The expected value of the game that you play will be negative 0.21.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
A pack contains 3 gold marbles, 6 silver marbles, and 29 dark marbles. Somebody offers to play this game: You haphazardly select one marble from the pack. Assuming it is gold, you win $3. Assuming it is silver, you win $2. Assuming it is dark, you lose $1.
The expected value is given as,
E(x) = 3(3/38) + 2(6/38) - 1(29/38)
E(x) = 0.2368 + 0.3158 - 0.7632
E(x) = -0.21
The expected value of the game that you play will be negative 0.21.
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1. The function below satisfies Rolle's Theorem on the specified interval. Find the value c in the interval (−4,−3)(-4,-3) such that f′(c)=0f'(c) = 0.
f(x)=x+12/x ; [−4,−3]
The value of c in the interval (-4 , -3) is -√12 such that f'(c) = 0 as
f'(-√12) = 0, so c = -√12.
Given, the function below satisfies Rolle's Theorem on the specified interval.
we have to find the value of c in the interval (-4 , -3) such that
f'(c) = 0.
the function given is,
f(x) = x + 12/x
First we have to find the derivative of the given function f(x).
f(x) = x + 12/x
f'(x) = 1 - 12/x²
Now, equating the derivative with 0 we get
f'(x) = 0
1 - 12/x² = 0
1 = 12/x²
x² = 12
x² - 12 = 0
(x + √12)(x - √12) = 0
x = √12 or x = -√12
we have two values of x be, ±√12.
but only -√12 lie in the interval (-4 , -3).
So, the value of c be -√12.
Hence, the value of c be -√12.
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mark dropped an object from a bridge 400400 feet above ground level with an initial velocity of 0.0. he knows that the gravitational pull of the earth is about 1616 feet per second squared. he wants to find how many seconds, t,t, it will take the object to hit the ground. match each expression with the correct equation that models this situation or solution
The correct equation is t = 5 seconds.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :
y(t) = -16t² + 0t + 400
and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:
0 = -16t² + 0t + 400
16t² + 0t - 400 = 0
which solving for "t" becomes:
16t² - 400 = 0
16t² = 400
t² = 25
t = √25
t = ± 5
So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.
That is: t = 5 seconds
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Work out the difference in minutes between 2 hour 35 minutes and 1 3/4 hours
Answer: The difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.
Step-by-step explanation:
To find the difference in minutes between 2 hours 35 minutes and 1 3/4 hours, we can first convert 1 3/4 hours to minutes.
There are 60 minutes in 1 hour, so 1 3/4 hours is equal to 1 + 3/4 = 1 3/4 hours = 1.75 hours.
Since there are 60 minutes in 1 hour, 1.75 hours is equal to 1.75 * 60 = 105 minutes.
Then, we can subtract 105 minutes from 2 hours 35 minutes to find the difference in minutes:
2 hours 35 minutes - 105 minutes = 135 minutes - 105 minutes = 30 minutes
So, the difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.
YOUR ANSWER IS IN THE ATTACHMENT
HOPE IT HELPS!!!!!!
MARK AS BRAINLIEST
Thankyou
g use the gas prices data set below to calculate a 3-month weighted moving average (wma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. use the weights of 0.6, 0.3, and 0.1 for the 3-month wma, where the first weight is used for the most recent month and the last weight is used for the least recent month. round your answer to two decimal places, if necessary.
We calculated 3-month weight moving average forecast = 0.417
What is weight moving average?It is a statistical expression of calculating average forecast that allows to keep heavier weight with the most recent data.
How to calculate weight moving average?Given, weights for the 3 months are 0.6, 0.3 and 0.1 where the first weight is used for the most recent month and the last weight is used for the least recent month.
the weighing factor will be n, n-1 and n-2
n is the number of periods and n=3
now, weight moving average = [W1 × n +W2 × (n-1) × W3 × (n-2)]/ [n+(n-1)+(n-2)]
[0.6 x 3 +0.3 x 2 + 0.1 x 1]/ [3+2+1] = 0.417
hence, weight moving average is 0.417
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Linda enrolls for 10 credit hours for each of two semesters at a cost of $550 per credit-hour (tuition and fees) in addition, textbooks cost $350 per semester. round your answer to the nearest dollar.
A) $488 B) $150 C) $1463 D) $975
Linda enrolls in two semesters for a total of 20 credits at a cost of $550 per credit hour (tuition and fees), plus $350 for each semester's textbooks. $488 is the total cost for one month. The right response in this case is option A.
In economics, the total cost is the total of all expenses a company incurs in order to produce a particular level of production.
The total cost is the sum of all the expenses a firm has expended to create a specific level of output. Product managers can assess their overall profit margin by adding together their fixed and variable costs. The sum of the fixed and variable expenses is the total cost.
The total cost for one semester = 10(550) + 350
= 5850
Total cost for one month = 5850/12
= 487.5 = $488
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let $c$ be a complex number. suppose there exist distinct complex numbers $r$, $s$, and $t$ such that for every complex number $z$, we have \[ (z - r)(z - s)(z - t)
There are four possible values of C if there exist distinct complex numbers.
A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,
a + bi
where a and b are real numbers.
Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so
z3 + Az2 + Bz + C ≡ z3+ cAz2 + c2Bz + c3C
⟹ (c−1)A = (c2−1)B = (c3−1)C = 0.
Solving this we can find the possible values of C.
A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.
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Question is incomplete. The complete question is:
Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have
(z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).
Compute the number of distinct possible values of c.
Find the difference between (1.5 × 108) and (7.4 × 107). Write the final answer in scientific notation.
7.6 × 10^8
7.6 × 10^7
5.9 × 10^−1
−5.9 × 10^1
Answer:
[tex]7.6 \times 10^7[/tex]
Step-by-step explanation:
[tex]1.5 \times 10^8-7.4 \times 10^7 \\ \\ =10^7 (15-7.4) \\ \\ =7.6 \times 10^7[/tex]
The difference between (1.5 x 10⁸) and (7.4 x 10⁷) is 7.6 x 10⁷.
What is subtraction?The mathematical operation is subtraction. It is employed to eliminate words or expression's objects.
To find the difference between (1.5 x 10⁸) and (7.4 x 10⁷) :
We subtract both the numbers,
(1.5 x 10⁸) - (7.4 x 10⁷)
To solve further, we take the common term outside the bracket.
(1.5 x 10⁸) - (7.4 x 10⁷)
= 10⁷ (15 - 7.4)
= 7.6 x 10⁷
Therefore, the difference is 7.6 x 10⁷.
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Help me place each point thank u
Answer: In the below pic attached
28. The table below shows the comparison of the cost, in dollars, of a
life insurance policy for female non-smokers at certain
$100,000
ages.
Age, a
31
32
33
34
35
Cost, C
170
172
176
178
182
Model the data with a linear function using age 32 and 35. Then
predict the cost of life insurance for a female non-smoker of
age 40. Round to the nearest dollar.
To model the data with a linear function, we can use the two data points for ages 32 and 35 to find the slope and y-intercept of the line. Since the cost of life insurance for a female non-smoker at age 32 is $172 and the cost at age 35 is $182, the slope of the line is given by the formula:
$m = \frac{\text{cost at age 35} - \text{cost at age 32}}{\text{age 35} - \text{age 32}} = \frac{182 - 172}{35 - 32} = \frac{10}{3} = 3.33$
We can then use the point-slope formula to find the y-intercept of the line:
$y - y_1 = m(x - x_1)$
$y - 172 = 3.33(x - 32)$
To find the y-intercept, we can set $x = 0$ and solve for $y$:
$y - 172 = 3.33(0 - 32)$
$y - 172 = -105.76$
$y = 66.24$
Therefore, the equation of the line that models the data is given by:
$y = 3.33x + 66.24$
To predict the cost of life insurance for a female non-smoker of age 40, we can substitute 40 for $x$ in the equation above:
$y = 3.33(40) + 66.24$
$y = \boxed{239.44}$
Therefore, the predicted cost of life insurance for a female non-smoker of age 40 is $239.44.
in the diagram, the number line is marked at consecutive integers, but the numbers themselves are not shown. the four larger dots represent two numbers that are multiples of 3 and two numbers that are multiples of 5. which point represents a number which is a multiple of 15?A. AB. BC. CD. D
A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line.
What is number line
A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. It is assumed that each real number on the number line corresponds to a point on the number line, and vice versa.
What are 3 examples of a line?Pencil. Edges of a ruler Edges of a paper
Pencil.
Edges of a ruler.
Edges of a paper.
What are different types of lines?Horizontal Line, Vertical Line, Perpendicular line, Intersecting lines.
Oblique Lines, Divergent lines, Convergent Lines, and Parallel Lines.
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The percentage of total variation in the dependent variable that is described by the independent variable is expressed by_________.
a. coefficient of determination
b. correlation coefficient
c. coefficient of covariation
d. regression coefficient
a. coefficient of determination
The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).
The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..
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Find the indefinite integral by using appropriate substitutions. (Use C for the constant of integration.) ∫In(cos(x)) tan(x) dx
Refer to the photo taken. Please rate :)
david and amy start at the same point and begin biking in different directions. david is biking west at a speed of 17 miles per hour. amy is biking south at a speed of 15 miles per hour. after how many hours will they be exactly 23 miles apart? round your answer to two decimal places.
The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.
Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.
David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.
According to Pythagoras theorem, and distance = Speed x time.
[tex](17t)^2 + (15t)^2 = 23^2[/tex]
[tex]289t^2 + 225t^2 = 529[/tex]
[tex]\therefore 514t^2 = 529[/tex]
[tex]t^2 = \frac{529}{514}[/tex]
[tex]t^2 = 1.029[/tex]
[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]
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The length of a rectangle is 5cm longer than its width. If the perimeter of the rectangle is 74cm , find its length and width.
Answer:
The width of the rectangle is 32cm and the length is 37cm.
Step-by-step explanation:
Let's call the width of the rectangle "w" and the length of the rectangle "l".We know that the perimeter of the rectangle is equal to 2 times the sum of the length and the width, or 2(w+l) = 74.We also know that the length is 5cm longer than the width, so we can set up the equation l = w + 5.We can substitute this expression for l in our first equation to get 2(w + (w + 5)) = 74.Combining like terms, we get 2w + 10 = 74.Dividing both sides by 2, we get w = 32.We can now use this value to find the length of the rectangle.Thus, the width of the rectangle is 32cm and the length is 37cm.how many parts of pat's garden do not have flowers. Explain? Fractions
Answer:GIVE A BETTER DETAILED QUESTION sorry for caps
Step-by-step explanation:
Aisha and David are reading a book that has 240 pages. Aisha has read
55% of the book, David has read 126 pages Which student has read
more pages so far? How many more pages has that student read?
Answer:
the answer that ur looking for is Aisha she has read more than David
Step-by-step explanation:
55% of 240=132
Answer:
Step-by-step explanation:
Ashia read more
Choose the graph that corresponds to the given system.
3x + y ≥-3
x + 2y ≤ 4
Answer:
See Attached Images
Step-by-step explanation:
First, draw the lines without < or > signs, just use equals signs:
3x + y = -3
y = -3x - 3 (slope of -3, y-intercept at (0,-3) )
x + 2y = 4
2y = -x + 4
y = -(1/2)x + 4
Now shade the region above and including line (1) and below and including line (2).
Note for similair problems: If you have to multiply or divide by a negative number when solving for y, remember to flip the < or > sign to the other one when determining where to shade on the graph.
suppose there is a game where you throw a marble and if it lands in a circle on the ground it is counted as a success. suppose that the probability of you throwing a marble and landing in the circle on the ground is 25%. using the normal distribution, approximate the probability of landing in the circle on the ground 10 times or less if you play the game for 30 rounds a. 56%
b. 65%
c. 71%
d. None of these
e. 47%
Using the Normal Distribution , the probability of landing in the circle on ground 10 times or less is 85.32 % , the correct option is (d) None of these .
The term Normal Distribution is defined as a continuous probability distribution where the values lie in a symmetrical fashion mostly situated around mean .
it is given that ,probability(p) of landing marble on ground is 25% = 0.25
game is played for 30 rounds (n) = 30 ; q = 1 - 0.25 = 0.75 .
we know the mean (μ) = n×p = 30 × 0.25 = 7.5 ;
the standard deviation is (σ) = √n×p×q = √30×0.25×0.75
= √5.625 = 2.38
By using Normal Distribution , X follows N(μ,σ²)
that is X follows N(7.5 , 2.38²) ;
we have to find P[X<10] = P[ (x-μ)/σ < (10 - 7.5)/2.38]
= P[ z < 2.5/2.38] = P[ z < 1.05 ] = 0.85314094 = 85.32 %
Therefore , the required probability is 85.32 % .
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which of the following is a correct factorization of -3x^2+10x-8
Answer:
Step-by-step explanation:
Sketch a graph of the polynomial function f(x) = x³ + 4x² + 3x. Use it to complete each statement.
• f(x) is
·
D
.
f(x) is
f(x) is
Choose...
Choose...
Choose...
f(x) is Choose...
on the intervals (-∞, -3) and (-1,0).
on the intervals (-∞, -2) and (-0.5, 00).
on the intervals (-3,-1) and (0, 00).
on the interval (-2,-0.5).
The graph of the polynomial is given below.
The interval of the polynomial is
(-∞, 3) U (-3, -1) U (-1, ∞).
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
f(x) = x³ + 4x² + 3x
The graph of this polynomial is given below.
The interval of the graph are:
(-∞, 3) U (-3, -1) U (-1, ∞)
Thus,
The graph is given below.
The interval of the graph is (-∞, 3) U (-3, -1) U (-1, ∞).
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Christa purchased ten bottles of shampoo in each of three different sizes: 312 ounces; 612 ounces; and 812 ounces. She used the expression (10×312)+(10×612)+(10×812) to show the total amount of shampoo purchased in ounces. Which expression is equivalent to the one Christa used?
Answer:
(10 * 312) + (10 * 612) + (10 * 812)
Step-by-step explanation:
To find the total amount of shampoo that Christa purchased in ounces, we can use the expression (10 * 312) + (10 * 612) + (10 * 812), which is equivalent to the expression that Christa used. This expression is also equivalent to 3120 + 6120 + 8120, which can be simplified to 3120 + 6120 + 8120 = 3120 + 6150 + 8100 = 9280 + 6150 = 15,430. Therefore, the expression (10 * 312) + (10 * 612) + (10 * 812) is equivalent to 15,430.
1. A study explored the effect of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 was water (control). Treatment 2 waas 1g of ethanol per kg of body weight, and Treatment 3 was 2g/kg. The amount of REM sleep (in minutes) in a 24hr period was recorded: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
(a) Graph the data. Why did you choose the graph that you did and what does it tell you?
(b) Create an ANOVA table for the data using the formulas provided in class. Show your work. You may use R to check your answers.
(c) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?
(d) Based on the ANOVA table, make a conclusion in the context of the problem.
(e) Create 95% CIs for all pairwise comparisons of means using the Tukey method. Do this without R show your work. (You may use R to check your work). Summarize your results using letter codes. What do you conclude?
We have to find a problem at the 5% significance level.
Sample size = 10.
If the Significant value is between five and ten, we lose one till the test. W. C. has a critical value of 44. We must perform a one-tailed analysis of the test. What tail is that?
If one is more efficient than the other, we are asked.
Here, almost everything is positive, and we discover what our values are. Mhm. The following data set, High bromide, was employed to get more sleep for 10 patients who used love level high school.
That's the control group minus the other one.
The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.
The right tail will be 44, the other tail will be divided by two, and 55 minutes will equal 44. It's extremely useful. Okay. It won't reject if it's less than 11, and it will if it's more than 44. Is the music good? There were 10 pupils in our class, and their scores were 1.9 plus 0.8 plus 1.1 plus 0.1. The value of our nut is 23.4. Okay. Critical value takes us directly to the center. This was only a right tail test because we were unable to rule out the null hypothesis. The results would change to 50 if we ran it again at the 1% significance threshold. ten tons and eleven
We failed to reject the hypothesis again.
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1. Part A: Graph quadrilateral WXYZ
with vertices W(-4,5), X(3,5), Y(3,-6), and
Z(-4,-6).
*plot this quadrilateral
Part B: Find the length of the following
sides
WX=
XY=
YZ=
WZ=
The lengths of the sides of the quadrilateral are:
WX = 7 units
XY = 11 units
YZ = 7 units
WZ = 11 units
What is a Quadrilateral?A quadrilateral is any polygon that has four sides and four interior angles.
Part A: The quadrilateral WXYZ has the following vertices,
W(-4, 5)
X(3, 5)
Y(3, -6)
Z(-4, -6)
Each of these vertices of quadrilateral WXYZ have been plotted in the graph that is attached below (see attachment).
Part B: To find the length of each of the sides of the quadrilateral, count the number of square boxes between two points on the graph, given that a square is equal to 1 unit.
Length of WX = 7 boxes = 7 units
Length of XY = 11 boxes = 11 units
Length of YZ = 7 boxes = 7 units
Length of WZ = 11 boxes = 11 units
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Find the value of x in the kite.
18
32
65.7
The value of x in the kite is 32 (option B)
Polygons are defined as plane (two-dimensional) and closed shapes that are formed by joining three or more line segments with each other.
A polygon can be categorized as regular and irregular polygon based on the length of its sides.
Given figure of kite is a polygon,
Three angles of kite are given as 100° , 101° and (4 + 3x)°
It is given that sides opposite sides are equal to each other
Therefore, opposite angles are also equal
=> 4 + 3x = 100
=> 3x = 96
=> x = 96 / 3
=> x = 32
Hence , Value of x in the kite is 32
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College question need help shark attack probability, in the next year, what is the probability there will be:
The probabilities, using the Poisson distribution, are given as follows:
11. A shark attack next year: 0.038.
12. More than one shark attack next year: 0.001.
13. At least one shark attack in the next 100 years: 0.982.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.Considering that there have been 8 attacks in 200 years, the mean for n years is given as follows:
[tex]\mu = \frac{8n}{200}[/tex]
Hence the probability of one shark attack in the next year(n = 1, mean = 0.04) is given as follows:
[tex]P(X = 1) = \frac{e^{-0.04}(0.04)^{1}}{(1)!} = 0.038[/tex]
The probability of more than one shark attack is obtained as follows:
P(X > 1) = 1 - P(X ≤ 1)
In which:
P(X ≤ 1) = P(X = 0) + P(X = 1).
Then:
P(X = 0) = e^(-0.04) = 0.961.P(X = 1) = 0.038.Thus:
P(X > 1) = 1 - (0.961 + 0.038) = 0.001.
For 100 years, the mean is of:
100 x 8/200 = 4.
Thus the probability of at least one attack is of:
P(X > 0) = 1 - e^(-4) = 0.982.
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a television camera is positioned 4,000 ft from the base of a rocket launching pad. the angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. let's assume the rocket rises vertically and its speed is 900 ft/s when it has risen 3,000 ft. (Round your answers to three decimal places.) (a) How fast is the distance from the television camera to the rocket changing at that moment? 480 ft/s (b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment? 0.002 rad/s
For the given height and distance the answer of the following questions are:
a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.
b. Change in the angle of elevation is equal to 0.144rad/sec.
As given in the question,
Let 'α' be the angle of elevation
'h' be the height of the rocket
'x' be the distance between the camera and the rising rocket.
a. Relation between x , h, and 4000 ft during launching pad is given by Pythagoras theorem:
x² = h² + 4000²
Differentiate with respect to time 't' we get,
2xdx/dt = 2hdh/dt + 0 __(1)
When h = 3000ft
x² = 3000² + 4000²
⇒x = 5000ft
dh/dt = 900ft/s
Substitute all values in (1) we get,
2(5000)dx/dt= 2(3000)(900)
⇒dx/dt = 5,400,000/ 10,000
⇒dx/dt = 540ft/sec.
b. tanα = h/4000 __(2)
when h = 3000ft
tanα = 3/4
⇒α = 0.6435
Differentiate (2) with respect to t we get,
sec²α dα/dt = (1/4000) dh/dt
⇒sec²(0.6435) dα/dt = (1/4000)(900)
⇒dα/dt = (0.225)/ 1.5625
⇒dα/dt = 0.144 rad/ sec.
Therefore, for the given height and distance the answer of the following questions are:
a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.
b. Change in the angle of elevation is equal to 0.144rad/sec.
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homework Algebra 1
tion Progress
9
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Write the following using algebraic notation, using the letter x for any
unknown numbers:
I think of a number, add one, then double the result.
Answer:
2(x + 1)
Step-by-step explanation:
x is the unknow number. Add 1 to that and then take that expression (x+1) and multiply it by 2.
g use the formula for the sum of a geometric series to find the sum or state that the series diverges 100/81 10/9 1 9/10 81/100 729/1000
The sum of geometric series is 12.34 and the series is converges
According to the question,
Geometric series is 100/81 + 10/9 + 1 + 9/10 + 81/100 + 729/1000 + . . .
The given series looks like to be in geometric progression with constant ratio r
r = 2nd term/1st term = a2/a1
= (10/9) / (100/81)
=> 9/10
We know that if the ‘r’ is less than 1 then it is convergent
Here 9/10 < 1, it is convergent.
Clearly, this is the sum of an infinite geometric series.
Sum of infinite series in GP = a/(1 - r)
Where a is the first term, 9/10 is the common ratio.
Sum of the geometric series = (100/81) / (1 - 9/10)
=> (100 / 81) / ( 1 / 10)
=> 100 / 8.1
=> 12.34
Therefore, the given series is convergent and its sum is 12.34
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g use the formula for the sum of a geometric series to find the sum or state that the series diverges 100/81 10/9 1 9/10 81/100 729/1000
On solving the provided question we can sat that, the geometric series' total is 12.34, and they care convergent.
What is geometric series?An infinite series in mathematics known as a geometric series has the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. One straightforward illustration is the geometric series with a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, totaling 2 (or 1 if the first term is locked out).
The answer to the query is
The geometric series is made up of the numbers 100/81, 10/9, 1, 9/10, 81/100, 729/1000, and so on.
The provided series appears to be moving forward geometrically with a fixed ratio r.
r = second term, first term, or a2, a1.
[tex]= (10/9) / (100/81)[/tex]
[tex]= > 9/10[/tex]
We are aware that convergence occurs when 'r' is smaller than 1.
In this case, 9/10 1 is convergent.
This sums up an endless geometric sequence, without a doubt.
Infinite series' sum in GP equals a. (1 - r)
The usual ratio is 9/10, where an is the first word.
The geometric series' sum is equal to (100/81) / (1 - 9/10).
[tex]= > (100 / 81) / ( 1 / 10)\\ = > 100 / 8.1\\ = > 12.34[/tex]
The given series is therefore convergent, and its total is 12.34.
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A child asks his parents for some money. The parents make the following offers.Father’s offer: The child flips a coin. If the coin lands heads up, the father will give the child $20. If the coin lands tails up, the father will give the child nothing.Mother’s offer: The child rolls a 6-sided die. The mother will give the child $3 for each dot on the upside of the die.Which offer has the greater expected value?answer choices:Mother's OfferFather's Offer
The mother will give the child $3 for each dot on the upside of the die. the greater expected value is Mother's Offer
The expected value of father's offer is $10, since the probability of getting heads is 50% and the reward for getting heads is $20.
The expected value of mother's offer is $3, since the probability of getting any number is 1/6 and the reward for getting any number is $3.
Therefore, the mother's offer has a greater expected value than the father's offer.
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