Answers
The analysis of the data to obtain the best fit line equations that model the data, indicates;
5. a. Quadratic
b. y = -0.1179·x² + 2.1124·x + 4.215
c. Please find the completed chart showing the predicted values and the in the residuals in the following section.
6. a. A linear model may not be appropriate for the data in the residual plot
b. 4
c. 5
4. a. The exponential model of the function is; y = 100·e^(-0.124·t)
b. The weight after 8 weeks is about 37.1 grams
c. The sample will be 4 grams in about 26 weeks
5. a. The equation is; y = 22.703·x + 2.5733
b. The predicted y-value at x = 10 is; y = 229.60
c. The first time is about x ≈ 3.54
What is the best fit line?The best fit line is a line that is drawn through a set of data points in such a way that it minimizes the sum of squared errors of the data.
5. The best fit model can be obtained by plotting a scatter plot of the graph, which indicates that the best fit line resembles the shape of a parabola.
Therefore;
a. The best fit equation is; Quadratic
b. The best fit equation, obtained using technology is; y = -0.1179·x² + 2.1124·x + 4.215
The square of the correlation coefficient is; R² = 0.9584
The chart can be filled with the best fit equation as follows;
[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-4}Distance (foot) & Height (foot) & Predicted Value &Residual \\ \cline{1-4}0 & 4 & 4.215 & -0.215 \\\cline{1-4}2 & 8.4 & 8.16588 & 0.23412 \\\cline{1-4}6 & 12.1 & 13.23804 & -1.13804 \\\cline{1-4}9 & 14.2 & 14.56626 & -0.36626\\\cline{1-4}12 & 13.2 & 13.77228 & -0.57228 \\\cline{1-4}13 & 10.5 & 13.03602 & -2.53602 \\\cline{1-4}15 & 9.8 & 10.8561 & -1.0561 \\\cline{1-4}\end{tabular}[/tex]
The predicted value are obtained by plugging in the x-value into the best fit equation and the residuals is the difference between the actual value and the predicted value.
6. a. A residual plot can be used to as assessment with regards to meeting the assumptions of a linear regression model.
A residual plot that is randomly scattered about zero indicates that a linear model is appropriate for the data.
The data points in the residual plot are not expressed as being randomly scattered around zero.
The pattern that exists in the residual plot indicates that the values are positive for x-values that are either low or high, and the middle x-values have a negative residuals. Therefr;
The pattern indicates that a linear regression model may not be appropriate for the datab. The number of positive residuals = 4
c. The number of negative residuals = 5
4. The general form of the exponential model of a function, y = A × e^(-k·t) can be used to find the function for the data as follows;
A = The initial amount = The value at 0 = 100
y = The amount of radioactive material at a given time t
e = Euler's number = 2.71828
The datapoints in the table indicates;
88.3 = 100 × e^(-k × 1)
k = -㏑(0.883) ≈ 0.124
The exponential model is therefore; y = 100 × e^(-0.124·t)
b. The weight of the sample after 8 weeks can be obtained by plugging in t = 8 in the exponential function for the weight of the radioactive substance as follows;
y = 100 × e^(-0.124 × 8) ≈ 37.1
The weight of the sample after 8 weeks is about 37.1 grams
c. When the sample is 4 grams we get;
y = 4
4 = 100 × e^(-0.124 × t)
e^(-0.124 × t) = 4/100 = 1/25
-0.124 × t = ln(1/25) = -ln(25)
t = ln(25)/0.124 ≈ 26
t ≈ 26 weeks
Therefore; The weight will be 4 grams after approximately 26 weeks
5. A linear regression can be performed using MS Excel to obtain the equation that models the data as follows;
y = 22.703·x + 2.5733
The square of the regression coefficient is; R² = 0.9995
a. The most appropriate equation to model the data in the table is; y = 22.703·x + 2.5733
b. The y-value when x = 10 can be predicted by plugging in x = 10 into the model equation for the data as follows;
y = 22.703 * 10 + 2.5733 ≈ 229.60
Therefore;
The predicted y-value when x is 10 is 229.60 (rounded to the nearest tenth)c. The first time the y-value is 83, can be found by setting y = 83 in the equation and solve for x as follows;
83 = 22.703·x + 2.5733
22.703·x = (83 - 2.5733)
x = (83 - 2.5733)/22.703 ≈ 3.54
Therefore, the first time the y-value is 83 is when x is approximately 3.54
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Related Questions
Let X be the time that Alice waits for a traffic light to turn green, and let Y be the time (at a different intersection) that Bob waits for a traffic light to turn green. Suppose that X and Y have joint density
f(x,y)=15e−3x−5y,x≥0,y≥0
The variance of 2X+3Y is
Answers
The variance of 2X + 3Y is 35.52.
The solution to the problem is as follows:
First, find the mean and variance of X and Y:
E(X) = 3/5
Var(X) = 3/25
E(Y) = 1
Var(Y) = 1/25
Then, use the properties of variance to find the variance of 2X + 3Y:
Var(2X + 3Y)
= 4Var(X) + 9Var(Y) + 12Cov(X,Y)Cov(X,Y)
= E[(2X - 6/5)(3Y - 1)]
= 6E(XY) - 6E(X) - 3E(Y) + 2
= 6 * (integral from 0 to infinity integral from 0 to infinity of xyf(x,y)dxdy) - 6 * 3/5 - 3 * 1 + 2 = 6 * (integral from 0 to infinity 15xye^-3xdydx) - 8
= 54/5
Therefore,
Var(2X + 3Y) = 4(3/25) + 9(1/25) + 12(54/5)
= 888/25
= 35.52.
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Ming took a cab across town. His fare was $22, and he leaves an 18% tip.
What is the total amount Ming pays the cab driver?
Answers
Answer:
$25.96
Step-by-step explanation:
Since the tip is 18% of the fare, he pays 118% of the fare.
118% of $22 =
= 1.18 × $22
= $25.96
your friend deposits $5000 in an investment account that earns 6.3% annual interest. find the balance after 6 years when the interest is compounded monthly
Answers
The balance after 6 years when the interest is compounded monthly is $7289.60
How to find the balance after 6 years when the interest is compoundedTo find the balance after 6 years when the interest is compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final balanceP = the principal amount (the initial deposit)r = the annual interest rate (as a decimal)n = the number of times the interest is compounded per yeart = the time in yearsIn this case, P = $5000, r = 6.3% = 0.063 (annual interest rate as a decimal), n = 12 (since interest is compounded monthly), and t = 6.
Plugging in these values, we get:
A = $5000(1 + 0.063/12)^(12*6)
Evaluate
A = $7289.60
Therefore, the balance after 6 years when the interest is compounded monthly is $7289.60
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How do you tell Linear vs. Nonlinear
Answers
Answer:
linear equations produce straight lines when graphed, and their rate of change remains constant
Nonlinear equations do not produce straight lines when graphed.
To determine whether its linear or nonlinear, you can graph it and see if it produces a straight line, or check if it can be written in the form y= Mx+b
Step-by-step explanation:
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
Answers
Answer:
The height of the water increases 2 inches per minute.
Step-by-step explanation:
The slope is the rate at which the pool is being filled.
A slope of 2 means a filling rate of 2 inches per minute.
Answer: The height of the water increases 2 inches per minute.
Find the distance between the points (9,7) and (6,3).
Answers
Let (x1, y1) = (9,7) and (x2, y2) = (6,3)
By distance formula,
d = (x2 - x1)² + (y2 - y1)²
d = (6 - 9)² + (3 - 7)²
d = (-3)² + (-4)²
d = 9 + 16
d = 25 units
I need help finding the subsets and proper subsets. Please help it’s due tonight!!
Answers
Answer:
Step-by-step explanation:
# elements = 292 - 268 - 1 = 23 elements
G has 2^23 subsets = 8388608
G has 2^23 - 1 proper subsets = 8388607
let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. which of the following is a possible graph of y=f(x)?
Answers
First, note that the degree of the polynomial is the highest power of x that appears in the expression. In this case, the degree is max(n, 5, m, 2).
How to determine graph?Next, consider the leading coefficient of the polynomial, which is the coefficient of the term with the highest power of x. In this case, the leading coefficient is a.
Based on this information, here are some possible general shapes of the graph of y=f(x):
If n is even and a > 0, the graph of y=f(x) looks like a "U" shape, with both ends pointing upwards.
If n is even and a < 0, the graph of y=f(x) looks like an upside-down "U", with both ends pointing downwards.
If n is odd and a > 0, the graph of y=f(x) looks like a "v" shape, with the vertex pointing upwards.
If n is odd and a < 0, the graph of y=f(x) looks like an upside-down "v", with the vertex pointing downwards.
Note that these are just general shapes, and the actual graph could be modified by the other terms in the polynomial. Additionally, the values of b, c, d, and the constants could also affect the shape and behavior of the graph.
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Complete Question is : let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. what is the possible graph of the function?
NEED ANSWER ASAP NOT WORRIED ABOUT AN EXPLANATION
Answers
Because a is a right angle that means the entire line is right which is 90° then you divide 90° by 30° and you get 3°
A 145 pound person burns 420 calories per hour riding an exercise bicycle at a rate of 15 miles per hour. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem related to the function
Answers
Answer: 580
Step-by-step explanation: i learned that just like 1 hour ago in school
PLEASEEEEE HELPPPPPPP!!!!!!!
A line segment contains endpoints A(-1, 2) and B(2, 5).
Determine the point that partitions line segment AB into a 3: 6 ratio.
A 4,5/3
B 0,3
C 1/3,3
D -2,1
Answers
Answer:
We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.
Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:
x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9
y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9
Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:
x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0
y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)
Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.
What is the answer to
(P-q) (3)
Answers
Answer:
3P-3q
Step-by-step explanation:
you want to distribute the 3, to the whole parenthesis.
Sam has 26 seashells.
He collects 31 more seashells.
Then he gives 14 seashells away.
What equation shows the number of seashells, Sam has now?
Answers
Answer:
43 seashells
Step-by-step explanation:
x = 26
x + 31 - 14
(26) + 31 - 14
57 - 14
= 43
at the farmers market there is a large pile of small cauliflowers. the mean weight of these cauliflowers is 400 grams with a standard deviation of 20 grams. assume the weight of theses cauliflowers is normally distributed. which has a greater probability, the mean weight of an individual cauliflower being between 400 and 409 grams or the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams?
Answers
The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.
Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:
z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)
μ = 400 grams (mean weight of the population)
σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0
Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:
P(400 < X < 409) = P(0 < Z < 0.45)
Using the standard normal distribution table, the probability is 0.1745.
The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:
(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)
σ = 20 grams (standard deviation)
n = 36 (number of samples)
Now, we need to standardize the sample mean. It will be as follows:
z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)
z = 0
As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.
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Oliver practices the piano 448 minutes in 4 weeks. At what rate did she practice, in
minutes per day?
Answers
Answer:
16
Step-by-step explanation:
First you figure out how many days are in 4 weeks which is 28. Then you do 448 divided by 28 which equals 16. There's your answer.
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++
0
Which division expression is shown in the model?
1
col
3
÷2
314
÷2 2÷
Divide Fractions: Fractional Quotients Quiz - Level F
13
2
3
-
+ +
3
Answers
The division expression shown in the model attached to this question is 1/2 ÷ 3
How to determine which division expression is shown in the model?The model missing in the question is added as an attachment
In the model, we have
Shaded sections = 3
Partitons = 1/2
This means that
Division expression = Partitons ÷ Shaded sections
Substituting the above expressions, we have
Division expression = 1/2 ÷ 3
This means that the division expression is 1/2 ÷ 3
When the expression is solved, we have
Division expression = 1/6
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Complete question
Which division expression is shown in the model?
See attachment
Help plis! Need process too
Answers
Answer:
Step-by-step explanation:
E
A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
Answers
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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2x^4 −15x^3 +27x^2 +2x +8 is divided by x−4
Answers
Answer:
Step-by-step explanation:
Standard: 2x^3 - 7x^2 -x-2
Quotient: 2x^3- 7x^2 -x-2
remainder: 0
the animal club is designing a large terrarium to house their pet gecko. the dimensions of the terrarium are shown (in terms of x). the volume of the terrarium will be 70 cubic feet. solve for x.
Answers
The answer of the given question based on the the volume of the terrarium will be 70 cubic feet to solve for x the answer is the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.
What is Formula?A formula is mathematical expression that shows relationship between different variables or quantities. It can be used to calculate value based on given inputs or to derive mathematical result from set of conditions or assumptions.
To find the value of x, we can use the formula for the volume of a rectangular prism, which is:
Volume = Length x Width x Height
We are given the dimensions of the terrarium in terms of x, so we can substitute them into the formula:
Volume = (x) * (x-2) * (x-5)
We know that the volume of the terrarium is 70 cubic feet, so we can set the equation equal to 70 and solve for x:
(x) * (x-2) * (x-5) = 70
Expanding left side of equation we get:
x^3 - 7x^2 + 10x = 70
We can simplify this equation by subtracting 70 from both sides:
x^3 - 7x^2 + 10x - 70 = 0
In this case, the constant term is -70 and the leading coefficient is 1, so the possible rational roots are:
±1,±2,±5,±7,±10,±14,±35,±70
We can use synthetic division to simplify the calculation. After testing all the possible roots, we find that the only rational root is x = 7.
This means that the dimensions of the terrarium are:
Length = x = 7 feet
Width = x - 2 = 5 feet
Height = x - 5 = 2 feet
Therefore, the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.
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A house on the market was valued at $442,000. After several years, the value decreased by 15%. By how much did the house's value decrease in dollars? What is the current
Answers
decrease = 0.15 x $442,000
decrease = $66,300
the house's value decreased by $66,300.
current value = original value - decrease
current value = $442,000 - $66,300
current value = $375,700
the current value of the house is $375,700.
HELP IS DUE TODAY!!!!!!!!!!!!!!!!!!
Answers
Using expressions,
4a. x= 0 is not possible.
4b. x= 1 is not possible.
5a. (9x-5)(9x+5)
5b. (x-3)(2x+1)
6. 1/(3x-7)
7a. x = (-5,∞)
7b. x = (∞,2]
7c. x = (-3,7]
What are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let's examine the writing of expressions.
The other number is x, and a number is 6 greater than half of it.
As a mathematical expression, this proposition is denoted by the expression x/2 + 6.
Here the values of x has to be such that the denominator is not equal to zero.
So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.
a. 81x²-25
= 81x² + 45x-45x-25
=9x(9x+5)-5(9x+5)
= (9x-5)(9x+5)
b. 2x²-5x-3
= 2x² + x - 6x -3
= x(2x+1)-3(2x+1)
=(x-3)(2x+1)
Next, the intervals for x are as follows:
x = (-5,∞)
x = (∞,2]
x = (-3,7]
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suppose is an matrix, all of whose rows are identical. suppose is an matrix, all of whose columns are identical. what can be said about the entries in
Answers
we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.
In the row-wise identical matrix, all entries in each row are the same, but the entries in different rows can be different.
In the column-wise identical matrix, all entries in each column are the same, but the entries in different columns can be different.
Thus, we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.
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What is the volume of the composite figures?
Answers
Total volume of the composite figure using volume of cuboid formula is = 120ft³.
Define volume?A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.
The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.
In the given figure,
Length of cuboid = 6ft.
Breadth of cuboid = 3ft.
Height of cuboid = 5ft.
Length of second cuboid = 4ft.
Height of second cuboid = 5ft.
Breadth of second cuboid = 3ft.
Volume of first cuboid = length × breadth × height.
= 6 × 3 × 5
= 90ft³
Volume of second cuboid = 4 × 3 × 5
= 60ft³
Now the second cuboid is half.
So, volume becomes = 60/2
= 30ft³.
So, total volume of the figure = 90 + 30 = 120ft³.
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Determine the exact surface area of the cylinder in terms of tt radius: 1 1/4 height: 2 3/4 A. 6 9/16 B: 10 C: 15 15/16 D: 19 3/8
Answers
Step-by-step explanation:
Total surface area is 2πr²+2πrh
2× 22/7 × 5/4× 5/4 + 2 × 22/7 × 5/4 × 11/4
continue like this to get your right answer
What are the approximate solutions to the equation-1+3=12x+5?
Answers
The value of x in this equation is -¼ so, the approximate solution to the equation "-1+3=12x+5" is (x = -¼).
As equation given is -1+3=12x+5
Thus, 2 = 12x+5
12x = -3
x = -3/12
x = -¼
Hence the value of x in this equation is -¼.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. A linear equation with two variables, however, has two solutions.
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The difference between
two numbers is 3. Their
sum is 47. What are the
numbers?
Answers
Answer:
25 and 22
Step-by-step explanation:
Laura has a flower with a stem that is 11/12
of a foot long. She cuts 3/12
of a foot off the stem. Complete the fraction to show the length of the flower's stem after it was cut
Answers
the length of the flower's stem after it was cut is 2/3 of a foot long.
Laura's flower has a stem that is 11/12 of a foot long. If she cuts 3/12 of a foot off the stem, we need to subtract 3/12 from 11/12 to find the length of the remaining stem. To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:
11/12 - 3/12 = 8/12
We can simplify the fraction 8/12 by dividing both the numerator and the denominator by their greatest common factor, which is 4. Therefore, we have:
8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3
the fraction to show the length of the flower's stem after it was cut
To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:
11/12 - 3/12 = 8/12
Therefore, the length of the flower's stem after it was cut is 2/3 of a foot long.
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when using multiple regression techniques, it is common to try out the resulting equation on a second sample to see if it still fits well. this process is known as
Answers
The process of trying out the resulting equation on a second sample to see if it still fits well is called “cross-validation”.
Cross-validation is a technique used to evaluate the performance of a statistical model on a new independent dataset, which was not used in training the model. This process helps to assess the generalization capability of the model and helps to determine whether the model is overfitting or underfitting the data. By testing the model on a new independent dataset, we can get a better idea of how well the model is likely to perform on new data in the future. Cross-validation can also help in selecting the best model from a set of competing models.
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two fair dice are tossed together once
a. draw the sample space for the following outcome
b. find the probability of getting a total of 7 and 8
Answers
Therefore, the probability of getting a total of 7 is 6/36, which reduces to 1/6. The probability of getting a total of 8 is 5/36.
What is probability?In mathematics, probability is a measure of the likelihood that an event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. The probability of an event A is denoted by P(A), and it is defined as the ratio of the number of outcomes favorable to A, to the total number of possible outcomes in the sample space.
Here,
a) The sample space for tossing two fair dice can be represented as a table, where each row represents the outcome of one die, and each column represents the outcome of the other die. The sample space for this experiment would consist of all possible combinations of the two dice outcomes. Here's how the sample space table would look like:
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
b) To find the probability of getting a total of 7 or 8, we need to count the number of possible outcomes that result in these totals, and then divide by the total number of possible outcomes in the sample space.
For a total of 7, there are 6 possible outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
=6/36
For a total of 8, there are 5 possible outcomes (2+6, 3+5, 4+4, 5+3, 6+2).
=5/36
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Complete question:
Two fair dice are tossed together once, what is:
a. draw the sample space for the following outcome
b. find the probability of getting a total of 7 and 8