Answer:
Option D is correct.
XY = 10 cm
Step-by-step explanation:
Complete Question
Which of the following statements must be true, given that ABC = XYZ and AB = 10 cm?
The diagram for the question is missing.
Solution
The diagram for the question isn't attached.
But from the condition, ABC = XYZ, it is evident that the two triangles are similar according to the SSS congruent theorem.
If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. And from the condition given, we can predict, without seeing the diagram for the question, that
(AB/XY) = (BC/YZ) = (CA/ZX)
We can also predict that the triangles are exactly the same and the proportionality bbetween is 1.
AB = XY
BC = YZ
CA = ZX
Hence, AB = XY = 10 cm.
Hope this Helps!!!
Evaluate. Write your answer as a fraction or whole number without exponents. 7^–1 =
Answer:
1/7 = 0.142857... repeating
Step-by-step explanation:
7^(-1) = 1/(7^1) =1/7 = 0.142857... repeating
Answer:
[tex] \frac{1}{7} [/tex]Solution,
[tex] {7}^{ - 1} \\ = \frac{1}{ {7}^{1} } \\ = \frac{1}{7} [/tex]
Laws of indices:Law of zero index:[tex] {x}^{0} = 1[/tex]
Product law of indices:[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
Power law of indices:[tex] {( {x}^{m} )}^{n} = {x}^{m \times n} [/tex]
law of negative index:[tex] {x}^{ - m} = \frac{1}{ {x}^{m} } [/tex]
Root law of indices:[tex] {x}^{ \frac{p}{q} } = \sqrt[q]{ {x}^{p} } [/tex]
[tex]( \frac{x}{y} ) ^{n} = \frac{ {x}^{n} }{ {y}^{n} } [/tex] [tex] {(xy)}^{m} = {x}^{m} {y}^{m} [/tex][tex] \sqrt[n]{x} = x \frac{1}{n} [/tex]Hope this helps ....
Good luck on your assignment...
[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Answer:
6 inches square by 3 inches high
Step-by-step explanation:
For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².
That is, the bottom is 6 inches square, and the sides are 3 inches high.
_____
Let x and h represent the base edge length and box height, respectively. Then we have ...
x² +4xh = 108 . . . . box surface area
Solving for height, we get ...
h = (108 -x²)/(4x) = 27/x -x/4
The volume is the product of base area and height, so is ...
V = x²h = x²(27/x -x/4) = 27x -x³/4
We want to maximize the volume, so we want to set its derivative to zero.
dV/dx = 0 = 27 -(3/4)x²
x² = (4/3)(27) = 36
x = 6
h = 108/x² = 3
The box is 6 inches square and 3 inches high.
_____
Comment on maximum volume, minimum area
In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².
If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
acccording to this diagram what is cos 28
Answer:
[tex] \frac{15}{17} [/tex]Option B is the correct option.
Here,
Adjacent=15
Hypotenuse=17
Now,
[tex]cos \: theta = \frac{adjacent}{hypotenuse} \\ cos \: 28 = \frac{15}{17} [/tex]
Hope this helps..
Good luck on your assignment..
Answer:
B. 15/17
Step-by-step explanation:
(see attached graphic for reference)
Because we have a right triangle (i.e one of the internal angles is 90 degrees), we can use trigonometry to solve
from the diagram, we can see that
cos 28° = adjacent length / hypotenuse
we can also see that the length adjacent to 28° = 15 units and the hypotenuse is 17 units,
hence, substituting these values into the equation:
cos 28° = 15 / 17 (answer)
edit: typo
For the triangle show, what are the values of x and y (urgent help needed)
we just have to use the Pythagoras theorem and then calculate the value of x and y.
Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 7 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3
Answer:
work done is equal to 384279168 lb-ft
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as [tex]\pi r^{2} h[/tex]
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = [tex]3.142* 7^{2}*200[/tex] = 30791.6 ft^3
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = 1921395.84 lb
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> work done is equal to 384279168 lb-ft
The required work done will be "384279168 lb-ft".
Work done:Whenever a force pushes anything across distances, work is performed. This same energy transmitted, as well as work done, maybe determined by calculating the force through the kilometers moved throughout the direction of the applied force.
According to the question,
Circular base of cylinder = 7 ft
Height of cylinder = 200 ft
Weight density of water = 62.4 lb/ft³
The Volume of cylinder be:
= πr²h
By substituting the values,
= [tex]3.142\times (7)^2\times 200[/tex]
= [tex]3.142\times 49\times 200[/tex]
= [tex]30791.6[/tex] ft³
Now,
The weight of water be:
= [tex]62.4\times 30791.6[/tex]
= [tex]1921395.84[/tex] lb
hence,
The work done be:
= Water's weight × Cylinder's height
= [tex]1921395.84\times 200[/tex]
= [tex]384279168[/tex] lb-ft
Thus the above answer is right.
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The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
31
z – 40-12
2
Solution
Answer:
31z-162
Step-by-step explanation:
[tex]-40-122=-162[/tex]
[tex]=31z-162[/tex]
a line pass through the point (4,-2) and has a slope of 1/2 what is the value of (-4,a)
Answer:
if you are trying to find the value of a then a= -6
Step-by-step explanation:
i used the information along with desmos graphing calculator and i graphed the line and got the second point (-4,-6)
Answer:
a=-6
Step-by-step explanation:
slope=(y2-y1)/x2-x1)
1/2=(a-(-2))/(-4-4)
1/2=(a+2)/-8
a+2=1/2×-8=-4
a=-4-2=-6
Tommy has "n" friends and he wants to give each friend 5 pencils. Write an expression to show how many pencils pencils Tommy will share.
Answer:
5n
Step-by-step explanation:
Think about it:
If Tommy has 4 friends (n = 4), then he will have to give 5 pencils to each person. The total number of pencils is 5 * n or 5 * 4 = 20.
Similarly, if Tommy has 0 friends (I can relate), then he will have to give 5 pencils to each of his imaginary friends. The total number of pencils he has to give out to his real friends is 5 * n or 5 * 0 = 0.
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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if my medical expenses are $30,000 per year for 35 years with inflation at 5.13% how much money would I have to put in an interest bearing account with a 5% return to cover all medical expenses and the account be $0 at the end of 35 years
Answer:
$1,021,337.13
Step-by-step explanation:
The sum of present values of medical expenses is ...
30,000/1.05 +30,000(1.0513)/1.05^2 +30,000(1.0513^2)/1.05^3 +...
So, the series has an initial value of 30,000/1.05 and a common ratio of 1.0513/1.05. Its sum is given by ...
S = a(r^n -1)/(r -1)
where a = 30,000/1.05, n = 35, r = 1.0513/1.05.
Filling in these values and doing the arithmetic, we get ...
S = $1,021,337.13
You need an initial deposit of $1,021,337.13 to cover rising expenses for 35 years.
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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I NEED HELP PLEASE, THANKS! :)
Answer:
68
Step-by-step explanation:
The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.
[tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]
The technician can test 68 chips in that time period.
Find the general formula for the following sequence.
300000, 480000, 768000, 1228800, 1966080, ....
Answer:
3,145,728
Step-by-step explanation:
x1.6
300000 x 1.6 = 4800000
480000 x 1.6 = 7680000
768000 x 1.6 = 1228800
122800 x 1.6 = 1966080
1966080 x 1.6 = 3145728
Among 20 golden hamster litters recorded, there was a sample mean of =7.72 baby hamsters, with a sample standard deviation of s=2.5 hamsters per liter. Create a 98% confidence interval for the mean number of baby hamsters per liter.
Answer:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\bar X= 7.72[/tex] represent the sample mean
[tex]s= 2.5[/tex] represent the sample deviation
[tex] n=20[/tex] represent the sample size
The confidence interval is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:
[tex] df= n-1 = 20-1=19[/tex]
And the critical value would be:
[tex] t_{\alpha/2}= 2.539[/tex]
And replacing we got:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
The 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.
The margin of error E is:
[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]
The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)
Hence the 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
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Who'd be better at speed answering? Datguy323 or some Helping Hand? (Not a serious question) Solve for the variables: [tex]x^3+y^7=28\\x^3=27[/tex]
Answer:
x = 3
y = 1
Step-by-step explanation:
The equations are:
[tex]x^3+y^7 = 28[/tex]
and
[tex]x^3 = 27[/tex]
Putting second equation in the first one:
=> [tex]27+y^7 = 28[/tex]
Subtracting 27 to both sides
=> [tex]y^7 = 28-27[/tex]
=> [tex]y^7 = 1[/tex]
Taking power 7 to both sides
=> y = 1
Now,
[tex]x^3 = 27[/tex]
Taking cube root on the both sides
x = 3
Answer: (3,1)
Step-by-step explanation:
First, to find x, simply take the cube root of 27, or 3. Thus, x = 3.
Then, simply plug it in:
[tex]27+y^7=28\\Subtract(27)\\y^7=1\\y=1[/tex]
Thus, y = 1
Hope it helps <3
p.s. for some reason, in a graphing calculator, it shows no solutions
Hope it helps <3
2 in a row!
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.80, 0.08, 0.10, and 0.02, respectively. A particular company offers three different policies: a $200 deductible with a $780 premium, a $500 deductible with a $700 premium, and a $1000 deductible with a $590 premium. (A $Y deductible means the insurance company pays X - Y for X Y and 0 for X Y.) Compute the expected profit for each policy.
Answer:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
Step-by-step explanation:
X values | Probability P(x)
0 | 0.80
1,000 | 0.08
5,000 | 0.10
10,000 | 0.02
A particular company offers three different policies:
Policy 1: $200 deductible with a $780 premium
Policy 2: $500 deductible with a $700 premium
Policy 3: $1000 deductible with a $590 premium
The company pays X - Y in damages if X > Y and 0 otherwise.
So the expected profit is given by
Expected profit = Premium amount - Expected payout
Expected profit = Premium amount - [ (X - deductible) × P(x) ]
Expected profit Policy 1:
E(x) = $780 - [ 0×0.80 + (1,000 - 200)×0.08 + (5,000 - 200)×0.10 + (10,000 - 200)×0.02 ]
E(x) = $780 - [ 0 + 64 + 480 + 196 ]
E(x) = $780 - $740
E(x) = $40
Expected profit Policy 2:
E(x) = $700 - [ 0×0.80 + (1,000 - 500)×0.08 + (5,000 - 500)×0.10 + (10,000 - 500)×0.02 ]
E(x) = $700 - [ 0 + 40 + 450 + 190 ]
E(x) = $700 - $680
E(x) = $20
Expected profit Policy 3:
E(x) = $590 - [ 0×0.80 + (1,000 - 1,000)×0.08 + (5,000 - 1,000)×0.10 + (10,000 - 1,000)×0.02 ]
E(x) = $590 - [ 0 + 0 + 400 + 180 ]
E(x) = $590 - $580
E(x) = $10
Therefore, the expected profits for the three policies are:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
The equation of a parabola in the xy-plane is given as
y= n(x + 5)(x - 3) where n is a non-zero constant. What
is the y-coordinate of the vertex of this parabola in
terms of n?
A. -18n
B. -16n
C. -15n
D. -12n
Answer:
B
Step-by-step explanation:
y=n(x+5)(x-3)
or y=n(x²-3x+5x-15)
or y=n(x²+2x-15)
=n(x²+2x+1-1-15)
=n(x+1)²-16n
y -coordinate of vertex=-16n
Find the slope of the line passing through (6,8) and (-10,3)
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
consider a politician discussion group consisting of eight Democrats three Republicans and seven Independents suppose that two group members are randomly selected in succession to attend political convention find the probability of selecting an independent and then a Democrat
Answer:
(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.
Step-by-step explanation:
You want to first add up everyone. So in total there are 18 people.
There is than a 38.8% chance that a independent will be picked first. 7/18.
But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.
There is now a 47% chance that a democrat will be picked next. 8/17.
Hartman Motors has $15 million in assets, which were financed with $6 million of debt and $9 million in equity. Hartman's beta is currently 1.4, and its tax rate is 30%. Use the Hamada equation to find Hartman's unlevered beta, bU. Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
Unlevered beta ≈ 1.09
Step-by-step explanation:
Unlevered beta is basically the unlevered weighted average cost as it shows the volatility of returns without financial leverage. Unlevered beta is also known as asset beta, while the levered beta is commonly known as equity beta. Unlevered beta is calculated from the hamada equation as:
Unlevered beta = Levered beta/[1 + ((1 - Tax rate) × (Debt / Equity))]
We are given;
Levered beta = 1.4
Tax rate = 30% = 0.3
Debt = $6 million
Equity = $15 million
Thus, plugging these into the hamada equation, we have;
Unlevered beta = 1.4/[1 + ((1 - 0.3) × (6/15))]
Unlevered beta = 1.4/(1 + (0.7 × 0.4)
Unlevered beta = 1.4/(1 + 0.28)
Unlevered beta = 1.4/1.28
Unlevered beta = 1.09375
To 2 decimal places;
Unlevered beta ≈ 1.09
For the following data at the near-ground level, which location will residents likely see dew on their lawns in the morning? Group of answer choices City C: Dew Point Temperature = 25°F, expected low Temperature = 20°F City A: Dew Point Temperature = 65°F, expected low Temperature = 60°F City B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Answer: CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Step-by-step explanation:
CITY C: Dew Point Temperature = 25°F, expected low Temperature = 20°F
CITY A: Dew Point Temperature = 65°F, expected low Temperature = 60°F
CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
city B is going to have dew on their lawn in the morning as the dew point temperature is less than the lowest temperature.
When surface temperature drops, eventually reaching the dew point, atmospheric water vapor condenses to form small droplets on the surface. Thus dew will be formed as the conditions are suitable only for city B.
If George is 33 1/3% richer than Pete, than Pete is what percent poorer than George?
Answer:
25%
Step-by-step explanation:
George is 33[tex]\frac{1}{3}[/tex]% ([tex]\frac{100}{3}[/tex]%) richer than Pete. Let Pete's percentage of wealth be 100%.
Thus George percentage of wealth = 100% + [tex]\frac{100}{3}[/tex]%
= [tex]\frac{400}{3}[/tex]%
= 133[tex]\frac{1}{3}[/tex]%
Pete's percent poorer than George can be determined by;
= [tex](\frac{100}{3})[/tex] ÷ [tex](\frac{400}{3} )[/tex] × 100
= [tex](\frac{100}{3})[/tex] × [tex]\frac{3}{400}[/tex] ×100
= 0.25 × 100
= 25%
Pete is 25% poorer than George.
Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
Find the value of x and the value of y. A.x = 15, y = 10 B.x = 20, y = 50 C.x = 50, y = 10 D.x = 50, y = 20
Answer:
X = 50
Step-by-step explanation:
(5x - 100) + (x - 20) = 180 (sum of angle on a straight line is = 180)
5x + x -100 -120 = 180
6x - 120 = 180
6x = 180 + 120
6x = 300
x = 300/6
x = 50
For y
3y + y + 140 = 180
4y = 180 -140
4y = 40
y = 40/4
y = 10
Pls help me help me
Answer:
C. -4/3
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4. Negate the fraction and find the reciprocal.
Negative: switch the sign
3/4 --> -3/4
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-3/4 --> -4/3
Line m has a slope of -4/3 and C is correct.
You obtain a simple interest loan from National city for $2500 at 7.6% for 5 years. Find the amount of interest on the loan
Answer:
950
Step-by-step explanation:
2500(0.076)(5) = 950
Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc
3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1
Answer:
x⁴ = -0.955939
x³ = 0.206897
x² = -2.07471
x = 2.65517
Step-by-step explanation:
Step 1: Rewrite equations in standard form
30x⁴ - 5x³ - 10x² + 3x = -1
-3x⁴ + 5x³ + 7x² + 4x = 0
-3x⁴ + x³ + x² = 1
6x⁴ - 10x³ - 2x² + x = -1
Step 2: Write in matrix form
Top Row: [30 -5 -10 3 | -1]
2nd Row: [-3 5 7 4 | 0]
3rd Row: [-3 1 1 0 0 | 1]
Bottom Row: [6 -10 -2 1 | -1]
Step 3: Plug in calc with RREF function
Top Row: [1 0 0 0 | -499/522]
2nd Row: [0 1 0 0 | 6/29]
3rd Row: [0 0 1 0 | -361/174]
4th Row: [0 0 0 1 | 77/29]