The p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.
What is the p-value?
The p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.
(a) Hypotheses:
H1 : Best ski area is independent of the level of the skier
H2 : Best ski area is dependent on the level of the skier
(b) Expected counts:
Beginner Intermediate Advanced Total
Tahoe Observed 20 30 40 90
Expected 12.41 31.03 46.55 90.00
Utah Observed 10 30 60 100
Expected 13.79 34.48 51.72 100.00
Colorado Observed 10 40 50 100
Expected 13.79 34.48 51.72 100.00
Total Observed 40 100 150 290
Expected 40.00 100.00 150.00 290.00
(c)
All the expected counts are > 5, so we can apply the test
(d) Test statistic:
Square Contingency Table Test for Independence
Beginner Intermediate Advanced Total
Tahoe Observed 20 30 40 90
Expected 12.41 31.03 46.55 90.00
O - E 7.59 -1.03 -6.55 0.00
(O - E)² / E 4.64 0.03 0.92 5.59
Utah Observed 10 30 60 100
Expected 13.79 34.48 51.72 100.00
O - E -3.79 -4.48 8.28 0.00
(O - E)² / E 1.04 0.58 1.32 2.95
Colorado Observed 10 40 50 100
Expected 13.79 34.48 51.72 100.00
O - E -3.79 5.52 -1.72 0.00
(O - E)² / E 1.04 0.88 0.06 1.98
Total Observed 40 100 150 290
Expected 40.00 100.00 150.00 290.00
O - E 0.00 0.00 0.00 0.00
(O - E)² / E 6.72 1.50 2.30 10.53
10.53 chi-square
4 df
0.0324 p-value
x² = 10.53 and p-value = 0.0324
(e) Since the p-value (0.0324) < α (0.10), we reject H1. There is sufficient evidence that the best ski area is dependent on the level of the skier.
Hence, the p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.
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Q.7.
The table below shows the numbers of pages Lenny can read in certain amounts of time.
Lenny's Reading Rate
Time
(minutes)
60
90
135
Pages
Read
108
162
243
Based on the table, which equation can be used to determine the number of pages (p) Lenny
can read in t minutes?
A. p = 1.5t
B.
p = 1.8t
C.
t = 1.5p
D.
t = 1.8p
Based on the table, the equation that can be used to determine the number of pages (p) Lenny can read in t minutes is B. p = 1.8t.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
For this equation, the slope, unit rate, or pages per minute is the quotient of the total number of pages read and the total time (in minutes) used.
Equations are depicted using the equation symbol (=) to show that two or more mathematical expressions are equal to one another.
Lenny's Reading Rate
Time (minutes) Pages Read Pages per Minute
60 108 1.8 (108/60)
90 162 1.8 (162/90)
135 243 1.8 (243/135)
Thus, we can conclude that we can find the number of pages Lenny can read in t minutes using the equation provided by Option B.
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Answer:
p=1.8
Step-by-step explanation:
unit rate 108/60=1.8
Consider the following line integral. C xy dx + x2y3 dy, c is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).(a) evaluate the given line integral directly. 20 correct: your answer is correct. (b) evaluate the given line integral by using green's theorem.
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.
How is Green's theorem demonstrated?M(x, c) M(x, d) dx is equivalent to = b M(x, c) dx + M(x, d) dx. So, by demonstrating that the two sides of a rectangle are equal, we have established Green's Theorem. The sum of rectangles theorem. Since each region can be as nearly approximated by a sum of rectangles as desired, Green's Theorem must apply to all regions.
It looks like the integral is
[tex]\int\limits^0_c {xy} + x^{2} y^{3} \, dy[/tex]
Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}
Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem
Compute the double integral:
From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by
C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}
The line integral over C' is
[tex]\int\limits^1_0 {(256t^{5} }+1280t^{4}+ 2560t^{3} - 2564t^{2} + 1288t - 260) \, dt[/tex]
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.
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7. (01.05 LC)
If x³ = 64, what is the value of x? (5 points)
04
8
21
61
Answer:
4
Step-by-step explanation:
Solve for x over the real numbers:
x^3 = 64
Take cube roots of both sides:
Answer: x = 4
4^2 = 16
4^3 = 64
Write the equation of the line that passes through the points (9, 4) and (−6, −8).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
The desired equation is then y -4 = 12/15 (x -9)
What is equation of line?Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.where a ≠ 0 and b ≠ 0.
We need this line's equation in the point-slope form, y - k = m. (x - h).
The point (h, k) in the point-slope form shown above can be chosen at random from the two points (9, 4) and (-6, -8). In the above point slope form, the other point is thus denoted by (x, y):
Let (x, y) be and (h, k) be (9,4). (-6,-8). Consequently, y - k = m(x - h) becomes
-8-4 = m (-6-9), so that -12 = m(-15), and the slope is thus m = 12/15
The desired equation is then y -4 = 12/15 (x -9) (which is in point-slope form).
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Question 3 of 5
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
Let x represent the canoe's speed with no water current (in still water) and y represent the speed of the water current, in miles per hour. Then the situation can be represented by this system of equations:
x+y=7
x-y=1
Choose the two correct options.
A. The speed of the canoe in still water is 3 miles per hour.
B. The speed of the water current is 4 miles per hour.
C. The speed of the canoe in still water is 4 miles per hour.
D. The speed of the water current is 3 miles per hour.
Two correct options are option (C) The speed of the canoe in still water is 4 miles per hour and option (D) The speed of the water current is 3 miles per hour.
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
x is the Canoe's speed with no water current in miles per hour
y is the speed of the water current, in miles per hour
The equations are
x + y = 7
x - y = 1
Here we have to use the elimination method
Add both the equation
2x = 7 + 1
2x = 8
x = 8/2
x = 4
Then substitute the value of x in the first equation
4 + y = 7
y = 7 -4
y = 3
Therefore, the correct options are option (C) and option (D)
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researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. which of the following should the researchers do to avoid the more consequential error?
Based on the null hypotheses, the type of error is Decrease the significance level to decrease the probability of Type I error.
According to the given question, the null hypothesis is that the new diagnostic tool is not effective in detecting the condition.
Here the more consequential error described is that the diagnostic tool is not effective, but the significance test indicated that it is effective. This is a type I error.
And in Hypothesis testing, a type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.
Therefore, it involves saying there is significant evidence to show that the new diagnostic tool is effective in detecting the condition when in reality, it isn't.
When the level of significance (α) of a hypothesis test directly gives the probability of a type I error. So, by setting it lower, we reduce the chances of a type I error.
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Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.
Repair Time
in Hours
2.9
3.0
4.8
1.8
2.9
4.9
4.2
4.8
4.4
45
Months Since
Last Service
2683279846
Type of Repair
Electrical
Mechanical
Electrical
Mechanical
Electrical
Electrical
Mechanical
Mechanical
Electrical
Electrical
Repairperson
Dave Newton
Dave Newton
Bob Jones
Dave Newton
Dave Newton
Bob Jones
Bob Jones
Bob Jones
Bob Jones
Dave Newton
Get solutions
a. ignore for now the months since the last maintenance service ( ) and the repairperson who performed the service. develop the estimated simple linear regression equation to predict the repair time () given the type of repair ( ). recall that if the type of repair is mechanical and if the type of repair is electrical (to 2 decimals). time
b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain
c. Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
d. Does the equation that you developed in part (c) provide a good fit for the observed data? Explain
The fitted regression model is y = 0.96+0.38x1 + 1.27 x2, and Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3.
a) simple linear regression equation is y=a+bx1+cx2
last maintenance service (x1), repair time (y) given the type of repair (x2).
If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. The Fitted regression model is y = 0.96+0.38x1 + 1.27 x2
b) Since R2 is 0.84.hence we say that x1 and x2 are 84% variation on. Hence we conclude that the above equation is best fit for the data.
c) simple linear regression equation is y=a+bx1+cx2+dx3
last maintenance service (x1), repair time (y) given the type of repair (x2).
If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. and x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
The Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3
d) Since R2 is 0.89.hence we say that x1 and x2 are 89% variation on y. Hence we conclude that the above equation is best fit for the data. compare to part (b).
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In the figure, m∠ 1=(3 x)° and m ∠2=(x+48)°
(a) Write an equation to find x. Make sure you use an = sign in your answer.
(b) Find the degree measure of each angle.
m ∠ 1=____°
m ∠ 2=____°
If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees
The equation to solve the value of x is
3x = x+48
The value of x = 33
The angle 1 = 99 degrees
The angle 2 = 81 degrees
The measure of angle 1 = 3x degrees
The measure of angle 2 = x + 48 degrees
The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.
∠1 + ∠2 = 180 degrees
Substitute the values in the equation
3x + x + 48 = 180
4x + 48 = 180
4x = 180 - 48
4x = 132
x = 132/4
x = 33
Part b
Then the measure of angle 1 = 3x
= 3 × 33
= 99 degrees
The measure of angle 2 = x + 48
= 33 + 48
= 81 degrees
Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively
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in the air, it had an average speed of 161616 \text{m/s}m/sstart text, m, slash, s, end text. in the water, it had an average speed of 333 \text{m/s}m/sstart text, m, slash, s, end text before hitting the seabed. the total distance from the top of the cliff to the seabed is 127127127 meters, and the stone's entire fall took 121212 seconds.
The time it takes for the stone to fall in the air is 7 seconds, and it takes 5 seconds for the stone to fall in the water in the seabed.
The average speed of the stone in air is shown here as 16 m/s.
The average speed of the stone in water is 3 meters per second.
The total distance from the top of the cliff to the seabed is 127 meters.
Total fall time = 12 seconds
Therefore
Let t1 represent the time spent by the stone in the air and
t2 = time spent by the stone in water
Now using the equations of motion we get :
Therefore, t₁ + t₂ = 12 s........(1)
16·t₁ + 3·t₂ = 127............(2)
From (1) t₁ = 12 - t₂
16×(12 - t₂) + 3×t₂ = 127
13t2 = 65 is the result.
and t2 equals 5 seconds
t1 = 12 - t2 = 12 - 5 = 7 sec
The time it takes for the stone to fall in the air is t1 = 7 seconds.
The time it takes for the stone to fall into the water is t2 = 5 seconds.
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19. The ___ is the amount or part that results from the base multiplied by the rate.
A. increase
B. percent
C. rate
D. portion
Answer: B, Percent
Step-by-step explanation: The formula to find a whole after a percent is:
Worth = Part percent * Wole number / 100
This is the same as the definition says, "the amount or part that results from the base multiplied by the rate."
Find the missing measure:
Answer:
46°
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°
take off from 180° the know angles and you will find "x".
180 - 68 - 66 =
46°
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
The composite solid has a volume equal to 2268π cubic feet.
How to determine the volume of a composite solid
In this problem we have the case of a solid as a result of the combination of a cylinder and a hemisphere. The volume formulas for the cylinder and the hemisphere are, respectively:
Volume of cylinder
V = π · r² · h
Volume of hemisphere
V = (2π / 3) · r³
Where:
r - Radius, in feeth - Height, in feetVolume of the composite solid:
V' = π · r² · h + (2π / 3) · r³
If we know that r = 9 ft and h = 22 ft, then the volume of the composite solid is:
V' = π · (9 ft)² · (22 ft) + (2π / 3) · (9 ft)³
V' = 2268π ft³
The volume of the composite solid is equal to 1053π cubic feet.
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X-3y = 16 4x-y=9
I’m so confused
Answer:
x = 1, y = -5.
Step-by-step explanation:
X-3y = 16 Equation (1)
4x- y = 9 Equation (2)
We can solve this by the Method of Elimination.
One way is to multiply the second equation by -3, as follows:
-3(4x - y = 9)
= -12x + 3y = -27 Call this equation (3)
Now if we add equation (3) to equation (1) we eliminate the y terms:
x - 3y = 16
-12x + 3y = -27 Adding:
-11x + 0 = -11
-11x = -11
x = -11/-11 = 1
Finally, we find the value of y by substituting x = 1 into equation (2):
4(1) - y = 9
-y = 9 - 4
-y = 5
y = -5.
So, the answer is x = 1, y = -5.
or we can write it as an ordered pair (1, -5).
Hope this helps.
Answer:
x=1 and
y= -5
t: w = 7:2
p:r = (4t+w) : (t +9w)
Calculate the ratio p : r.
Give your answer in its simplest form.
The ratio of p:r is 6/5
What is ratio?A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.
From the information given, we have that;
t: w = 7:2
We have that;
t =7w = 2p:r = (4t+w) : (t +9w)Now, substitute the values into the formula
p = 4t + w
p = 4(7) + 2
expand the bracket
p = 28 + 2
Add the values
p = 30
r = t + 9w
r = 7 + 9(2)
expand the bracket
r = 25
The ratio, p:r
p:r = 30/25
p: r = 6/5
Hence, the value is 6/5
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HELP PLEASE FAST!! Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
Answer:
26
Step-by-step explanation:
One leg measures 7.
One leg measures 8.
a² + b² = c²
7² + 8² = c²
c² = √113 = 10.630 = 11
perimeter = 7 + 8 + 11
perimeter = 26
Help me solve it 79 points for the answer
Answer:
Step-by-step explanation:
2. Unit Rate: 1:2
3. A class has 26 kids. Johnny is trying to figure out the number of ears everyone has in total. You can use the ration 1:2. For every kid there are 2 ears. Therefore there are 52 ears total. [tex]\frac{1}{2}=\frac{26}{52}[/tex]
4. Multiplication
5. No, you can't have half an ear
Calculator
The fine for speeding is based on the formula F = 45+ 10( s - 60), where F is the fine, in
fined $375, how fast was she driving?
Use linear approximation to estimate the amount of paint in cubic centimetres needed to apply a coat of paint 0.070000cm thick to a hemispherical dome with a diameter of 40.000 meters.
Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.
Given that,
We have to find applying a coat of paint 0.07cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated volume of paint in cubic centimeters, which may be calculated using a linear approximation.
We know that,
Volume of a sphere = 4/3 πr³
Volume of a hemisphere is
V= 2/3 πr³
dV = 2πr² dr
Here,
dr=0.07cm
r=(1/2)×40m=2000cm
Let plug in the formula
dV = 2×π×(2000²)×(0.07)
dV=1759291.886 cubic centimeters
Therefore, Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.
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Plot the GNP series, gnp, and then test for a unit root against the alternative that the process is explosive. State your conclusion.
Hint: [in R]
library(astsa)
library(tseries)
head(gnp)
print(gnp)
there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).
The United States is super power and has multiple resources to maintain itself and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.
The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.
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A fish tank requires 8 liters of water to fill. Alejandro filled the tank with 2 liters of
water. Anthony poured 1- less than Alejandro into the tank. How much water does the tank
still need for it to be filled?
The tank needs 5 more liters of water to be filled.
What is Subtraction?Subtraction is one of the basic operations of mathematics where we remove numbers or expressions or objects away from a given value.
Amount of water needed to fill the tank = 8 liters
Amount of water Alejandro filled = 2 liters
Amount of water Anthony filled = 1 less than Alejandro = 2 - 1 = 1 liter.
Total amount of water filled = 2 liters + 1 liter = 3 liters
Remaining space can be filled with 8 liter - 3 liter = 5 liters.
Hence tank still need 5 liters of water to be filled.
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Create an inequality with 0-9
Answer:
The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .
What is 8 divided by 2/5 in simplest form?
Answer:
20
Step-by-step explanation:
20.
Step-by-step explanation:1. Write the expression.[tex]\frac{8}{\frac{2}{5} }[/tex]
2. Apply the fraction rules.Check the attached image below.
[tex]\frac{8}{1}* \frac{5}{2}[/tex]
3. Simplify.[tex]\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20[/tex]
4. Conclude.[tex]\frac{8}{\frac{2}{5} }=20[/tex].
give an example of a function that is discontinous at one and only one point in its domain but is continous at every other point
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.
This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
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possible values of residualconsider solving the least squares problem where which of the following vectors is a possible value of the residual ?
To find a least squares solution using the normal equations, compute AT A and AT b, then solve the new system AT Ax = AT b. Each solution will be a least squares solution x to Ax = b.
What is least square method with example?
By reducing the total of the offsets or residuals of points from the plotted curve, the least squares method is a statistical technique for determining the best fit for a set of data points. In order to forecast the behavior of dependent variables, least squares regression is performed.
The least squares approach, sometimes referred to as the linear or simple least squares method, typically fits a straight line across the provided points. The sum of squares of the distances from the points is reduced along this line, which is known as the line of best fit.
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A manufacturer of floor mops would like her product to last 700 hours, on the average. She hopes the mean number of hours is not a lot less than 700 (people will not continue to buy her product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that sample mean = 675 and sample standard deviation = 77 hours. Use the significance level α=.05. What is the appropriate test to perform? Regarding the hypothesis testing in question 1, what is the rejection region? Regarding the hypothesis testing in question 1, what is the p-value of the test? Round your answer to four decimal places Regarding the hypothesis testing in question 1, what is your conlusion?
There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.
We are supposed to use Israel and
significance level α=.05 to perform hypothesis test on the statement of the manufacturer.
So Let's move into our worksheet, our population is 700, our sample size is 48.
The sample mean is 675
Sample standard deviation is 77.
So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.
This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.
So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.
So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.
So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.
Our degree of freedom is the sample size minus one.
48-1=47
And our T score uh is minus two points 249.
So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.
We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.
As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.
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Solve for 2 sin A sin B =
2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).
What is 2SinASinB Identity?
2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].
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Fill in the Venn Diagram and Answer the Questions.
The Venn Diagram is shown at the end of the answer.
Then the amounts are given as follows:
History or did not take dance: 1769.History or math, but not dance: 917.Dance and Math, but not history: 343.History, Dance or Math: 2153.None: 248.How to fill the Venn Diagram?The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.
286 students took all three courses, hence:
V = 286.
629 students were taking history and dance, hence:
VI + V = 629
VI + 286 = 629
VI = 343.
605 students took history and math, hence:
IV + V = 605
IV = 605 - 286
IV = 319.
604 students took dance and math, hence:
II + V = 604
II = 318.
1236 students took dance, hence:
III + II + VI + V = 1236
III + 318 + 343 + 286 = 1236
III = 1236 - (318 + 343 + 286)
III = 289
1295 students took math, hence:
VIII + IV + V + VI = 1295
VIII + 319 + 286 + 343 = 1295
VIII = 1295 - (319 + 286 + 343)
VII = 347
1174 students took history, hence:
I + II + IV + V = 1174
I + 318 + 319 + 286 = 1174
I = 1174 - (318 + 319 + 286)
I = 251
Then the number of students who took at least one of the subjects is of:
251 + 318 + 289 + 319 + 286 + 343 + 347 = 2153.
The number of students who took none of the subjects is of:
2401 - 2153 = 248.
(VIII = 248 on the diagram).
The remaining amounts are then calculated as follows:
History or did not take dance: 1174(history) + 347(math) + 248(none) = 1769.History or math, but not dance: I + IV + VII = 251 + 319 + 347 = 917.Dance and Math, but not history: VI = 343.More can be learned about Venn Diagrams at brainly.com/question/24713052
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Athena Investment Company is considering the purchase of an office property. After a careful review of the market and the leases that are in place, Athena believes that next year’s cash flow will be $100,000. It also believes that the cash flow will rise in the amount of $5,400 each year for the foreseeable future. It plans to own the property for at least 10 years. Based on a review of sales of properties that are now 10 years older than the subject property, Athena has determined that cap rates are in a range of 0.10. Athena believes that it should earn an IRR (required return) of at least 11 percent.
Required:
a. What is the estimated value of this office property (assume a 0.10 terminal cap rate)?
b. What is the current, or going-in, cap rate for this property?
Cap rate (going in) = 5.6%
The estimated value of this property = 17,85,714.2 $
What is the required rate of return?The needed rate of return is the rate of return that investors are looking for on assets that are similar. The value of the property and the needed rate of return are inversely related. Property value will fall as the needed rate of return rises, and the opposite is also true.
given cash flow is $100,000 and it increases by 5400$ every year hence growth rate would be 5.4 %.
Cash flows = $1,000,00
Growth rate = 5.4%
Required rate of return = 11%
the required rate of the property = cash flow / ( Required rate of return - growth)
the required rate of the property = 100,000 / (11 -5.4 ) = 17,85,714.2 $
Cap rate (going in) = Required rate of return - a growth rate of the property
Cap rate (going in) = (11 - 5.4) %
Cap rate (going in) = 5.6%
Thus, it can be concluded that the decrease in the required rate of return is the cause of the increase in the value of the property.
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In the figure, if AD=DB, what is the length pf DE?
a. 6
c. 9
b. 9 √2
d. 12
In triangle ABC, where AD = DB , BC = 18 units then length of DE is equal to 9 units.
As given in the question,
In the given triangle ABC,
BC = 18 units
AD = DB
⇒ 'D' is the mid-point of AB.
From the given figure of triangle ABC,
DE is parallel to BC.
⇒E is the midpoint of AC.
Using mid-point theorem,
'D' and 'E' are midpoint of AB and AC and parallel to the opposite side BC then DE is half the measure of BC.
DE = ( 1/2) BC.
⇒ DE = ( 1/2) (18)
⇒ DE = 9 units
Therefore, in the given triangle ABC, the length of DE is equal to 9 units.
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Which of the following rational functions is graphed below?
A. F(x)=1/-x²
B. F(x)=1/(x+1)²
c.
D. F(x)=1/x²
The following rational functions is graphed below is D . F ( x ) = 1 / x^2 .
Given :
f the following rational functions is graphed below
we know that ,
Rational functions in the form a / b
y = 1 / x^2
Table :
x -2 -1 1 2
y 1 / 4 1 1 1 / 4
on plotting the above points we get the graph which is shown in figure .
here vertical asymptote x = 0 and
Horizontal asymptote y = 0
Therefore F ( x ) = 1 / x^2 is the rational function graphed below .
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