The total number of popsicle sticks needed to make one snowman using the given conditions for system of equations is equal to 9.
Let us consider 'x' is the number of popsicle sticks required to make one pencil cup.
And 'y' represents the number of popsicle sticks required to make one snowman.
The required set up two equations are,
8x + 15y = 271 ___(1)
14x + 15y = 373 ___(2)
Multiplying both sides of equation (1) by 14 and both sides of equation (2) by -8 we get,
112x + 210y = 3794
-112x - 120y = -2984
Add both the above equations to eliminate the x variable we get,
⇒ 112x + (-112x) + 210y + (-120y) = 3794 + (-2984)
Simplifying the equation we get,
⇒90y = 810
Dividing both sides by 90 we get,
⇒ y = 9
Therefore, number of popsicle sticks required to make one snowman is equal to 9.
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The table below shows a cumulative frequency
distribution of runners' ages.
Cumulative Frequency Distribution
of Runners' Ages
Age Group. Total
20-29 8
20-39 18
20-49 25
20-59 31
20-69 35
According to the table, how many runners are in
their forties?
1) 25
2) 10
3) 7
4) 6
(b) Suppose you wanted to estimate the true proportion of all student loan borrowers who have loans
totaling more than $40,000 with 95% confidence to within 1%. Calculate the sample size you would
need. Use the sample proportion to estimate the population proportion
The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:
n = 9604.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The margin of error is modeled as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We have no estimate of the proportion, hence it is used as follows:
[tex]\pi = 0.5[/tex]
The margin of error is of M = 0.01, hence the sample size is obtained as follows:
[tex]0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = 98[/tex]
n = 98²
n = 9604.
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I NEED HELP ON THIS ASAP!!!
Step-by-step explanation:
Refer to pic...........
Identify the domain and range of (f(x)=4[(x-2)^(1/2)]-8 To type in your answer, type the domain first, then a comma and space, and finally the range.
The domain of the function f(x) = 4[(x-2)^(1/2)]-8 is the set of all real numbers x such that x ≥ 2.
This is because the expression (x-2)^(1/2) is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)^(1/2)]-8 is always greater than or equal to -8 for all values of x in the domain.
So, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)
In conclusion, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are [2, ∞), [-8, ∞).
The domain of the function f(x) = 4[(x-2)1/2]-8 is the set of all real numbers x such that x ≥ 2. This is because the expression (x-2)1/2 is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)1/2]-8 is always greater than or equal to -8 for all values of x in the domain.
So, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)
In conclusion, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are [2, ∞), [-8, ∞).
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A drawing of a 78-foot long building was built using a scale of 1in:8ft. What is the length of the drawing??
Answer:
Step-by-step explanation:
Given: Length of the building = 78 ft
Scale = 1 in : 8 ft
To find: Length of the building in the drawing
Now we have the scale where
8 ft = 1 inch
So using unit rule
1 ft = (1/8) in
So
78 ft = (1/8)(78) in = 9.75 inch
So length of the building in the drawing is 9.75 inch.
The length of the drawing is 9.75 inches.
To calculate the length of the drawing, find out how many inches correspond to 78 feet using the scale provided.
Since the scale is 1in:8ft, this means that 1 inch on the drawing represents 8 feet in real life.
To determine the length of the drawing, divide the length of the building by the scale factor:
Length of drawing = Length of building / Scale factor
Length of drawing = 78 ft / 8
Length of drawing = 9.75 inches
Hence, the drawing is 9.75 inches long.
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Need help to complete the proof.
Y is the midpoint of UW. Prove △VWY ≅ △XUY. Arrange the following reasons to complete the proof.
Reasons: Given, Given, Definition of midpoint, ASA, Vertical Angle Theorem
Mr. Whyte buys a new television. He pays down a payment of $99 and promises to make 12 monthly payments of $75. What is the total cost of the television?
Answer:$999
Step-by-step explanation:
You are going to want to multiply 75 by 12 since you are giving 75 dollars 12 times- then you are going to add $99 for the down payment- and you’ve got your answer!
Answer:
999
Step-by-step explanation:
of means "x"
12 monthly payments of $75
12 x 75 = total for 12 payments
then add down-payment
u get total cost
The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ have no solution, are
Aλ=3,μ=10
Bλ=3,μ=10
Cλ=3,μ=10
DNone of these
The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ are none of this. The correct answer is option D, None of these.
To find the value of λ and μ for which the system of equations has no solution, we can use the determinant method. The determinant of a system of equations is given by:
| a1 b1 c1 |
| a2 b2 c2 | = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
| a3 b3 c3 |
For the given system of equations, the determinant is:
| 1 1 1 |
| 1 2 3 | = 1(2λ - 3μ) - 1(3 - 3) + 1(2 - 2)
| 1 2 λ |
Simplifying, we get:
2λ - 3μ = 0
For the system of equations to have no solution, the determinant must be equal to 0. Therefore, we need to find the values of λ and μ that satisfy the equation 2λ - 3μ = 0.
None of the given options satisfy this equation, therefore the correct answer is option D, None of these.
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Can someone explain how to do this? I'm confused. Anything helps.
Thank you so much!
Answer:
28 and 152 degrees
Step-by-step explanation:
Using sine inverse, the answer is 28 or 152 degrees.
Answer:48.87°
Step-by-step explanation:
The average weekly spending of students in ABC University follow a normal distribution. It is known that 10% of the students spend more than $50 per week, while 30% spend more than $48 weekly. How do we find the mean and standard deviation of this distribution?
To find the mean and standard deviation of the distribution, we can use the z-scores for the given percentages and the corresponding spending amounts. The mean of the distribution is $46.63 and the standard deviation is $2.63.
By using the z-scores for the specified percentages and related spending amounts, we can determine the mean and standard deviation of the distribution. The z-score for 10% is 1.28 and the z-score for 30% is 0.52. Using the formula
z = (x - mean)/standard deviation, we can set up two equations:
1.28 = ($50 - mean)/standard deviation
0.52 = ($48 - mean)/standard deviation
We can rearrange the equations to solve for the mean and standard deviation:
mean = $50 - (1.28)(standard deviation)
mean = $48 - (0.52)(standard deviation)
Subtracting the second equation from the first gives us:
0 = $2 - (0.76)(standard deviation)
Solving for standard deviation gives us:
standard deviation = $2/0.76 = $2.63
Plugging this back into the first equation gives us:
mean = $50 - (1.28)($2.63) = $46.63
Therefore, the mean of the distribution is $46.63 and the standard deviation is $2.63.
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Suppose g(x)=x+3/2. Evaluate g(g(1)) and g(g(g(1)))
Answer: g(g(1)) = 4 and g(g(g(1))) = 5 1/2
Step-by-step explanation:
We will first find g(1). To do so, we plug 1 in for x.
g(1) = (1) + 3/2 = 5/2 = 2 1/2
To find g(g(1)) we will plug in 5/2 for x.
g(g(1)) = (5/2) + 3/2 = 8/2 = 4
To find g(g(g(1))) we will plug in 4 for x.
g(g(g(1))) = (4) + 3/2 = 11/2 = 5 1/2
Hope this helps!
Consider the equation x^(2)+bx+9=0 where b is a real number. Enter a value for b so that the equation has no real solutions.
This inequality will be true when b is between -6 and 6. So any value of b in this range will result in no real solutions for the equation. For example, we could choose b=4, and the equation would have no real solutions.
To find a value for b that results in no real solutions for the equation x^(2)+bx+9=0, we need to use the discriminant. The discriminant is the part of the quadratic formula under the square root sign: b^(2)-4ac. If the discriminant is less than 0, the equation will have no real solutions.
In this case, a=1, b=b, and c=9. Plugging these values into the discriminant gives us:
b^(2)-4(1)(9)=b^(2)-36
We want this to be less than 0, so:
b^(2)-36<0
We can solve this inequality by factoring:
(b+6)(b-6)<0
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Calculate the next term in the arithmetic sequence that
increases by 21, if the current term is 55.
What is the next term if the first two terms of a
Fibonacci sequence are 2, 25?
Find the 72th term o
3525
The next term in the arithmetic sequence that increases by 21, starting at 55, is 76. The next two terms of the Fibonacci sequence are 67 and 109, and the 72nd term is 3525.
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Use the table to complete the statements.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 50, 0, negative 6, negative 4, negative 6, 0.
The x-intercepts shown in the table are _____
and ______.
The y-intercept shown in the table is _______.
Answer:
-2, 2
-4
Step-by-step explanation:
The x-intercept is the point where the graph crosses the x-axis. At that point, the y-coordinate equals zero. At the x-intercept, f(x) = 0.
Look below f(x) and find where f(x) = 0. Which x values correspond to f(x) = 0?
There are two x values: x = -2, and x = 2
The x-intercepts shown in the table are -2 and 2.
The y-intercept is the point where the graph crosses the y-axis. At that point, the x-coordinate equals zero. At the y-intercept, x = 0.
Look below x and find where x = 0. Which f(x) value corresponds to x = 0?
There is one f(x) value: f(x) = -4
The y-intercept shown in the table is -4.
The measure of an angle is 19.5°. What is the measure of its complementary angle?
Answer:
70.5
In Maths, two angles are said to be complementary, when the angles add up to 90 degrees. The complementary angle need not be adjacent to each other, but its sum should be equal to 90 degrees. For example, 47° and 43° are complementary angles.
Example:
To find out another angle if one of the complementary angles is 60°
Solution:
We know that the sum of complementary angles is 90
Let the unknown angle be x
Thus,
60° + x = 90°
X = 90° – 60°
X = 30°
Hence, the unknown angle is 30°
Helppppppppppppppppppppp
Answer: 3. 200ft 4. 21ft
5. 37.5m 6. h=4.2ft
Step-by-step explanation:
What is the approximate measure of the central angle that is created by an arc of (32pi)/9 units in a circle with a radius of 7 units?
the options are
A- 156
B-91
C-26
D-11
9. Determine the 6-day SMA for the 10-consecutive-trading-day closing
prices for SunEdison Inc. listed below.
$2.65 $2.63 $2.70 $2.63 $2.50 $2.65 $2.66 $2.56 $2.52 $2.37
The 6-day SMA for the given closing prices is as follows:
Day 1: 2.63
Day 2: 2.63
Day 3: 2.61
Day 4: 2.59
Day 5: 2.54
Calculating Simple Moving Average (SMA)To calculate the 6-day Simple Moving Average (SMA) for the given closing prices, we need to take the sum of the last six closing prices and divide it by 6. Then we move one day forward and repeat the process until we have calculated the SMA for each day.
Here are the calculations:
Day 1: SMA = (2.65 + 2.63 + 2.70 + 2.63 + 2.50 + 2.65) / 6 = 2.63
Day 2: SMA = (2.63 + 2.70 + 2.63 + 2.50 + 2.65 + 2.66) / 6 = 2.63
Day 3: SMA = (2.70 + 2.63 + 2.50 + 2.65 + 2.66 + 2.56) / 6 = 2.61
Day 4: SMA = (2.63 + 2.50 + 2.65 + 2.66 + 2.56 + 2.52) / 6 = 2.59
Day 5: SMA = (2.50 + 2.65 + 2.66 + 2.56 + 2.52 + 2.37) / 6 = 2.54
Therefore, the 6-day SMA for the given closing prices is as follows:
Day 1: 2.63
Day 2: 2.63
Day 3: 2.61
Day 4: 2.59
Day 5: 2.54
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O POLYNOMIALS AND FACTORING Polynomial long division: Problem type 1 Divide. (3x^(2)+20x+30)-:(x+5) Your answer should give the quotient and the remainder.
The quotient of the polynomial long division problem (3x2 + 20x + 30) : (x + 5) is 3x + 25 and the remainder is 0.
To solve this, use polynomial long division. First, divide the leading coefficient of the dividend (3) by the leading coefficient of the divisor (1). The quotient is 3 and this is placed above the dividend.
Then, multiply the quotient (3) by the divisor (x + 5) and subtract the product from the dividend (3x2 + 20x + 30). The difference is 3x + 25.
Finally, multiply the quotient (3x + 25) by the divisor (x + 5) and subtract the product from the difference (3x + 25). Since the difference is 0, the remainder is 0.
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The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.
The following values represent the rollercoaster graph scenario most accurately:
is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6
Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5
Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)
For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6
Define graphs?The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.
The Latin word Datum, which meaning "something provided," is where the word data first appeared.
In the question, where at x = 0, Red(x) = 10,
at x = 5, Red(x) = 2.5
For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5 if 6 ≤ x < 10
Given, where at x = 10, Green (x) = 7,
So, at x = 6, Green (x) = 2.0
For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15
Given, where at x = 10, Purple (x) = 7,
at x = 15, Purple (x) = 0
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The complete question is:
The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.
3. Note this example is using weeks instead of years to calculate the interest. Mr. Lindsey is
going to start a fund for the student who completes the highest amount of classwork
assignments during the rest of the quarter. He puts in $50 at the beginning of week one and
that money will draw interest at a given rate each week for 5 weeks. At the beginning of week 3
his honey business is going so well that he puts another 25 dollars in to draw interest for the
remaining 3 weeks. He puts another 30 at the beginning of week 4.
a) Write an expression to model this situation 50/5)
b) If I paid 4% interest over that period, how much money would the winner get?
Answer: Your welcome!
Step-by-step explanation:
a) The expression to model this situation is (50/5) + (25/3) + (30/2). This expression represents the amount of money Mr. Lindsey has in the fund at each week, starting at $50 for the first 5 weeks, then adding $25 for the remaining 3 weeks, and then adding $30 for the last 2 weeks.
b) If 4% interest is paid over the period, the winner of the fund will get a total of $70.14. This is calculated by multiplying the expression from part a) by 1.04 (1.04 = 1 + 4%) to get the total amount of money in the fund at the end of the period. In this case, (50/5) + (25/3) + (30/2) * 1.04 = 70.14.
-8y + 25 ≤ -31
Please Answer
Answer:
Hi
Step-by-step explanation:
im pretty sure this the answer
hope this helps
good luck;)
Answer:
y≤7
Step-by-step explanation:
-8y+25≤-31
take away 25 from both sides
-8y≤-56
then divided by -8 on both sides
y≤7
ind the difference and write the resulting polynom (19x^(4)-17x-18)-(12x^(4)-8x+5)
The difference of the two polynomials is 7x^(4) - 9x - 23.
The difference of the two polynomials (19x^(4)-17x-18)-(12x^(4)-8x+5) can be found by subtracting the corresponding terms of the two polynomials.
Subtract the first term of the second polynomial from the first term of the first polynomial: 19x^(4) - 12x^(4) = 7x^(4)
Subtract the second term of the second polynomial from the second term of the first polynomial: -17x - (-8x) = -17x + 8x = -9x
Subtract the third term of the second polynomial from the third term of the first polynomial: -18 - 5 = -23
Write the resulting polynomial by combining the terms 7x^(4) - 9x - 23
Therefore, the difference of the two polynomials is 7x^(4) - 9x - 23.
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5000 people visit mueum during a month how many visitors were there for each age group. 18 and under, age 19 to 44, 45 to 64, age 65 and over
The number of degrees for each part of the museum visitors graph would be Age 18 and under: 108 degrees, Age 19 – 44: 180 degrees, Age 45 – 64: 54 degrees, and Age 65 and over: 18 degrees.
To find the number of degrees for each part of the museum visitors graph, we need to know the total number of visitors for that month. Let's assume that the total number of visitors for the month is 10,000.
Age 18 and under:
Let's assume that the number of visitors aged 18 and under is 3,000. To find the number of degrees for this section of the graph, we need to use the formula: (Number of visitors in the age group / Total number of visitors) x 360 degrees. So, (3000/10000) x 360 = 108 degrees.
Age 19 – 44:
Let's assume that the number of visitors aged 19-44 is 5,000. Using the same formula as above, we get (5000/10000) x 360 = 180 degrees.
Age 45 – 64:
Let's assume that the number of visitors aged 45-64 is 1,500. Using the same formula as above, we get (1500/10000) x 360 = 54 degrees.
Age 65 and over:
Let's assume that the number of visitors aged 65 and over is 500. Using the same formula as above, we get (500/10000) x 360 = 18 degrees.
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For any invertible matrix BEM nxn(K), define a function TB: Mnxn(K) → M nxn(K) by
TB (A) = BAB-¹,
where A EM nxn(K). Prove that TB is an isomorphism.
TB is both one-to-one and onto, it is an isomorphism.
To prove that TB is an isomorphism, we need to show that it is both one-to-one and onto.
One-to-one: Assume TB(A) = TB(C) for some A, C EM nxn(K). Then, BAB-¹ = CBC-¹. Multiplying both sides by B-¹ on the left and B on the right gives B-¹BAB = B-¹CBC. Since B is invertible, B-¹B = I and we have A = C. Therefore, TB is one-to-one.
Onto: Let D EM nxn(K). Then, we can define A = B-¹DB. Since B is invertible, A EM nxn(K) and TB(A) = BAB-¹ = B(B-¹DB)B-¹ = D. Therefore, TB is onto.
Since TB is both one-to-one and onto, it is an isomorphism.
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Use ELIMINATION to solve for (x) and (y). 2y=x-5 2y=x+5 x+2y=13 -x+4y=11 Upload a file that shows each step to solve for (x) and (y).
The solution to the system of equations using elimination is:
x = 1058/1890
y = 26/90
To solve this system of equations using elimination, we will add the two equations together and rearrange the terms.
2y = x - 5
2y = x + 5
Add the equations together:
2y + 2y = x - 5 + x + 5
4y = 2x + 0
Rearrange the terms:
4y - 2x = 0
We will now use this equation and the equation x + 2y = 13 to solve for x and y.
Substitute 4y - 2x = 0 into x + 2y = 13:
x + 2(4y - 2x) = 13
x + 8y - 4x = 13
Rearrange the terms:
5x + 8y = 13
Substitute 4y - 2x = 0 into 5x + 8y = 13:
5x + 8(4y - 2x) = 13
5x + 32y - 16x = 13
Rearrange the terms:
21x + 32y = 13
Divide by 21:
x + (32/21)y = 13/21
Rearrange the terms:
x = 13/21 - (32/21)y
Substitute x = 13/21 - (32/21)y into 4y - 2x = 0:
4y - 2(13/21 - (32/21)y) = 0
4y - (26/21) + (64/21)y = 0
Rearrange the terms:
(90/21)y = 26/21
y = (26/21) / (90/21)
y = 26/90
Substitute y = 26/90 into x = 13/21 - (32/21)y:
x = 13/21 - (32/21)(26/90)
x = 13/21 - (832/1890)
x = 1058/1890
The solution to the system of equations is:
x = 1058/1890
y = 26/90
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Describe how to map figure J onto
Figure L, complete the statement
Find the period of the function f(x) = cos(2.22x+0.19). Provide four decimal places. Answer:______ Find the period of the function f(x) = sin(1.05x). Provide four decimal places. Answer:______
The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x) is 5.9834
The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.
For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323
For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834
So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.
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Given f(x)=-x^3+6x^3-9x
a) identify end behavior
b) the degree is?
c)Maximum number of turning points
d) The leading coefficient
e) so the end behavior is:
Given g(x)=x(x+2)(x-2)^2
The same questions
1) a) X approaches negative infinity, f(x) approaches positive infinity.
b) The degree of f(x) is 3.
c) The maximum number of turning points for f(x) is 2.
d) The leading coefficient of f(x) is -1.
e) The end behavior of f(x) is "as x approaches infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.
2) a) a) The end behavior of g(x) is determined by the leading term x⁴. As x approaches infinity, g(x) approaches positive infinity. As x approaches negative infinity, g(x) approaches positive infinity.
b) The degree of g(x) is 4.
c) The maximum number of turning points for g(x) is 3.
d)The leading coefficient of g(x) is 1.
e)The end behavior of g(x) is "as x approaches infinity, g(x) approaches positive infinity; as x approaches negative infinity, g(x) approaches positive infinity.
Given f(x)=-x³ + 6x³ - 9x
a) The end behavior of f(x) is determined by the leading term -x³. As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.
b) The degree of f(x) is 3, as the highest exponent in the polynomial is 3.
c) The maximum number of turning points for f(x) is 2, as it is one less than the degree of the polynomial.
d) The leading coefficient of f(x) is -1, as it is the coefficient of the leading term -x³.
Given g(x)=x(x+2)(x-2)²
b) The degree of g(x) is 4, as the highest exponent in the polynomial is 4.
c) The maximum number of turning points for g(x) is 3, as it is one less than the degree of the polynomial.
d) The leading coefficient of g(x) is 1, as it is the coefficient of the leading term x⁴.
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Exercise 2 An engineer analyses the presence (Yes-present, No= not present) of a specific terms in received messages (100 messages), to filter spams. These terms are: Donation, Ransom, Shows, Unsubscribe The analysis is based on the data shown below: No Donation Ransom Shows Unsubscribe Total
Yes No Yes No Yes No Yes No
Spam 4/20 16/20 10/20 10/20 0/20 20/20 12/20 8/20 20
Ham 1/80 79/80 14/80 66/80 8/80 71/80 23/80 57/80 80
Total 5/100 95/100 24/100 76/100 8/100 91/100 35/100 65/100 100 Suppose that you receive a new message that contains the terms Donation and Unsubscribe, but does not contain either Ransom or Shows. In your opinion, this new message will be classified as spam or ham? (assume class conditional independence: P(An B/C) = P(A/C)P(B/C) and use conditional probability)
The new message is more likely to be classified as spam.
Based on the given data, we can use the class conditional independence to calculate the probability that a message containing the terms Donation and Unsubscribe, but not Ransom or Shows, will be classified as spam or ham. By applying Bayes' Theorem, we can calculate that the probability of the message being classified as spam is P(spam/Donation, Unsubscribe) = (P(Donation/spam)P(Unsubscribe/spam)) / P(Donation, Unsubscribe) = (4/20 x 10/20) / (5/100 x 8/100) = 0.8. Therefore, the new message is more likely to be classified as spam.
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