Choose the correct answer
1. ______is the ratio of 300 to 100.
a) 3 : 1 b) 1 : 3 c) 300 : 1 d) 100 : 3
2. If the weight of 20 books is 80Kg, then the weight of 1 book is..
a) 4 Kg b) 20 Kg c) 40 Kg d) 8 Kg
3. An equivalent ratio of 3 : 2 is
a) 3 : 4 b) 6 : 4 c) 9 : 4 d) 3 : 6
4. The middle terms of 3:15 = 21:105 are.
a) 3 and 15 b) 21 and 105 c) 3 and 21 d) 15 and 21
5. Which of the following is not proportional?
a) 8 : 4 :: 8 : 16 b) 4 : 8 :: 8 : 16 c) 16 : 8 :: 8 : 4 d) 8 : 16 :: 4 : 8
6. If two ratios are equal, then they are in ____________
7. The ratio of 20 boys to 15 girls is _____________
8. Express the following ratios in the simplest form.
a) 14 to 42 b) 56 to 80
9. Check whether the following are in proportion or not.
a) 4, 6, 8, 12. b) 15, 45, 5, 25.
10. If the cost of 6 cans of Juice is ₹ 210, then what will be the cost of 4 Juice?
11. Taniya earns ₹ 150,000 and saves ₹ 50,000. Find the ratio of
a) Her earning to her expenditure b) Her earning to her savings
12. Find the ratio of 15 cm to 2 meters.
Answers
Answer:
1) A, 2) A, 3) B, 4) D, 5) A, 6) proportion, 7) 4 : 3, 8) a) The simplest ratio of 14 : 42 is 1 : 3, b) The simplest ratio of 56 : 80 is 7 : 10, 9) a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units, b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series, 10) 4 cans of juice cost 140, 11) a) 3 : 2, b) 3 : 1, 12) The ratio of 15 centimeters to 2 meters is 3 : 40.
Step-by-step explanation:
1) The ratio is determined by following operation:
\(x = \frac{300}{100}\)
\(x = \frac{3}{1}\)
3 : 1 is the ratio of 300 to 100. (Answer: A)
2) The weight of 1 book is found by the total weight of books divided by the total amount of books, that is:
\(x = \frac{80\,kg}{20}\)
\(x = 4\,kg\)
The weight of 1 book is 4 kilograms. (Answer: A)
3) The equivalent ratio of 3 : 2 is found by multiplicating both numerator and denominator by a given positive number:
\(x = \frac{3\times 2}{2\times 2}\)
\(x = \frac{9}{4}\)
An equivalent ratio of 3 : 2 is 6 : 4. (Answer: B)
4) The middle terms of ratio correspond with the denominator of the ratio on the left and the numerator of the ratio on the right. Hence, the middle terms of 3 : 15 = 21 : 105 are 15 and 21. (Answer: D)
5) 8 : 4 is not proportional to 8 : 16, since both numerators and denominators are not multiplied by the same number. That is:
\(x = \frac{8\times 1}{4\times 4}\)
\(x = \frac{8}{16}\)
8 : 4 :: 8 : 16 is not proportional. (Answer: A)
6) If two ratios are equal, then they are in proportion. That is:
\(a \,:\,b \,::c\,:\,d\), where \(r = \frac{c}{a} = \frac{d}{b}\), \(\forall\,r > 0\).
If two ratios are equal, then they are in proportion. (Answer: proportion)
7) The ratio of 20 boys to 15 girls is derived of 20 divided by 15 until a denominator of the least integer is found by simplifying the fraction:
\(\frac{20}{15} = \frac{4}{3}\)
The ratio of 20 boys to 15 girls is 4 : 3. (Answer: 4 : 3)
8) Express the following ratios in the simplest form:
a) \(\frac{14}{42} = \frac{7}{21} = \frac{1}{3}\).
The simplest ratio of 14 : 42 is 1 : 3.
b) \(\frac{56}{80} = \frac{28}{40} = \frac{14}{20} = \frac{7}{10}\)
The simplest ratio of 56 : 80 is 7 : 10.
9) When a series is in proportion, it must be in increasing or decreasing order at constant rate.
a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units.
b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series.
10) We determine the cost of 4 cans of juice by simple rule of three:
\(x = \frac{4\,cans}{6\,cans}\times 210\)
\(x = 140\)
4 cans of juice cost 140.
11) a) The ratio of her earning to her expenditure is:
\(x = \frac{150000}{150000-50000}\)
\(x = \frac{3}{2}\)
The earning to expenditure ratio is 3 : 2.
b) The ratio of her earning to her savings is:
\(x = \frac{150000}{50000}\)
\(x = 3\)
The earning to savings ratio is 3 : 1.
12) 1 meter equals 100 centimeters. Then, the given ratio is:
\(x = \frac{15\,cm}{200\,cm}\)
\(x = \frac{3}{40}\)
The ratio of 15 centimeters to 2 meters is 3 : 40.
Related Questions
Find an equation of the tangent plane to the given parametric surface at the specified point. Graph the surface and the tangent plane.r(u,v)=u2i+2usinvj+ucosvk; u=1, v=0.
Answers
The equation of the tangent plane to the given parametric surface at the specific point is -2x + 4z = 0 .
In the question ,
it is given that ,
the function is r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .
Now,
According to the give function,
r(u,v) = (u² , 2usin(v) , ucos(v))
Then, solving it , We get ,
r(u,v) = (u² , 2usin(v) , ucos(v))
\(r_{u}\) = (u , 2sin(v) , cos(v))
\(r_{u}\) (1,0) = (2 , 0 , 1)
\(r_{v}\) = (0 , 2ucos(u) , -sin(v))
\(r_{v}\) (1,0) = (0 , 2 , 0)
So , the matrix become
\(\left[\begin{array}{ccc}i&j&k\\2&0&1\\0&2&0\end{array}\right]\)
On simplifying , we get
i(−2) −j(0) \(+\) k(4) = (−2 , 0 , 4)
r(2,0) = (2 , 0 , 1)
The plane is
r = −2x \(+\) 4z
r(2,0,1) = −2(2) \(+\) 4(1) = d
−4 \(+\) 4 \(=\) d
d = 0
Therefore , the equation of tangent is -2x + 4z = 0 .
The given question is incomplete , the complete question is
Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .
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The Vikings score 14 more
points than the Chargers. The
total of their points was 50.
How many points did the
Chargers score?
A- 14 B- 18 C- 32. D- 17
Answers
Answer:
18
Step-by-step explanation:
x= Chargers
x+14= Vikings
x + x + 14 = 50 Combine the x's to be 2X
2x + 14 = 50 Subtract 14 from both sides
2x -14 = -14
2x = 36 Divide 2 into to 2x and 36
2x /2 = 36 /2
x= 18
find the percent of discountOriginal price Sale Price
$60
% $45
Answers
Answer:
25% Discount
Step-by-step explanation:
find the percent of discountOriginal price Sale Price
$60
% $45 =
$60 was the SP
$45 is the MP
discount = 60/45 * 100 = 75
100 - 75 = 25%
please help if you can!!!!!!!
Answers
Answer:
-7
Step-by-step explanation:
hope this helps it might not be the right answer!
A man and another man were selling oranges the first man said to the other man " give me one of your oranges so that I can get double" but than The man said " no give me one of your oranges and we will have equal oranges" how much oranges does the man and the other man have 
Answers
Answer:
The first man has 7 oranges and the other man has 5 oranges
Step-by-step explanation:
System of Equations
To solve the problem, we set the variables:
x = number of oranges of the first man
y = number of oranges of the other man
If the other man gives one orange to the first man:
x + 1 = one more orange for the first man
y - 1 = one less orange for the second man
The first condition is: if the other man gives one orange to the first man, the latter would have double oranges:
x + 1 = 2 (y - 1)
Operating:
x + 1 = 2y - 2
x = 2y - 3 [1]
The second conditions states if the first man gives one orange to the other man, they would have the same number of oranges:
x - 1 = y + 1 [2]
Substituting [1] in [2]
2y - 3 - 1 = y + 1
Subtracting y and operating:
2y - y - 4 = 1
y = 1 + 4
y = 5
From [1]:
x = 2(5) - 3
x = 7
The first man has 7 oranges and the other man has 5 oranges
Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of x = 1 + r. $1,000 is deposited at the start of the first year, an
additional $300 is deposited at the start of the next year, and $500 at the start of the following year.
Write an expression for the value of the account at the end of three years in terms of the growth factor x.
Answers
The polynomial expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500x
Interest earned per year, x = 1 + r
First year :
deposit = $1000Year end balance = 1000 × x = 1000x
Second year :
Initial balance = 1000x + 300Year end balance = (1000x + 300)x = 1000x² + 300x
Third year :
Initial balance = 1000x² + 300x + 500Year end balance = (1000x² + 300x + 500)x = 1000x³ + 300x² + 500x
Therefore, the expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500
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a friend of yours who works in the it department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., monday through saturday. what is this restriction an example of?
Answers
Given restriction is an example of Time-of-day restrictions
The correct answer is an option (C)
In this question we have been given a friend tells you that tellers
are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday through Saturday.
We need to identify the type of restriction in this example.
We know that time-of-day restrictions are the restrictions that often used to limit the hours during which a user is allowed to log into or access a system.
This type of restrictions helps prevent unauthorized access outside that user's normal working hours .
Therefore, given restriction present in this example: Time-of-day restrictions
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The complete question is:
A friend of yours who works in the IT department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday
through Saturday. What is this restriction an example of?
A. User auditing
B. Least privilege
C. Time-of-day restrictions
D. Account verification
The four control points in 2D plane are Po(0,0) ?, (1, 1), P₂ (2,-1) and P3 (3,0). The tangent veehrs at the end points are Po'(1,1) & P3'(1,1). Determine the intermiclate points on the Humite curve at t = 1/3 & 2/3
Answers
The Hermite curve with four control points P0(0,0), P1(1,1), P2(2,-1), and P3(3,0) has tangent vectors P0'(1,1) and P3'(1,1) at the endpoints. To determine the intermediate points on the curve at t = 1/3 and t = 2/3, we can use the Hermite interpolation formula.
The Hermite interpolation formula allows us to construct a curve based on given control points and tangent vectors. In this case, we have four control points P0, P1, P2, and P3, and tangent vectors P0' and P3'.
To find the intermediate point at t = 1/3, we use the Hermite interpolation formula:
P(t) = \((2t^3 - 3t^2 + 1)P0 + (-2t^3 + 3t^2)P3 + (t^3 - 2t^2 + t)P0' + (t^3 - t^2)P3'\)
Substituting the given values:
\(P(1/3) = (2(1/3)^3 - 3(1/3)^2 + 1)(0,0) + (-2(1/3)^3 + 3(1/3)^2)(3,0) + ((1/3)^3 - 2(1/3)^2 + (1/3))(1,1) + ((1/3)^3 - (1/3)^2)(1,1)\)
Simplifying the equation, we can find the coordinates of the intermediate point at t = 1/3.
Similarly, for t = 2/3, we use the same formula:
\(P(2/3) = (2(2/3)^3 - 3(2/3)^2 + 1)(0,0) + (-2(2/3)^3 + 3(2/3)^2)(3,0) + ((2/3)^3 - 2(2/3)^2 + (2/3))(1,1) + ((2/3)^3 - (2/3)^2)(1,1)\)
Calculating the equation yields the coordinates of the intermediate point at t = 2/3.
In this way, we can use the Hermite interpolation formula to determine the intermediate points on the Hermite curve at t = 1/3 and t = 2/3 based on the given control points and tangent vectors.
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it costed $50 to rent a bike for 9 hours how many dollars does it cost per hour of bike use
Answers
The cost of per hour bike use is $5.56 when it costed $50 to rent a bike for 9 hours.
According to the question,
We have the following information:
It costed $50 to rent a bike for 9 hours.
Now, we can easily find the cost of per hour bike use by dividing the total cost by the number of hours.
So, we have the following expression:
9 hours = $50
1 hour = 50/9
1 hour = $5.56
(Note that this is the approximate cost after rounding off the obtained result.)
Hence, the cost of per hour bike is $5.56.
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If a 159 pound man can have 1020 mg of a medicine in a day how much can a 127 pound woman have?
Answers
Answer
A 127 pound woman can have 814.7 mg of medicine in as day
Explanation
Let the amount of medicine a 127 pound woman can have be x mg
Assuming the amount of medicine doesn't depend on gender and only depends on weight,
159 pound man = 1020 mg
127 pound woman = x mg
We can write a mathematical relationship for this by cross multiplying
(159) (x) = (127) (1020)
159x = 129,540
Divide both sides by 159
(159x/159) = (129,540/159)
x = 814.7 mg
Hope this Helps!!!
Question 1: Given the following expression
6 - 3w – w4
Classify the polynomial
Monomial
Binomial
Trinomial
Answers
A movie rental company deducts $7 from Serena’s account every month for a year. After 1 year, how much do movie rental fees change Serena’s account
Answers
5. A parabola has a directrix of y = -3 and a vertex
at (2,1). Which ordered pair is the focus of the
parabola?
Answers
The ordered pair of the force of the parabola will be (2, -1).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
A parabola has a directrix of y = - 3 and a vertex at (2,1).
Since the directrix is upward, utilize the condition of a parabola that opens up or down.
(x − h)² = 4p(y − k)
The separation from the concentration to the vertex and from the vertex to the directrix is |p|. Deduct the worth of the directrix from the y direction of the vertex to track down p.
p = − 1 + 1 / 2
p = − 1/2
Then the equation is given as,
(x − 2)² = 4(1/2)(y + 1)
(x − 2)² = 2(y + 1)
The ordered pair of the force of the parabola will be (2, -1).
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marked price of an item is 4000, what will be it's selling price having 20% discount and 10% vat.
Answers
Answer:
I HOPE IT WILL HELP
EXPLANATION IS IN THE PHOTO .
Multiplying the original value by the discounted percent, the percent taxed but add one to it.
(4,000)(.80)(1+10/100)= 3,520
4000 is the original value
.80 is the value of the item with 20% off
1.1 gives value after tax, adding the one allows you to see the value of the item after tax.
Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of -0.524. Which statement best summarizes this result? O There is a strong positive correlation between the variables. O There is a strong negative correlation between the variables. O There is a moderate positive correlation between the variables.O There is a moderate negative correlation between the variables.
Answers
The best summarizes for the result is:
O There is a moderate negative correlation between the variables.
CORRELATION COEFFICIENTA correlation coefficient measures the strength and direction of the relationship between two variables. The coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
In this case, the correlation coefficient of -0.524 indicates a moderate negative correlation between the variables. This means that as the value of one variable increases, the value of the other variable decreases, and vice versa. The negative sign indicates that the relationship is negative, and the absolute value of the coefficient (0.524) indicates that the relationship is moderate in strength.
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Two lines that have the same slope and different y intercepts do not intersect at any points.
True
False
Answers
Answer:
True
Step-by-step explanation:
one number is 4 less than 3 times another number. If their sum is increased by five,the result is 25. Find both the numbers.
Answers
Answer:
6 and 14
Step-by-step explanation:
let the second number=x
the first number=3x-4
(x+3x-4)+5=25
4x-4+5=25
4x+1=25
4x=25-1
4x=24
x=6
Since x is the first number,the first number is 6
second number=3•6-4
=18-4=14
The perimeter of an isosceles trapezoid is 78 ft. The bases of the trapezoid are 30 ft and 14 ft. Find the area of the Trapezoid.
Answers
Answer:The perimeter of a trapezoid is equal to the sum of the lengths of all its sides.
Let's call the height of the trapezoid "h".
Then, the length of the two sides equal (78 - 30 - 14) / 2 = 22 ft.
The area of the trapezoid is equal to (30 + 14) / 2 * h = 22 * h.
We can now find h using the formula:
h = (2 * area) / (30 + 14) = (2 * area) / 44.
We don't know the area, so we cannot find h.
Step-by-step explanation:
use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.
Answers
The counterclockwise circulation around c is 12 and the outward flux through c is zero.
Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.
In this case,
we have a field f=(7x−4y)i+(9y−4x)j and
a square curve c bounded by x=0, x=4, y=0, y=4.
To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.
The curl of f is given by (0,0,3), so the line integral evaluates to 12.
To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.
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What is the solution to x + 7 = 23?
3 of 12 QUESTIONS
X= 14
X=7
X = 30
X = 16
SUBMIT
Answers
Answer:
x=16
Step-by-step explanation:
x+7=23
23-7=x
x=16
Factorise x^2+4x+3
Write your steps as well please
Answers
Step-by-step explanation:
x²+4+3x²+x+3x+3x(x+1)+3(x+1)(x+1)(x+3)hope it helps.
stay safe healthy and happy...The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 18 chickens shows they laid an average of 20 eggs per month with a standard deviation of 5 eggs per month.
(a-1) What is the value of the population mean?
20
It is unknown.
5
(a-2) What is the best estimate of this value?
Best estimate
(c)
For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
Value of t
(d)
Determine the 95% confidence interval for the population mean. is (Round your answers to 2 decimal places.)
Confidence interval to
(e-1) Would it be reasonable to conclude that the population mean is 17 eggs?
No
Yes
(e-2) What about 18 eggs?
Yes
No
Answers
(a-1) The value of the population mean is unknown.
(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.
(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).
(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.
(e-2) It would be reasonable to conclude that the population mean is 18 eggs.
(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.
(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.
(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.
Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.
In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.
(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.
(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.
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US
Solve.
73
When solving exponential expressions, you must
multiply the base by itself as many times as the
value of the exponent.
7x7x7
[?] x 7
Hint: First calculate and enter the value of 7.7.
M
Answers
\( {7}^{3} \\ = 7 \times 7 \times 7 \\ = 7^{1 + 1} \times 7 \\ = {7}^{2} \times 7 \\ = 49 \times 7\)
Answer:\(49\)
Hope it helps...ray4918 here to help
Simplify the expression.
16-4 [3+2 divide (9-7)]
Answers
Answer:
0
Step-by-step explanation:
16-4 (3+2÷2)
16-4 (3+1)
16-4×4
16-16
0 ans.
help me solve the blanks pleaseeee
Answers
Answer: hi
Step-by-step explanation:
does anyone know the answer for top and bottom? please help
Answers
Answer:
15/18=5/6
14/18=7/9
the last symbol
Step-by-step explanation:
Answer:
For the first part (the part on the top), you have to make the fractions have the same denominator. To do this, you must find the LCM (least common multiple) of 6 and 9. The LCM of 6 and 9 would be 18 because 6x3=18 and 9x2=18. Now, both of the denominators are 18. But we still have to change the numerators! To change the numerators, we must multiply them by the same numbers that we multiplied the denominators by. So for 5/6, we would multiply the 5 (the numerator) by 3 because that is what we multiplied the 6 by. 5x3=15. So now the first fraction, 5/6, is 15/18 (that's the answer). For 7/9, we still have to multiply the 7 (the numerator) by 2. 7x2=14. So now this fraction, 7/9, is 14/18 (that's the answer).
So basically what I was saying is that 5/6=15/18 and 7/9=14/18.
For the second part (the part on the bottom), you have to compare the fractions. It is difficult right now as it is written as 5/6 and 7/9. But remember what we did for the first part! Think about these fractions as 15/18 and 14/18. 15/18 is larger than 14/18. So the answer for the part on the bottom is 5/6 > 7/9.
Hope this helps! :)
the sum of the squared deviation scores is ss = 20 for a population of n = 5 scores. what is the variance for this population? group of answer choices 4 5 80 100
Answers
The variance for this population is 5.Hence, the correct option is 5.
Given that, the sum of the squared deviation scores is ss = 20 for a population of n = 5 scores. Now we have to find the variance for this population.
Variances can be found using the formula: variance = s^2 = SS / (n - 1)Here, SS = 20n = 5 We have to substitute the given values into the variance formula, which gives us: s^2 = 20 / (5 - 1)s^2 = 20 / 4s^2 = 5.
So, the variance for this population is 5. Hence, the correct option is 5.
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Which of the following shows the graph of y=-(2)^x-1
Answers
Answer:
option c
Step-by-step explanation:
Geoffrey draws a triangle. One of the angles measures 75° and one of the angles measures 40°. What is the measure of the third angle?
A. 180°
B. 115°
C. 105°
D. 65°
Answers
Answer:
D) 65°
Step-by-step explanation:
Remember, all the angles of a triangle are 180 degrees and 75 + 40 + 65 = 180 degrees. Please if you can, support my channel. In the images you can find the information ;)
A "pay-what-you-pull" raffle is an alternative to a standard raffle where a person blindly draws a raffle ticket, say out of bag, and agrees to pay the amount written on the raffle ticket (as opposed to having one fixed price for each raffle ticket). The raffle ticket is then entered into a draw for a prize. Suppose you draw 2 raffle tickets without replacement from a bag with 4 tickets which have prices $1, $2, $3 and $4. How much can you expected to pay for your 2 raffle tickets?
Answers
To find the expected amount you would pay for your two raffle tickets, we need to calculate the expected value of the sum of the prices on the tickets.
Let's denote the prices on the tickets as follows:
Ticket 1: $1
Ticket 2: $2
Ticket 3: $3
Ticket 4: $4
Since you are drawing two tickets without replacement, there are a total of 4C2 = 6 possible combinations of two tickets.
The expected value (E) can be calculated by summing up the products of each combination and its corresponding probability. The probability of each combination is 1/6 since all combinations are equally likely.
The expected amount you would pay for your two raffle tickets is given by:
\(\[E = \frac{1}{6}(\$1 + \$2) + \frac{1}{6}(\$1 + \$3) + \frac{1}{6}(\$1 + \$4) + \frac{1}{6}(\$2 + \$3) + \frac{1}{6}(\$2 + \$4) + \frac{1}{6}(\$3 + \$4)\]\)
Simplifying the expression, we find:
\(\[E = \frac{\$3 + \$4 + \$5 + \$5 + \$6 + \$7}{6} = \$5\]\)
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