The computer output below gives results from the linear regression analysis for predicting the pounds of fuel consumed based on the distance traveled in miles for passenger aircraft. Data used for this analysis were obtained from ten randomly selected flights. Predictor Constant Distance (miles) Coef -4702.64 21.282 SE Coef 1657 0.833 T -2.84 25.54 P 0.022 0.000 S = 2766.57 R-Sq - 98.8% R-Sqladj)=98.3% (a) What is the equation of the least-squares regression line that describes the relationship between the distance traveled in miles and the pounds of fuel consumed? Define any variables used in this equation. (b) Below is a residual plot for the ten flights. Is it appropriate to use the linear regression equation to make predictions? Explain. 6000 Residual (lbs) -6000 C) Interpret the y-intercept in the context of the problem. Is this value statistically meaningful

Answer:

29

Step-by-step explanation:

primes up to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47

Answer:

5, 7, 13, 23, 37, 55

Step-by-step explanation:

The sequence is, +2, +6, +10 so it should be +14 next and then +18

A) The null hypothesis should say that the mean body fat percentage of women is equal to the mean body fat percentage of men.

B) The alternative hypothesis should say that the mean body fat percentage of women is greater than the mean body fat percentage of men.

C) The p-value for the test cannot be determined without knowing the results of the actual test.

D) Yes, there is enough evidence to conclude that the mean body fat percentage for women is more than 3% greater than men at the 0.05 significance level, because the difference between the means is 7.34% (22.29% - 14.95%) which is greater than 3%.

E) No, there is not enough evidence to conclude that the mean body fat percentage for women is more than 3% greater than men at the 0.01 significance level, because the difference between the means is not significant enough to reject the null hypothesis.

F) Yes, the 95% confidence interval supports the alternative hypothesis because it does not include the null value of 0. The confidence interval for the difference between the means is (1.63%, 12.05%).

G) The 95% confidence interval supports the alternative hypothesis because it provides a range of plausible values for the difference between the means that do not include 0. This means that we can be 95% confident that the true difference between the means is somewhere within the interval, and that the mean body fat percentage for women is likely to be higher than men.

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Answer:

19

Step-by-step explanation:

Since the median is 18, we know that the missing number must be between 17 and 21. To find their average, we add them together and divide by 2:

(17 + 21) / 2 = 19

The E-M algorithm is used to estimate the parameters mu and Sigma. The implementation in R involves defining the likelihood function, initializing the estimates, and using the E-M steps to update the estimates.

The E-M algorithm for estimating the mean and covariance matrix of a multivariate normal distribution from a set of observations can be performed in the following steps

Initialization: Choose initial values for the mean vector and covariance matrix.

Expectation step: Calculate the posterior probabilities of each observation belonging to each component of the mixture model using Bayes' theorem and the current parameter estimates.

Maximization step: Use the posterior probabilities to update the estimates of the mean vector and covariance matrix for each component of the mixture model.

Repeat steps 2 and 3 until convergence (i.e., until the change in the parameter estimates falls below a specified tolerance level).

In this case, we have a single multivariate normal distribution with unknown mean vector and covariance matrix. Therefore, we can perform the E-M algorithm to estimate these parameters directly.

Here is the R code for implementing the E-M algorithm

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The depth of the ocean is 650 feets at the bottom of the sunlight zone.

The distance travelled by echo sound is given by the formula -

Speed = 2×distance/time

So, calculating the speed of sound from the formula using distance and time

Speed = 2×25/(1/100)

Speed = 50×1000

Speed of sound = 5000 feet/second

Now, calculating the distance or depth of ocean at the bottom of the sunlight zone -

Distance = (speed×time)/2

Distance = (5000×26/100)/2

Distance = 1300/2

Distance = 650 feets

Hence, the depth of ocean is 650 feets.

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The correct interpretation for the confidence interval is that with 95% confidence, the true proportion of people with kids will be in the above interval.

This means that if we were to repeat the same survey or study multiple times, about 95% of the time, the true proportion of people with kids would fall within the given interval.

It is important to note that we cannot say with certainty that the true proportion falls within the interval, as there is always a chance for sampling error or variability.

However, we can say with a high degree of confidence that the true proportion is likely to fall within the interval. Option A is incorrect because we cannot say with certainty that the true proportion is within the interval, even though it is likely. Option c is also incorrect because the confidence level refers to the long-run proportion of intervals that will contain the true value, not a probability statement about a single interval.

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To find the change of coordinates matrix P_C_H_B, given the change of coordinates matrix P_B_C = [1, 3; 0, 1] and the coordinates matrices H and B, follow these steps:

1. Write down the given matrix P_B_C:
  P_B_C = [1, 3;
           0, 1]

2. Write down the coordinates matrices H and B:
  H = [h1; h2]
  B = [b1; b2]

3. Calculate P_C_H_B by multiplying P_B_C with the difference between the coordinates matrices H and B:
  P_C_H_B = P_B_C * (H - B)

4. Substitute the given matrices into the equation and perform the matrix subtraction:
  P_C_H_B = [1, 3; 0, 1] * ([h1 - b1; h2 - b2])

5. Multiply the matrices:
  P_C_H_B = [1*(h1 - b1) + 3*(h2 - b2); 0*(h1 - b1) + 1*(h2 - b2)]

6. Simplify the resulting matrix:
  P_C_H_B = [(h1 - b1) + 3*(h2 - b2); h2 - b2]

So, the change of coordinates matrix P_C_H_B is [(h1 - b1) + 3*(h2 - b2); h2 - b2].

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The required solution for the given right angle triangle is given below.

Blank #1: We can use the Pythagorean theorem to find AB:

[tex]AB = \sqrt{AC^2 + CB^2} \\= \sqrt{12^2 + 9^2}\\ =15[/tex]

Therefore, AB = 15.

Blank #2: We can use the inverse tangent function to find the angle A:

tan(A) = opposite / adjacent = CB / AC = 9 / 12

[tex]A = tan^{-1}(9/12) = 36.86^o[/tex]

Therefore, angle A ≈ 36 degrees.

Blank #3: We can use the inverse cosine function to find the angle C:

cos(C) = adjacent / hypotenuse = CB / AB = 9 / 15

C = arccos(9/15) ≈ 53.14

Therefore, angle C ≈ 53.14 degrees.

Blank #4: We can use the fact that the sum of angles in a triangle is 180 degrees to find angle B:

B = 180 - A - C ≈

B= 90

Therefore, angle B ≈ 90

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When a person walking [tex] \frac{1}{5}[/tex] mile in [tex] \frac{1}{15}[/tex] hour, then the speed ( distance travelled per unit time) of person is equals to the 3 miles per hour.

The speed is defined as the rate at which a particular object covers a certain amount of distance. This speed can be fast or slow. That is simply defined as the rate of change in distance per unit of time. It is defined as Speed=[tex]\frac{d}{t }[/tex]

We have a person who is walks along the road. The distance travelled by person =

[tex] \frac{1}{5}[/tex] mile

Time taken by him to travel the distance 1/5 mile [tex]= \frac{ 1}{15}[/tex] hours.

We have to determine the persons speed per hour. Using the speed formula, now the speed of person, [tex]s = \frac{ \frac{ 1}{5} }{\frac{1}{15} }[/tex]

= 3 miles/hour

Hence, required value of speed is 3 miles per hour.

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If the economy starts to weaken and the FOMC determines that employment is falling short of maximum employment, an appropriate policy implementation would be to lower the interest on reserve balances rate, ON RRP offering rate, and discount rate.

This would make it cheaper for banks to borrow money and encourage them to lend more, which could stimulate economic activity and create more job opportunities. Option c, Lower the interest on reserve balances rate, ON RRP offering rate, and discount rate, is the best answer. The other options are not as effective in this scenario - raising rates would likely make it more expensive for businesses and consumers to borrow money, which could further slow down the economy, while using open market operations to decrease reserves could lead to a shortage of liquidity in the banking system.

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Answer:

y = 8 + x

350x + 70y = 1,400----->5x + y = 20

5x + 8 + x = 20

6x + 8 = 20

6x = 12

x = 2, y = 10

2 sliders, 10 onion rings

Generator for D = ABCE + AE + BE + CE + (AB + AC + BC)E

= ABCE + AE + BE + CE + ABE + ACE + BCE

This simplifies to:

Generator for D = ABCE + AE + BE + CE + ABE + ACE + BCE.

The generator for column D is ABCE.

To see this, note that column D depends on the factors B, C, and E, as well as on the interaction between A and B, A and C, and A and E. These six terms are the only ones that involve A, B, C, and E, and so they must be included in the generator. We can write this as:

Generator for D = ABCE + AB + AC + AE + BC + BE + CE

Simplifying this expression, we can combine the last five terms into a single term using the property that in GF(2), any number added to itself is equal to zero:

Generator for D = ABCE + AB + AC + AE + BC + BE + CE

= ABCE + AB + AC + AE + BC + BE + CE + ABC + ABE + ACE + BCE

= ABCE + AB + AC + AE + BC + BE + CE + (AB + AC + BC)E

We can then remove the redundant terms AB, AC, and BC from the generator, since they are already included in ABCE:

Generator for D = ABCE + AE + BE + CE + (AB + AC + BC)E

= ABCE + AE + BE + CE + ABE + ACE + BCE

This simplifies to:

Generator for D = ABCE + AE + BE + CE + ABE + ACE + BCE.

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Maria sells each scarf for  $33 if Maura spends $5.50 in materials to make a scarf and she sells each scarf for 600% of the cost of material

Given that Maura spends $5.50 in materials to make a scarf.

Maura sells each scarf for 600% of the cost of material

Let us find 600 % of 5.50

600/100×5.50

6×5.50

$33

Maria sells each scarf for 600% of the cost of materials, which means she sells each scarf for 6 times the cost of materials.

Therefore, Maria sells each scarf for  $33.

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For the first part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3), (3,2)}. This relation is reflexive because every element in A is related to itself, and it is symmetric because if (x,y) is in R, then (y,x) is also in R. However, it is not transitive because (1,2) and (2,3) are in R, but (1,3) is not in R.

For the second part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (3,4), (1,3), (2,4)}. This relation is reflexive because every element in A is related to itself, and it is transitive because if (x,y) and (y,z) are in R, then (x,z) is also in R. However, it is not symmetric because (1,2) is in R, but (2,1) is not in R.

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We can say with 99% confidence that the true mean length of all Hollywood movies made in the last 10 years is between 107.2 and 116.0 minutes.

We are given:

Sample size (n) = 45

Sample mean (x) = 111.6 minutes

Sample standard deviation (s) = 14.3 minutes

Confidence level = 99%

To construct the confidence interval, we can use the formula:

Confidence interval = x ± zα/2 * (s/√n)

Where:

x = sample mean

zα/2 = the z-score associated with the desired confidence level (in this case, 99% corresponds to a z-score of 2.576)

s = sample standard deviation

n = sample size

Substituting the given values, we get:

Confidence interval = 111.6 ± 2.576 * (14.3/√45)

Confidence interval = 111.6 ± 4.36

Confidence interval = (107.2, 116.0)

Therefore, we can say with 99% confidence that the true mean length of all Hollywood movies made in the last 10 years is between 107.2 and 116.0 minutes.

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Answer:

A legal question an interviewer may ask an application at a job interview is does the applicant has a criminal history.,

z1 = (78.1 - 83) / (7/√49) ≈ -1.49 and z2 = (85.2 - 83) / (7/√49) ≈ 0.85. Using a standard normal distribution table or calculator, we find that P(-1.49 < z < 0.85) ≈ 0.6924. Therefore, P(78.1 < x < 85.2) ≈ 0.6924.

(a) Since the sample size is large enough (n ≥ 30) and the population standard deviation is known, the central limit theorem can be applied to conclude that the sampling distribution of the sample mean, x, is approximately normal with mean µ = 83 and standard deviation σ/√n = 7/√49 = 1.

(b) To find P(x > 84.9), we need to standardize the value of 84.9 using the formula z = (x - µ) / (σ/√n). Thus, z = (84.9 - 83) / (7/√49) = 1.9. Using a standard normal distribution table or calculator, we find that P(z > 1.9) ≈ 0.0287. Therefore, P(x > 84.9) ≈ 0.0287.

(c) To find P(x ≤ 76.7), we again need to standardize the value of 76.7 using the formula z = (x - µ) / (σ/√n). Thus, z = (76.7 - 83) / (7/√49) = -1.86. Using a standard normal distribution table or calculator, we find that P(z < -1.86) ≈ 0.0317. Therefore, P(x ≤ 76.7) ≈ 0.0317.

(d) To find P(78.1 < x < 85.2), we first standardize the values of 78.1 and 85.2 using the formula z = (x - µ) / (σ/√n). Thus, z1 = (78.1 - 83) / (7/√49) ≈ -1.49 and z2 = (85.2 - 83) / (7/√49) ≈ 0.85. Using a standard normal distribution table or calculator, we find that P(-1.49 < z < 0.85) ≈ 0.6924. Therefore, P(78.1 < x < 85.2) ≈ 0.6924.

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The probability that at least one random number is greater than 4.55 is 0.718 (rounded to three decimal places).

The probability of at least one number exceeding 4.55 can be calculated as the complement of the probability that all ten numbers are less than or equal to 4.55.

The probability density function of a uniform distribution on the interval [0, 5] is:

f(x) = 1/5, 0 <= x <= 5

The probability that one number is less than or equal to 4.55 is given by:

P(X <= 4.55) = ∫₀⁴.₅₅ f(x) dx = ∫₀⁴.₅₅ (1/5) dx = (1/5) * (4.55 - 0) = 0.91

So, the probability that all ten numbers are less than or equal to 4.55 is:

P(X₁ <= 4.55, X₂ <= 4.55, ..., X₁₀ <= 4.55) = (0.91)^10 = 0.2824

Therefore, the probability that at least one number exceeds 4.55 is:

P(at least one number > 4.55) = 1 - P(all numbers <= 4.55) = 1 - 0.2824 = 0.7176

So the probability that at least one random number is greater than 4.55 is 0.718 (rounded to three decimal places).

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Answer:

The correct answer is:

E) We are 90% confident that the difference between the true population proportions of procedures performed in the large and small intestines is between 0.1714 and 0.1886.

Step-by-step explanation:

To calculate the confidence interval, we use the formula:

[tex]CI = (p1 - p2) ± z*SE[/tex]

where p1 and p2 are the sample proportions of surgeries performed in the large and small intestines, z is the z-score corresponding to the desired confidence level (90% in this case), and SE is the standard error of the difference in proportions, given by:

[tex]SE = sqrt((p1(1-p1)/nlarge) + (p2(1-p2)/nsmall))[/tex]

Substituting the given values, we have:

p1 = 0.4, nlarge = 15000

p2 = 0.22, nsmall = 15000

z = 1.645 (from the standard normal distribution for a 90% confidence level)

SE = sqrt((0.40.6/15000) + (0.220.78/15000)) = 0.0097 (rounded to 4 decimal places)

Therefore, the confidence interval is:

CI = (0.4 - 0.22) ± 1.645*0.0097 = 0.18 ± 0.0159

So we are 90% confident that the true difference in proportions of surgeries performed on the large and small intestines is between 0.1714 (0.4 - 0.0159) and 0.1886 (0.22 + 0.0159). Option E correctly represents this interpretation of the confidence interval.

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The angle ∠ABC is 83 degrees.

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Using the theorem for cyclic quadrilateral angles and arc angles,

67 = 1 / 2 (78 + x)

where

x = ∠DC

67 = 39 + 0.5x

67  - 39 = 0.5x

28  = 0.5x

divide both sides by 0.5

x = 28 / 0.5

x  = 56 degrees

Hence,

Arc ∠AC = 110 + 56 = 166 degrees

Therefore,

∠ABC = 1 / 2 (166)

∠ABC = 83 degrees

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Answer:

A sample is a subset of the population.

Answer: 3025 m^3.

Step-by-step explanation:

Answer:

67.6 grams

Step-by-step explanation:

First, find the volume of the cylindrical container which should provide the volume of water in the sample

Volume, V,  of a cylinder is given by the formula

[tex]V = \pi r^2h[/tex]

where,
r = radius of the cylinder
h = height of the cylinder

Given r = 8 cm and h = 11.6 cm. the volume of the container used by Parker
V = π · 8² · 11.6

   = 2332.31838 cubic centimeters

There are 0.029 grams of trace element for every cubic centimeter of water

Therefore the amount of trace element in 2332.31838 cc of water
= 2332.31838 x 0.029
= 67.63723302 grams'

Rounded to the nearest tenth that would be 67.6 grams

Answer:

Step-by-step explanation:

2332.31838 x 0.029

= 67.63723302 grams'

there the asnwer

The equation for the total cost of ordering the shirts by mail is Total = 10 * 5 + 5 * 7.5 + 8 * 12 + 0.50

From the question, we have the following parameters that can be used in our computation:

The total cost of ordering the shirts by mail is then represented as

Total = Sum of price * order + Mail order charge

Using the above as a guide, we have the following:

Total = 10 * 5 + 5 * 7.5 + 8 * 12 + 0.50

When evaluated, we have

Total = 184

Hence, the total amount of order is $184

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The Q-matrix is,

Q = | -λ1-λ2     λ2     λ1     0  |
   |    μ1  -μ1-λ2     0     λ2  |
   |    λ1     0  -μ1-λ1     μ2  |
   |    0      μ1     μ2  -μ1-μ2 |

In this problem, two salesmen are working in a small office selling shares in a mutual fund. Each salesman i is on the phone for an exponential amount of time with rate μi and then off the phone for an exponential amount of time with rate λi. We will formulate a Markov chain model for this system with state space {00, 01, 10, 11} and find the Q-matrix (generator matrix) of the Markov chain.

The state space has four possible states:
- 00: Both salesmen are off the phone
- 01: Salesman 1 is off the phone and Salesman 2 is on the phone
- 10: Salesman 1 is on the phone and Salesman 2 is off the phone
- 11: Both salesmen are on the phone

The Q-matrix (generator matrix) is a 4x4 matrix that describes the transition rates between states. We can find the Q-matrix as follows:

Q = | -λ1-λ2     λ2     λ1     0  |
   |    μ1  -μ1-λ2     0     λ2  |
   |    λ1     0  -μ1-λ1     μ2  |
   |    0      μ1     μ2  -μ1-μ2 |

In this matrix, the diagonal elements are negative sums of the transition rates out of the respective state, and the off-diagonal elements represent the transition rates between states.

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The quarter circle represents a distance of one-fourth of the circumference of a circle with a radius equal to the velocity of the object. Since the time interval is six seconds, the angular displacement of the quarter circle is (1/4) x 2π = π/2 radians. Therefore, the distance traveled along the quarter circle is [(π/2) x velocity + a + b]/6

To calculate the object's average speed during the six-second interval, we will first determine the distance traveled in each segment and then divide the total distance by the total time. In this case, the object moves in three parts: a quarter circle and two line segments.

Step 1: Determine the radius of the quarter circle using the given information (such as velocity or distance). To find the average speed of the object during the six-second interval represented by the quarter circle and two line segments, we need to first calculate the total distance traveled by the object.

Step 2: Calculate the circumference of the entire circle by using the formula C = 2πr, where C is the circumference and r is the radius.

Step 3: Find the length of the quarter circle by dividing the circumference by 4, as a quarter circle represents one-fourth of the entire circle.

Step 4: Determine the lengths of the two line segments using the given information.

Step 5: Add the length of the quarter circle and the lengths of the two line segments to find the total distance traveled.

Step 6: Divide the total distance traveled by the total time of six seconds to find the object's average speed during the six-second interval.
The two line segments represent the remaining distance traveled by the object. Let's assume the lengths of the two line segments are a and b, respectively. Then, the total distance traveled by the object is (π/2) x velocity + a + b.

Now, we can calculate the average speed of the object as the total distance traveled divided by the time interval of six seconds:
Average speed = (Total distance traveled) / (Total time)

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(a) The probability of selecting a senior on any given selection is 0.65. The probability of selecting a non-senior (either a junior or a sophomore) is 0.35. To select exactly three award-winners until a senior is selected, we need to select two non-seniors followed by a senior. The probability of this sequence is:

0.35 * 0.35 * 0.65 = 0.080

So the probability of selecting exactly three award-winners until a senior is selected is 0.080.

(b) The probability of selecting a junior on any given selection is 0.24. The probability of selecting a non-junior (either a senior or a sophomore) is 0.76. To select at least three award-winners until a junior is selected, we need to select two or more non-juniors followed by a junior. The probability of this sequence is:

(0.76 * 0.76 * 0.24) + (0.76 * 0.24) + (0.24) = 0.334

So the probability of selecting at least three award-winners until a junior is selected is 0.334.

(c) The probability of selecting a sophomore on any given selection is 0.11. The probability of selecting a non-sophomore (either a senior or a junior) is 0.89. To select 2 or fewer award-winners until a sophomore is selected, we need to select 1 or 2 non-sophomores followed by a sophomore. The probability of these sequences is:

(0.89 * 0.89 * 0.11) + (0.89 * 0.11) + (0.11) = 0.214

So the probability of selecting 2 or fewer award-winners, until a sophomore is selected, is 0.214.
(a) To find the probability that we will select exactly three award-winners, and the third one is a SENIOR, we need to consider the following probabilities:

1. First student is not a senior (i.e., a junior or a sophomore)
2. Second student is not a senior (i.e., a junior or a sophomore)
3. Third student is a senior

Probability (not a senior) = 1 - Probability (senior) = 1 - 0.65 = 0.35
Probability (exactly 3 award-winners with the third being a senior) = 0.35 * 0.35 * 0.65 ≈ 0.079625

(b) To find the probability that we will select at least three award-winners until a JUNIOR is selected, we can find the probability of selecting 1 or 2 award-winners and subtract it from 1.

Probability (1 award-winner and it's a junior) = 0.24
Probability (2 award-winners, first is not a junior and second is a junior) = (1-0.24) * 0.24 = 0.1816

Total probability (1 or 2 award-winners) = 0.24 + 0.1816 = 0.4216
Probability (at least 3 award-winners) = 1 - 0.4216 ≈ 0.5784

(c) To find the probability that we will select 2 or fewer award-winners until a SOPHOMORE is selected:

Probability (1 award-winner and it's a sophomore) = 0.11
Probability (2 award-winners, first is not a sophomore and second is a sophomore) = (1-0.11) * 0.11 ≈ 0.0989

Total probability (2 or fewer award-winners) = 0.11 + 0.0989 ≈ 0.2089

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The coordinates of the reflected points are:

Point A': (4, -4)

Point B': (0, 0)

Point C': (-2, -5)

As we know that a point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

As per the question, given that ΔABC has vertices at (-4, 4), (0,0), and (-5,-2).

To find the coordinates of the reflected points, we need to swap the x and y-coordinates of each point.

Point A (-4, 4) becomes A' (4, -4)

Point B (0, 0) remains the same B' (0, 0)

Point C (-5, -2) becomes C' (-2, -5)

Therefore, the coordinates of the reflected points are:

Point A': (4, -4)

Point B': (0, 0)

Point C': (-2, -5)

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The quantity q(t) of a radioactive substance left at time t > 0 with a half-life of 3200 years can be found using the formula: q(t) =

[tex]q(0) * 0.5^(t/3200)[/tex]

after 6400 years, only 10 grams of the substance will be left. where q(0) is the initial quantity of the substance.

Given q(0) = 20 g, we can find q(t) for any time t > 0 using the formula above. For example, if we want to find q(6400) - the quantity of the substance left after 6400 years - we can substitute t = 6400 in the formula and get: q(6400) =

[tex]20 * 0.5^(6400/3200)[/tex]

= 10 g.

After 6400 years, only 10 grams of the substance will be left. It is important to note that the half-life of a radioactive substance is the time it takes for half of the substance to decay.

After one half-life (3200 years), the initial quantity of the substance will be reduced to half (10 g). After two half-lives (6400 years), it will be reduced to one-fourth (5 g), and so on.

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Answer:

The answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape

Step-by-step explanation:

We are given that, Julia had a bag filled with gumballs. There were 3 lemon-lime, 4 watermelon, and 6 grape gumballs.

There are 3 lemon-lime: Elements in sample space are lemon-lime, lemon-lime, lemon-lime

There are also 4 watermelon: Elements in sample space are watermelon, watermelon, watermelon, watermelon

Lastly there are 6 grape: Elements in sample space are grape, grape, grape, grape, grape, grape

Which can lead to the problem of:

3 + 4 + 6 = 13. Same as option B

Thus the answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape