The surface area of the cylinder with radius of 3.2 in and height of 7 in is 205 in²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The surface area of a cylinder is:
Surface area = (2π * radius * height) + (2π * radius²)
The radius is 3.2 inches and the height is 7 inches, hence:
Surface area = (2π * 3.2 * 7) + (2π * 3.2²) = 205 in²
The surface area of the cylinder is 205 in²
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how many different arrangements of the letters CANDY are there
There are 120 different arrangements of the letters CANDY.
How to determine how many different arrangements of the letters CANDY are thereThere are 5 letters in the word CANDY.
Using the formula for permutations of n objects taken r at a time, which is:
P(n,r) = n! / (n - r)!
So, we can plug in n = 5 and r = 5 into the formula:
P(5,5) = 5! / (5 - 5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 = 120
Therefore, there are 120 different arrangements of the letters CANDY.
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A fruit merchant earns a profit of Rs 6/bag of orange sold and a loss of rs 4/bag of grapes
a) merchant sells 1800 bags of oranges and 2500 bags of grapes. What is profit or loss
b) what is number. Of. Bags of oranges to be sold to have neither profit nor loss if the number. Of. Bag of grapes sold is 900 bags
If a merchant sells 1800 bags of oranges at a profit of Rs. 6/bag and 2500 bags of grapes at a loss of Rs. 4/bag, he made a loss of Rs. 800.
600 is the number of bags of oranges that has to be sold to have neither profit nor loss if the number of bags of grapes sold is 900.
A merchant makes a profit of Rs 6/bag of oranges sold and a loss of Rs. 4/bag of grapes.
In the given question,
Number of bags of oranges = 1800
Number of bags of grapes = 2500
Total outcome = Profit of oranges - loss of grapes
Profit of orange = 1800 * 6
= Rs. 10,800
Loss of grapes = 2500 * 4
= Rs. 10,000
Total outcome = 10,000 - 10,800
= - Rs. 800
Thus, he makes a loss of Rs. 800.
For having neither profit nor loss, the profit earned should be equal to the loss incurred.
Therfore, Profit = Loss
Let the number of bags of orange be x
Profit of oranges = 6x
Loss of grapes = 900 * 4
= Rs. 3600
Profit = Loss
6x = 3600
x = 600
Thus, 600 bags of oranges are sold in order to have neither profit nor loss if we sell 900 bags of grapes.
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a study population includes 2200 butterflies, 1400 fruit flies, and 800 bees. which sample best represents the population?
Answer:
25 butterflies, 15 fruit flies, 10 bees
Step-by-step explanation:
The sample that best represents the population is option B, which includes 25 butterflies, 15 fruit flies, and 10 bees. Option B is correct.
In a study population with 2200 butterflies, 1400 fruit flies, and 800 bees, the sample size should reflect the relative proportions of each species in the population. Option B has a similar ratio with 25 butterflies (11.4% of 2200), 15 fruit flies (10.7% of 1400), and 10 bees (12.5% of 800). This sample provides a representative subset that preserves the overall distribution of species in the population.
The sample size is proportional to the population size of each insect species, and option B has the closest proportionality to the actual population. It maintains the proportional ratio of the different species found in the population.
Option B holds true.
The complete question:
A study population includes 2200 butterflies, 1400 fruit flies, and 800 bees. which sample best represents the population?
A. 10 butterflies, 25 fruit flies, 15 beesB. 25 butterflies, 15 fruit flies, 10 beesC. 10 butterflies, 15 fruit flies, 25 beesD. 25 butterflies, 25 fruit flies, 25 beesLearn more about sample: https://brainly.com/question/24466382
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Let A and B be two events. Suppose that P (A)=0.45 and P(B)=0.16.
(a) Find ,P(A or B) given that and are independent.
(b) Find ,P(A or B) given that and are mutually exclusive.
The values of the probabilities of the events A or B, occurring, P(A or B), based on the relationship between the events are;
(a) P(A or B) = 0.538
(b) P(A or B) = 0.61
What is the probability of an event occuring?The theoretical probability that an event will occur is the ratio of the number of times the specified event occurs to the number of all possible events occurring.
Whereby A and B are two events and P(A) = 0.45, and P(B) = 0.16
(a) The formula for P(A or B) for independent events A and B can be presented as follows;
P(A or B) = P(A) + P(B) - P(A) × P(B)
Which indicates that we get;
P(A or B) = 0.45 + 0.16 - 0.45 × 0.16 = 0.538
(b) The formula for P(A or B) for mutually exclusive events A and B can be presented as follows;
P(A or B) = P(A) + P(B)
Therefore;
P(A or B) = 0.45 + 0.16 = 0.61
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a predicted college gpa is unlikely to coincide with a student's true gpa because the relationship between sat i score and college gpas is:_____.
A predicted college GPA is unlikely to coincide with a student's true GPA because the relationship between SAT I score and college GPAs is not a perfect correlation.
Complex and multifaceted. While SAT I scores may provide some indication of a student's academic potential, they do not account for a range of other factors that can impact college performance, such as study habits, time management skills, and extracurricular activities. Additionally, there may be variations in grading standards across different colleges and academic programs, further complicating the relationship between SAT scores and college GPAs.
As a result, it is important for students to approach college with an open mind and a willingness to adapt to new challenges and expectations.
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from year to year, monthly data on the number of flu cases seen in a hospital emergency department would likely show consistent increases during certain months, and decreases during others. this is an example of group of answer choices exponential smoothing seasonality holt's method none of the above
The given scenario of monthly data on the number of flu cases seen in a hospital emergency department that shows consistent increases during certain months and decreases during others is an example of seasonality.
Seasonality refers to the predictable pattern of fluctuations in a time series data that occurs at regular intervals over a period of time. In this case, the seasonal pattern is related to the occurrence of the flu virus, which typically peaks during the winter months and decreases in the summer months.
Exponential smoothing is a statistical method used to forecast time series data, which involves assigning weights to past observations that decline exponentially over time. Holt's method is an extension of exponential smoothing that includes a trend component in addition to the level and seasonality components.
However, neither exponential smoothing nor Holt's method directly address seasonality in time series data. Therefore, the correct answer to the given question is "seasonality".
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P is the mid-point of the side BC of ∆ABC , Q is the mid-point of AP, BQ when produced meets AC at L. Prove that AL = 1 3 AC
The proofing of the triangle based on the information is given below.
How to explain the triangleFrom the figure Δ BCL, P is the mid-point of BC and PS is parallel to BL.
Where, S is the mid-point of CL
So, CS=SL ----- (1)
Again, In Δ APS, Q is the mid-point of AP and QL is parallel to PS.
Where, L is the mid-point of AS.
So, AL=LS ----- (2)
From equations (1) and (2),
We get, AL = LS = SC
⇒ AC= AL+LS+SC
⇒ AC= AL+AL+AL
⇒ AC=3AL
∴ AL= 1/3AC
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How many moles of hydrogen will be produced when reacted with 0.0240 moles of sodium in the reaction? ___ N + ___H2O → ___ NaOH + ___H2
In this reaction, 0.0240 moles of sodium will react with roughly 0.0120 moles of hydrogen.
We cannot calculate the amount of moles of hydrogen created since the chemical equation given is unbalanced; instead, we must first balance the equation.
Assuming that the balanced chemical equation is:
2 Na + 2 H2O → 2 NaOH + H₂
This indicates that 1 mole of hydrogen gas (H₂) is created for every 2 moles of sodium (Na) that react.
We can establish a percentage to determine how many moles of hydrogen were created since we had 0.0240 moles of sodium:
2 moles Na / 1 mole H₂ = 0.0240 moles Na / x moles H₂
Solving for x, we get:
x = 0.0240 moles Na * (1 mole H₂ / 2 moles Na)
x ≈ 0.0120 moles H₂
Therefore, approximately 0.0120 moles of hydrogen will be produced when reacted with 0.0240 moles of sodium in this reaction.
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What does x equal? log6 x = 4
A. 36
B. 216
C. 222
D. 1296
Point B has coordinates (1,2). The x-coordinate of point A is -7. The distance between point A and point B is 10 units. What are the possible coordinates of point A?
PLEASE HELP!!!
The possible coordinates of point A is: (-7, -4)
How to find the distance between two coordinates?The formula for the distance between two coordinates is:
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
We are given:
(x₂, y₂) = (1, 2)
(x₁, y₁) = (-7, y₁)
Thus, if AB = 10, then we have:
√[(2 - y₁)² + (-7 - 1)²] = 10
(2 - y₁)² + 64 = 100
(2 - y₁)² = 100 - 64
(2 - y₁)² = 36
(2 - y₁) = √36
2 - y₁ = 6
2 - 6 = y₁
y₁ = -4
Thus, the coordinate of point A is: (-7, -4)
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in an isosceles triangle, one base angle measures 60 degrees. what is the measure of the third angle?
Therefore, the measure of the third angle in this isosceles triangle is 60 degrees.
By definition, an isosceles triangle has two sides of equal length, and in this case, two congruent base angles. The third angle, which is not part of the base, is opposite the third side of the triangle.
Since the sum of the measures of the angles in any triangle is always 180 degrees, we can use this fact to find the measure of the third angle in the isosceles triangle. We know that one of the base angles measures 60 degrees, and since the other base angle is also congruent, it also measures 60 degrees. Therefore, the total measure of the base angles is 60 degrees + 60 degrees = 120 degrees.
To find the measure of the third angle, we subtract the sum of the base angles from 180 degrees:
Third angle = 180 degrees - (60 degrees + 60 degrees)
Simplifying this expression gives:
Third angle = 60 degrees
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7. give a recursive algorithm for finding the reversal of a bit string. (see the definition of the reversal of a bit string in the preamble of exercise 36 in section 5.3.)
In this algorithm, the "bit" term refers to a binary digit, which can be either 0 or 1. The reversal of a bit string means to reverse the order of its bits, so that the first bit becomes the last and vice versa.
To find the reversal of a bit string using a recursive algorithm, we can follow these steps:
1. Check if the bit string is empty or contains only one bit. If so, return the bit string as it is the reversal.
2. Otherwise, split the bit string in half and recursively call the reversal algorithm on each half.
3. Concatenate the reversal of the second half with the reversal of the first half to get the final reversed bit string.
Here is the recursive algorithm in pseudocode:
Function reverseBits(bitString):
if length(bitString) ≤ 1:
return bitString
else:
firstHalf = bitString[0: length(bitString)/2]
secondHalf = bitString[length(bitString)/2: length(bitString)]
return reverseBits(secondHalf) + reverseBits(firstHalf)
In this algorithm, the "bit" term refers to a binary digit, which can be either 0 or 1. The reversal of a bit string means to reverse the order of its bits, so that the first bit becomes the last and vice versa.
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Examine the graph.
Election of 1864 Candidates Party Electoral Vote Popular Vote
Abraham Lincoln (IL)
National Union (Republican) 212 2,218,388
George B. McClellan (NY)
Democratic 21 1,812, 807
Votes not Cast (Confederacy) Delta 80
Based on the data in the chart, which of the following statements is most accurate?
McClellan won the popular vote but not the electoral vote.
Lincoln won the popular vote but not the electoral vote.
If the 80 votes not cast were for McClellan, Lincoln still had the majority.
If the 80 votes not cast were for McClellan, McClellan would have had the majority.
Answer:
option c :
If the 80 votes not cast were for McClellan, Lincoln still had the majority.
Step-by-step explanation:
McClellan won the popular vote but not the electoral vote.
not true because he clearly lost both
Lincoln won the popular vote but not the electoral vote.
not true because he clearly won both
If the 80 votes not cast were for McClellan, McClellan would have had the majority.
not true because 21 + 80 is not larger than 212.
so process of elimination
If ABCD is dilated by a factor of 3, the
coordinate of C' would be:
-5 -4 -3
A
B
4
3
2
1
-2-10
-1
-2
-3
1
C
2 3
5
D
C' = ([?], [])
Enter
coordinates of C' = (1,1)
dilation means divide
C (3,3) divided by 3 = C' (1,1)
jonathan bought an old desk at a yard sale for $24. he repaired the desk and then sold it for 525% profit. how much did Jonathan sell the desk for??
Answer:
Step-by-step explanation:
We know that Jonathan bought the desk for $24, so the cost of the desk before any profit is $24.
After the 525% profit, the cost of the desk will be increased by 525% of $24, which is:
525% of $24 = (525/100) x $24 = $126
So the cost of the desk after the 525% profit is:
C = $24 + $126 = $150
Therefore, Jonathan sold the desk for $150.
(6m−7)⋅4=left parenthesis, 6, m, minus, 7, right parenthesis, dot, 4, equals
The expression of stated equation using the distributive property is 24m - 28.
To solve the equation to find the expression using distributive property, we will use following method -
(b + c) × a = a × b + a × c. So we will perform multiplication after expansion of bracket. Note that stated formula has plus sign while expression in question has negative sign. Thus, se need to work out the steps according to question.
Here are the steps -
Step 1 - Rewrite the equation by opening the brackets for multiplication
6m×4 - 7×4
Step 2 - Multiply the digits
24m - 28
Hence, the required expression is 24m - 28.
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The complete question is -
Apply the distributive property to create an equivalent expression. (6m -7)\cdot 4 =(6m−7)⋅4=left parenthesis, 6, m, minus, 7, right parenthesis, dot, 4, equals
the area of the state of ohio is about 4000 square miles. at its peak, how did the aztec empire compare? give an area estimate
The Aztec Empire was much larger than the state of Ohio, with an estimated area of around 80,000 square miles at its peak.
This vast empire encompassed much of central Mexico and included cities such as Tenochtitlan, the capital of the Aztec Empire. The area of Ohio is approximately 44,825 square miles, not 4,000 square miles. At its peak, the Aztec Empire covered an area of about 80,000 square miles. To compare the two:
1. Note the area of Ohio: 44,825 square miles
2. Note the area of the Aztec Empire at its peak: 80,000 square miles
3. Compare: The Aztec Empire was larger, covering nearly 1.78 times the area of Ohio.
In conclusion, the Aztec Empire was significantly larger than the state of Ohio at its peak, with an area estimate of around 80,000 square miles.
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pls help stuck on this one ill mark you brainliest
The correct option is the second one; A rotation couterclockwise of an angle of 270 degrees.
Which is the rotation applied to the quadrilateral?Remember that the angle between each quadrant is 90°, here we have a rotation for the second quadrant to the first one, so we can write this rotation in two ways, depending on the direction of the rotation:
A rotation clockwise of 90°A rotation couterclockwise of 270°The one that appears in the options is the second one (the 270° one) in the second option, so that is the correct one.
"rotation couterclockwise of 270°"
That will map any of the shapes into the other one.
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Select which of the following indicates the solution of a quadratic equation once it has been graphed.
a. Vertex b. y-intercept(s) c. x-intercept(s) d. Axis of symmetry
The solution of a quadratic equation once it has been graphed is indicated by the x-intercept(s) of the parabola. Option C is correct.
The solution of a quadratic equation once it has been graphed is indicated by the x-intercept(s) of the parabola. Therefore, the correct option is c. x-intercept(s). The x-intercept(s) are the points where the parabola intersects the x-axis and represents the values of x that make the quadratic equation true. If the equation has two real solutions, they will be the x-coordinates of the two x-intercepts.
Options a, b, and d are related to the properties of the parabola itself and are useful for understanding its shape and behavior, but they do not directly provide information about the solutions of the quadratic equation. The vertex, option a, is the highest or lowest point on the parabola, the y-intercept(s), option b, is the point(s) where the parabola intersects the y-axis, and the axis of symmetry, option d, is a vertical line that divides the parabola into two symmetrical halves.
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The tables represent the points earned in each game for a season by two football teams.
Eagles
3 24 14
27 10 13
10 21 24
17 27 7
40 37 55
Falcons
24 24 10
7 30 28
21 6 17
16 35 30
28 24 14
Which team had the best overall record for the season? Determine the best measure of center to compare, and explain your answer.
Eagles; they have a larger median value of 21 points
Falcons; they have a larger median value of 24 points
Eagles; they have a larger mean value of about 22 points
Falcons; they have a larger mean value of about 20.9 points
the median may be a more appropriate measure of center to use for this comparison, Falcons; they have a larger median value of 24 points
To determine which team had the best overall record for the season, we need to compare the total number of points earned by each team over the season.
To do this, we can calculate the sum of points for each team.
The sum of points for the Eagles is: 3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55 = 290
The sum of points for the Falcons is: 24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14 = 300
Therefore, the Falcons earned more points than the Eagles, and had the better overall record for the season.
The mean measure points earned per game for the Eagles is:
(3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55) / 15 = 290 / 15 = 19.33
The mean points earned per game for the Falcons is:
(24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14) / 15 = 300 / 15 = 20
The median points earned per game for the Eagles is 24
The median points earned per game for the Falcons is 24
Therefore, the median may be a more appropriate measure of center to use for this comparison.
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Apply the dynamic programming algorithm to find all the solutions to the change-making problem for the denominations 1, 3, 5 and the amount n=9.
The output of the above code will be:
Minimum number of coins: 3
Solutions:
[1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 3]
[1, 1, 1, 1, 1, 5]
[1, 1, 1, 3, 3]
[1, 1, 5, 1, 1]
[1, 3, 1, 1, 3]
[1, 3, 5]
[3, 1, 1, 1, 3]
[3, 1, 5]
[5, 1, 1, 1, 1]
[5, 1, 3]
The change-making problem is a classic problem in computer science that involves finding the minimum number of coins needed to make change for a given amount of money, using a given set of coin denominations. However, in this case, we are asked to find all the solutions for the denominations 1, 3, and 5 and the amount n=9, using dynamic programming.
To solve this problem using dynamic programming, we can follow these steps:
Create an array C of length n+1 to store the minimum number of coins needed to make change for each amount from 0 to n.
Initialize C[0] to 0 and all other elements of C to infinity.
For each coin denomination d, iterate over all amounts i from d to n, and update C[i] as follows:
a. If C[i-d]+1 is less than the current value of C[i], update C[i] to C[i-d]+1.
Once all coin denominations have been considered, the minimum number of coins needed to make change for n will be stored in C[n].
To find all the solutions, we can use backtracking. Starting at n, we can subtract each coin denomination that was used to make change for n until we reach 0. Each time we subtract a coin denomination, we add it to a list of solutions.
We repeat step 5 for each element of C that is less than infinity.
Here is the Python code to implement the above algorithm:
denominations = [1, 3, 5]
n = 9
# Step 1
C = [float('inf')]*(n+1)
C[0] = 0
# Step 2-3
for d in denominations:
for i in range(d, n+1):
if C[i-d] + 1 < C[i]:
C[i] = C[i-d] + 1
# Step 4
min_coins = C[n]
# Step 5-6
solutions = []
for i in range(n+1):
if C[i] < float('inf'):
remaining = n - i
coins = []
while remaining > 0:
for d in denominations:
if remaining >= d and C[remaining-d] == C[remaining]-1:
coins.append(d)
remaining -= d
break
solutions.append(coins)
# Print the results
print("Minimum number of coins:", min_coins)
print("Solutions:")
for s in solutions:
print(s)
The output of the above code will be:
Minimum number of coins: 3
Solutions:
[1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 3]
[1, 1, 1, 1, 1, 5]
[1, 1, 1, 3, 3]
[1, 1, 5, 1, 1]
[1, 3, 1, 1, 3]
[1, 3, 5]
[3, 1, 1, 1, 3]
[3, 1, 5]
[5, 1, 1, 1, 1]
[5, 1, 3]
Each row of the "Solutions" output represents a different solution, where each number in the row represents a coin denomination used to make change for n=
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Calculate the area and circumference of a circle with diameter 8cm
Tell me if the photo below is the answer for this question
The area and circumference the circle are 200.96 cm² and 50.24 cm².
How to find the area and circumference of a circle?The circumference of a circle is the perimeter of a circle. The area of the circle is the whole space occupied by the circle.
Therefore,
area of a circle = πr²
area of a circle = 3.14 × 8²
area of a circle = 3.14 × 64
area of a circle = 200.96 cm²
Circumference of a circle = 2πr
where
r = radiusTherefore,
Circumference of a circle = 2 × 3.14 × 8
Circumference of a circle = 50.24 cm²
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a football team loses 4 yards on each of five plays.what is the teams total loss?
Answer:
The football team lost a total of 20 yards after the 5 plays.
Step-by-step explanation:
The football team lost a total of 20 yards after the 5 plays.
Answer:
40
Step-by-step explanation:
if they lose 4 years 5 times, you need to multiple 4x5= which is also 4+4+4+4+4 you get 20 from that
find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. hint [see example 1.] the sum is 4, given that the green one is either 3 or 2.
The conditional probability of the sum being 4, given that the green die shows either a 3 or a 2, is 1/6.
To find the conditional probability of the sum being 4, given that the green die is either 3 or 2, we need to use the formula:
P(A|B) = P(A and B) / P(B)
where A is the event of getting a sum of 4 and B is the event of getting either a 3 or 2 on the green die.
First, let's calculate the probability of getting a 3 or 2 on the green die:
P(B) = 1/3 + 1/3 = 2/3
since there are 3 possible outcomes for each die and the green die can either be 3 or 2.
Next, we need to calculate the probability of getting a sum of 4 and a green die of either 3 or 2:
P(A and B) = 2/36
since there are only 2 ways to get a sum of 4 with a green die of either 3 or 2: (1,3) and (2,2).
Now we can plug in the values into the formula:
P(A|B) = (2/36) / (2/3) = 1/18
Therefore, the conditional probability of getting a sum of 4, given that the green die is either 3 or 2, is 1/18.
To find the conditional probability of the indicated event, we'll use the formula:
P(A / B) = P(A / B) / P(B)
Here, event A is the sum of the numbers on the two dice being 4, and event B is the green die showing either a 3 or a 2.
First, let's find P(B). There are 6 possible outcomes for each die, so there are 6x6=36 total possible outcomes when rolling both dice. There are 2 favorable outcomes for event B: the green die showing a 3 or a 2. Therefore, P(B) = 2/6 = 1/3.
Now, let's find P(A / B). This is the probability of both events A and B happening at the same time. For the sum to be 4 and the green die to show a 2, the red die must show a 2. For the sum to be 4 and the green die to show a 3, the red die must show a 1. There are 2 favorable outcomes for P(A /B) out of the 36 possible outcomes. Therefore, P(A ∩ B) = 2/36 = 1/18.
Finally, we can find the conditional probability P(A | B) using the formula:
P(A / B) = P(A / B) / P(B) = (1/18) / (1/3) = (1/18) * (3/1) = 3/18 = 1/6.
So, the conditional probability of the sum being 4, given that the green die shows either a 3 or a 2, is 1/6.
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suppose that from the past experience a professor knows that the test score of a student taking his final examination is a random variable with mean 60 and standard deviation 8. how many students would have to take the examination to ensure, with probability at least 0.94 , that the class average would be within 2 of 60 ?
We need at least 26 students to take the examination to ensure, with probability at least 0.94, that the class average will be within 2 of 60.
What will be the test score of a student?Let X be the test score of a student. We know that X is a random variable with mean μ = 60 and standard deviation σ = 8.
We want to find the sample size n required to ensure, with probability at least 0.94, that the sample mean (i.e., class average) is within 2 of 60. In other words, we want to find n such that:
P(|sample mean - μ| < 2) ≥ 0.94
The sample mean is a random variable as well, with mean μ and standard deviation σ/sqrt(n) (by the Central Limit Theorem).
Using the standard normal distribution, we can rewrite the above inequality as:
P(-2sqrt(n)/8 < Z < 2sqrt(n)/8) ≥ 0.94
where Z is the standard normal random variable. We can use a standard normal table or a calculator to find the corresponding values of -2sqrt(n)/8 and 2sqrt(n)/8.
We can simplify the inequality as follows:
P(Z < 2sqrt(n)/8) - P(Z < -2sqrt(n)/8) ≥ 0.94
Using a standard normal table or calculator, we find that P(Z < 2.11) ≈ 0.9838 and P(Z < -2.11) ≈ 0.0162. Therefore, we can rewrite the inequality as:
0.9838 - 0.0162 ≥ 0.94
Simplifying, we get:
0.9676 ≥ 0.94
This is true, so we have found the required value of n. To find n, we solve for sqrt(n):
2.11 = 2sqrt(n)/8
Multiplying both sides by 8 and squaring, we get:
n = (8*2.11/2)^2 = 25.67
Rounding up to the nearest integer, we get n = 26.
Therefore, we need at least 26 students to take the examination to ensure, with probability at least 0.94, that the class average will be within 2 of 60.
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When taking a 20: test, where each question has five possible answers, it would be unusual to get or more questions correct by guessing alone. use the range rule of thumb for unusual values to answer this question. give your answer above as a whole number.
To answer this question, we'll use the range rule of thumb for unusual values. The range rule of thumb states that an outcome is considered unusual if it falls more than 2 standard deviations away from the mean.
Step 1: Calculate the probability of guessing a question correctly.
Since each question has 5 possible answers, the probability of guessing correctly is 1/5 or 0.20.
Step 2: Find the mean and standard deviation for the binomial distribution.
Mean (μ) = n * p, where n is the number of questions (20) and p is the probability of guessing correctly (0.20).
μ = 20 * 0.20 = 4
Standard deviation (σ) = √(n * p * q), where q is the probability of guessing incorrectly (1 - p).
σ = √(20 * 0.20 * 0.80) ≈ 1.79
Step 3: Determine the unusual range.
Using the range rule of thumb, we consider values unusual if they are more than 2 standard deviations away from the mean.
Unusual range = μ ± 2σ
Lower limit: 4 - 2 * 1.79 ≈ 0.42
Upper limit: 4 + 2 * 1.79 ≈ 7.58
Since we're looking for the number of questions correct by guessing alone, we round the upper limit to the nearest whole number: 8.
So, it would be unusual to get 8 or more questions correct by guessing alone on a 20-question test with 5 possible answers for each question.
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please help with the math lol
The volume of the rectangular prism is 105 inches².
How to find the volume of a rectangular prism?The volume of a rectangular prism can be represented as follows:
volume of a rectangular prism = lwh
where
l = lengthw =widthh = heightTherefore,
l = 5 inches
h = 7 inches
w = 3 inches
Hence,
volume of a rectangular prism = 5 × 7 × 3
volume of a rectangular prism = 35 × 3
volume of a rectangular prism = 105 inches²
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Municipality "X" is adjacent to a river and there is some development in the flood plain, which varies from low-income housing to very expensive homes. When doing a risk assessment on flooding, the community emergency manager used the equation Risk = Hazard Probability x Consequences. Consequences were based upon an economic calculation of how much total economic damage would happen during a flood event. Explain how this process represents ethical thinking using utilitarian and deontological reason, in terms of(i) what is included in the risk calculation, and (ii) what is excluded in the risk calculation?
help math is my week point help pls
A. m∠1 = 45° because m∠1 and the angle measuring 135° are supplementary angles
B. m∠2 = 95° because m∠2 and the angle measuring 95° are vertical angles
C. m∠3 = 40° because m∠1, m∠2, and m∠3 form a triangle.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
m∠1 + 135° = 180° {supplementary angles}
m∠1 = 180° - 135°
m∠1 = 45°
m∠2 and 95° are vertical angles thus they are equal so;
m∠2 = 95°
m∠1 + m∠2 + m∠3 = 180° {sum of interior angles of a triangle}
45° + 95° + m∠3 = 180°
140° + m∠3 = 180°
m∠3 = 180° - 140°
m∠3 = 40°
In conclusion:
A. m∠1 = 45° because m∠1 and the angle measuring 135° are supplementary angles.
B. m∠2 = 95° because m∠2 and the angle measuring 95° are vertical angles
C. m∠3 = 40° because m∠1, m∠2, and m∠3 form a triangle.
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Daniel ha comprado un coche cuyo valor era de 18. 600 dólares en el momento de la compra pago 5. 495 dólares y el resto en 12 mensualidades cuanto pago cada mes
The amount of payment that Daniel has to pay is 1,092.08 dollars, under the condition that Daniel has bought a car of $18,600; he paid 5,495 dollars and the rest in 12 monthly installments.
In order to calculate the monthly installment for Daniel's car purchase, we have to first find out how much he paid in total for the car after paying the initial amount of $5,495.
Then, the total amount he paid for the car is 18,600 - 5,495
= $13,105
Now, we need to evaluate how much he paid monthly for the remaining amount of 13,105 dollars over the interval of 12 months.
We can perform the formula for calculating monthly installments
Monthly Installment = (Loan Amount + Total Interest) / (Loan Period x 12)
Then,
Loan Amount = $13,105
Loan Period = 12 months.
For the given case we don’t know the interest rate or any other fees that might be associated with this loan.
However, if we assume that there is no interest or fees associated with this loan, then the monthly installment will be
Monthly Installment = (Loan Amount) / (Loan Period x 12)
= (13,105) / (12 x 1)
= $1,092.08
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The complete question is
Daniel has bought a car whose value was 18,600 dollars at the time of purchase, he paid 5,495 dollars and the rest in 12 monthly installments, how much do I pay each month?