Answer:
Step-by-step explanation:
To solve this problem, we can use the following formula:
(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture
Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.
We know that:
The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.
The store owner wants to sell the final mixture for $2.10 per pound.
The black tea is worth $1.80 per pound.
Using the formula above, we can write:
(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10
Simplifying this equation, we get:
84 + 1.8x = 73.5 + 2.1x
0.3x = 10.5
x = 35
Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.
I hope this helps! Let me know if you have any other questions.
Answer:
Step-by-step explanation:
Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.
The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:
Cost of oolong tea = 35 pounds × $2.40/pound = $84
The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:
Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x
Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:
$73.5 + $2.10x = $84
Now, let's solve for x to find the amount of black tea needed:
$2.10x = $84 - $73.5
$2.10x = $10.5
x = $10.5 / $2.10
x ≈ 5
Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.
Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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How many ways can you arange 2 Letters picked
from A, B, C, D? order matters
When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).
Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 x 3 x 2 x 1) / (2 x 1)
= 24 / 2
= 12
Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.
~~~Harsha~~~
Answer:
Step-by-step explanation:
When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.
In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).
Using the formula, we can calculate:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 × 3 × 2 × 1) / (2 × 1)
= 24 / 2
= 12
Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.
The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth of coffee makers, which of the following is a valid possible price for them?
A. $15
B. $30
C. $40
D. $55
The possible price for the items if the store sells $600 is (c) $40
How to determine the possible price for the items?From the question, we have the following parameters that can be used in our computation:
The supply-demand graph
If the store sells $600, then there is a supply worth of $600
The equation of the supply line is calculated as
y = mx + c
Where
c = y = 0
i.e. c = 100
So, we have
y = mx + 100
Using another point on the graph, we have
30m + 10 = 400
So, we have
m = 13
This means that
y = 13x + 100
For a supply of 600, we have
13x + 100 = 600
So, we have
13x = 500
Divide by 13
x = 38.4
Approximate
x = 40
Hence, the possible price for the items is (c) $40
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PLS HELP THANK YOUUUUUUU
¿De cuántas maneras es posible formar los grupos del torneo de liga de futbol de primera división? Recordemos que en la primera división del futbol en México participan 18 equipos, y para el torneo de la liga se forman dos grupos de cinco equipos y dos grupos de 4 equipos. Se sugiere que al resolverlo se vaya restando la cantidad de equipos que se han considerado para el primer grupo, después para el segundo grupo y así para cada grupo. Finalmente aplicar la regla del producto para encontrar las diferentes formas.
Note that his is solved using the principle of Combination, and there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
How is this so ?Let 's compute the number of ways to form the groups using combinations.
First group - 5 teams
C(18, 5) = 18! / (5! * (18-5)!) = 8568
Second group - 5 teams
C(13, 5) = 13! / (5! * (13-5)!) = 1,287
Third group - 4 teams
C(8, 4) = 8! / (4! * (8-4)!) = 70
Fourth group - 4 teams
C(4, 4) = 4! / (4! * (4-4)!) = 1
Now, applying the product rule
Total ways = 8568 x 1,287 x 70 x 1 = 771891120
Therefore, there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
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Translation
In how many ways is it possible to form the groups of the first division soccer league tournament? Let's remember that 18 teams participate in the first division of soccer in Mexico, and for the league tournament, two groups of five teams and two groups of 4 teams are formed. It is suggested that when solving it, the number of teams that have been considered for the first group be subtracted, then for the second group and so on for each group. Finally apply the product rule to find the different shapes.
Kristin left the movie theater and traveled
toward the lake at an average speed of 33
km/h. Jennifer left sometime later
traveling in the opposite direction with an
average speed of 45 km/h. After Kristin
had traveled for two hours they were 156
km apart. How long did Jennifer travel?
AnswerTherefore, Jennifer traveled for 2 hours.
Step-by-step explanation:
Let x be the time Jennifer traveled.
Kristin traveled for 2 hours at 33 km/h, so she had traveled 66 km when Jennifer started traveling.
After x hours, Jennifer had traveled 45x km.
The total distance between them was 156 km.
So, we have:
66 km + 45x km = 156 km
Simplifying the equation, we get:
45x km = 90 km
x = 2 hours
Therefore, Jennifer traveled for 2 hours.
1. Find the value of x for which is parallel to m. The figure is not to scale. 60 150 90 30 30° Y 60° ро
The value of x for which the two lines are parallel is given as follows:
x = 60º.
What are consecutive interior angles?We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.
Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:
x + 2x = 180
3x = 180º
x = 180º/3
x = 60º.
Missing InformationThe figure is given by the image presented at the end of the answer.
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Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x-10)^2-49
Answer:f(x) = (x-10)^2-49
f(x) = (x-10+7)(x-10-7)
f(x) = (x-3)(x-17)
The zeros of the function are 3 and 17.
Step-by-step explanation:
A population of values has a normal distribution with �=189.7 and �=96.7. You intend to draw a random sample of size �=62.
Find the probability that a single randomly selected value is between 189.7 and 213.
P(189.7 < X < 213) =
Find the probability that a sample of size �=62 is randomly selected with a mean between 189.7 and 213.
P(189.7 < M < 213) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.
Step 1: Calculate the z-scores for the given values using the formula:
z = (x - μ) / σ
For 189.7:
z1 = (189.7 - 189.7) / 96.7 = 0
For 213:
z2 = (213 - 189.7) / 96.7 ≈ 0.2417
Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.
P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939
Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.
To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance
Step 1: Calculate the standard error of the mean (σ_m) using the formula:
σ_m = σ / sqrt(n)
σ_m = 96.7 / sqrt(62) ≈ 12.2878
Step 2: Convert the given qualities to z-scores utilizing the equation:
z = (x - μ) / σ_m
For 189.7:
z1 = (189.7 - 189.7) / 12.2878 = 0
For 213:
z2 = (213 - 189.7) / 12.2878 ≈ 1.8967
Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.
P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702
Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
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The mean rounded to the nearest 10th of the following data set is 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
Answer:
17.5
Step-by-step explanation:
You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.
In this case, your data set is:
15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19 (12 numbers).
Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]
Next, divide 210 (total sum) with the amount of terms in total (12):
[tex]\frac{(210)}{(12)} = 17.5[/tex]
17.5 is already in the tenth digit place value, and so you do not need to round.
17.5 is your answer.
~
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A group of ten students recorded the number of minutes they spent on one math homework problem. The mean amount of time was 9 minutes, but the MAD was 7 minutes. Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label your axis.
Answer:
Here is an example of a dot plot (in text, did as best as I could to represent it) that matches the description you provided:
Number of Minutes Spent on Math Homework Problem
|
10| o
9| o
8|
7| o
6|
5| o
4|
3| o
2|
1| o
0|___________________
1 2 3 4 5 6 7 8 9 10
Students
This dot plot shows the number of minutes spent on a math homework problem by ten students. The mean amount of time is represented by the dot at the y-value of 9, and the MAD (Mean Absolute Deviation) is represented by the spread of the data around the mean.
PLS HELP MEEEE PLSSS The number of defective watches manufactured by a watch company, with regard to the total number of watches manufactured for each
order, are shown in the scatter plot below.
Which of the equations below would be the line of best fit?
A. y = 1/5x
B. y = 1/50x
C. y = 1/50x-10
D. y = 1/50x+10
The equation line is y= 1/50x.
We have a graph from which we can take two points as
(100, 2) and (200, 4).
So, the slope of line
= (change in y)/ (change in x)
= (4-2)/ (200- 100)
= 2/ 100
= 1/50
Now, the equation line is
(y - 2)= 1/50 (x - 100)
y-2 = 1/50 x - 2
y= 1/50x
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Tom buys a UNC jersey with a 20% discount coupon.
Which response accurately calculates his new cost C
with respect to the original costs x?
a. C=x-0.20
B. C = 0.80x
C. C = 1.20x
d. C = x-0.80
A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answer:
Perimeter:[tex]4x+10[/tex] feet
Area:[tex]x^{2}+5x+6[/tex] feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=[tex]x^{2}+2x+3x+6=x^{2}+5x+6[/tex]
i am going toget a detention if i dont do this please help me
challenging was 0.92, with a margin of error of 0.07.
Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.
The confidence interval using a margin of error of 0.07 is (0.85,0.99)
Confidence IntervalSample proportion = 0.92
Margin of error = 0.07
Lower bound of the confidence interval = Sample proportion - Margin of error
Lower bound = 0.92 - 0.07 = 0.85
Upper bound of the confidence interval = Sample proportion + Margin of error
Upper bound = 0.92 + 0.07 = 0.99
Confidence interval = [Lower bound, Upper bound]
Confidence interval = [0.85, 0.99]
Therefore, the confidence interval for the proportion of math majors who found the curriculum challenging is approximately 0.85 to 0.99.
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I need help with this!
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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e:
3) Find the value of x if RZ-2x+7 and SW= 5x-23
Applying the properties of the diagonal of a rectangle, the value of x is calculated as: x = 37.
How to Find the Value of x Using the Properties of the Diagonals of a Rectangle?A rectangle is a quadrilateral that has two equal diagonals which bisect each other, to form equal segment. Rectangle RSTW has two diagonals RT and SW, therefore:
2(RZ) = SW
Given the following:
RZ = 2x + 7
SW = 5x - 23
Plug in the values:
2(2x + 7) = 5x - 23
4x + 14 = 5x - 23
4x - 5x = -14 - 23
x = 37
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the three consecutive term of geometric series be increased by their middle term, then prove that the resulting term will be in Harmonic series.
Let x, xr , xr² be the terms of GP.
After the increase, the terms are : x+xr , xr+xr , xr²+xr
or in simplified manner : x(1+r), 2xr, xr (r+1) .
For these terms to be in Harmonic Progression, their reciprocals should be in Arithmetic Progression .
Thus,
Arithmetic mean of first and last terms should be equal to the middle term.
First term = 1/[x(1+r)] ; Middle term= 1/(2xr) ; Last term = 1/[xr(r+1)]
Assume,
A = Arithmetic mean of first and last term
A= [1/[x(1+r)]+[1/[xr(r+1)] /2
A= (1/2)[(r+1)/(xr(1+r))]
A= (1/2)(1/xr)
A= 1/(2xr)
A = Middle term
Thus, the reciprocals are in AP.
Hence x(1+r), 2xr, xr(r+1) in HP.
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Isosceles trapezoid 3 The minor base, the height and oblique side of a trapezoid isosceles measure respectively 34 m. 20m and 29m. Calculate the perimeter and area of the trapezius.
The perimeter of the trapezoid is 106 meters.
The area of the trapezoid is 1360 square meters.
To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:
The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).
First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.
So, the length of the major base is also 34 m.
The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:
Perimeter = length of minor base + length of major base + 2 × length of oblique side
Perimeter = 34 m + 34 m + 2 × 29 m
Perimeter = 34 m + 34 m + 58 m
Perimeter = 106 m
To calculate the area of the trapezoid, we can use the formula:
Area = (sum of the lengths of the bases) × height / 2
Area = (34 m + 34 m) × 20 m / 2
Area = 68 m × 20 m / 2
Area = 1360 m²
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heres the equation...
2/3 * P = 5
P=?
Answer:
p=7.5 or 7 1/2
Step-by-step explanation:
To solve this equation you need to isolate the P
1) We can multiply P and the numerator (In this case 2) since it is the same thing. The rewritten equation is 2p/3=5.
2) Now we can multiply both sides by 3 to isolate 2p. The equation is now 2p=15
3) The next step is to divide both sides by 2 so we can isolate the p. We now have p=7.5 or 7 1/2
Hope this helps :)
enter the number that belongs in the green box
The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.
We have,
To find the angle opposite to side BC in triangle ABC, we can use the Law of Cosines.
The Law of Cosines states that in a triangle with sides of lengths a, b, and c, and the angle opposite to side c being denoted as C, the following equation holds:
c² = a² + b² - 2ab x cos(C)
In this case,
Side a is BC with length 12, side b is AC with length 20, and side c is AB with length 11. We want to find the angle C, which is opposite to side BC.
Plugging the given values into the Law of Cosines equation:
11² = 12² + 20² - 2 x 12 x 20 x cos C
121 = 144 + 400 - 480 x cos C
121 = 544 - 480 x cos C
480 x cos C = 544 - 121
480 x cos C = 423
cos C = 423/480
Now, we can find the angle C by taking the inverse cosine (arccos) of (423/480):
C = arccos(423/480)
Using a calculator, we find that C is approximately 38.213 degrees.
Therefore,
The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.
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What is the product?
(4x)(-3x³)(-7x³)
O -84x¹2
O-84x24
O 84x¹2
O 84x24
Answer:
-84x^7
Step-by-step explanation:
The product of (4x)(-3x³)(-7x³) is -84x^8.
To calculate the product, we multiply the coefficients together and add the exponents of the variables:
4 * (-3) * (-7) = 84
x^1 * x^3 * x^3 = x^(1+3+3) = x^7
Combining the coefficient and the variable, we get -84x^7.
Out of a pool of 26 men and 29 women what is the probability of 12 women jurors being chosen?
The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.
The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:
C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.
The number of ways to choose 12 women from a pool of 29 is given by the combination formula:
C(29, 12) = 29! / (12! * (29-12)!) = 7726160.
Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:
P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.
Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
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The figure below represents
marked central angle.
I
of a full circle. Find the measure of the
A full circle has [tex]360^{\circ}[/tex].
[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]
The mark angle is [tex]160^{\circ}[/tex].
What is the numerical probability of selecting 10 men and 2 women out of 26 men and 29 women?
Hello!
men = 10/26 = 5/13
women = 2/29
P = 5/13 x 2/29 = 10/377
PLEASE HELP ME I REALLY NEED THIS SOLVED
total angles of the triangle = 180°
∠BAC + ∠ABC + ∠ACB = 180°
40° + 90° + ∠ACB = 180°
130° + ∠ACB = 180°
∠ACB = 180° - 130°
∠ACB = 50°
∠ACB and ∠ECD is opposite angles. So, that two angles are equal.
∠ACD = ∠ECD = 50° (B)
That's it :)
Step-by-step explanation:
50°
abc is right angle and
a is 40°
b is 90°
c is 50°
so angle acb is vertical opposite to angle ecd and it is equal
Heather has a bag with 8 balls numbered 1 through 8. She is playing a game of chance.
This game is this: Heather chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected,$8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $13 if 7 or 8 is selected.(a) Find the expected value of playing the game.
(b) What can Heather expect in the long run, after playing the game many times?
(She replaces the ball in the bag each time.)
Heather can expect to gain money.
Heather can expect to lose money.
Heather can expect to break even (neither gain nor lose money).
(a) The expected value of playing the game is 0.
(b) Heather can expect to break even in the long run.
To find the expected value of playing the game, we need to calculate the weighted average of the possible outcomes.
Expected value calculation:
The probability of selecting each ball is the same since Heather replaces the ball in the bag each time.
The probability of selecting any particular number is 1/8.
Expected value = (Probability of outcome 1 × Value of outcome 1) + (Probability of outcome 2 × Value of outcome 2) + ... + (Probability of outcome 8 × Value of outcome 8)
Expected value = (1/8 × 1) + (1/8 × 2) + (1/8 × 5) + (1/8 × 6) + (1/8 × 8) + (1/8 × 10) + (1/8 × (-13)) + (1/8 × (-13))
Expected value = (1/8) + (2/8) + (5/8) + (6/8) + (8/8) + (10/8) + (-13/8) + (-13/8)
Expected value = 26/8 - 26/8
Expected value = 0
Since the expected value of playing the game is 0 On average, she neither gains nor loses money over multiple plays of the game.
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What is the multiplicative identity of 1/2
Answer:
Multiplicative identity for any real number is 1.
Step-by-step explanation:
9. Difference between the place values of "1" in 3116365 is
