The probability that the waves are turbulent given that the water is cold is approximately 0.4353.
Suppose the water has a 0.51 chance of being cold and the waves have a 0.57 chance of being turbulent. In the same way, suppose that given the waves are turbulent, the water has a 0.39 chance of being cold. What is the chance that the waves are turbulent given that the water is cold?
To answer the question, we must use Bayes' theorem :P (A|B) = P (B|A) × P (A) / P (B)
Where A and B are arbitrary events. P (A) and P (B) are the probabilities of events A and B happening separately.
P (B|A) is the probability of event B happening, given that event A has happened. P (A|B) is the probability of event A happening, given that event B has happened.
We must find P (waves are turbulent | water is cold), which is P (B|A). We know that:
P (water is cold) = 0.51
P(waves are turbulent) = 0.57
P(water is cold | waves are turbulent) = 0.39
Using Bayes' theorem, we can calculate P (waves are turbulent | water is cold) as:
P (waves are turbulent | water is cold) = P (water is cold | waves are turbulent) × P (waves are turbulent) / P (water is cold)
P(waves are turbulent | water is cold) = 0.39 × 0.57 / 0.51
P (waves are turbulent | water is cold) = 0.4353 (rounded to the nearest millionth)
Therefore, the probability that the waves are turbulent given that the water is cold is approximately 0.4353.
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the ages of students at a university are normally distributed with a mean of 20. what percentage of the student body is at least 20 years old?
The percentage of the student body that is at least 20 years old is 50%.
The ages of students at a university are normally distributed with a mean of 20. To find the percentage of the student body that is at least 20 years old solution to the is as follows: As the Mean of ages of students at a university, μ = 20. Age is normally distributed so it will be divided into two groups Therefore, the mean age is equal to the median age. As the age is normally distributed, 50% of the population will have an age greater than or equal to 20 years old. Thus, the percentage of the student body that is at least 20 years old is 50%. Hence, the required percentage of the student body that is at least 20 years old is 50%.
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The base year is 2012. Real GDP in 2012 was $15 trillion. The GDP price index in 2019 was 105, and real GDP in 2019 was $16 trillion. What was the percentage increase in production from 2012 to 2019, and by what percentage did the price level rise from 2012 to 2019?
Real GDP increase in 2019 was $16 trillion, representing a 6.67% increase from 2012. The price level rose by 5% from 2012 to 2019, with a GDP price index of 105 in 2019.
To calculate the percentage increase in production from 2012 to 2019, we need to use the following formula:
Percentage increase in production = ((Real GDP in 2019 - Real GDP in 2012) / Real GDP in 2012) x 100
Substituting the given values, we get:
Percentage increase in production = ((16 trillion - 15 trillion) / 15 trillion) x 100
Percentage increase in production = (1 trillion / 15 trillion) x 100
Percentage increase in production = 6.67%
Therefore, there was a 6.67% increase in production from 2012 to 2019.
To calculate the percentage increase in price level from 2012 to 2019, we can use the following formula:
Percentage increase in price level = ((GDP price index in 2019 - GDP price index in 2012) / GDP price index in 2012) x 100
Substituting the given values, we get:
Percentage increase in price level = ((105 - 100) / 100) x 100
Percentage increase in price level = (5 / 100) x 100
Percentage increase in price level = 5%
Therefore, the price level rose by 5% from 2012 to 2019.
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A window is 150cm wide and 90cm high what is the area of the window in square metres
For any acute angle A if sin A = 2x-1/2x+1, what is the value of cos A cot A?
The trigonometric expression cosAcotA = 8x/(4x² - 1)
What is a trigonometric expression?A trigonometric expression is an expression that contains trigonometric ratios.
Given that for any acute angle A if sin A = 2x-1/2x+1, we desire to find the value of cos A cot A?
So, we proceed as follows
cosAcotA = cosA × cosA/sinA (since cotA = cosA/sinA)
= cos²A/sinA
Now using the trigonometric identity
sin²A + cos²A = 1
⇒ cos²A = 1 - sin²A
So, substituting this into the equation, we have that
cosAcotA = cos²A/sinA
= (1 - sin²A)/sinA
= 1/sinA - sin²A/sinA
= 1/sinA - sinA
Substituting the value of sinA into the equation, we have
= 1/(2x - 1)/(2x + 1) - (2x - 1)/(2x + 1)
= (2x + 1)/(2x - 1) - (2x - 1)/(2x + 1)
Taking the L.C.M, (2x - 1)(2x + 1), we have
= [(2x + 1)² - (2x - 1)²]/[(2x - 1)(2x+ 1)]
= [(2x + 1)² - (2x - 1)²]/[(2x)² - 1²)]
= [(2x + 1 + 2x - 1)(2x + 1 - (2x - 1)]/(2x)² - 1²)
= [(2x + 1 + 2x - 1)(2x + 1 - 2x + 1)]/4x² - 1)
= [(4x)(2)]/4x² - 1)
= 8x/(4x² - 1)
So, cosAcotA = 8x/(4x² - 1)
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please help me with these questions plaese hurry need these today
For numbers 1-6, using the order of operations to evaluate each expression is given as follows:
[tex](8.15 x 4 + 5) x 3.2 = 120.32\\12 + 5 + 32 x 2.2 = 87.4\\17 + 8 x (2.7 + 6) - 3 = 83.6\\38.9 - 2.3 x 1.5 + 2.6 = 37.05\\0.2 x (5 - 0.7) + 1.8 + 2 = 4.66\\5 + (8.06 - 12.5 + 2) = 4.56[/tex]
Define pοlynοmial equatiοn.A pοlynοmial equatiοn is an equatiοn in which a pοlynοmial expressiοn is set equal tο anοther expressiοn οr tο zerο. It is an algebraic equatiοn that invοlves οne οr mοre terms in which the variables are raised tο a pοsitive integer pοwer and multiplied tοgether. The degree οf the pοlynοmial is the highest pοwer οf the variable in the pοlynοmial equatiοn.
(8.15 x 4/5) x 3.2
= (6.52) x 3.2 (Perfοrming multiplicatiοn befοre divisiοn)
= 20.86
2. 12/5+32 x 2.2
= 2.4 + 70.4 (Perfοrming multiplicatiοn befοre additiοn)
= 72.8
3. 17+8 x (2.7/6)-3
= 17 + 1.2 - 3.0 (Perfοrming divisiοn befοre multiplicatiοn and subtractiοn)
= 15.2
4. 38.9 - 2.3 x 1.5 + 2.6
= 38.9 - 3.45 + 2.6 (Perfοrming multiplicatiοn befοre subtractiοn)
= 37.05
5. 0.2 x (5 - 0.7) + 1.8 / 2
= 0.2 x 4.3 + 0.9 (Perfοrming subtractiοn inside the parentheses)
= 1.12
6. 21.5/5+(8.06-12.5/2)
= 4.3 + 1.53 (Perfοrming divisiοn befοre subtractiοn and additiοn inside the parentheses)
= 5.83
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While birdwatching, Vicki saw 7 red birds, 9 white birds, and 19 black birds. Johnny saw 9 red birds, 12 blue birds, and 29 brown birds. Estimate how many more birds Johnny saw by rounding all numbers to the nearest ten before adding and subtracting.
Answer:
10
Step-by-step explanation:
7 rounds to 10
9 rounds to 10
19 rounds to 20
so Vicki has 40 birds
9 rounds to 10
12 rounds to 10
29 rounds to 30
so johnny has 50 birds
now subtract 50-40=10
I need help with this problem. Joe bought a gallon of gasoline for 2. 85 per gallon and c cans of oil for 3. 15 per can
From the given information provided, the expression that need to determine the total amount is Total cost = $2.85/gallon x g gallons + $3.15/can x c cans.
The expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = Cost of gasoline + Cost of oil
We can represent the cost of gasoline as:
Cost of gasoline = price per gallon x number of gallons
Substituting the given values, we get:
Cost of gasoline = $2.85/gallon x g gallons
Similarly, we can represent the cost of oil as:
Cost of oil = price per can x number of cans
Substituting the given values, we get:
Cost of oil = $3.15/can x c cans
Putting it all together, we get:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Question - Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
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probability sampling procedures are question 13 options: a) instances where every unit in the population has a non-zero chance of being selected b) every possible answer is correct c) typically used when population parameters are known to exist d) certain to eliminate random sample error
Probability sampling procedures are instances where every unit in the population has a non-zero chance of being selected. (Option a)
Probability sampling is a type of sampling method used in statistical analysis, where each member of the population has a known and equal probability of being selected. This means that every possible unit in the population has a non-zero chance of being selected for the sample.
Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. These methods are typically used when population parameters are unknown or when the researcher wants to make generalizations about the population based on the sample data.
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ten chairs are arranged in a circle. find the number of subsets of this set of chairs that contain at least three adjacent chairs.
Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
The given that 10 chairs arranged in a circle.
Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.
To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.
This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.
The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.
Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:
Length of subset number of ways to select the subset number of ways to add chairs
Total number of subsets31 (adjacent)
= 10 ---43 (adjacent) 10*2
=20---55 (adjacent)10*4
=40---67 (adjacent)10*6
=60---79 (adjacent)10*8
=80---810 (adjacent)10*10
=100---
As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:
Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100
= 310
Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
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11. Hannah recorded the number of miles she jogged. She started jogging 3 41 miles. Every week she jogged an additional
1 21 miles. Select all true statements. The y-intercept is the rate of change. The y-intercept is the starting value. The slope is 121. The slope is 3 41. The y-intercept is 1 21. The y-intercept is 3 41
Using coordinate geometry,
The y-intercept is the starting value (true).The slope is 1/2 or 0.5, not 121 or 3/41 (false).The y-intercept is 3/41 is also false as it contradicts the first true statement, therefore, the y-intercept is the starting value and the y-intercept of 3/41 is also true.The problem provides two pieces of information about Hannah's jogging routine: she started with 3 41 miles and added 1/21 miles every week. We can use this information to create a linear equation that represents the number of miles Hannah jogged as a function of the number of weeks she has been jogging.
To create this equation, we first identify the starting value, which is 3 41 miles. This is also the y-intercept of the line. Next, we determine the slope of the line, which is the rate at which the number of miles increases each week. The slope is equal to the change in y (miles) divided by the change in x (weeks), which in this case is (1/21 - 3/41)/1 = -2/1 = -2. Therefore, the slope of the line is -2.
Putting these two pieces of information together, we get the equation y = -2x + 3 41, where y is the number of miles jogging and x is the number of weeks of jogging. This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 3 41.
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What is the volume of the cone expressed in terms of pi?
Answer: V≈339.29 in
Step-by-step explanation:
9. A helicopter spots two landing pads below. The straight-line distance
from the helicopter to the pads is 14 miles to Landing Pad A and 8 miles
to Landing Pad B. If the landing pads are 20 miles apart, find the angle
of depression from the helicopter to Landing Pad B.
In response to the stated question, we may state that As a result, the Pythagorean theorem angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.
what is Pythagorean theorem?The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.
We can calculate the angle of depression from the helicopter to Landing Pad B using trigonometry.
Let we make a diagram:
B
/|
/ |
/ | 8 miles
14 / |
/θ |
/ |
/ |
/______|______ A
20 miles
Using trigonometry, we can deduce:
tan(θ) = opposite / adjacent
The opposing side in this example is 14 - 8 = 6 miles (since the helicopter is 14 miles from Landing Pad A and 8 miles from Landing Pad B, and the pads are 20 miles apart). The distance between the two sides is 20 miles (the distance between the landing pads).
tan(θ) = 6 / 20
tan(θ) = 0.3
θ = arctan(0.3)
θ ≈ 16.7 degrees
As a result, the angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.
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what's a drawback to using a histogram?
Answer:
Step-by-step explanation:
One potential drawback of using a histogram is that it can be sensitive to the choice of bin width or bin size. If the bin size is too small, the histogram may appear too noisy or have too many empty bins, which can obscure patterns in the data. If the bin size is too large, important features of the distribution may be lost or smoothed out. Additionally, histograms do not always show the actual values of the data points, but rather a summary of the data. This means that some details about the data may be lost, such as the exact values of outliers or individual data points.
ANSWER THIS WITHIN ONE HOUR OR ELSE I WILL BE DOOMED
mARKING BRAINLIEST
PS: FILL IN THE SHEET DONT JUST GIVE AN ANSWER
The prompt on fractions is given as follows:
1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10
3) (1/3) ÷ 5 = 1/15
4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.
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SOMEONE HELP PLEASE
Kiki runs 4 3/7 miles during the first week of track practice she runs 6 2/3 miles during the second week of track practice. How much longer does kiki run during the second week of track practice than the first week of track practice
Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.
We have, a runner Kiki and she runs on track for practice. In first week,
Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]
which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,
Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]
After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].
taking least common multiple of (3,7)= 21
=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]
[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].
Hence, required distance value is
[tex]3\frac{2}{21} [/tex].
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sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, what minimal sample size of the random sample should be used?
Sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, 368 is the minimal sample size of the random sample should be used
The appropriate sample size for probability estimates of the sample proportion of female students in the business statistics class is determined by the margin of error (m) and the level of confidence (Z).
The formula for sample size calculation is as follows:
N = [tex](Z^2\times p \times q) / m^2[/tex]
where
N is the sample size
Z is the z-score that corresponds to the level of confidence
p is the estimated proportion of female students
q is 1 - p (proportion of male students)m is the margin of error.
Since we don't have any margin of error, we can assume it to be a standard value of 5%. And a z-score of 1.96 is appropriate for a 95% level of confidence.
As a result, the sample size for estimating the sample proportion of female students in the business statistics class is given by
N = [tex](1.96^2\times0.60\times0.40) / (0.05^2)[/tex]
N = 368 students
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function “p” is in the form y = ax 2+c. if the values of “a” and “c” are both less than 0. which graph could represent “p”?
Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.
Answer: p= 2+c
Step-by-step explanation:
Subtract the following polynomials.
The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x
How to subtract polynomials?A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.
(3.1x + 2.8z) - (4.3x - 1.2z)
open parenthesis
3.1x + 2.8z - 4.3x + 1.2z
combine like terms
3.1x - 4.3x + 2.8z + 1.2z
-1.2x + 4x
Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.
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Please help 30 points I've been struggling
Identify the Slope and y - intercept from the graph
Slope (m) =
b =
Write the equation of the line in Slope-Intercept form
Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.
A′(−4, −1), B′(0, 1), C′(−2, −4)
A′(−4, 7), B′(0, 9), C′(−2, 4)
A′(0, 3), B′(4, 4), C′(3, 0)
A′(−8, 7), B′(−4, 9), C′(−6, 4)
The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).
What is meant by preimage?
In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.
To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:
A′(-4, 3-4) = (-4, -1)
B′(0, 5-4) = (0, 1)
C′(-2, 0-4) = (-2, -4)
Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).
So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).
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On a certain hot summers day, 402 people used the public swimming pool. The daily prices are 1. 50$ for children and 2. 00$ for adults. The receipts for admission totaled 648. 50$. How many children and how many adults swam at the public pool that day?
From the given information provided, there were 311 children who swam at the pool that day.
Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.
From the problem, we know that:
C + A = 402 (Equation 1) (The total number of people who used the pool was 402)
1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)
To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:
1.50C + 1.50A = 603 (Equation 3)
Now we can subtract Equation 3 from Equation 2 to eliminate C:
2.00A - 1.50A = 648.50 - 603
0.50A = 45.50
A = 91
So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:
C + 91 = 402
C = 311
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The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line
The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).
For option 1: intersection point (1,1)
substitute the values of x & y in the given equation.
1 = 3 (1) - 2
1 = 1
LHS = RHS
For option 2: point (1,1)
substitute the values of x & y in the given equation.
1 = 2 (1) + 3
1 = 5
LHS ≠ RHS
For option 3: point (1,1)
substitute the values of x & y in the given equation.
1 = -2 (1) + 3
1 = 1
LHS = RHS
For option 4: point (1,1)
substitute the values of x & y in the given equation.
1 = - [tex]\frac{1}{2}[/tex] (1) + 3
1 = [tex]\frac{5}{2}[/tex]
LHS ≠ RHS
For option 5: point (1,1)
substitute the values of x & y in the given equation.
1 = - [tex]\frac{1}{3}[/tex] (1) + 3
1 = [tex]\frac{8}{9}[/tex]
LHS ≠ RHS
Therefore, correct option for the given graph is option 1 and option 3.
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the area of the figure
Answer:
432
Step-by-step explanation:
go 16x27 and that is your answer
Answer:
The area of the figureo will be 432
BECAUSE :-
You have to multiply 16 × 27 = 432
Hope Its Help You !!
What is the height of the tree?
Answer:
72 ft
Step-by-step explanation:
Alright so two ways you can solve this, but the easier one (imo) is to find the scale factor by doing 24/2 since its an enlargement, and multiplying 6 by the scale factor (12)
for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. 5.1
Bending moment curve equation below point A will be:
M = 15x - 3x² for 0 ≤ x ≤ b
Determination of shear and bending moment curves.
For the beam and loading shown, we can do the following:
Equation of shear curve (above point A):V = RA - w.x
For x = a,V = RA - w.a
For x = b,V = RA - w.b
Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b
Equation of shear curve (below point A):
V = RA - w.x
For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a
The shear curve equation becomes;
V = 15k for 0 ≤ x ≤ a
V = 15 - 6a for a ≤ x ≤ b
Equation of bending moment curve (above point A):
M = RAx - ½w.x²For 0 ≤ x ≤ a,
M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,
M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²
The bending moment curve equation above point A becomes:
M = 15x - 3x² for 0 ≤ x ≤ a
M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b
Equation of bending moment curve (below point A):
M = RAx - ½w.x²For 0 ≤ x ≤ b,
M = 15x - ½(6x²) = 15x - 3x²
The bending moment curve equation below point A becomes;
M = 15x - 3x² for 0 ≤ x ≤ b
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The graph below shows a company's profit f(x), in dollars, depending on the price of goods x, in dollars, being sold by the company:
f(x)
150
120
Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit for the company in the situation
described?
Part C: What is an approximate average rate of change of the graph from x= 1 to x= 3, and what does this rate represent in context of the described situation?
The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice
How to explain the graphThe higher or largest number of the chart is the maximum reach
B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about:
(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50
The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.
If we take the peak profit to be $270 we can write f(x) as:
f(x) 16.875x(x-8)
Then f(1) = 118.15 and average rate of change is 50.625.
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a bag contains red balls, green balls, and yellow balls. if balls are drawn one at a time without replacement, the probability that the first yellow ball is drawn on the eighth draw is , what is the value of ?
The probability of drawing the first yellow ball on the eighth draw is 1/2772.
The probability of drawing a yellow ball on the eighth draw is the probability of drawing 7 non-yellow balls followed by a yellow ball.
The probability of drawing a non-yellow ball on the first draw is 7/12 since there are 7 non-yellow balls out of a total of 12 balls in the bag. After the first non-yellow ball is drawn, there will be 6 non-yellow balls left out of a total of 11 balls. So the probability of drawing a non-yellow ball on the second draw is 6/11. Continuing in this manner, the probability of drawing 7 non-yellow balls in a row is
(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6)
Now, there are 5 yellow balls left out of a total of 5 + 7 + 3 = 15 balls. So the probability of drawing a yellow ball on the eighth draw is 5/15.
Therefore, the probability of drawing the first yellow ball on the eighth draw is
(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6) × (5/15)
Simplifying this expression, we get
(7 × 6 × 5 × 4 × 3 × 2 × 1 × 5) / (12 × 11 × 10 × 9 × 8 × 7 × 6 × 15)
which simplifies to:
1/2772
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The given question is incomplete, the complete question is:
A bag contains 3 red balls, 4 green balls, and 5 yellow balls. If balls are drawn one at a time without replacement, what is the probability that the first yellow ball is drawn on the eighth draw?
f scores are normally distributed with a mean of 35 and a standard deviation of 10, what percent of the scores is: (a) greater than 34?
The percentage of scores greater than 34 is 0.5398 or 53.98%.
Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.
z = (x - μ) / σ
Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1
We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.
The percentage of scores greater than 34 is 0.5398 or 53.98%.
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Select the correct answer.
The subtraction property of equality is used for the justification of step 2 in the solution.
How to use the subtraction property of equality?The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality.
Therefore, Justify the property used for step 2 in the equality.
1 / 2 r + 1 / 2 = - 2 / 7 r + 6 / 7 - 5
Step 1 : 1 / 2 r + 1 / 2 = - 2 / 7 r - 29 / 7
Step 2: 1 / 2 r = - 2 / 7 r - 65 / 14
We had to subtract 1 / 2 from both sides of the equation to arrive at step 2. Therefore, the subtraction property of equality is the justification for step 2 in the solution.
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there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season?
There are a total of 48 soccer games in the season.
Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:
Number of day games = Total number of games - Number of night games
= 12 games/month x 4 months - 8 night games/month x 4 months
= 48 games - 32 games
= 16 games
Therefore, the total number of games in the season is:
Total number of games = Number of day games + Number of night games
= 16 games + 32 games
= 48 games
So, there are 48 soccer games in the season.
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