The value of local maximum and local minimum for the function f(x) = x^2/(x -1 ) is equal to f(0) = 0 at x = 0 and f(2) = 4 at x = 4 respectively.
Local maximum and minimum values of the function
f(x) = x^2 / (x - 1),
Use both the first and second derivative tests.
First, let's find the critical points of the function,
By setting its derivative equal to zero and solving for x,
f'(x) = [2x(x - 1) - x^2] / (x - 1)^2
⇒ [2x(x - 1) - x^2] / (x - 1)^2 = 0
Simplifying this expression, we get,
x(x - 2) = 0
This gives us two critical points,
x = 0 and x = 2.
These critical points correspond to local maxima, local minima, or neither.
Use the second derivative test,
f''(x) = [2(x - 1)^2 - 2x(x - 1) + 2x^2] / (x - 1)^3
At x = 0, we have,
f''(0) = 2 / (-1)^3
= -2
Since the second derivative is negative at x = 0, this critical point corresponds to a local maximum.
f(0) = 0^2/ (0 -1 )
= 0
At x = 2, we have,
f''(2) = 2 / 1^3
= 2
Since the second derivative is positive at x = 2, this critical point corresponds to a local minimum.
f(2) = 2^2/ (2 - 1)
= 4
Therefore, at x = 0, the local maximum value is f(0) = 0, and at x = 2, the local minimum value is f(2) = 4.
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How many beats are in each of these measures?
תחנת J
A3
B. 2
) c. 4
D. 6
Answer:
Step-by-step explanation:
2
can you help me to solve this question?
The slope of tangent line is, m= [tex]-\frac{1}{14}[/tex]
Equation of tangent line, for m= [tex]-\frac{1}{14}[/tex] and b= [tex]\frac{53}{7}[/tex] is, 14y = -x + 106
Define the term slope of line?The slope of a line is a measure of how steeply it rises or falls as it moves horizontally. It is calculated by dividing the change in the vertical coordinate by the change in the horizontal coordinate between two points on the line.
Slope of tangent, m = [tex]\frac{dy}{dx}[/tex]
f(x) = y = [tex]\sqrt{57-x}[/tex]
y = [tex](57-x)^{\frac{1}{2}}[/tex]
Differentiate the above equation y with respect to x.
[tex]\frac{dy}{dx} = \frac{1}{2} * (57-x)^{1-\frac{1}{2} }* (-1)[/tex]
[tex]\frac{dy}{dx} = -\frac{1}{2} * (57-x)^{-\frac{1}{2} }[/tex]
[tex]\frac{dy}{dx} = -\frac{1}{2\sqrt{57-x} }[/tex]
Therefore, the slope (m) of tangent line f(x) at point (8, 7) is,
[tex]\frac{dy}{dx} | _{(8, 7)} = -\frac{1}{2\sqrt{57-8} } = - \frac{1}{14}[/tex]
Equation of tangent line f(x) at point (8, 7) is,
y = mx + b
7 = [tex]-\frac{1}{14}[/tex] × 8 + b
b = [tex]\frac{53}{7}[/tex]
So, Equation is, y = [tex]-\frac{1}{14}x + \frac{53}{7}[/tex]
Therefore, 14y = -x + 106
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Question 1 of 20
What is the solution to the following inequality?
Is this figure a polygon dont answer if you don’t know the answer
Polygon - a plane figure with at least three straight sides and angles, and typically five or more.
Answer:
No
Step-by-step explanation:
Since a polygon has straight sides, with 3 or more, it cannot be a polygon since one side is curved.
The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5) calculate the corresponding z-scores for the following 6 American’s weekly beer intake.
The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
1. 5 beers per week: z-score = -1
2. 8 beers per week: z-score = +1
3. 10 beers per week: z-score = +2
4. 4 beers per week: z-score = -2
5. 6 beers per week: z-score = -0.5
6. 12 beers per week: z-score = +3
To calculate a z-score, we need to know the mean (μ) and standard deviation (σ) of the population. In the given problem, the mean is 7 beers per week, and the standard deviation is 1.5.
A z-score is the number of standard deviations away from the mean. Therefore, to calculate the z-scores, we subtract the mean from the given data point and divide by the standard deviation.
For example, for 5 beers per week, the z-score is (-1). This is calculated by subtracting the mean (7) from the data point (5) and dividing by the standard deviation (1.5). Therefore, (5-7)/1.5 = -1.
Similarly, the z-score for 8 beers per week is (+1). This is calculated by (8-7)/1.5 = +1. The z-score for 10 beers per week is (+2). This is calculated by (10-7)/1.5 = +2. The z-score for 4 beers per week is (-2). This is calculated by (4-7)/1.5 = -2. The z-score for 6 beers per week is (-0.5). This is calculated by (6-7)/1.5 = -0.5.The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
the complete question is :
The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5), calculate the corresponding z-scores for the following 6 Americans’ weekly beer intake:
a) Bob drinks 9 beers per week
b) Sarah drinks 6 beers per week
c) John drinks 4 beers per week
d) Emily drinks 8 beers per week
e) Michael drinks 10 beers per week
f) Rachel drinks 5 beers per week
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1. Investigations have revealed that 60% of the road accident deaths occurred on highways
and 40% on rural roads. If out of a sample 100 accidents investigated, the number of accidents
on highways was 80 and rural roads 20. Determine the number of accidents on highways and
rural roads after 4 years.
Answer: To determine the number of accidents on highways and rural roads after 4 years, we need more information. The given data only tells us about the distribution of accidents in a sample of 100 accidents investigated, but it doesn't provide any information about the rate of change or trend of accidents over time.
Assuming that the rate of accidents on highways and rural roads remains the same, we can make a projection based on the given data. If 60% of the road accident deaths occur on highways and 40% on rural roads, we can estimate the number of accidents on highways and rural roads after 4 years as follows:
Number of accidents on highways after 4 years = 80 * (100/60) = 133.33 (rounded to 133)
Number of accidents on rural roads after 4 years = 20 * (100/40) = 50
Note that this is only a projection based on the assumption that the rate of accidents remains the same. In reality, the number of accidents can vary depending on various factors such as changes in traffic volume, weather conditions, road infrastructure, and driver behavior, among others. Therefore, this projection should be taken as an estimate and not as an accurate prediction.
Step-by-step explanation:
A mark on the side of a pier shows the
water is 4 feet deep. At high tide, the
water level rises 21 feet. About how deep
is the water at high tide?
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble?
A) 11
B) 33
C) 32
D) 22
Answer:
B) 33 times.
Step-by-step explanation:
The total amount of pebbles is 50. There is 22 yellow pebbles.
Note that 3/2 * 50 is 75. 3/2 * 22 = 33.
He should expect to choose a yellow pebble B) 33 times.
HELP ASAP! 10 POINTS! PLEASE HELP ME FIND THE AREA AND THE PERIMETER!!!!
The area of the composite shape using the area formula for the different shapes is 460.48ft².
What are composite shapes?The area of composite shapes refers to the space occupied by any composite shape. A composite shape is a shape that is made by connecting a few polygons to form the required shape.
These figures or shapes can be built from a wide range of shapes, such as triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.
Now in the question,
First let us find the area of the semi-circle.
Area of semi-circle = πr²/2
= [3.14 × (16/2) ²]/2
= (3.14 × 8²)/2
= 200.96/2
= 100.48ft²
Now coming to the rectangle,
area of the rectangle = l × b
= 20 × 15
= 300ft²
Now for calculating the area of the triangle,
area = 1/2 × b × h
= 1/2 × 12 × 10
= 60ft²
Therefore, the area of the total figure = 100.48 + 300 + 60 = 460.48ft².
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I will mark you brainiest!
Perpendicular lines form acute angles.
A) True
B) False
Answer:
B) False
Step-by-step explanation:
Perpendicular lines form right angles. It does not form acute angles.
find the linear approximation of f (x )equals fifth root of x when x equals 32.
This is the linear approximation of f(x) = 5th root of x when x = 32. To find the linear approximation of f(x) = 5th root of x when x = 32, we need to first find the equation of the tangent line at x = 32.
The derivative of f(x) = 5th root of x is: f'(x) = 1/(5x⁴/⁵)
So, at x = 32, we have f(32) = 2 and f'(32) = 1/80.
Using the point-slope form of a line, we can write the equation of the tangent line as:
y - 2 = (1/80)(x - 32)
Simplifying this equation, we get:
y = (1/80)x + (79/40)
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What percent of 2160 is 270?
The percent of the number 2160 which is 270 is 12.5%.
Given a number 2160.
It is required to find the percent of this number which is 270.
Let x be the percent of 2160 which is 270.
Then, this can be written as:
2160 × (x/100) = 270
2160 × x = 270 × 100
2160 × x = 27000
x = 27000 / 2160
= 12.5
Hence the required percentage is 12.5%.
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A physical inventory of Liverpool Company taken at December 31 reveals the following.
Per Unit
Item Units Cost Market
Car audio equipment
Speakers 350 $ 105 $ 113
Stereos 265 126 116
Amplifiers 331 101 110
Subwoofers 209 67 57
Security equipment
Alarms 485 165 155
Locks 296 108 98
Cameras 217 327 337
Binocular equipment
Tripods 190 89 99
Stabilizers 175 110 120
Required:
1. Calculate the lower of cost or market for the inventory applied separately to each item.
2. If the market amount is less than the recorded cost of the inventory, then record the LCM adjustment to the Merchandise Inventory account.
The net realizable value οf the inventοry is the anticipated sale price in the nοrmal cοurse οf business less the prοjected cοsts fοr cοmpletiοn, destructiοn, and transpοrtatiοn after the LCM adjustment has been made.
What dοes a math's unit mean?The rightmοst place in an integer οr the number οne can be cοnsidered a unit in mathematics. The unit number inside the number 6713 in this case is 3. The standard measuring units can alsο be referred tο as a unit.
1. We must evaluate the price per piece and selling price per unit and select the lesser οf the twο in οrder tο get the lοwer οf price οr marketplace (LCM) fοr each item. The calculatiοns lοοk like this:
Speakers: LCM = min($105, $113) = $105 per unit
Stereοs: LCM = min($116, $126) = $116 per unit
Amplifiers: LCM = min($101, $110) = $101 per unit
Subwοοfers: LCM = min($57, $67) = $57 per unit
Alarms: LCM = min($155, $165) = $155 per unit
Lοcks: LCM = min($98, $108) = $98 per unit
Cameras: LCM = min($327, $337) = $327 per unit
Tripοds: LCM = min($89, $99) = $89 per unit
Stabilizers: LCM = min($110, $120) = $110 per unit
2. We must evaluate the entire cοst οf inventοry as well as the tοtal selling price οf inventοry in οrder tο determine whether an LCM adjustment is required. We must change the value οf the inventοry tο reflect the lesser οf the cοst οr market if indeed the market value falls shοrt οf the cοst. The calculatiοns lοοk like this:
Tοtal cοst οf inventοry = (350 x $105) + (265 x $126) + (331 x $101) + (209 x $67) + (485 x $165) + (296 x $108) + (217 x $327) + (190 x $89) + (175 x $110)
= $70,657
Tοtal market value οf inventοry = (350 x $113) + (265 x $116) + (331 x $110) + (209 x $57) + (485 x $155) + (296 x $98) + (217 x $327) + (190 x $99) + (175 x $110)
= $70,273
We must make an LCM mοdificatiοn tο the Merchandise Accοunting system because the market price is lοwer than the cοst. The distinctiοn amοng the tοtal cοst and the tοtal market value is the adjustment amοunt, which is:
$70,657 - $70,273 = $384
The LCM adjustment's jοurnal entry is as fοllοws:
Merchandise Inventοry 384
LCM Adjustment 384
The LCM adjustment reduces the inventοry value tο its net realizable value, which is the estimated selling price in the οrdinary cοurse οf business, less the estimated cοsts οf cοmpletiοn, dispοsal, and transpοrtatiοn.
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find the center and radius of the circle whose equation is x^2+y^2+4x+12y =-15
Answer:
center: (-2,-6)
radius: 5
Step-by-step explanation:
You have to complete the square again. This time the x's and the y's both need work. So first, organize. Put the x's together and put the y's together. Leave a little room to work. Take the x term and the y term and CUT them in HALF and Square 'em. That is what you add in to complete the square. Add the same thing to both sides.
see image.
Determine the equation of the ellipse with foci (2,4) and (2,-8), and co-vertices (10,-2) and (-6,-2).
Answer:
To find the equation of the ellipse, we need to use the standard form of the equation for an ellipse centered at the origin:
((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1
where (h, k) is the center of the ellipse, a is the distance from the center to the end of the major axis, and b is the distance from the center to the end of the minor axis.
Step 1: Find the center of the ellipse
The center of the ellipse is halfway between the two foci:
center = ((2+2)/2, (4-8)/2) = (2,-2)
Step 2: Find the length of the major axis
The distance between the two foci is 12 units (the absolute value of the difference in the y-coordinates):
c = 12
The length of the minor axis is the distance between the two co-vertices, which is 16 units:
2b = 16
b = 8
To find the length of the major axis, we use the relationship between a, b, and c in an ellipse:
c^2 = a^2 - b^2
a^2 = b^2 + c^2
a^2 = 8^2 + 12^2
a^2 = 256
a = 16
Step 3: Plug in the values to the standard form of the equation
((x-2)^2)/16^2 + ((y+2)^2)/8^2 = 1
Therefore, the equation of the ellipse is:
((x-2)^2)/256 + ((y+2)^2)/64 = 1
Executive Bonuses A random sample of bonuses (in millions of dollars) paid by large companies to their executives is shown. Find the mean and modal class for the data. Class boundaries Frequency 0.5-3.5 3.5-6.5 6.5-9.5 9.5-12.5 12.5-15.5 11 12 4 2 1
The mean bonus paid by large companies to their executives is $5 million and the modal class is 3.5-6.5.
How to calculate the mean and the modal class for the dataTo find the mean, we need to find the midpoint of each class and multiply it by the frequency, then add up all of these values and divide by the total frequency:
Class boundaries Midpoint Frequency Midpoint x Frequency
0.5-3.5 2 11 22
3.5-6.5 5 12 60
6.5-9.5 8 4 32
9.5-12.5 11 2 22
12.5-15.5 14 1 14
Total 150
Mean = (Midpoint x Frequency) / Total Frequency
Mean = 150 / 30
Mean = 5
Therefore, the mean bonus paid by large companies to their executives is $5 million.
To find the modal class, we need to look for the class with the highest frequency. In this case, the class with the highest frequency is 3.5-6.5, with a frequency of 12. Therefore, the modal class is 3.5-6.5.
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Would appreciate any help
Answer:
Step-by-step explanation:
I don’t know how to do that it
Find the volume of a frustum of a right circular cone with height 30, lower base radius 21 and top radius 11. Volume =?????
Please Show your steps!!!!!!!
The volume of the frustum of right circular cone = 7730 cube
The volume of the frustum of the right circular cone:
The formula for the Volume of Frustum of Cone (V)=[tex]\frac{1}{3} \pi H (R^2+r^2+Rr )[/tex]
where,
H = Height of frustum
R = Radius of lower base
r = Radius of top base
According to given question,
Height of frustum(H) = 30 units
Radius of lower base(R) = 21 units
Radius of top base (r) = 11 units
Substituting all the given values in the formula of volume of the frustum of the cone we will get,
The volume of a frustum of a right circular cone(V) =[tex]\frac{1}{3} \pi H (R^2+r^2+Rr )[/tex]
[tex]=\frac{1}{3}*30(21^2+11^2+21*11)\\\\=10*(441+121+211)\\=10*(773)\\=7730 unit^3[/tex]
The volume of the frustum of the right circular cone = 271.22
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6TH GRADE MATH, SOMEONE PLS FIND THE SLOPE IN THIS EQUATION TY
Answer:
slope is -2
Step-by-step explanation:
100% correct :)
The slope is what is next to the x in y=mx+b
so if it was like this y=3x + 2
3 is the slope
hope that makes sense
so you need to select 6 varieties without replacement from 10 varieties: c(10,6) b) if there are at least two varieties.
The number of ways to select half dozen donuts from 10 varieties is 210 ways.
The total number of varieties of donuts is = 10 varieties;
we have to select half a dozen donuts, which means we have to select 6 varieties of donuts from the total of 10 varieties of donuts.
Using formula of Combination, we can compute the number of ways to choose a half dozen donuts from 10 varieties:
which is written as :
⇒ ¹⁰C₆ = 10! / (6!×4!) = (10×9×8×7)/(4×3×2×1) = 210,
Therefore, there are total of 210 ways in which half dozen donuts can be selected from 10 varieties, where no two donuts are of the same variety.
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The given question is incomplete, the complete question is
How many ways are there to choose a half dozen donuts from 10 varieties, If there are no two donuts of the same variety (means you need to select 6 varieties without replacement from 10)?
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a)
The bases for the row space and null space of A, we put A into reduced row echelon form and solve for the null space. The dot product of basis vectors shows they are orthogonal.
To find the bases for the row space and null space of A, we perform row operations on A until it is in reduced row echelon form:
[ 1 -1 3 | 5 ] [ 1 -1 3 | 5 ]
[ 2 1 -5 | -9 ] -> [ 0 3 -11 | -19]
[-1 -1 2 | 2 ] [ 0 0 0 | 0 ]
[ 1 1 -1 | -1 ] [ 0 0 0 | 0 ]
The reduced row echelon form of A tells us that there are two pivot columns, corresponding to the first and second columns of A. The third and fourth columns are free variables. Therefore, a basis for the row space of A is given by the first two rows of the reduced row echelon form of A:
[ 1 -1 3 | 5 ]
[ 0 3 -11 | -19]
To find a basis for the null space of A, we solve the system Ax = 0. Since the third and fourth columns of A are free variables, we can express the solution in terms of those variables. Setting s = column 3 and t = column 4, we have:
x1 - x2 + 3x3 + 5x4 = 0
2x1 + x2 - 5x3 - 9x4 = 0
-x1 - x2 + 2x3 + 2x4 = 0
x1 + x2 - x3 - x4 = 0
Solving for x1, x2, x3, and x4 in terms of s and t, we get:
x1 = -3s - 5t
x2 = s + 2t
x3 = s
x4 = t
Therefore, a basis for the null space of A is given by the vectors:
[-3 1 1 0]
[ 5 2 0 1]
To verify that every vector in the row space of A is orthogonal to every vector in the null space of A, we compute the dot product of each basis vector for the row space with each basis vector for the null space:
[ 1 -1 3 | 5 ] dot [-3 1 1 0] = 0
[ 1 -1 3 | 5 ] dot [ 5 2 0 1] = 0
[ 0 3 -11 | -19] dot [-3 1 1 0] = 0
[ 0 3 -11 | -19] dot [ 5 2 0 1] = 0
Since all dot products are equal to zero, we have verified that every vector in the row space of A is orthogonal to every vector in the null space of A.
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_____The given question is incomplete, the complete question is given below:
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a). a = [ 1 -1 3 5 2 1 0 1 -2 -1 -1 1]
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.08°C and 1.68°C.
The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
What are the four types of probability?Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.
The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.
To solve this problem, we must use the z-score formula to standardise the values:
z = (x - μ) / σ
where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.
The lower bound is -0.08°C:
z1 = (-0.08 - 0) / 1.00 = -0.08
1.68°C is the upper bound:
z2 = (1.68 - 0) / 1.00 = 1.68
We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.
The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:
P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854
As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
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44567/23467-456*2445+34566/33
Answer:
-32,723.92295785232
Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2
pls help me soon
Christine has a six-sided dice numbered from 1 to 6. She rolled it a total of 50 times. It landed on an odd number 21 times. a) Work out the relative frequency of the dice landing on an odd number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probablity of it landing on an odd number be? Give your answer as a decimal. c) Is the dice definitely biased or definetely not biased, or is it impossible to tell? Write a sentence to explain your answer.
A) Relative frequency is number of times an event happened over total number of events:
Answer is 21/50 = 0.42
B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50
C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.
Which graph represents the function f(x)=∣x+1∣−3?
By looking at the vertex of the graph, we can see that the fourth graph is the correct option.
Which graph represents the function f(x)=∣x+1∣−3?Here we want to see which one of the given graphs represents the given absolute value function.
Remember that for the absolute value function:
f(x) = |x - a| + b
Has a vertex at the point (a, b) and opens up.
Then in this particular case, with the function f(x)=∣x+1∣−3, the vertex will be at the point (-1, -3), so we just need to identify which one of the given graphs has that vertex, we can see that the correct option is the fourth option.
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Debra, Alan, and Shen have a total of 122 in their wallets. Alan has less than $7 Debra. She has 3 times what Alan has. How much do they have in their wallets?
Answer:
Debra has $10.50, Alan has $3.50, and Shen has $108.
Step-by-step explanation:
Set up a system of equations to represent the situation.
Let a represent Alan's money, d represent Debra's money, and s represent Shen's money.
1. a + d + s = 122
2. a = d - 7
3. d = 3a
Use equation's 1 and 2 alone to calculate a and d. Substitute Eq 3 into Eq 2 such that
a = 3a - 7
-2a = -7
a = $3.50
Use Alan's money to calculate Debra's money.
d = 3(3.5)
d = $10.50
Now use values of a and d to calulate Shen's money, given the total.
s + 3.5 + 10.5 = 122
s + 14 = 122
s = $108
So, Debra has $10.50, Alan has $3.50, and Shen has $108.
Please help me, can’t figure out which one is actually correct for Jackson
If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or phenomena. It is the measure of the likelihood or chance of an event or set of events occurring.
If Jackson does not take the final exam, the average of his three highest scores would be:
(72 + 73 + 70)/3 = 71.67.
If Jackson takes the final exam, there are two possibilities:
If Jackson scores lower than any of his previous exam scores, then his lowest score will be dropped, and his grade will be calculated based on his four highest scores, which would be:
(73 + 72 + 70 + X)/4.
where X is his score on the final exam. In this case, taking the final exam would not benefit Jackson, as his grade would be based on his three highest scores (72, 73, and 70) regardless of his performance on the final exam.
If Jackson scores higher than any of his previous exam scores, then his lowest score will be the lowest of his first four exams, and his grade will be calculated based on his four highest scores, which would be:
(73 + 72 + X1 + X2)/4.
Therefore, If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.
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An 8 foot long ladder is leaning against a wall. The top of the ladder is sliding down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall.
"The rate at which the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall is calculated to be 3.464 ft/s."
At a pace of 2 feet per second, the lower end of the ladder is being pulled away from the wall.
At a specific moment, when the lower end of the ladder is 4 feet from the wall, we should determine the rate at which the bottom of the ladder is lowering.
From the point t, the bottom of the ladder is x m, the top of the ladder is y m from the wall.
x² + y² = 64
Differentiating the given relationship with regard to t,
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
We need to find out dx/dt at x = 4.
dy/dt = -2
At x = 4, we have,
x² + y² = 64
16 + y² = 64
y² = 48
y = 4√3
Put in the known values to find out dx/dt,
x dx/dt + y dy/dt = 0
4 dx/dt + 4√3 (-2) = 0
4 dx/dt = 8√3
dx/dt = 2√3 = 3.464
Thus, the bottom of the ladder is calculated to be moving at the rate 3.464 ft/s.
The figure can be drawn as shown in the attachment.
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(b) do these data appear to follow a normal distribution? explain your reasoning using the graphs provided below.
a)There are total 25 data values so for the given data, 100% data lies within 3 standard deviations of mean.
b). Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities
a) Here we have μ=61.52 and [tex]\sigma=4.58[/tex]
The 68-95-99.7% rule states that 68% of the data must be within one standard deviation of the mean. Thus, 68% of the data should fall between 61.52-4.58=56.94 and 61.52+4.58=66.1. 19 data values in the provided data are within one standard deviation of the mean. As there are a total of 25 data points, 76% of the data for the given data (19/25)*100=1 standard deviation of the mean.
The 68-95-99.7% rule states that 95% of the data should be within two standard deviations of the mean.
Specifically, 95% of the data should fall between 61.52+2*4.58=70.68 and 61.52-2*4.58=52.36. 24 data values in the provided data are within two standard deviations of the mean.
As there are a total of 25 data points, (24/25)*100=96% of the data for the given data is contained within two standard deviations of the mean.
The 68-95-99.7% rule states that 99.7% of the data should be within three standard deviations of the mean.
It follows that 99.7% of the data should fall between 61.52+3*4.58=75.26 and 61.52-3*4.58=47.78. 25 data values in the provided data are within three standard deviations of the mean.
As there are a total of 25 data points, (25/25)*100=100% of the data falls within three standard deviations of the mean for the given data.
Although not exactly, it appears that the distribution of height follows a normal distribution.
b) Both graphs demonstrate that the height distribution is essentially normal. Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities.
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The complete question is:
Heights of female college students. Below are heights of 25 female college students.
(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.
(b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.