The mathematical expectation is a weighted sum:
[tex]E(X) = \displaystyle \sum_{i=1}^n x_ip(x_i)[/tex]
i.e. we multiply each outcome with its probability, and sum all these terms.
There are 16 possible outcomes for the spin, and here's table with wins/losses:
[tex]\begin{array}{c|cccc}&1&4&4&5\\1&L&L&L&L\\4&L&W&W&W\\4&L&W&W&W\\5&L&W&W&W\end{array}[/tex]
So, there are 9 winning spins and 7 losing spins. Since all the spins have the same probability, the probablity of winning $8 is 9/16, and the probability of losing $2 is 7/16. This leads to a mathematical expectation of
[tex]E(A) = 8\cdot \dfrac{9}{16}-2\dfrac{7}{16} = \dfrac{29}{8}[/tex]
In the case of the three coin flips, all triplets have the same probability of 1/8, and the eight triplets are
TTT, TTH, THT, HTT, THH, HTH, HHT, TTT
So, Danielle wins with 3 triplets, and loses with 5 triplets. The mathematical expectation is
[tex]E(B) = 6\cdot \dfrac{3}{8}-1\dfrac{5}{8} = \dfrac{13}{8}[/tex]
So, the first method is better, and the difference is 29/8-13/8 = 2.
After calculating the expected values, Danielle expects to make $0.875 more by choosing Option B over Option A, as it has a higher mathematical expectation.
To calculate which option has a greater mathematical expectation (expected value), we must consider the possible outcomes of each option and their probabilities. We then multiply each outcome by its probability and sum the results.
Option A: SpinnerWe have 3 possible sums that would result in Danielle winning $8: 5+4, 4+5, and 4+4. Any other sum results in losing $2. The probability of spinning a 5 on the first spin is 1/4, and so is the probability of spinning a 4. Therefore, the probability of getting a sum greater than 6 is:
P(sum > 6) = P(5+4) + P(4+5) + P(4+4) = (1/4)*(1/4) + (1/4)*(1/4) + (1/4)*(1/4) = 3/16.
The probability of getting a sum of 6 or less is 1 - 3/16 = 13/16. The expected value for Option A is:
E(A) = (3/16)*$8 + (13/16)*(-$2) = $0.25.
Option B: Coin FlipDanielle wins $6 if she gets exactly one head. The probability of getting exactly one head in three flips (HHT, HTH, THH) is:
P(exactly one head) = [tex](1/2)^3 + (1/2)^3 + (1/2)^3 = 3/8[/tex].
The probability of not getting exactly one head is 1 - 3/8 = 5/8. The expected value for Option B is:
E(B) = (3/8)*$6 + (5/8)*(-$1) = $1.125.
Comparing the expected values, Option B has a higher expected value than Option A. Therefore, the amount Danielle expects to make by choosing Option B over Option A is:
E(B) - E(A) = $1.125 - $0.25 = $0.875.
Danielle expects to make $0.875 more by choosing Option B.
Solve 8 sin ( 5 x ) = 3 for the two smallest positive solutions a and b, with a < b
The two smallest positive solutions, with a < b, are approximately
x ≈ 0.384 and x ≈ 1.64.
We have,
Isolate the sine function by dividing both sides by 8.
sin(5x) = 3/8
The inverse sine function (also called arcsin) is on both sides of the equation.
5x = arcsin(3/8).
Divide both sides by 5.
x = (1/5) arcsin(3/8)
Now,
arcsin(3/8) is approximately 0.4115.
So,
x = (1/5) * 0.4115
x = 0.384.
Since the sine function repeats itself every 2π radians, we add multiples of 2π/5 to the solution to find other valid values of x.
The second smallest positive solution
x = 0.384 + (2π/5) = 1.64.
Therefore,
The two smallest positive solutions, with a < b, are approximately
x ≈ 0.384 and x ≈ 1.64.
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The equation 8 sin(5x) = 3 is solved by isolating the variable term, using inverse sine to get an angle, and considering the period of the sine function when finding additional solutions.
Explanation:To solve the equation 8 sin (5x) = 3, we first isolate the term involving the variable 'x'. Start by dividing both sides by 8. We get sin(5x) = 3/8.
The inverse sine (also known as arcsin or sin^-1) is used to get the angle whose sine is 3/8. So we have 5x = sin^-1(3/8).
To solve for 'x', we then divide both sides by 5: x = sin^-1(3/8) / 5.
This value of 'x' is a solution, but sine function repeats every 2π intervals, so we add multiples of 2π/5 to 'x' to get additional solutions.
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A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
20 centimeters
Step-by-step explanation:
27 / x = 12
x = 2.25 times
width would be 45 / 2.25 = 20 centimeters
Gavin and Jack are practicing shots against their goalie. On their last 15 attempts, Gavin made 6 and Jack made 7. Based on this performance, what is the probability that they both make their next shot?
Answer:
[tex]\dfrac{14}{75}[/tex]
Step-by-step explanation:
Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be successful is
[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]
Jack made 7 out of 15 shots, so the probability that Jack's next shot will be successful is
[tex]\dfrac{7}{15}[/tex]
The probability that they both make their next shot successfully is
[tex]\dfrac{2}{5}\cdot \dfrac{7}{15}=\dfrac{14}{75}[/tex]
Linda received the following scores on her essay tests.
64, 65, 63, 66, 60, 65, 66, 68, 69, 66, 63
What is the mean of her scores?
A.64.5
B.65
C.65.5
D.66
The answer to your question is B. 65
Answer:
b
Step-by-step explanation:
you add them all together and divide 11 because there are 11 numbers.
i used to have problem on mean, median, and mode too.
You select a letter randomly from a bag containing the letters s, p, i, n, n, e, and r. find the probability of selecting an s. description
Answer:
1/7
Step-by-step explanation:
Answer:
i think it would be 1/7 also
Step-by-step explanation:
If Ruth contributed $10,000 toward the total group investment of $200,000 for the purchase of a seafood restaurant, what percentage of the company does she own?
Answer:
20 %
Step-by-step explanation:
10000/200000
The percentage of the company she owns is equivalent to 5%.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that if Ruth contributed $10,000 toward the total group investment of $200,000 for the purchase of a seafood restaurant.
Assume that the percentage of the company she owns is equivalent to [x] percent. So, we can write -
10000 = [x]% 0f 200000
10000 = [x]/100 × 200000
10000 = [x] × 2000
[x] = (10000/2000)
[x] = 5%
Therefore, the percentage of the company she owns is equivalent to 5%.
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(3^2)^6 = _____
A) 3^-4
B) 3^4
C) 3^8
D) 3^12
The answer is:
The correct option is:
D) [tex](3^{2})^{6}=3^{12}[/tex]
Why?To solve the problem, we need to remember the power of a power property, it's defined by the following way:
[tex](a^{m})^{n}=a^{m*n}[/tex]
When we have a power of a power, we must keep the base and then, the new exponent will be the product between the two original exponents.
So, we are given the expression:
[tex](3^{2})^{6}[/tex]
Then, calculating we have:
[tex](3^{2})^{6}=3^{2*6}=3^{12}[/tex]
Hence, we have that the correct option is:
D) [tex](3^{2})^{6}=3^{12}[/tex]
Answer:
The correct answer is option D). 3^12
Step-by-step explanation:
Points to remember
Identities
(xᵃ)ᵇ = xᵃᵇ
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
It is given that (3^2)^6
To find the correct option
(3^2)^6 can be written as, (3²)⁶
By using above identities,
(3²)⁶ = 3⁽² ˣ ⁶⁾
= 3¹²
Therefore the correct answer is option D). 3^12
Divide and write in simplest form
3 1/3 divided by 2 3/5
Answer:
Step-by-step explanation:
If we change those mixed fractions to improper we will have a much easier time with them:
[tex]\frac{\frac{10}{3} }{\frac{13}{5} }[/tex]
Now that looks horrible. The rule for dividing fractions by fractions is a simple one, thankfully. Bring the bottom fraction up next to the top fraction, then flip it upside down and change the sign to multiplication:
[tex]\frac{10}{3}[/tex]×[tex]\frac{5}{13}[/tex]
Multiply straight across the top and straight across the bottom to get
[tex]\frac{50}{39}[/tex]
Depending upon what your teacher calls "simplest form", this form may be the simplest, or the mixed fraction may be the simplest. The mixed fraction equivalent to this improper is
[tex]1\frac{11}{39}[/tex]
A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probability that both are silver hoop earrings? Write your answer as a fraction or percent rounded to the nearest tenth. The probability that both are silver hoop earrings is .
Answer:
fraction is 2/4
Step-by-step explanation:
Which shows reflection
Is it c?
Will give BRAINLIEST. Can't see these very well
Answer:
B
Step-by-step explanation:
You could take these images (if you can visualize it)
And paste it into SM paint, and then reflect it.
But, if you look closely, A is just the notes higher, but not reflected, or changed in any other way.
C the second note is lower in the reflection. The notes shouldn't change in a reflection. Just the order.
It’s simple but my teacher has “33 ft” as an answer and Idk why...
Answer:
33 ft
Step-by-step explanation:
The distance of interest is apparently not the straight-line distance from the top of the vertical ladder to the ground (20 ft), but the length of the arc the top of the ladder makes as it rotates. That arc length (s) is given by ...
s = r·θ . . . . . where θ is the angle in radians subtended by the arc
Here, the radius is 20 ft, and the angle is the supplement of 85°, or 95° = (95/180)π radians.
s ≈ (20 ft)·(1.65806 radians) ≈ 33.16 ft ≈ 33 ft
What questions can you ask yourself as you decide on a career field?
What do I love to do?
What brings me joy?
What am I naturally good at?
All of the above
Answer:
What do I love to do?
What brings me joy?
What am I naturally good at?
Answer is all of the above - last choice
HELP ME OUT PLEASE!! A circular plot with a 250 ft diameter is watered by a spray irrigation system. To the nearest square foot, what is the area that is watered as the sprinkler rotates through an angle of 58∘?
≈ 41,179 ft^2
≈ 31,634 ft^2
≈ 2,517 ft^2
≈ 7,909 ft^2
Answer:
7,909 ft²
Step-by-step explanation:
If the diameter is 250 ft, that must mean the radius is 125 ft. For this problem, use the formula for area of a sector.
[tex]\frac{58}{360} \pi 125^{2}[/tex]
Answer:
≈ 7,909 ft^2
Step-by-step explanation:
Find the next term of the arithmetic sequence shown. 23, 28, 33, 38, . . .
A) 42
B) 43
C) 45
D) 48
ANSWER
B) 43
EXPLANATION
The given arithmetic sequence is 23, 28, 33, 38, . . .
We can observe the following pattern,
23+5=28
28+5=33
33+5=38
To obtain the subsequent terms, we add 5.
Therefore the next term is
38+5=43
After a group of 24 parts were tested. 5 were found defective. About what percent of the parts were defective
Answer:
20.8%
Step-by-step explanation:
5/24= defective
^divide, and multiply by 100 to get percent
:)
The required percentage of defective parts is 20.8%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
After a group of 24 parts was tested. 5 were found defective.
The required percentage of the defective parts is given as,
= 5 / 24 × 100%
= 0.208 × 100%
= 20.8%
Thus, the required percentage of defective parts is 20.8%.
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How do you evaluate the limit?
Answer:
Step-by-step explanation:
First of all the answer.
[tex]\lim_{n \to -\infty}2^x= 1/ \lim_{n \to \infty}1/2^x = 0[/tex]
[tex]\lim_{n \to -\infty} 1-2^x = 1[/tex]
This approaches 0/1 = 0
The graph is included to show that this is the answer I get.
6.
What is the value of x?
24
30
40
38
You must do pythagorean theorem:
a^2 + b^2 = c^2
a and b are the legs and c is the hypotenuse
In this triangle...
a = 16
b = x
c = 34
so...
16^2 + x^2 = 34^2
256 + x ^2 = 1156
x^2 = 900
Then to isolate x square root both sides. This will get rid of the square on the x value.
This will give you...
30
x is 30
Hope this helped!
Answer: second option
Step-by-step explanation:
You need to apply the Pythagorean theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
In the figure you can observe the value the hypotenuse of the right triangle and the value of one of this leg. Then, you need to solve for the other leg from [tex]a^2=b^2+c^2[/tex]:
[tex]b^2=a^2-c^2[/tex]
[tex]b=\sqrt{a^2-c^2}[/tex]
Substituting values, you get that the value of "x" is:
[tex]b=\sqrt{(34)^2-(16)^2}[/tex]
[tex]b=30[/tex]
The population of California is approximately 3.8 × 107, and the population of Nebraska is approximately 1.9 × 106. Which state has the larger population, and by how many times is its population larger than the other state’s?
Answer:
california by 205.2
Step-by-step explanation:
3.8 times 107=406.6-California
1.9 times 106=201.4-Nebraska
205.2
Answer: The Population of California is larger than the population of Nebraska by 20 times
Step-by-step explanation:
Given
Population of California , [tex]P_C=3.8\times 10^{7}[/tex]
and population of Nebraska, [tex]P_N=1.9\times 10^{6}[/tex]
From above data it is clear that the population of California is larger than the population of Nebraska
And Ratio, [tex]\frac{P_C}{P_N}=\frac{3.8\times 10^{7}}{1.9\times 10^{6}}=\frac{38}{1.9}=20[/tex]
Thus the population of California is larger than the population of Nebraska by 20 times
Find the coordinates of the point on the directed segment from (3,2) to (6,8) that divides into a ratio of 1:3.
a. (4.5, 5.5)
b. (5.25, 6.25)
c. (3.75, 3.5)
d. (4,4)
Answer:
c. (3.75, 3.5)
Step-by-step explanation:
Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.
There are a couple of ways you can get there.
1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...
P-A = (1/(1+3))·(B-A)
We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...
P = A + (.75, 1.5) = (3.75, 3.5)
__
2. Finish working out the equation above to solve for P:
4(P -A) = B -A
4P = B + 3A
P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa
P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)
_____
Comment on choosing an answer
You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.
Find a cubic function with the given zeros. 7, -3, 2 (1 point)
ANSWER
[tex]f(x) =x^3-6x^2-13x+42[/tex]
EXPLANATION
The zeros of the cubic function is given as:
x=7,x=-3,x=2
This implies that, x-7,x+3,x-2 are factors of the given cubic polynomial function.
We can write the completely factored form as a function of x to get:
[tex]f(x) = (x - 7)(x + 3)(x - 2)[/tex]
We expand to get:
[tex]f(x) = (x - 7)(x^2+ x-6)[/tex]
[tex]f(x) =x^3-6x^2-13x+42[/tex]
This is a cubic function because the highest degree is 3.
What is the smallest fractional portion of an inch that you can measure with the ruler shown in Exam Figure A1?
A. 1/32"
B. 1/16"
C. 1/8"
D. 1/64"
Answer:
The minimun portion of inches that can be measured with the ruler is 1/16''.
Step-by-step explanation:
The precision , what is the minimun measurement that can be aprecciated by the ruler can be determined counting the number of disivion within 2 units. To this ruler we can count 16 division bwtween one unit and asecutive one.
There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys
The problem describes a situation with 16 girls who are four more than twice the number of boys. By setting up and solving the simple algebra equation 2x + 4 = 16, we find there are 6 boys in the club.
Explanation:This is a word problem which can be solved using simple algebra. Given that there are 16 girls in the club and the number of girls is four more than twice the number of boys, we can set up the equation:
2x + 4 = 16
Where x stands for the number of boys. Solving this equation, we subtract 4 from both sides to get: 2x = 12. Dividing both sides by 2, we find that there are x = 6 boys in the club.
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(25 points)
Mr. Price earns $350 per week working in an appliance store. In addition, he earns 3% commission on all of his sales.
Last week, he sold $3, 800 worth of appliances.
What was Mr. Price's total income for the week?
A) $114
B) $236
C) $464
D) $556
Answer:
c
Step-by-step explanation:
commission is basically 3 percent of what he sells he gets, sooooo 3 percent of 3800 is 114 (3800 × .03 because change the percent to decimal) and add it to his pay :)
Answer:
D
Step-by-step explanation:
quadrilateral ABCD is located at A(-2,2) B (-2,4) C(2,4) D(2,2). The quadrilateral is then transformed using the rule (x-2, y+8) to form A’B’C’D’. Describe what characteristics you would find if the corresponding vertices were connected with line segments !!! HELP WILL MARK AS BRAINLIEST PLS HELP!!
Answer:
Those line segments are parallel and all the same length.
Step-by-step explanation:
Translation modifies the coordinates of each point the same way, moving the point some distance in some direction. Hence the line segments connecting original to image points will all have the same length and direction.
_____
Comment on the question
The question is pretty open-ended. If it is multiple choice, perhaps there is a choice that more or less expresses the idea above. Otherwise, it is hard to tell what the question is driving at.
A rabbit and a turtle were to start a race at the same place. the rabbit was feeling very confident and slept for 8 hours before starting. the turtle ran at a pace of 1 mile per hour, and the rabbit ran at 5 miles per hour. the race was a distance of 10 miles. who won the race?
Answer:
Step-by-step explanation:
D=RT
10=1T
T=10 HOURS FOR THE TURTLE.
10=5(T-8)
10=5T-40
5T=10+40
5T=50
T=50/5
T=10 HOURS FOR THE RABBIT.
LOOKS LIKE A TIE .
Which numbers are necessary to solve this problem? Franklin brought 4 jump ropes to the park. Each jump rope can be used by 3 people at a time. Fifteen friends came to the park to jump rope. How many friends could play jump rope if all of Franklin's ropes were being used? A. 4 jump ropes, 3 people B. 3 people, 15 friends C. 4 jump ropes, 15 friends D. 4 jump ropes, 3 people, 15 friends
Answer:
D. 4 jump ropes, 3 people, 15 friends
Step-by-step explanation:
In order to answer the question how many friends could play, you need to be able to determine the smaller of ...
(number of ropes) × (friends per rope)number of friendsYou can find the first of these numbers using the values of answer A, but if the number of Franklin's friends is smaller than 12, then you need to know that in order to properly answer the question. Hence, we believe you need to know ...
the number of jump ropesthe number of friends per ropethe number of friendsOn the first day of the month, John counted his money and found he had 28.35. Since then, he has received an additional 17.26 from the jobs he does after school. How much money does he have now
Answer: He has 45.61
Step-by-step explanation:The answer is 45.61 because you add the decimals, 28.35+17.26, then you aline the decimal points and add, then get 45.61
1 1
28.35
+ 17.26
45.61
Total money John has now is 45.61.
On the first day of the month, John had $28.35 and received an additional $17.26.
To find out how much money John has now, you need to add the initial amount to the additional money he received. Therefore, John now has
28.35 + 17.26 = 45.61 money
the surface area of the figure below is 50.80m^2 True or False
For this case we have that by definition, the surface area of a cone is given by:
[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]
Where:
A: It's the radio
s: It's the slant
Substituting according to the data we have:
[tex]SA = \pi * 2.1 * 5.6 + \pi * (2.1) ^ 2\\SA = 36.9264 + 13.8474\\SA = 50.7738 \ m ^ 2[/tex]
If we round:
[tex]SA = 50.8 \ m ^ 2[/tex]
Answer:
True
At the movie theatre, child admission is $5.70 and adult admission is $9.40. On Wednesday, 173tickets were sold for a total sales of $1345.00. How many child tickets were sold that day?
Answer: 76 child tickets were sold that day.
Step-by-step explanation:
You need to set up a system of equations.
Let be "c" the number of child tickets sold that Wednesday and "a" the number of adult tickets sold that Wednesday.
Then:
[tex]\left \{ {{a+c=173} \atop {9.40a+5.70c=1345.0}} \right.[/tex]
Using the Method of Elimination, you can multiply the first equation by -9.40, then add both equations and finally solve for "c":
[tex]\left \{ {{-9.40a-9.40c=-1626.2} \atop {9.40a+5.70=1345.0}} \right.\\..................................\\-3.7c=-281.2\\\\c=\frac{-281.2}{-3.7}\\\\c=76[/tex]
A science teacher needs to choose 12 students out of 16 to serve as peer tutors how many different ways can the teacher choose the12 students
He can ask the student to raise their hands and pick them
the teacher can ask them to pick the closest number. the teacher can choose the students with the highest grades.