A constant of dilation is a number used to change the size of a figure while preserving its shape. It is also known as a scale factor.
The constant of dilation is used in a dilation transformation, a type of transformation that changes the size of a figure without changing its shape or orientation.
The constant of dilation is typically represented by the letter "k" and is a number greater than 0. If the constant of dilation is greater than 1, the dilation will increase the size of the figure. If the constant of dilation is less than 1, the dilation will reduce the size of the figure. And if the constant of dilation is equal to 1, the dilation will not change the size of the figure.
It's important to note that the constant of dilation is a factor that applies to all the points of the figure, and it's the same for all the points of a figure during a dilation transformation.
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HELP PLS!!!! i don’t get it
Answer:
153
Step-by-step explanation:
i = square root of -1
i = √-1
(3+12√-1) (3-12√-1)
√a times √b = √ab
a√b times c√d = (a times c) √ (b times d)
9 - (36√-1) + (36√-1) - (144(√-1)^2) =
9 - 0 - (144 * -1) =
9 - 0 - (-144) =
9 - (-144) =
9 + 144 =
153
*** funny thing is if you put
(3+12i) (3-12i)
in a calculator
it works!
it gives you the answer 153
another way:
Expand the expression using
(a-b) (a+b) =
a²-b² :
3²-(12i)²
Simplify using exponent rule with same exponent
(a*b)^n =
a^n*b^n:
3²-12²* i²
Calculate the power:
9-144* i²
Rewrite by definition
i²=-1:
9–144×(−1)
Calculate the product or quotient: 9+144
Calculate the sum or difference: 153
Answer: 153
gathmath
can someone help me with answer C? its the last one i need
Using the monthly payment formula, it is found that her down payment should be of $1,419.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
A = 250, r = 0.072, n = 72.
Hence:
r/12 = 0.072/12 = 0.006.
We solve for P to find the total amount of the monthly payments, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]
0.0171452057P = 250
P = 250/0.0171452057
P = $14,581.
The total payment is of $16,000, hence her down payment should be of:
16000 - 14581 = $1,419.
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Please help!! a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y=-30x^2+1325x-8569
The widgets should be sold for $22.08 for the company to make the maximum profit.
To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.
Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.
In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.
The function given is:
y = -30x² + 1325x - 8569.
Differentiating this with respect to x, we get:
y' = -60x + 1325.
To find the point of inflection, we equate this to zero, to get:
0 = -60x+ 1325,
or, x = 1325/60 = 22.0833
Now, we differentiate, y' = -60x + 1325, with respect to x, to get:
y'' = -60 < 0, thus we have a maximum at x = 22.0833.
Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.
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I need help with these questions because I don't understand it.
Evaluating the given expressions and inequalities, we have;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b) = 4
[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex] 16) \: x \geq 11\frac{2}{3} [/tex]
17) k > 9
18) v > 9
20) m ≤ 16
Which method can be used to evaluate the expressions and inequalities?The given expressions are;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]
Where x = 4, and y = 6, we have;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]
Therefore;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b)
Where a = 3 and b = 2, we have;
(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4
Therefore;
(8•a - 5•b) - 2•(a + b) = 4[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]
Where a = 7, and p = 6, we have;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]
Therefore;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]
Where m = 5, and n = 6, we have;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]
Therefore;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]
Which gives;
[tex] \frac{7}{6} \times 10 \leq x [/tex]
[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]
[tex] x \geq 11\frac{2}{3} [/tex]
17) 20 < k + 11
Therefore;
k > 20 - 11 = 9
k > 918) 6•v > 54
v > 54 ÷ 6 = 9
Therefore;
v > 9[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]
Therefore;
2 × 8 = 16 ≥ m
Which gives;
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I WILL GIVE BRAINLIEST!!!!
2 step equation:
4x + 3 = 19
2 step equation w/ fractions:
(4/3)x + 5 = 17
Distributive Property:
4x(6 - 2) - 10 = 20
Decimals:
4.3x + 0.7 = 5
Real world equation:
Sharon's restaurant is bringing in money from customers, and she needs to know how much she needs to pay off the bill for the electricity to run the place. To turn the electricity on, she has to pay $25. For every hour that the electricity is on for, she has to pay $4. How many hours can she have the electricity on for if she makes $49 profit?
i really need some help solving these
The answers to the questions are:
1. x = 4
2. x = 1.5
3. x = 1.875
4. x = 1
2 step equation:1. 4x + 3 = 19
4x = 19 - 3
4x = 16
divide by 4
x = 4
2 step equation w/ fractions:(4/3)x + 5 = 17
= 1.33x + 5 = 7
Take like terms
1.33x = 7-5
1.33x = 2
divide through by 1.33x to get 2
x = 2/1.33
x = 1.5
3. Distributive Property:4x(6 - 2) - 10 = 20
Multiply and open the bracket
24x - 8x - 10 = 20
Take like terms
16x = 20+10
16x = 30
x = 30/16
= 1.875
4. Decimals:4.3x + 0.7 = 5
4.3x = 5 - 0.7
4.3x = 4.3
x = 1
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Sarita showed the steps to solving the equation. 5 (x minus 3) 7 (x 4) = 73 steps sarita’s solution sarita’s verification 1 5 x minus 15 7 x 28 = 73 5 (5 minus 3) 7 (5 4) = 73. 5 (negative 2) 7 (9) = 73. negative 10 63 = 73. 53 not-equal-to 73. 2 (5 7) x (negative 15 28) = 73 3 12 x 13 = 73 4 12 x 60 5 x = 5 when sarita tried to verify her answer, she found it was wrong. which explains her mistake? sarita’s solution is correct. she made an error in her verification. sarita was supposed to add the 5 and 7 in the first step. sarita added 13 instead of negative 13 in the fourth step. sarita was supposed to use the division property of equality in the third step.
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
What is linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.
Given the following equation:
5(x-3) + 7(x+4) = 73
The steps to solve it are:
Apply the Distributive property:
5x - 15 + 7x + 28 = 73
12x + 13 = 73
Subtract 13 from both side
12x + 13 - 13 = 73 -13
12x = 60
Divide both side by 12
12x/12 = 60/12
x = 5.
To verify it, put the x = 5 in to the equation:
5(5 - 3) + 7(5 + 4) = 73
After solving it, we get
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
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Chanda is planning to visit universities over the summer to help decide where she wants to attend college. The first two universities on her proposed route are 6 inches apart on Claudias map. In real life, this distance is 30 miles. What scale does the map use? 1 in = _____ miles.
The map scale to use would be: 1 in. = 5 miles.
What is Map Scale?The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.
Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:
6/30 = 1/x
Solve for x
x = (30 × 1)/6
x = 5.
Therefore, the scale of the map is: 1 in = 5 miles.
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Can someone please help me on this?
Answer:
[tex]\frac{9\pi }{4}[/tex] inches
Step-by-step explanation:
I suppose they are asking you for the length of the red part.
18[tex]\pi \\[/tex] * [tex]\frac{45}{360}[/tex] = [tex]\frac{9\pi }{4}[/tex] inches
Answer:
L = 7.07 in
Step-by-step explanation:
L = arc lenght
[tex]L=\frac{\pi (45)(9)}{180} =2.25\pi =7.07in.[/tex]
Hope this helps
Two pulses are moving along a string. one pulse is moving to the right and the second is moving to the left. both pulses reach point x at the same instant. an illustration of a triangular trough traveling right and the same size and shape crest traveling left both toward point x. they are equidistant from x. will there be an instance in which the wave interference is at the same level as point x? no, the interfering waves will always be above x. no, the interfering waves will always fall below x. yes, the overlap will occur during the slope of the waves. yes, the overlap will occur when the first wave hits point x.
The sum of the pulses allows us to find that the answer for the sum at a point x is
There is no interference pattern as the amplitude does not remain constant.Traveling waves can add up as they travel, leading to different results.in which the wave interference is at the same level as point x?If the waves travel in the same direction, their sum gives resulting waves that can be maximum or minimum depending on the phase between them, un stationary patterns.
If the directions are coincident directions, they add place to the interference processes, in this case, stationary patterns are formed on a screen.
If the waves travel in the opposite direction the sum of the two waves gives rise to a wave that maximum is the sum of the amplitudes of the two pulses
In the case of a pulse that corresponds to a single wavelength, the result is an instantaneous maximum, which after the pulse passes, returns to zero.
Consequently, there is no stationary pattern, so there is no interference between the two pulses.
In conclusion with the sum of the pulses, we can find that the answer is No interference pattern is produced as the amplitude does not remain constant.
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There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the first ticket, since 5 out of 26 letters are vogal, the probability is:
5/26.
For the second ticket, since there is no replacement, the probability is:
4/25.
The probability of both tickets is:
[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]
0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
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In your opinion, what are the pros and cons of each projection? What are the limitations? In which circumstances, environments, or occupations is one type of projection likely preferred over the other? Describe any special tools that might be needed to create the projection. Which projection is easiest for you to interpret visually? Why?
The projection discussed are the isometric and the orthographic projection.
How to illustrate the information?The isometric projection is how the object look to the eyes when seen from a distance. It should be noted that orthographic projection give the actual measurements of the object.
The isometric drawing is through 100% true measurement of the height, width, and the depth.
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¿Cuál de los siguientes números NO es un decimal periódico?
A.
11
30
B.
11
400
C.
11
600
D.
111
90
El número decimal que no es un decimal periódico es dado por:
B. [tex]\frac{11}{400}[/tex].
¿Que es un número decimal periódico?Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.
La conversión de las fracciones para decimales són:
11/30 = 0.366666 -> Periódico.11/400 -> 0.0275 -> No es periódico.11/600 -> 0.018333333 -> Periódico, en razón de lá repetición de el 3.11/90 = 0.1222222 -> Periódico.Puede-se aprender más a cerca de números decimales periódicos en https://brainly.com/question/1192529
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How many of the 960 dvd players were repaired in the first year
if you get the right answer you get a 20k gaming setup
(D) 200 DVD players were repaired in the first year.
What are DVD players?A DVD player is a device that plays DVDs that adhere to both the DVD-Video and DVD-Audio technical standards, which are incompatible. Some DVD players are also capable of playing audio CDs.Given:
The DVD player shipped 960 players last month
There is a record that out of every 24 players, the 5 would be repaired.
So we need to find the number of DVD players that were repaired in these 960 players.
So,
[tex]\frac{960*5}{24} \\=200[/tex]
Therefore, (D) 200 DVD players were repaired in the first year.
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The question you are looking for is here:
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?
A: 40
B: 120
C: 192
D: 200
If sint=18 , and t is in quadrant i, find the exact value of sin(2t) , cos(2t) , and tan(2t) algebraically without solving for t
The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
According to the statement
we have given that the sint=1/8 then we have to find the exact value of
sin(2t) , cos(2t) , and tan(2t).
Here the value of Sint = 18
then sin2t becomes
sin2t = 2*1/8 then
sin2t = 1/4.
And
(Cos2t)^2 = 1 - (Sin2t)^2
(Cos2t)^2 = 1 - 1/16
(Cos2t)^2 = (16 - 1)/16
(Cos2t)^2 = 15/16
(Cos2t) = (15/16)^1/2
then
tan2t = sin2t/cos2t
tan2t = (1/4)/(15)^1/2 / 4
tan2t = 1/(15)^1/2
these are the values of given terms.
So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
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A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to
participate in a probability experiment. Compute the probability that
a) a male is selected, then a female.
b) a female is selected, then a male.
c) two males are selected.
d) two females are selected.
e) no males are selected.
The probability that a male is selected, then a female is 0.26
The probability that a female is selected, then a male is 0.26
The probability that two males are selected is 0.18
The probability that two females are selected is 0.30.
The probability that no males are selected is 0.30.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26
The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26
The probability that two males are selected = (11/25) x (10/24) = 0.18
The probability that two females are selected = (14/25) x (13 / 24) = 0.30
The probability that no males are selected = (14/25) x (13 / 24) = 0.30
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What are the domain and range ofWhat are the domain and range of ?
D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)
Answer:
Domain:[-4,∞)
Range:[0, ∞)
Thus, choice C is the exact answer
Which of the following lists of ordered pairs is a function?
OA. (2, 4), (3, 9), (4, 16), (5,25)
OB. (2, 4), (-2, 4), (3,9), (-2,-4)
OC. (1, 1), (2, 3), (1, 5), (4,7)
OD. (0, 2), (4, 2), (0, -4), (4, -2)
Answer:
OA
Step-by-step explanation:
because it only got a y parameter for each x
Answer:
Option A. (2,4),(3,9),(4,16),(5,25)
Find the equation of the line through point (−1,4) and parallel to 5x+y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
The equation of the parallel line is y = -5x - 1
How to determine the line equation?The equation is given as:
5x + y = 4
Make y the subject
y = -5x + 4
The slope of the above equation is
m = -5
Parallel lines have equal slope.
This means that the slope of the new line is 5
The equation is then calculated as:
y = m(x - x1) + y1
So, we have:
y = -5(x + 1) + 4
Expand
y = -5x - 5 + 4
Evaluate
y = -5x - 1
Hence, the equation of the parallel line is y = -5x - 1
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WORTH 50 points pls answer.
The two polygons are similar. Find the values of x and y
Answer:
y = 120
x = 10.6
Step-by-step explanation:
Given polygons are parallelograms.
In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.
Since two parallelograms are similar:
60 + y = 180 subtract 60 from both sides
y = 120
To find the value of x:
side lengths are proportional because these are similar polygons
[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions
18x + 72 = 264 subtract 72 from both sides
18x = 192 divide both sides by 18
x = 10.6 approximately
what is the derivative of this
The derivative of the natural logarithm function is given by:
[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]
What is the derivative of the natural logarithm function?Suppose we have a composite natural logarithm function given as follows:
[tex]f(x) = \ln{g(x)}[/tex]
The derivative of the function is given as follows:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]
In this problem, the function, which is already a first derivative, it given by:
[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]
The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:
[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]
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If we sample from a small finite population without replacement, the binomial distribution should not be used because
the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types,
we can use the hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are
of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and
n-x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor
selects four numbers from 1 to 54 (without repetition), and a winning four-number combination is later randomly
selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A = 4, B = 50, n = 4, and
x=2.)
P(x)=
A!
B!
(A + B)!
(A-x)!x! (B-n+x)!(n-x)! (A+B-n)!n!
+
P(2)=
(Round to four decimal places as needed.)
Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the parameters are given as follows:
N =A + B = 54, k = 4, n = 4.
The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]
There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
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Olivia is making 15 bead bracelets for her friends what is the proportional relationship?
5 minutes per bracelet.
because 15/3 = 5 mins.
To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality =15/3= 5 minutes.
Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Step-by-step explanation:
The answer is 8 2 / 5 because ...
[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]
Answer:
Here your ans and dont forget to say dhanwyad ok.
=
Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.
Given right triangle RST, what is the value of sin(S)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Thirteen-twelfths
Answer:
Step-by-step explanation:
I would use the law of sins.
13/sin90 = 5/sin s
sin s = (5 sin 90)/13
sin s = .3846.
Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.
Answer:
22.6 = 113/5
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Simplify the following polynomial expression.
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
-
x +
The simplification of the polynomial expression will give 3x² - 20x + 8.
How to illustrate the polynomial?The polynomial expression is given as:
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7
Then collect like terms
= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19
= 3x² - 20x + 8.
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What is the perimeter of a regular heptagon with a side length of 8 units? 48 units 56 units 72 units 32 units
Answer:
The answer to your question is P=56
Step-by-step explanation:
P=7a=7·8=56
I hope this helps and have a good day!
Can you construct an example of a discrete random variable which does not have a finite expectation?
Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
For the given question,
A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.
It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.
Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,
[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]
⇒ [tex]E(X)=\infty[/tex]
Consider the following example,
You throw a coin until it lands tails.
Let n be the number of heads
Then number of heads can be found by, 2ⁿ
Now, the expected value function is
[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]
⇒ [tex]E(X)=\infty[/tex]
Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.
Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
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Please help ASAP!! Thank you :D
Answer:
Obtuse, scalene.
Step-by-step explanation:
In ΔSVU, one angle is 120° which is obtuse angle.
So, ΔSVU is a obtuse triangle.
All the sides have different measurements. So, It is a Scalene triangle.
The binomial 5x – 4 is a factor of 10x^2 – 23x + 12. What is the other factor?
Answer:
2x - 3
Step-by-step explanation:
10x²-23x+ 12 ÷ 5x-4
Answer:
2x - 3
Step-by-step explanation:
[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]
Hope this helps
Select all that apply.
Which functions have a range of {y ∈ all real numbers | -∞ < y < ∞}?
f(x) = -(x + 1)^2 - 4
f(x) = -4x + 11
f(x) = 2/3x - 8
f(x) = 2^x+3
f(x) = x^2 + 7x - 9
The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.
What are the domain and range of a function?The domain is the set of all the possible values of x that are taken as inputs for the function.The range is the set of all the values(output) that are obtained for the domain of x.So, domain = {input values(x)} and range = {output values(y)}Calculation:Step 1: Finding the range for the function f(x) = -(x + 1)² - 4
The given function is quadratic in the form of a(x - h)² + k,
So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0
For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4
∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}
Step 2: Finding the range for the function f(x) = -4x + 11
This is a linear function. So, the range is R.
∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}
Step 3: Finding the range for the function f(x) = 2/3x - 8
This is also a linear function. So, the range is R.
∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}
Step 4: Finding the range for the function f(x) = 2^x + 3
This is an exponential function. So, the range is y > k
Here k = 3.
∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}
Step 5: Finding the range for the function f(x) = x² + 7x - 9
This is a quadratic function.
we can write it as,
f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9
= (x + 7/2)² - 85/4
This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4
Since a > 0, the range of the function is y ≥ -85/4
∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}
Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}
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