The amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
What is the probability of an event?The probability of an event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
How to solve the question?In the question, we are given that in a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses.
We are asked the amount the woman should pay to play the game if it is fair.
The amount that the woman should pay to play the game is her expected return from the game.
Her expected return can be shown as E(X), where X represents all possible returns, which is calculated as:
E(X) = ∑ x.P(x), where P(x) is the probability of x.
The values of x can be:
3 when she draws a jack or a queen,
5 when she draws a king or an ace, and
0 when she draws any other card.
The probabilities of drawing a:-
The total number of possible outcomes remains constant throughout as 52.
Jack or a queen:
Number of favorable outcomes = 8 {4 jacks + 4 queens}.
Thus, the probability = 8/52 = 2/13.
King or an ace:
Number of favorable outcomes = 8 {4 kings + 4 ace}.
Thus, the probability = 8/52 = 2/13.
Any other card:
Number of favorable outcomes = 36 {All remaining cards, that is, 52 - 8 - 8 = 36}.
Thus, the probability = 36/52 = 9/13.
Thus, the expected return:
E(X) = ∑ x.P(x),
or, E(X) = 0.(9/13) + 3.(2/13) + 5(2/13),
or, E(X) = 0 + 6/13 + 10/13,
or, E(X) = 16/13 = 1.23.
Thus, the amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
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Create a factorable polynomial with a GCF of 2. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
Which of the following graphs represent a function? 4072-01-02-01- a. Graph A and Graph C b. Graph A c. Graph D d. Graph B and Graph D
The graph which represent a graph of a function is:
Graph A and Graph C
Step-by-step explanation:We know that a graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to y-axis should intersect the curve exactly once i.e. corresponding to each x-value there is exactly one y-value.
Hence, from the figure attached to the answer we see that the Graph which is a function is:
Graph A and Graph C
Graph A represents a function.
Explanation:A function is a relation in which each input has only one output. In other words, for every x-value, there can only be one y-value. To determine if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. Looking at the given graphs, Graph B and Graph D do not pass the vertical line test, as there are vertical lines that intersect these graphs at multiple points. Therefore, the correct answer is Graph A.
Kaia needs braces, which will cost $2,400. Her insurance deductible is $1500, after which her insurance pays 80% of all costs. How much will Kaia need to pay for her braces?
A.$2,200
B.$1,680
C.$180
D.$480
Kaia will pay a $1,500 deductible and the remaining 20% not covered by insurance after the deductible, totaling to $1,680 for her braces.
To calculate how much Kaia will need to pay for her braces, we need to take into account her insurance deductible and the percentage her insurance will cover after that deductible is paid. Kaia's braces cost $2,400, so let's break it down step-by-step:
Kaia pays her insurance deductible, which is $1,500. So, $2,400 - $1,500 = $900 remains.
Her insurance then covers 80% of the remaining $900. To calculate this, we use 80% of $900: ($900 x 0.80) = $720.
Since the insurance pays $720 of the remaining cost, Kaia is left with 20% of $900 to pay out of her pocket. To calculate this, we take 20% of $900: ($900 x 0.20) = $180.
Therefore, Kaia will need to pay $1,500 (deductible) plus $180, for a total of $1,680.
What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?
A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
The daily population growth function is P=25,000((1.0095)1/365.25)t, and the daily growth rate is approximately 1.000026 or an increase of about 0.0026% per day.
Explanation:The city population growth function given, P=25,000(1.0095)t, is an exponential function. To identify the daily growth rate, we need to rewrite this function in terms of days. As there are approximately 365.25 days in a year, we substitute this into the formula for t. Hence, the daily population growth function becomes P=25,000(1.0095)t/365.25.
To find the approximate daily growth rate, we solve for the base of the exponent. Using the fact that (ab)c = abc, we can rewrite the function as P=25,000((1.0095)1/365.25)t.
Thus, the daily growth rate of the population is approximately the value of (1.0095)1/365.25, which calculates to about 1.000026, or an increase of about 0.0026% per day.
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Helene is finding the sum (9 + 10i) + (–8 + 11i). She rewrites the sum as (–8 + 11)i + (9 + 10)i. Which statement explains the property of addition that she made an error in using?
Answer:
answer is d
Step-by-step explanation:
[ 3+ ( 18 - 4 ) / 7 ] * 8
Nick bought a pair of glasses for $200. He later saw the same glasses advertised for 20% less than what he originally paid. What price were the glasses being advertised for?
Solve the polynomial equation. State the multiplicity of each root. x3 + 15x2 + 75x + 125 = 0
what 3050 divided by 100
can someone please express 105/20 as a mixed number in simplist form
write the following decimal as a fraction or mixed number in lowest terms 0.85
There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)
Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.
Aurella wants to enlarge a 4-inch by 6 inch photo so that it has a width of 15 inches. Use a ratio table to determine the new length of the photo
The quotient Of 30 and the sum of -4 and -6
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? Zach's method is linear because the number of minutes increased by an equal factor every month. Victoria's method is linear because the number of minutes increased by an equal number every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
(NEVER MIND GUYS IM GOING WITH A)
At time t = π /6 , the position x(t) = 6 cos(t) is given by the following. x (π/6) = 6 cos (π /6 )
I NEED ANSWER RIGHT NOW!!!!!!!!! (30 POINTS + BRAINIEST ANSWER REWARD!!!!)
The graph below shows the velocity f(t) of a runner during a certain time interval:
graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 8 and 8, 0. Label on the x axis is time in seconds and label on the y axis is velocity in meters per second
Which of the following describes the intercepts on the graph?
A. The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.
B. The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
C. The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
D. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 seconds.
Solve the following equation exactly on the interval 0 ≤ θ ≤ 2π ? cos 2θ + sin θ = 0
for halloween, lana received 7 4/8 pounds of candy. after a week her family had eaten 3 6/8 pounds, how many pounds does she have left?
Answer To Questions :
3 3/4
hich numbers are to solve this problem? A bicycle shop sold 60 road bikes, 50 racing bikes, and 75 mountain bikes each month for 15 months. How many more mountain bikes than road bikes did the shop sell in the 15 months?
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does not react with water but it does react with nitric acid. Silver tarnishes when exposed to air or light. What is a physical property of silver?
Answer:
The density of silver is 10.49 g/cm3.
Step-by-step explanation:
Physical properties are those that can be observed without any change in the identity of the element in question. In this case, the physical property that is mentioned is density. Other examples include color and hardness. On the other hand, chemical properties describe how a substance can change into a different substance. This would include characteristics such as flammability and corrosion resistance.
factor 2x^3+3x^3-18x-27
After combining like terms, the polynomial simplifies to 5x^3 - 18x - 27. It cannot be factored using basic techniques due to the lack of common factors and its incompatibility with simple factoring patterns.
Explanation:To factor the polynomial 2x^3 + 3x^3 - 18x - 27, we first combine like terms and then look for common factors or patterns that we can use to factor the polynomial.
Combining Like Terms
Combining the cubic terms, we get 5x^3. Therefore, the polynomial simplifies to 5x^3 - 18x - 27.
Factoring
We look for a greatest common factor (GCF) among the terms. In this case, there are no common factors other than 1.
Since there is no obvious way to factor by grouping, and the polynomial does not fit the patterns for difference of cubes or sum of cubes, we'd have to consider other methods such as Rational Root Theorem or synthetic division to find if the polynomial has rational roots and can be factored further. However, those methods are more complex and require trial and error or a systematic approach that typically isn't covered until more advanced algebra classes or college algebra.
Conclusion
Without additional methods, we conclude that the polynomial 5x^3 - 18x - 27 cannot be factored over the rationals using basic factoring techniques commonly taught in high school algebra.
To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors and factor out those common factors.
Explanation:To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors. The first two terms, 2x^3 and 3x^3, have a common factor of x^3. The last two terms, -18x and -27, have a common factor of -9. Factoring out these common factors, we get:
2x^3 + 3x^3 - 18x - 27 = x^3(2 + 3) - 9(2 + 3) = x^3(5) - 9(5) = 5x^3 - 45
So, the factored form of the expression is 5x^3 - 45.
Let f be the function defined by f(x) = x + lnx. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1, 4]?
Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis
ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx
=√14(x4+2+1x4)dx=√122(x2+1x2)2dx
=12(x2+1x2)dx
how do the 8 differ in 38108
Allie wants to arrange her flower garden in eight equal rows.
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width is 10 cm. if he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
The area of the rectangle board, including the wooden border, is 280 cm².
The student's question pertains to finding the new area of the rectangle board after adding a 2 cm wooden border around it. Initially, the board has dimensions of 16 cm in length and 10 cm in width. To account for the new wooden border, we add 2 cm to each side of the board. This means that the new length will be 16 cm + 4 cm (2 cm for each side of the length) and the new width will be 10 cm + 4 cm (2 cm for each side of the width).
The calculation will be as follows:
New Length = 16 cm + 4 cm = 20 cm
New Width = 10 cm + 4 cm = 14 cm
Area = New Length * New Width
Area = 20 cm * 14 cm
Area = 280 cm²
Therefore, the area of the rectangle board with a 2 cm border added around it will be 280 cm².
Which of the following rules describes the function graphed below? a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
Answer:
Option C
output=0.5(input)+1.5
Step-by-step explanation:
Let
y------> the output
x------> the input
we have
[tex]A(-1,1), B(5,4)[/tex]
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{4-1}{5+1}[/tex]
[tex]m=\frac{3}{6}=0.5[/tex]
Find the equation of the line
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=0.5[/tex]
[tex]A(-1,1)[/tex]
substitute
[tex]y-1=0.5(x+1)[/tex]
[tex]y=0.5x+0.5+1[/tex]
[tex]y=0.5x+1.5[/tex]
remember that
y=output
x=input
substitute
output=0.5(imput)+1.5
What percent of 450 is 60? Round to the nearest hundredth of a percent.