Answers
Answer:
x = 75°
Step-by-step explanation:
In a cyclic quadrilateral, opposite angles are supplementary.
x + 105 = 180
Subtract 105 from both sides,
x = 180 - 105
[tex]\boxed{\bf x = 75^\circ}[/tex]
Related Questions
A group consists of men and women. people are selected to attend a conference.
a. In how many ways can people be selected from this group of ?
b. In how many ways can women be selected from the women?
c. Find the probability that the selected group will consist of all women.
Answers
a) The number of ways to choose three people from a set of eleven is given as follows: 165.
b) The number of ways to choose three women from a set of five women is given as follows: 10.
c) The probability that the group will consist of all women is given as follows: 0.0606 = 6.06%.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The number of ways to choose 3 people from a set of 11 is given as follows:
C(11,3) = 11!/(3! x 8!) = 165.
The number of ways to choose 3 women from a set of 5 is given as follows:
C(5,3) = 5!/(2! x 3!) = 10.
Hence the probability that the group will consist of all women is given as follows:
10/165 = 0.0606 = 6.06%.
Missing Informationa group consists of six men and five women.Three people are selected to attend a conference. a) how many ways can three people be selected from this group of eleven?
In how many ways can three women be selected from the five women?
Find the probability that selected group will consist of all women.
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For the expression
15x² + 25x² + 5x+2/
(5x +1)
which sum represents the correct form of the partial fraction decomposition?
Answers
Answer:
15×2
Step-by-step explanation:
5×+2/(5× +1) =15×2^
According to the manufacturer, a sandwich cookie weighs on average 11.3 grams. A statistics class is wondering if this is true, so they randomly select 37 sandwich cookies and weigh them. Their sample of 37 sandwich cookies had the following statistics: grams grams.
Answers
Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.
What is standard deviation?Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.
The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.
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Compare the dimensions of the prisms. How many times greater is the surface area of the red prism than the surface area of the blue prism?
4 m
3m
2m
12 m
The dimensions of the red prism are
The surface area of the red prism is
9 m
6 m
times the dimensions of the blue prism.
times the surface area of the blue prism.
Answers
Answer:
3, 9
Step-by-step explanation:
Surface A = 2(wl + hl + hw)
Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3
Lenght 12/4 =3
Width 6/2 =3
Height 9/3 =3
Calculate surface are of red prism
SA = 2( 6x12 + 9x12 + 9x6)
SA = 2( 72 +108+54)
SA = 2(234) = 468 m²
Calculate surface area of blue prism
SA = 2(2x4 + 3x4 + 3x2)
SA = 2(8 +12+6)
SA = 2(26)
SA =52
Area of red /area of blue = 468/52
Ans =9
3) What is the translation rule that describes the result of the composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)?
Answers
The composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5) is (x, y) --> ( x - 1 , y - 6).
What is Composition of transformation ?
Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines)
Given :
1st Translation : (x, y) --> (x+4, y-1)
It means 4 units to the right and 1 unit down.
2nd Translation : (x, y) --> (x-5, y-5)
It means 5 units to the left and 5 units down.
Now, The composition will be as follows:
(x, y) --> ( x +4 -5 , y - 1 - 5)
(x, y) --> ( x - 1 , y - 6)
It means 1 unit to the left and 6 units down.
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Mary works for a company that pays time and a half for hours over 40 in a week and double time for holidays. This week she worked 8 hours on Monday (which was a holiday), 10 hours on Tuesday, 10 hours on Wednesday, 9 hours on Thursday, and 8 hours on Friday. If Mary earns $8 per hour, what is the total of Mary’s earnings for the week?
Answers
Total Earnings = (8 x 1.5 x 8) + (10 x 2) + (10 x 1) + (9 x 1) + (8 x 1) = $136. Once we have all the calculations, we can add them together to find Mary’s total earnings amount for the week. In this case, Mary’s total earnings is $136.
To calculate Mary’s total earnings for the week, we need to take into account the time and a half for hours over 40 and the double time for holidays. First, we multiply the 8 hours worked on Monday (a holiday) by 1.5 to calculate the time and a half earnings for that day. Then we multiply the 10 hours worked on Tuesday and Wednesday by 1 to calculate the regular earnings for those days. We multiply the 9 hours worked on Thursday by 1 to calculate regular earnings for that day. Finally, we multiply the 8 hours worked on Friday by 1 to calculate regular earnings for that day. Once we have all the calculations, we can add them together to find Mary’s total earnings for the week. In this case, Mary’s total earnings is $136 amount.
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Question 5, please help
5/10
Answers
Answer:
1.5 gallons per minute
Step-by-step explanation:
To solve this question we have to figure out how much water there was in every time scale calculated. To do this we simply have to divide both values...
12 ÷ 8 = 1.59 ÷ 6 = 1.56 ÷ 4 = 1.53 ÷ 2 = 1.5We don't need to figure out the 0 as no time has passed for water to fill up!
We can see that for each one the answer is 1.5, so our average rate would be 1.5 gallons per minute!
Hope this helps, have a lovely day! :)
On Saturday mornings, Ronald volunteers at the hospital where his mother works. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 40 minutes delivering flowers to patients' rooms. In all, Ronald volunteers at the hospital for 90 minutes that day. Which equation can you use to find the amount of time , that Ronald answers phone calls?
Answers
Ronald spent 50 minutes answering phone calls on Saturday morning. The equation used to find this value is x + 40 = 90.
Let's assume that Ronald spent "x" minutes answering phone calls. We know that he spent a total of 90 minutes volunteering, and 40 minutes delivering flowers. So the time he spent answering phone calls and delivering flowers can be expressed as:
x + 40
We also know that the total time he spent volunteering was 90 minutes. So we can write:
x + 40 = 90
To solve for "x", we can subtract 40 from both sides of the equation:
x + 40 - 40 = 90 - 40
Simplifying:
x = 50
where x represents the amount of time Ronald spent answering phone calls.
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Write (10 + √2)÷(14+ √2) in the form a+b√2/c
where a, b and c are all integers.
Answers
Answer:
[tex]\frac{69+2\sqrt{2}}{97}[/tex]
Step-by-step explanation:
(10 + √2)÷(14+ √2)= [tex]\frac{10+\sqrt{2} }{14+\sqrt{2} }[/tex]
= [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{(14+\sqrt{2}) x (14-\sqrt{2}) }[/tex]
= [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{14^{2}-(\sqrt{2}^{2})}[/tex]
= [tex]\frac{{(10+\sqrt{2}) x (14-\sqrt{2})}}{196-2}[/tex]
= [tex]\frac{140-10\sqrt{2}+14\sqrt{2}-2}{194}[/tex]
= [tex]\frac{138+4\sqrt{2}}{194}[/tex]
= [tex]\frac{2 x (69+2\sqrt{2})}{194}[/tex]
= [tex]\frac{69+2\sqrt{2}}{97}[/tex]
∴ the answer is [tex]\frac{69+2\sqrt{2}}{97}[/tex] in the form [tex]\frac{a+b\sqrt{2}}{c}[/tex]
(10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.
What are integers?A number that includes zero, positive numbers, and negative numbers, is an integer. Integer's can never be a fraction, a decimal, or a percent, it should be noted.
To write (10 + √2)÷(14+ √2) in the form a+b√2/c, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 14 - √2.
[(10 + √2) ÷ (14 + √2)] x [(14 - √2) ÷ (14 - √2)]
= [(10 + √2) x (14 - √2)] ÷ [(14 + √2) x (14 - √2)]
= [140 + 8√2 - 2√2 - 2] ÷ [196 - 2]
= (138 + 6√2) ÷ 194
= (69 + 3√2) ÷ 97
Therefore, (10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.
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what would the answer to y = 11.7x + 96.7 be?
Answers
The answer to given linear equation will be When y = 200, x = 8.82.
The values of x and y utilised will determine the solution to the equation y = 11.7x + 96.7.
You can solve for y by substituting a particular value of x into the equation. For instance, if x equals 2, then:
y = 11.7(2) + 96.7
y = 23.4 + 96.7
y = 120.1
Hence, at x = 2, y = 120.1.
Nevertheless, you might choose a different value of y and solve for x by substituting it into the equation. For instance, if y equals 200, then
200 = 11.7x + 96.7
103.3 = 11.7x
x = 8.82
Hence, x equals 8.82 when y is 200.
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What type of shape is the box of Cremora
Answers
The box of Cremora is typically rectangular in shape, with six rectangular faces and twelve edges.
Which describes a possible independent variable for the given dependent variable?
The amount of money you earn
1. Who you call most often each day
2. The number of miles you run each day
3. The number of hours you work
4. The color of your new car
Answers
Answer:
3. The number of hours you work.
Step-by-step explanation:
Independent variable means that the occurrence of the event is not dependent on another event occurring.
In this case, the independent variable is the amount of hours you work, as you can, assumingly for the question, can work any amount you would like. However, the pay would be on the basis of how much work you do, and is dependent on the amount of hours you do (assuming you are on hourly).
~
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1) What is the total amount in the account if the interest rate is 4.5% each year?
2) After 6 years $275 is added to the account. What does R(x) equal after 6 years ? What is the new expression for A(x) ?
Answers
The simple interest has an expression and the total amount after an year at an interest rate of 4.5% is approximately $2478.33. The value of R(x) after 6 years is 275 and the new expression for A(x) is 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
What is the total amount in the account if the rate is 4.5%1. To find the total amount in the account after 5 years with an interest rate of 4.5%, we can simply plug in x = 1.045 (1 + 0.045) into the expression for A(x):
A(1.045) = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045)
≈ 2478.33
So the total amount in the account after 5 years with an interest rate of 4.5% is approximately $2478.33
2. After 6 years, the expression for A(x) would become:
A(x) + 275
We can find the new expression for R(x) by subtracting the original expression for A(x) from the new expression:
R(x) = A(x) + 275 - A(x)
= 275
So the new expression for R(x) after 6 years is simply R(x) = 275.
3. The original expression for A(x) was:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x
To find the new expression for A(x) after 6 years, we can simply plug in x = 1.045 (1 + 0.045) and add 275:
A(1.045) + 275 = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045) + 275
≈ 2923.97
So the new expression for A(x) after 6 years is:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
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An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
(Score for Question 1: ___ of 2 points)
1. Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.
Option A:
Week
1
2
3
4
5
6
Amount Paid
Option B:
Week
1
2
3
4
5
6
Amount Paid
Answer:
(Score for Question 2: ___ of 8 points)
2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
(a) Determine the iterative rule for each sequence. Show your work.
(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.
Answer:
(Score for Question 3: ___ of 5 points)
3. Consider the iterative rules you wrote in Problem 2.
(c) Explain why the rules are functions.
(d) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. How would you respond to your friend’s comment?
(e) Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her outputs are meaningless in this situation. What would you tell her about the inputs she can use?
Answer:
(Score for Question 4: ___ of 5 points)
4. The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.
Answers
Answer: A
Week Amount Paid
1 $200
2 $250
3 $300
4 $350
5 $400
6 $450
Option B:
Week Amount Paid
1 $200
2 $220
3 $242
4 $266.20
5 $292.82
6 $322.10
Your welcome stranger. (:
Use a property to write an equivalent expression 12 times (100-5).which property did you use?
Answers
Answer: distributive property
Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.
Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer:
2
Step-by-step explanation:
-3x - 12 = 40 - 8x - 21x
-3x + 8x + 21x = 40 + 12
26x = 52
x = 52/26
x = 2
Answer:
x=-14/13, or -1 1/13
Step-by-step explanation:
Jill bakes an apple pie in a pie
pan that is 10" in diameter. What is
the circumference of Jill's pie?
2
Answers
Answer: the circumference of Jill's pie is 31.4 inches.
Step-by-step explanation:
The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle and π (pi) is a constant approximately equal to 3.14.
In this case, the diameter of Jill's pie is 10", so we can use the formula to find the circumference:
C = πd
C = 3.14 x 10
C = 31.4 inches
Therefore, the circumference of Jill's pie is 31.4 inches.
Answer:
10pi or 31.42
Step-by-step explanation:
the formula for circumference of a circle is 2pir (yes, i can't find the symbol for pi... sorry...) (and r = the radius)
since the diameter is 2*r, the radius is 5 inches.
2*5*pi = 10pi, which is about 31.42
The figures shown are similar. What is the measure of side DE? 2 trapezoids. First trapezoid has points B, C, D, E. Distance from B to E (4.5 centimeters); B to C (6 centimeters); C to D (4.5 centimeters). Second trapezoid has points F, G, H, I. Distance from F to G (4 centimeters); G to H (3 centimeters); H to I (2 centimeters); F to I (3 centimeters). help me
Answers
The measurement of side DE is 3 centimeters.
What is the trapezoids?
A trapezoid is a 2D geometric shape that has four sides, with two sides parallel to each other and two sides non-parallel.
To solve this question, we can use the fact that similar figures have corresponding sides in proportion. Let's label the lengths of the sides of the trapezoids as follows:
First trapezoid: BE = 4.5 cm, BC = 6 cm, CD = 4.5 cm
Second trapezoid: FG = 4 cm, GH = 3 cm, HI = 2 cm, FI = 3 cm
Since the trapezoids are similar, we know that the ratio of corresponding sides is the same. Let's call this ratio k.
For the first trapezoid, the parallel sides are DE and BC, so we have:
k = DE / BC
For the second trapezoid, the parallel sides are FG and HI, so we have:
k = HI / FG
Since the trapezoids are similar, these ratios must be equal:
DE / BC = HI / FG
Substituting in the given lengths, we get:
DE / 6 = 2 / 4
Simplifying, we get:
DE = 3 cm
Therefore, the measurement of side DE is 3 centimeters.
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Question 6 of 10 Which of the following is the correct factorization of the polynomial below? p³-125q³ A. (p-5q) (p² + 5pq+25q²) B. (p-25q) (p2 + 25pq+25q²) C. (p² +10g)(p³ +25pq+5q²) D. The polynomial is irreducible.
Answers
Answer:
the answer is A
Step-by-step explanation:
p³-125q³
(p-5q)³
but if expand A
it will give the same p³-125q³
(p-5q)(p²+5pq+25q²)
expanding will give
p3+5p²q+25pq²-5p²q-25pq²-125q³
C.L.T
p³+5p²q-5p²q+25pq²-25pq²-125q³
p³-125q³
Find the area of the rhombus
Answers
If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².
What is the area of the rhombus?
The Area of a Rhombus = A = ½ × d1 × d2,
Where d1 and d2 are the diagonals of the rhombus.
The area of a rhombus can be found using the formula:
Area = (diagonal 1 x diagonal 2) / 2
or
Area = (base x height) / 2
We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.
Using the Pythagorean theorem, we can find the length of the other diagonal:
diagonal 2 = 2(radius) = 2(4) = 8 m
Now we can use the formula to find the area of the rhombus:
Area = (diagonal 1 x diagonal 2) / 2
Area = (6 m x 8 m) / 2
Area = 24 m²
Therefore, the area of the rhombus is 24 m².
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Identify the correct leading coefficient, degree, and end behavior of P(x) = 4x^(5) + 9x^(4) + 6x^(3) - x^(2) + 2x - 7.
Answers
The leading coefficients of a polynomial is the factor of the term with the greatest degree. The largest exponent of a polynomial's variable is its degree. The coefficient for the given polynomial is [tex]4[/tex], and the degree is [tex]5[/tex].
What in mathematics is a polynomial?An expression that consists of variables, constants, and exponents that is combined using arithmetic computations like addition, subtraction, multiplication, and division is referred to as a polynomial.
What distinguishes a polynomial?By noticing which formulas only contain the operations of adding, subtract, manipulation, and quasi integer exponents, the polynomials may be located.
In the given polynomial [tex]P(x) = 4x^5 + 9x^4 + 6x^3 - x^2 + 2x - 7[/tex], the highest degree of the polynomial is [tex]5[/tex], which means it is a [tex]5^{0}[/tex] polynomial.
The coefficient of the term with the highest degree, which is [tex]4x^5[/tex], is [tex]4[/tex]. Therefore, the leading coefficient is [tex]4[/tex].
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How long is this triangles hypotenuse?
Answers
Answer:
17.
Step-by-step explanation:
[tex]a^2+b^2 = c^2[/tex] is the formula used to find the hypotenuse (also known as the Pythagora's Theorem).
Substitute the given values into the equation.
[tex]8^2+15^2=c^2[/tex]
64 + 225 = [tex]c^2[/tex]
289 = [tex]c^2[/tex]
[tex]\sqrt{289}[/tex] = c
c = 17
A farmer has built circular pens for her animals behind the barn.
She needs to determine how far the center of each pen is from the barn in order to install
underground wiring for lights.
Here's what she knows:
The distance between the center of the cow pen and the center of the horse pen is 15 yards.
The distance between the center of the cow pen and the center of the pig pen is 10 yards.
All radii are whole numbers, and all are greater than 3 yards
No two pens are the same size.
She has labeled distances between the barn & points of tangency to the pens in her diagram.
You can help her decide which animal goes in which pen.
1. Now help her find the distance from the barn to the center of each pen! Show all of your work.
Use the page below for workspace as needed.
Distance from barn to center of...
Horse pen:
Cow pen:
Pig pen:
18.25
9.5 yds
+
75 yds.
Pig
COW
112248
8.75 yds.
24.75
horse
16 yds.
Answers
The distances from the barn to the center of each pen are: Horse pen: 47 yards , Cow pen: 50.25 yards , Pig pen: 64.75 yards.
Define Pythagorean theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
To solve for the distances from the barn to the center of each pen, we can use the following steps:
Draw a diagram of the situation, labeling the radii of each pen and the distances between the pens.
Use the Pythagorean theorem to solve for the radius of each pen. Let r1 be the radius of the horse pen, r2 be the radius of the cow pen, and r3 be the radius of the pig pen.
For the horse pen:
r1² = (15 + 16)² + (18)²
r1²= 961
r1 = 31 (rounded to the nearest whole number)
For the pig pen:
r3² = (10 + 24.75)² + (18)²
r3²= 1640.06
r3 = 40 (rounded to the nearest whole number)
Use the distance from the barn to the point of tangency of each pen to solve for the distance from the barn to the center of each pen. Let d1 be the distance from the barn to the center of the horse pen, d2 be the distance from the barn to the center of the cow pen, and d3 be the distance from the barn to the center of the pig pen.
For the horse pen:
d1 = 16 + r1
d1 = 16 + 31
d1 = 47 yards
For the cow pen:
d2 = 75 - r2
d2 = 75 - 24.75
d2 = 50.25 yards
For the pig pen:
d3 = 24.75 + r3
d3 = 24.75 + 40
d3 = 64.75 yards
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Henry has 3 bunches of flowers. If there are 5 flowers in each bunch, which of the following shows how to find the total number of flowers he has?
A) 3 divided by 5
B) 3 times 5
C) 3 plus 5
Answers
Given the following profit payoff table: s1�1 s2�2 s3�3 d1�1 130 100 330 d2�2 230 -50 310 d3�3 70 -100 370 Construct an opportunity loss (regret) table by completing the following table. s1�1 s2�2 s3�3 d1�1 d2�2 d3�3 Given the probabilities of the states of nature are P(s1)�(�1) = 0.2, P(s2)�(�2) = 0.3, and P(s3)�(�3) = 0.5, calculate the minimum expected opportunity loss. Minimum EOL��� = What is the best alternative based on expected opportunity loss? d1�1 d2�2 d3�3 s1�1 s2�2 s3�3 What is the EVPI����?
Answers
Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
Answer:To solve this problem, we will have to first calculate the regret for each option. We will do that by finding the maximum payoff for each column and subtracting the current payoff from that. That gives us the opportunity loss. We will then multiply the opportunity loss with the probabilities of the events to calculate the expected opportunity loss. We will find the minimum expected opportunity loss by selecting the minimum value in each row. We will then add the minimum expected opportunity loss to the minimum payoff for each option to calculate the maximum regret. Finally, we will calculate the EVPI by subtracting the maximum regret from the maximum payoff. Here are the tables that we need to construct: Regret table: Minimum expected opportunity loss table: Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
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Which expression is equivalent to the expression 10a - 14c
Answers
The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Given the equation:
10a - 14c
We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:
10a - 14c
2(5a - 7c)
The expression 10a - 14c is equivalent to 2(5a - 7c)
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Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. About ______% of the area is between z=−3.5 and z=3.5 (or within 3.5 standard deviations of the mean).
Answers
99.96% of area lies between given value range under the curve.
We can use a standard normal distribution table or a calculator with a normal distribution function to determine the area under the curve of the standard normal distribution between z = -3.5 and z = 3.5. The difference between the area to the left of z = 3.5 and the area to the left of z = -3.5 is the area under the curve between these two numbers.
We determine the region to the left of z = 3.5 and z = -3.5 using a typical normal distribution table. Left of z = 3.5 is an area of 0.9998, whereas left of z = -3.5 is an area of 0.0002. Hence, the region between z = -3.5 and z = 3.5 is as follows:
0.9998 - 0.0002 = 0.9996
To turn this to a percentage, we multiply by 100:
0.9996 x 100 = 99.96%
In other words, 99.96% of the area is within 3.5 standard deviations of the mean, or between z = -3.5 and z = 3.5. This shows that most values in a normal distribution fall within a few standard deviations of the mean and accounts for a sizeable portion of the overall area under the curve.
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Finding values of an Inverse Using a Table values. =.31.f−1(5) 34. f(f−1(6)) ax. f−1(f(1)) 36. f−1(f−1(0)) 37−48= Inverse Function Property we une inverse Funge . Property to show that f and g are inverses of each other. 37. f(x)=x−6:g(x)=x+6 38. f(x)=3x,g(x)=3x e.39. f(x)=3x+4;g(x)=3x−4 40. f(x)=2−5x;g(x)=52−x 41. f(x)=x1;g(x)=x1 42. f(x)=x5;g(x)=5x
43. f(x)=x2−9,x≥0;g(x)=x+9
,x≥−9 44. f(x)=x3+1;g(x)=(x−1)1/3 45. f(x)=x−11;g(x)=x1+1
Answers
31.f(f-1(6)) = 6
34.f-1(f(1)) = 1
36.f-1(f-1(0)) = 0
37.f(g(x)) = f(x + 6) = x + 6 - 6 = x g(f(x)) = g(x - 6) = x - 6 + 6 = x
39.f(g(x)) = f(3x) = 3(3x) = x g(f(x)) = g(3x) = 3(3x) = x
40.f(g(x)) = f(3x - 4) = 3(3x - 4) + 4 = x g(f(x)) = g(3x + 4) = 3(3x + 4) - 4 = x
41. f(g(x)) = f(5/2 - x) = 2 - 5(5/2 - x) = x g(f(x)) = g(2 - 5x) = 5/2 - (2 - 5x) = x
42. f(g(x)) = f(x2) = (x2)1/2 = x g(f(x)) = g(x1/2) = (x1/2)2 = x
43.f(g(x)) = f(x + 9) = (x + 9)2 - 9 = x g(f(x)) = g(x2 - 9) = x2 - 9 + 9 = x
44.f(g(x)) = f((x - 1)1/3) = (x - 1)1/33 + 1 = x g(f(x)) = g(x3 + 1) = (x3 + 1 - 1)1/3 = x
45.f(g(x)) = f(x1/2 + 1) = x1/2 + 1 - 11 = x g(f(x)) = g(x - 11) = (x - 11)1/2 + 1 = x
To answer your questions, here is the following information:
1. Finding values of an Inverse Using a Table values: f-1(5) = 0.31
f(f-1(6)) = 6
f-1(f(1)) = 1
f-1(f-1(0)) = 0
2. Inverse Function Property: To show that f and g are inverses of each other, you must use the Inverse Function Property which states that if f and g are two inverse functions, then f(g(x)) = x and g(f(x)) = x.
3. Examples:
f(g(x)) = f(x + 6) = x + 6 - 6 = xg(f(x)) = g(x - 6) = x - 6 + 6 = xf(x) = 3x, g(x) = 3x
f(g(x)) = f(3x) = 3(3x) = xg(f(x)) = g(3x) = 3(3x) = xf(x) = 3x + 4, g(x) = 3x - 4
f(g(x)) = f(3x - 4) = 3(3x - 4) + 4 = xg(f(x)) = g(3x + 4) = 3(3x + 4) - 4 = xf(x) = 2 - 5x, g(x) = 5/2 - x
f(g(x)) = f(5/2 - x) = 2 - 5(5/2 - x) = xg(f(x)) = g(2 - 5x) = 5/2 - (2 - 5x) = xf(x) = x1/2, g(x) = x2f(g(x)) = f(x2) = (x2)1/2 = xg(f(x)) = g(x1/2) = (x1/2)2 = xf(x) = x2 - 9, x ≥ 0, g(x) = x + 9
f(g(x)) = f(x + 9) = (x + 9)2 - 9 = xg(f(x)) = g(x2 - 9) = x2 - 9 + 9 = xf(x) = x3 + 1, g(x) = (x - 1)1/3f(g(x)) = f((x - 1)1/3) = (x - 1)1/33 + 1 = xg(f(x)) = g(x3 + 1) = (x3 + 1 - 1)1/3 = xf(x) = x - 11, g(x) = x1/2 + 1
f(g(x)) = f(x1/2 + 1) = x1/2 + 1 - 11 = xg(f(x)) = g(x - 11) = (x - 11)1/2 + 1 = x
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A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Answers
If a curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. The equation of the curve is y = 5e^(²x).
How to find the equation?Let's assume that the equation of the curve is y = f(x), where f(x) is some unknown function.
We are given that the slope of the curve at every point P is twice the y-coordinate of P. This means that:
f'(x) = 2f(x)
where:
f'(x) is the derivative of f(x) with respect to x.
We can solve this differential equation by separating the variables and integrating:
1/f(x) df/dx = 2
Integrating both sides with respect to x, we get:
ln|f(x)| = 2x + C
where C is a constant of integration.
To find the value of C, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:
ln|f(0)| = C
Since ln|f(0)| is just a constant, we can write it as another constant, say A. Therefore:
ln|f(x)| = 2x + A
Taking the exponential of both sides, we get:
|f(x)| = e^(²x+A)
Since f(x) cannot be negative (otherwise, the slope of the curve would be negative at some points), we can drop the absolute value signs:
f(x) = e^(²x+A)
To find the value of A, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:
f(0) = e^A = 5
Therefore, A = ln(5). Substituting this value into the equation, we get:
f(x) = e^(²x+ln(5)) = 5e^(²x)
So the equation of the curve is y = 5e^(²x).
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(6e−3f−4)⋅2=left parenthesis, 6, e, minus, 3, f, minus, 4, right parenthesis, dot, 2, equals
Answers
The final result of the expression (6e−3f−4)⋅2 is e3f−8.
The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.
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