Final answer:
The expected value of the gambling game with a cost of $5, and potential winnings of $10 for a sum of 10 or $20 for a sum 3, is −$2.78. The calculation shows the player will lose $2.78 on average per game, indicating it is not a profitable game to play long term. So, option (b) is correct.
Explanation:
The student is interested in determining the expected value of a gambling game where rolling two dice can result in either winning money or losing the cost to play. To find the expected value, we must consider the probability of each outcome and its associated payoff.
First, we calculate the chances of rolling a sum of 10 with two dice. There are three combinations that give a sum of 10: (4,6), (5,5), and (6,4). Since there are 36 possible outcomes when rolling two dice, the probability of obtaining a sum of 10 is 3/36 or 1/12.
Similarly, the only combinations that result in a sum of 3 are (1,2) and (2,1). Thus, the probability of rolling a sum of 3 is 2/36 or 1/18.
The expected value (EV) can be calculated using the formula:
EV = (−cost to play) + [P(sum of 10) × winnings for 10] + [P(sum of 3) × winnings for 3]
Substituting the given values yields:
EV = (−5) + [(1/12) × 10] + [(1/18) × 20]
After calculating, we find tha-
EV = −$2.78.
Since the expected value is negative, this implies that, on average, the player will lose $2.78 per game. Therefore, playing this game would result in an average loss over time.
Sheldon bought a $20 book at a 35% discount. He wrote an expression to find the discounted price.
20−0.35(20)
Which expression is equivalent to discounted price Sheldon paid?
A. (1−0.35)20
B.(1+0.35)20
C.(20−0.35)20
D. 20+0.35(20)
The line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1. Please don't respond if you can't explain how to get out of an impossible square root. Thanks
To evaluate the line integral, calculate the arclength element and substitute it into the integral. Expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.
Explanation:To evaluate the line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1, we need to find the arclength element ds and substitute it into the integral. The arclength element ds can be calculated using the formula ds = sqrt(dx^2 + dy^2 + dz^2). In this case, dx = dt, dy = 2t dt, and dz = 3t^2 dt. Substituting these values into the arclength element formula, we get ds = sqrt(dt^2 + 4t^2 dt^2 + 9t^4 dt^2) = sqrt(1 + 4t^2 + 9t^4) dt.
Substituting ds into the line integral, we get the integral of (2x+9z) * sqrt(1 + 4t^2 + 9t^4) dt. To evaluate this integral, you can expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.
However, it seems that there might be a typo in the original question regarding the curve parametrization. The curve given by x=t, y=t^2, z=t^3 is actually a parabolic curve, not a line. If you need further clarification or assistance, please let me know.
Joe Traffic gained 986 yards during football season.Ziggy Fumble lost 118 yards during the season.What was the difference in their yardage gains
Joe is positive 986 yards
Ziggy is negative 118 yards
the total difference is 986 +118 = 1,104 yards
Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. g
An equation regarding the length of the sides of an isosceles right triangle is required.
The required equation is [tex]2x^2=h^2[/tex]
The length of the legs of triangle which are equal in length is [tex]x[/tex]
The length of the hypotenuse is [tex]h[/tex]
From the Pythagoras theorem we have
[tex]x^2+x^2=h^2\\\Rightarrow 2x^2=h^2[/tex]
Hence, in the above equation the length of the legs and the hypotenuse lengths are related.
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PLEASE HELP!!! WILL GIVE BRAINLIEST!!
Katrina is 69.75 inches tall. Her best friend, Allison, is 64.85 inches in height.
How many inches taller is Katrina than Allison?
A) 4.10
B) 4.90
C) 5.10
D) 5.90
Use the chain rule to find ∂z∂s and ∂z∂t, where z=x2+xy+y2,x=10s+7t,y=10s+3t
rewrite 3/8 and 5/14 to have a common denominator
How can ΔWXY be mapped to ΔMNQ?
Which number is Not a rational number?
A.-5 4/11
B. sqrt of 31
C. 7.608
D. 18.46...
Answer:
[tex]\sqrt{31}[/tex]
Step-by-step explanation:
A.[tex]-5 \frac{4}{11} =\frac{-59}{11}[/tex]
Since it in in p/q form so it is a rational number
B. [tex]\sqrt{31} =5.5677643.......[/tex]
Since it cannot be represented in the form of p/q . So, it is irrational number .
C. 7.608
[tex]\frac{7608}{1000}[/tex]
Since it can be represented in p/q form . So, it is rational number.
D. 18.46...
18.4666.. Since 6 is repeating in decimal place . So, 18.46.. can be written in p/q form .
Hence Option B sqrt of 31 is not a rational number .
Select the function that represents a geometric sequence.
Answer:
Option B
Step-by-step explanation:
Given are 4 sequences and we have to find which one represents a geometric sequence.
We know that geometric sequence will be of the form
a, ar, ar^2,....
On scrutinising the options we get first option does not have the term multiplied by common ratio
OPtion I is incorrect
Option II is a geometric sequence with common ratio (1+i)
Option III is not a geometric sequence since the exponents are all real numbers
Option IV is also incorrect.
The function that represents a geometric sequence is [tex]A(n) = P(1 + i)^{n- 1}[/tex]
How to determine the function?A geometric function is represented as:
[tex]A(n) = ar^n[/tex]
The above function can be modified as follows:
[tex]A(n) = a(r)^n[/tex]
Looking through the options, we have:
[tex]A(n) = a(r)^n[/tex] is similar to [tex]A(n) = P(1 + i)^{n- 1}[/tex]
Hence, the function that represents a geometric sequence is [tex]A(n) = P(1 + i)^{n- 1}[/tex]
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an engineering technician makes $25 for the first 40 hours she works during a week $32 an hour for each hour over 40 hours which piecewise equation models her total weekly pay
A piecewise equation to model the total weekly pay for an engineering technician who earns different rates for hours within and beyond 40 hours is P(h) = {25h if h ≤ 40, 1000 + 32(h - 40) if h > 40}.
Explanation:The question asks for a piecewise equation to model the total weekly pay of an engineering technician who makes $25 per hour for the first 40 hours and $32 an hour for each hour over 40 hours. The piecewise function is made up of two parts:
When written as a piecewise function, it will look something like this:
P(h) =
\{
\begin{array}{ll}
25h & \text{if } h ≤ 40,\\
1000 + 32(h - 40) & \text{if } h > 40.
\end{array}
\}
A line passes through the point (-1,5) and has a slope of -6
write an equation in slope intercept form for this line
what is the quotient of 6/7 and 3/14
WILL GIVE BRAINEST
The values in the table...
Answer:
the answer is A which is 14. help this helps
Step-by-step explanation:
One integer is 2 times another. If the product of the two integers is 32, then find the integers
Final answer:
The two integers that satisfy the conditions of being twice of each other and having a product of 32 are either (4, 8) or (-4, -8).
Explanation:
The two integers as x and y, with y being 2 times x (y = 2x). According to the problem, the product of these two integers is 32 (x * y = 32). If we substitute y in the equation with 2x, we obtain the following: x * 2x = 32. Simplifying this equation gives us a quadratic equation, x² = 16.
To find x, we take the square root of both sides. The square root of 16 is 4, so x can be either 4 or -4. Consequently, y can be either 8 or -8, depending on whether x is positive or negative.
Therefore, the two sets of integers that satisfy the equation x*y = 32 are (4, 8) and (-4, -8), as both pairs have a product of 32 and one integer is exactly twice the other.
A florist is making 5 identical bridesmaid bouquets for a wedding. she has $610 to spend (including tax) and wants 24 flowers for each bouquet. roses cost $6 each, tulips cost $4 each, and lilies cost $3 each. she wants to have twice as many roses as the other 2 flowers combined in each bouquet. how many roses, tulips, and lilies are in each bouquet?
Each bouquet contains 16 roses, 4 tulips, and 4 lilies.
Explanation:To determine the number of roses, tulips, and lilies in each bouquet, we need to set up a system of equations based on the given information. Let's denote the number of roses as 'r', the number of tulips as 't', and the number of lilies as 'l'.
From the problem, we are told that there are twice as many roses as the other two flowers combined in each bouquet. This can be represented by the equation:
r = 2(t + l)
Next, we are given that the florist wants 24 flowers in each bouquet. So the total number of flowers is:
r + t + l = 24
Now we can solve these two equations simultaneously to find the values of 'r', 't', and 'l'.
Substituting the first equation into the second equation, we get:
2(t + l) + t + l = 24
3t + 3l = 24
t + l = 8
Solving this equation, we find t = 4 and l = 4. Plugging these values back into the first equation, we get:
r = 2(4 + 4)
r = 16
So each bouquet contains 16 roses, 4 tulips, and 4 lilies.
Which expression results in a product that is rational?
(a)square root of 7 times square root of 10
(b)square root of 8 times square root of 10
(c) square root of 9 times square root of 10
(d)square root of 10 times square root of 10
Final answer:
The expression that results in a rational product is √10 times √10, as this simplifies to the rational number 10.
Explanation:
To find which expression results in a product that is a rational number, we need to identify which pair of square roots can be multiplied to produce a non-radical number.
Multiplication of square roots is analogous to the multiplication of exponents. When the same base is multiplied, the exponents are added. Utilizing this property, we know:
√7 × √10 = √(7 × 10) = √70 (which is irrational since 70 is not a perfect square).
√8 × √10 = √(8 × 10) = √80 (which is irrational since 80 is not a perfect square).
√9 × √10 = √(9 × 10) = √90 (which is irrational since 90 is not a perfect square).
√10 × √10 = √(10 × 10) = √100 = 10 (which is rational since 100 is a perfect square).
Therefore, the expression that results in a rational product is √10 × √10, which simplifies to 10.
True or false: outliers "inflate" standard deviation.
Which statement is the converse of the following statement? If planes are parallel, then they do not intersect.
Anna wants to call Holly. Holly is on vacation in Asia. It is a time difference of ten hours. Holly's time is always later than Anna's time. If it is 7:35 P.M. where Anna lives, then what time is it where Holly is?
This was everything that was on paper I hope i gave enough
information!
If the population density of ocotillo in a desert is 15 per square kilometer, how many plants would be expected in an area that is 5 km by 3 km?
In an area that is 5 km by 3 km, with an ocotillo population density of 15 plants per square kilometer, we would expect to find 225 ocotillo plants.
The student's question pertains to calculating the expected number of ocotillo plants in a given area based on the known population density. First, we need to find the total area of the region in question, which in this case is a desert area that measures 5 km by 3 km. We calculate the area by multiplying the length by the width: 5 km x 3 km = 15 km2.
Since the population density of ocotillo is given as 15 plants per square kilometer, we can find the total number of ocotillos by multiplying the density by the total area:
15 plants/km2 x 15 km2 = 225 plants.
Therefore, in an area that is 5 km by 3 km, we would expect to find 225 ocotillo plants.
If 6 chocolates cost $0.93, how much do 22 chocolates cost?
I would be $3.41 first you figure out how much one cost by dividing 0.93 by 6 then you multiply your answer by 22
The length of a rectangle is 5 yd less than twice the width, and the area of the rectangle is 52 yd^2. Find the dimensions of the rectangle.
Please help ASAP!
To find the dimensions of the rectangle, we set up an equation using the area formula and solve for 'x'.
Explanation:Let's assume that the width of the rectangle is 'x' yards. Since the length is 5 yards less than twice the width, we can express the length as (2x - 5) yards. The area of a rectangle is given by the formula A = length * width, so we can set up the equation:
A = (2x - 5) * x = 52
Expanding the equation:
2x^2 - 5x - 52 = 0
Using the quadratic formula or factoring, we can solve for 'x'. Once we find the value of 'x', we can substitute it back into the expressions for length and width to find the dimensions of the rectangle.
Dimensions of the rectangle: Width = x yards, Length = (2x - 5) yards
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Phillip invested $6000 compounded continuously at 7.5% interest. How long will it take him to reach $10000
The quadratic x^2-4x-14=3x+16 has two solutions. What is the positive difference between these solutions?
To find the positive difference between the solutions of the quadratic equation x^2-4x-14=3x+16, we simplify it to x^2-7x-30=0 and use the quadratic formula. Calculating the solutions, we get 10 and -3, and the positive difference between these solutions is 13.
Explanation:To find the positive difference between the solutions of the quadratic equation x2-4x-14=3x+16, we first need to simplify the equation by subtracting 3x and 16 from both sides to set it equal to zero.
x2 - 7x - 30 = 0
Now, we use the quadratic formula, which is x = ∛(-b ± √(b2 - 4ac))/(2a), to find the solutions for x, where a = 1, b = -7, and c = -30.
∛(-(-7) ± √((-7)2 - 4*1*(-30)))/(2*1)
The solutions are:
x = (7 + √(49 + 120))/2x = (7 - √(49 + 120))/2Calculating the square root and simplifying, we find:
x = (7 + √169)/2x = (7 - √169)/2The solutions then become:
x = (7 + 13)/2 = 20/2 = 10x = (7 - 13)/2 = -6/2 = -3The positive difference between the solutions 10 and -3 is:
10 - (-3) = 13
Therefore, the positive difference between the solutions is 13.
The positive difference between the two solutions is 13.
Start by rearranging the equation [tex]\(x^2 - 4x - 14 = 3x + 16\)[/tex] into standard quadratic form:
[tex]\[ x^2 - 4x - 14 = 3x + 16 \][/tex]
Combine like terms:
[tex]\[ x^2 - 4x - 14 - 3x - 16 = 0 \][/tex]
[tex]\[ x^2 - 7x - 30 = 0 \][/tex]
Now, to find the solutions to this quadratic equation, we can use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
For the equation [tex]\(x^2 - 7x - 30 = 0\)[/tex], the coefficients are:
[tex]\[ a = 1, \quad b = -7, \quad c = -30 \][/tex]
Let's substitute these values into the quadratic formula:
[tex]\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-30)}}{2(1)} \ \\\\\\[ x = \frac{7 \pm \sqrt{49 + 120}}{2} \ \\\\\\[ x = \frac{7 \pm \sqrt{169}}{2} \ \\\\\\[ x = \frac{7 \pm 13}{2} \][/tex]
So, the solutions are:
[tex]\[ x = \frac{7 + 13}{2} = 10 \ \\\\\\[ x = \frac{7 - 13}{2} = -3 \][/tex]
The positive difference between these solutions is:
[tex]\[ \text{Positive difference} = |10 - (-3)| = |10 + 3| = 13 \][/tex]
Therefore, the positive difference between the two solutions is 13.
There were 3,515 shirts at the stadium store before the game. After the game, there were 1,396 shirts left. How many were sold during the game?
Answer: 2119 shirts
Step-by-step explanation:
Given : There were 3,515 shirts at the stadium store before the game.
After the game, there were 1,396 shirts left.
The by using SUBTRACTION OPERATION, the number of shirts were sold during the game will be:-
[tex]3515-1396=2119[/tex]
Hence, 2119 shirts were sold during the game.
Andrew has 10 more goldfish than Todd. Together, they have 50. goldfish. How many goldfish does each boy have?
a painter charges $35 per hour for labor plus 40$ for a ladder rental when he paints a house.the costomer provides the paint.total charge to paint a costomer hoise was 950. how many hours did the painter spend painting this house
rolls are being prepared to go to the grocery store. Divide 72 rolls into 2 groups so the ratio is 3 to 5
Little Boy Kuku needs help!
Miriam works at the ballpark. She gets paid $45 each day she works. She is given a 10% raise for being a good employee.
If she works 20 days next month, how much will she earn?
A.$900
B.$990
C.$1000
D.$1100
Answer:
990
Step-by-step explanation: