE (1) possible cause for favourable in direct labour rate and efficiency variances (4 marks) [25 Mark] Variable overhead expenditure
To calculate the variances, we need to compare the actual costs and quantities with the standard costs and quantities. Let's calculate each variance step by step:
(a) Direct material price variance:
Actual cost of direct material = 160,000 litres x RM14/litre = RM2,240,000
Standard cost of direct material = 160,000 litres x RM15/litre = RM2,400,000
Direct material price variance = Actual cost - Standard cost
= RM2,240,000 - RM2,400,000
= -RM160,000 (unfavourable)
(b) Direct material usage variance:
Actual usage of direct material = 160,000 litres
Standard usage of direct material = 120,000 cans x 12 litres/can = 1,440,000 litres
Direct material usage variance = Standard cost - Actual cost
= RM2,400,000 - RM2,240,000
= RM160,000 (favourable)
(c) Direct labour rate variance:
Actual cost of direct labour = 55,000 hours x RM12.50/hour = RM687,500
Standard cost of direct labour = 120,000 cans x 4 hours/can x RM12/hour = RM5,760,000
Direct labour rate variance = Actual cost - Standard cost
= RM687,500 - RM5,760,000
= -RM5,072,500 (unfavourable)
(d) Direct labour efficiency variance:
Actual hours worked = 55,000 hours
Standard hours allowed = 120,000 cans x 4 hours/can = 480,000 hours
Direct labour efficiency variance = Standard cost - Actual cost
= RM5,760,000 - RM687,500
= RM5,072,500 (favourable)
(e) Variable overhead expenditure variance:
Actual variable overhead = RM828,000
Standard variable overhead = 55,000 hours x RM16/hour = RM880,000
Variable overhead expenditure variance = Actual variable overhead - Standard variable overhead
= RM828,000 - RM880,000
= -RM52,000 (unfavourable)
(f) Fixed overhead efficiency variance:
Actual hours worked = 55,000 hours
Standard hours allowed = 120,000 cans x 4 hours/can = 480,000 hours
Fixed overhead efficiency variance = Standard fixed overhead - Actual fixed overhead
= RM440,000 - (55,000 hours x RM10/hour)
= RM440,000 - RM550,000
= -RM110,000 (unfavourable)
(g) Fixed overhead expenditure variance:
Actual fixed overhead = RM440,000
Standard fixed overhead = 55,000 hours x RM10/hour = RM550,000
Fixed overhead expenditure variance = Actual fixed overhead - Standard fixed overhead
= RM440,000 - RM550,000
= -RM110,000 (unfavourable)
(h) Possible cause for favourable direct labour rate and efficiency variances:
One possible cause for favourable direct labour rate and efficiency variances could be improved productivity or efficiency in the production process. It could be due to employees working more effectively, reducing the time required to complete tasks and thus resulting in lower costs. Additionally, the company may have negotiated lower labour rates or implemented cost-saving measures in the labour component.
Note: It's important to consider the given units and values while performing the calculations, and to round the variances appropriately based on the given requirements.
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If 15 people start a race, in how many different ways can the top 3 finishers be determined?
Hence, 15 people out of 3 people can be chosen in 35 ways.
Combinations:It is a method that helps us to determine the number of possible ways an item can be chosen given that the order of selection does not matter. Hence we are free to select the items in any order.Combinations are often confused with permutations. Permutations are the number of ways the given items can be arranged. Here the order is important.The formula for combinations:If we have 'n' items and we are required to choose 'r' items, the number of ways in which it can be done is calculated as:\(^{n}C_{r} }\) = \(\frac{n!}{(n-r)!r!}\)It is given that:
The total number of people in a race, n = 15
The number of finalists, r = 3.
Hence, the number of ways in which 3 people out of the 15 people can be finishers are:
\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.
Hence, 15 people out of 3 people can be chosen in 35 ways.
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f(x,y)=x³-12x+y³ +3y²-9y Ans: Max (-2,-3); Saddle point (2,-3) and (-2,1); Min (2,1)
The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).
To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.
Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:
∂F/∂x = 3x² - 12
∂F/∂y = 3y² + 6y - 9
To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:
3x² - 12 = 0 --> x² = 4 --> x = ±2
3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1
Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).
To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:
∂²F/∂x² = 6x
∂²F/∂y² = 6y + 6
Now, let's evaluate the second partial derivatives at each critical point:
At (-2, -3):
∂²F/∂x² = 6(-2) = -12 (negative)
∂²F/∂y² = 6(-3) + 6 = -12 (negative)
Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.
At (2, -3):
∂²F/∂x² = 6(2) = 12 (positive)
∂²F/∂y² = 6(-3) + 6 = -12 (negative)
Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.
At (-2, 1):
∂²F/∂x² = 6(-2) = -12 (negative)
∂²F/∂y² = 6(1) + 6 = 12 (positive)
Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.
Therefore, the critical points are classified as follows:
Local maximum: (-2, -3)
Saddle points: (2, -3) and (-2, 1)
Local minimum: (2, 1)
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The angle of sector of cicle of diameter 8cm is 135 . find the area of the sector
Answer:
18.85 cm²
Step-by-step explanation:
The formula to find the area of a sector = θ/360 × πr²
We are given:
θ = Angle of the sector = 135°
Radius = Diameter/2
Diameter = 8cm , Hence Radius = 8cm/2 = 4cm
Hence,
Area of a sector = 135/360 × π ×(4cm)²
= 18.849555922 cm²
Approximately to the nearest hundredth = 18.85 cm²
Therefore, the area of the sector is 18.85 cm²
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is ________ .a. urinaryb. bladderc. fissured. supravesical
The correct option of the given question is option (c) fissure.
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.
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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.
In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.
The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.
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Biologists stocked a lake with 400 fish and estimated the carrying capacity ( the maximal population of the species that the lake can support) to be 5400. The number of fish tripled in the first year.
a. Assuming that the size of the fish population satisfies the logistic equation dP/dt=kP(1−Pk), determine the constant k and then solve the equation to find an expression for the size of the population after t years.
b. How long will it take the population to reach 2700?
It will take approximately 6.96 years for the fish population to reach 2700. The initial fish population (P0) is 400, and after the first year, the population triples, making it 1200. The carrying capacity (K) is 5400. We can use these values to find the constant k.
a. To determine the constant k, we can use the initial conditions given in the problem. In the first year, the number of fish tripled, which means the population increased by a factor of 3. Therefore, we can set P(1) = 3(400) = 1200. We also know that the carrying capacity is 5400, so we can set K = r(1-Pmax/P0) where r is the intrinsic growth rate and P0 is the initial population. Substituting in the values we get K = 0.372.
Now we can solve the logistic equation:
dP/dt = kP(1-P/5400)
Separating variables and integrating, we get:
ln|P/ (5400-P)| = 0.372t + C
where C is the constant of integration. To find C, we can use the initial condition that P(0) = 400:
ln|400/5000| = C
C = -4.605
Substituting C back into the equation, we get:
ln|P/ (5400-P)| = 0.372t - 4.605
Taking the exponential of both sides:
|P/ (5400-P)| = e^(0.372t-4.605)
Multiplying both sides by the denominator and simplifying:
P = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))
b. We want to find the time t when the population reaches 2700. So we can set P = 2700 and solve for t:
2700 = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))
Multiplying both sides by the denominator and simplifying:
2700 + 2700e^(0.372t-4.605) = 5400e^(0.372t-4.605)
Dividing both sides by 2700 and simplifying:
1 + e^(0.372t-4.605) = 2
Taking the natural logarithm of both sides:
0.372t - 4.605 = ln(1)
0.372t = 4.605
t = 12.4 years
Therefore, it will take approximately 12.4 years for the population to reach 2700.
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Fundamentally, pressure is defined as force per unit area. what is the source of the force in a gas sample?
The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container
What is the relationship between Force and Pressure?We are given that;
Pressure = Force /Area
Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.
Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container
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17. Macro mineral needed to build strong bones and teeth
A- iron
B -calcium
18. Bodies inability to break down lactose due to absence of the enzyme lactase
A- Lactose Intolerant
B- Celiac Disease
Please HELP ME ITS DUE LIKE RN
Answer:
b
Step-by-step explanation:
b because its just the only stand out answer
What do the results tell us about the population of all celebrities? O A. The results tell us that all celebrities are expected to have amounts of net worth approximately equal to one of the measures of center found in parts (a) through (d). O B. Apart from the fact that all other celebrities have amounts of net worth lower than those given, the results in parts (a), (b), and (d) do not given meaningful results.
The result of population of all celebrities tell us option (C)Apart rom the fact that all other celebrities have amounts of net worth lower than those given nothing meaningful can be known about the population
The results obtained from the given information only provide limited information about the net worth of a small sample of celebrities. The measures of center, such as mean, median, mode, and midrange, provide a snapshot of the sample data but cannot be used to draw conclusions about the entire population of all celebrities. For instance, the most common net worth found in part c only provides information about the net worth that is the most frequent in the given sample, but it does not give us an idea of the range of net worth that exists in the population of all celebrities.
To make any meaningful conclusions about the population of all celebrities, a more comprehensive and representative sample needs to be considered. A larger sample size would allow us to capture the diversity of net worth that exists among celebrities. Additionally, the sample should be chosen in such a way that it is representative of the entire population of all celebrities. Only then can we use statistical measures to provide reliable insights into the net worth of all celebrities.
Therefore, the correct option is (C) Apart rom the fact that all other celebrities have amounts of net worth lower than those given nothing meaningful can be known about the population
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The given question is incomplete, the complete question is:
What do the results tell us about the population of all celebrities'? 。A. The results tell us that all celebrities are expected to have amounts of net worth approximately equal to one of the measures of center found in parts a through d 。B. part o the act that all other celebrities have amounts of net worth lower than those given, the results in parts a), b), and d) do not given mean full results. However, the result from part c) shows that the most common celebrity О С Apart rom the fact that all other celebrities have amounts of net worth lower than those given nothing meaningful can be known about the pop a n. 。D. The results tell us that the most common colet rity net worth is the mode, but all other celo ritios are expected to have net worths approximat hy equal to the mean, median, or midrange
Can Someone help me please I don't understand
Answer: 55 Gallons.
Step-by-step explanation: you can trust me on this, and I promise it will be correct.
What is
7/4
written as a decimal?
Answer:
1.75
Step-by-step explanation:
a travel weekly international air transport association survey asked business travelers about the purpose for their most recent business trip. nineteen percent responded that it was for an internal company visit. suppose 950 business travelers are randomly selected. what is the probability that between 133 and 171 of the business travelers say that the reason for their most recent business trip was an internal company visit?
To solve this problem, we can use the binomial distribution formula, which calculates the probability of a certain number of successes (in this case, business travelers who say their reason for the trip was an internal company visit) out of a given number of trials (950 business travelers). The formula is:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
- P(x) is the probability of getting x successes
- n is the number of trials (950 business travelers)
- x is the number of successes we're interested in (between 133 and 171)
- p is the probability of success (19% or 0.19)
To find the probability that between 133 and 171 business travelers say their reason for the trip was an internal company visit, we need to calculate the sum of the probabilities of getting 133, 134, 135,..., 170, 171 successes. This can be quite tedious to do by hand, but fortunately, we can use a calculator or a statistical software program to do it for us.
Assuming that we use a calculator or software, we can find that the probability of getting between 133 and 171 business travelers who say their reason for the trip was an internal company visit is approximately 0.919. This means that out of three random paragraphs of this length, it's likely that one would show the probability of the business travelers who say their reason for the trip was an internal company visit to be between 133 and 171.
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The floor plan of a hoise is drawn at a scale of 1/4 in = 1 ft. The length of the house is in the floor plan is 15 1/2 inches. What is the actual length if the house?
Answer: 62 ft
Step-by-step explanation:
The scale shows that for every 1/4 inches on the paper, the distance of the actual house is 1 ft.
If the floor plan lists the length as 15 ¹/₂ inches therefore, the length in inches feet is:
= 15 ¹/₂ ÷ 1/4
= 31/2 ÷ 1/4
= 31/2 * 4/1
= 62 ft
When dividing by a fraction, you can multiply its inverse.
How to do This item ? help me please!!!!
Answer:
I don't know if this will be helpful but here,
Step-by-step explanation:
The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. An article presented the following summary data on stance duration (ms) for samples of both older and younger adults. Age Sample Size Sample Mean Sample SD Older 27 802 116 Younger 19 770 73 Assume that both stance duration distributions are normal.
The Confidence Interval is \(763.885\leq \mu\leq 840.115\) and the true average stance duration is not larger among elderly individuals than among younger individuals.
Given the sample size of the older, \(n_1\) = 27
The sample mean of the older, \(\bar x_1\) = 802
The sample Standard Deviation, \(s_1\) = 116
Here the population mean \(\mu\) is unknown.
So the confidence interval for true average (population mean) is given by \(\bar x_1-t_\frac{\alpha }{2} \frac{s_1}{\sqrt{n_1-1} } \leq \mu\leq \bar x_1+t_\frac{\alpha }{2} \frac{s_1}{\sqrt{n_1-1} }\)
Here \(t_\frac{\alpha }{2}\) can be found from the tables of Student's 't' distribution for \(\alpha =0.01\) ,the level of significance and m-1 = 26 degrees of freedom.
\(\alpha\) is taken as 0.01 since we will be finding a 99% confidence interval for the true average stance duration among elderly individuals.
So here the \(t_\frac{\alpha }{2}\) = 1.706
Hence the confidence interval will be
\(802-1.706 \times \frac{116}{\sqrt{26} }\leq \mu\leq 802+1.706 \times \frac{116}{\sqrt{26} }\)
That is, \(763.885\leq \mu\leq 840.115\) is the 99% confidence interval for true average stance duration among elderly individuals.
We will carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than among younger individuals.
Testing of hypothesis concerning the true average stance among elderly and younger individuals.
That is, \(H_0:\mu_1=\mu_2\)
against \(H_1:\mu_1 > \mu_2\) ,the alternative hypothesis.
where \(\mu_1\) is the true average for the older and \(\mu_2\) is the true average for the younger.
Here the significance level, \(\alpha =0.05\). Hence \(t_\alpha = 1.65\).
The test statistic is,
\(t=\frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }\)
i.e., \(t=\frac{802 - 770}{\sqrt{\frac{116^2}{27} +\frac{73^2}{19} } }\)
= 1.147
Here \(t < t_\alpha\) . So we cannot reject the null hypothesis \(H_0\).
Thus the true average stance duration is not larger among elderly individuals than among younger individuals.
Your question is incomplete. Here you can find the full question:
The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. An article presented the following summary data on stance duration (ms) for samples of both older and younger adults. Age Sample Size Sample Mean Sample SD Older 27 802 116 Younger 19 770 73 Assume that both stance duration distributions are normal.
a) Calculate and interpret a 99% Confidence interval for true average stance duration among elderly individuals.
b) Carry out a test hypothesis at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than among younger individuals.
Find out more about testing of hypothesis at https://brainly.com/question/14042255
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