f(g(-4)) = 3(-4)^2 -2(-4)
f(g(-4)) = 56
g(f(2)) = + 3 ?
g(f(2))= 3 ???
(I guess you didn't write the whole question, all you have to do is to replace "x" with the given value, in this case for g(f(2)) the given value is 2)
Create an equation to show the relationship between m and g.
Answer:
Step-by-step explanation:
m = 32g
The derivation of the Quadratic Formula is shown by completing the square and applying square roots. What is the missing step?
A. x^2+b/a · x+c=0
B. ax^2+b/a · x+c/a=0
C. ax^2+b/a · x+c=0
D. x^2+b/a · x+c/a=0
In the derivation of the Quadratic Formula is shown by completing the square and applying square roots. The missing step is D. x^2 + b/a + c/a = 0.
How to explain the informationThe quadratic formula derivation requires the initial equation of ax^2 + bx + c = 0, where a, b and c are constants; it is also necessary that a cannot be zero.
the step simplifies the division of a:
0 divided by anything is still zero, so you can remove the a denominator
a/a = 1, and is therefore irrelevant, so ax^2 / a = x^2
The correct option is D
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What is the best way to multiply a chain of matrix with dimensions 10x3, 3x5, 5x10,10x12,12x1 show the steps performed in your work to get to the result.
The final matrix product has dimensions 10x1.
To multiply a chain of matrices with given dimensions, we need to follow the associative property of matrix multiplication and multiply the matrices in a certain order.
Given the dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, we need to multiply them in the order of (10x3) x (3x5) x (5x10) x (10x12) x (12x1).
Step 1: Multiply the first two matrices, (10x3) and (3x5), to get a resulting matrix of dimension (10x5).
Step 2: Multiply the resulting matrix from step 1, which is (10x5), with the next matrix, (5x10), to get a new matrix of dimension (10x10).
Step 3: Multiply the resulting matrix from step 2, which is (10x10), with the next matrix, (10x12), to get a new matrix of dimension (10x12).
Step 4: Multiply the resulting matrix from step 3, which is (10x12), with the last matrix, (12x1), to get a final matrix of dimension (10x1).
Therefore, the final answer obtained by multiplying the chain of matrices in the given order is a matrix of dimension (10x1).
The steps performed in the multiplication of the chain of matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1 are as follows:
(10x3) x (3x5) = (10x5)
(10x5) x (5x10) = (10x10)
(10x10) x (10x12) = (10x12)
(10x12) x (12x1) = (10x1)
To multiply a chain of matrices efficiently, you should follow the Matrix Chain Multiplication algorithm, which determines the optimal parenthesization to minimize the number of scalar multiplications. For your matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, here's the best way to multiply them:
1. Start by finding the optimal parenthesization:
- Multiply the 10x3 and 3x5 matrices first, resulting in a 10x5 matrix.
- Then, multiply the 5x10 and 10x12 matrices, resulting in a 5x12 matrix.
- Finally, multiply the 10x5 and 5x12 matrices, and then the resulting 10x12 matrix with the 12x1 matrix.
2. Perform the multiplications:
- A = 10x3 * 3x5 = 10x5
- B = 5x10 * 10x12 = 5x12
- C = A * B = 10x5 * 5x12 = 10x12
- D = C * 12x1 = 10x12 * 12x1 = 10x1
By following this approach, you minimize the total number of scalar multiplications, resulting in a more efficient calculation. The final matrix product has dimensions 10x1.
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consider the function l(x,y)shown in the contour diagram at the right.l(x,y)is the percentage a student earns on an exam as a function of x,the number of hours the student slept the night before,and y.how full their stomach is before the exam on a scale of 1 to 10.
Sleeping is more important than the having full stomach when it comes to doing well on an exam
Based on the contour diagram, it seems that the percentage a student earns on an exam (l) is affected by both x and y. In other words, the more hours a student sleeps (x), the higher their percentage in the exam tends to be. Similarly, the fuller a student's stomach is (y), the higher their percentage in the exam tends to be.
It's important to note that the impact of x and y on l isn't necessarily equal. For example, if a student sleeps for 10hours (x=10) and has a full stomach (y=10), their percentage in the exam appears to be close to 100%. However, if they only sleep for 5 hours (x=5) and have a full stomach (y=10), their percentage in the exam appears to be closer to 70%. This suggests that sleeping is more important than having a full stomach when it comes to doing well on an exam.
Overall, this function seems to demonstrate that the amount a student sleeps and their level of hunger can impact their performance on an exam. However, it's important to note that this is just one function and may not apply to every student or every exam.
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A manager's sample estimated the standard deviation of number of credit cards per employee to be 3 cards. You are researching the average number of credit cards per employee. You want to know how many people you should survey if you want to know, at a 95% confidence level, that the sample mean credit cards per employee is within 1point of the true number of credit cards per employee.
Use a calculator to find the value of z that you should use in the sample size formula
To find the value of z for a 95% confidence level, we can use a z-score table or a calculator. The z-score corresponding to a 95% confidence level is 1.96.
To determine the sample size, we can use the formula:
n = (z^2 * s^2) / E^2
where:
n = sample size
z = z-score (1.96 for 95% confidence level)
s = estimated standard deviation (3 cards)
E = margin of error (1 card)
Plugging in the values, we get:
n = (1.96^2 * 3^2) / 1^2
n = 34.56
We need to round up to the nearest whole number, so the sample size should be 35 people. This means that if we randomly select 35 employees and calculate their average number of credit cards, we can be 95% confident that the true average number of credit cards per employee is within 1 card of our sample mean.
To determine the required sample size for your survey with a 95% confidence level and a margin of error of 1 point, you'll need to use the sample size formula and find the appropriate z-value.
The sample size formula is: n = (z^2 * σ^2) / E^2
Where:
- n is the sample size
- z is the z-value corresponding to the desired confidence level (95% in this case)
- σ is the estimated standard deviation of the population (3 credit cards per employee)
- E is the margin of error (1 point)
For a 95% confidence level, the z-value is approximately 1.96. You can find this value using a z-table or an online calculator.
Now, plug the values into the formula:
n = (1.96^2 * 3^2) / 1^2
n = (3.8416 * 9) / 1
n ≈ 34.5744
Since you cannot survey a fraction of a person, round up to the nearest whole number. Therefore, you should survey approximately 35 people to achieve a 95% confidence level with a margin of error of 1 point for the average number of credit cards per employee.
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The diagram in Fig. 15.17 is an equi- lateral triangle with its given dimen- sions in cm. Find the perimeter of the triangle. x+8 y +4 4x-y
The perimeter of the equlateral triangle is 42 units
Finding the perimeter of the triangle.The dimensions of the triangle are given as
x + 8, y + 4 and 4x - y
The side lengths of an equilateral triangle are equal
So, we have
x + 8 = y + 4
4x - y = y + 4
When evaluated, we have
x = 6 and y = 10
So, we have
Perimeter = 3 * (y + 4)
This gives
Perimeter = 3 * (10 + 4)
Evaluate
Perimeter = 42
Hence, the perimeter is 42 units
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4. The department of fish and wildlife want to estimate the size of alligator population in
Louisiana. The department issued 937 tags to hunters in 2018. The average length of the
alligators was 11.2 ft with a standard deviation of 2.06 feet. What is the mean and
standard deviation of the population?
A sports photographer sells team pictures. The cost of each picture is based on its are. Wallet-sized pictures measure 5 cm by 7 cm and cost $1.93 each. The photographer sells a larger picture that is two times the length and two times the width of the wallet-size picture. How much does the larger picture cost?
The larger picture costs $7.72
To find the cost of the larger pictureThe wallet-sized image has the following area:
A1 = length x width = 5 cm x 7 cm = 35 cm2.
The bigger image has the following measurements because it is twice as long and wide as the wallet-sized image:
Length equals 2 x 5 cm = 10 cm
width equals 2 x 7 cm = 14 cm
The size of the larger image is given by the formula:
A2 = length x width = 10 cm x 14 cm = 140 cm^2
The price per square centimeter is something we must know. By dividing the price of the wallet-sized photo by its surface area, we can determine this:
Cost per cm^2 = $1.93 / 35 cm^2 = $0.05514 per cm^2
By dividing the area of the larger image by the price per square centimeter, we can now determine its cost:
Cost of larger picture = A2 x Cost per cm^2
= 140 cm^2 x $0.05514 per cm^2
= $7.7196
Therefore, the larger picture costs $7.72
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A rectangular prism has a volume of 7800 cubic feet width of 40 feet and a height of 13 feet, find its length in feet
The length of the rectangular prism is 15 feet.
What is the length of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that: the volume of the rectangular prism is 7800 cubic feet, the width is 40 feet, and the height is 13 feet.
We can substitute these values into the formula and solve for the length:
V = w × h × l
7800 = 40 × 13 × l
7800 = 520 × l
l = 7800 / 520
l = 15 ft
Therefore, the measure of the length is 15 feet.
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refer to information in the above question. if it takes 6 days for the order placed to arrive, at what level of inventory should the product be reordered, assuming a 30-day month (i.e what's the reorder point)? group of answer choices 83 gallons 100 gallons 500 gallons 537 gallons none of the above
To calculate the reorder point, we need to consider the lead time (6 days) and the average daily usage of the product. Assuming a 30-day month, the average daily usage can be calculated as:
Product used per day = Total product used in a month / Number of days in a month
Product used per day = Inventory / 30
To determine the reorder point, we need to know the daily consumption rate of the product and the lead time (number of days it takes for the order to arrive).
1. Calculate the daily consumption rate: Since we have a 30-day month, we will divide the monthly consumption by 30.
Total consumption in a month = X gallons (Information not provided)
Daily consumption rate = X gallons / 30 days
2. Calculate the lead time demand: Since it takes 6 days for the order to arrive, we need to find out how many gallons are consumed during this time.
Lead time demand = Daily consumption rate * Lead time
Lead time demand = (X gallons / 30 days) * 6 days
3. Determine the reorder point: The reorder point is the level of inventory at which the product should be reordered to ensure that there is enough stock to cover the lead time demand.
Reorder point = Lead time demand
Reorder point = (X gallons / 30 days) * 6 days
Let's assume that the reorder point is the level of inventory at which we need to place a new order to avoid running out of stock. So, the reorder point can be calculated as:
Reorder point = Lead time demand + Safety stock
Here, the lead time demand is the product used during the lead time (6 days) and the safety stock is the buffer inventory kept to avoid stockouts. Let's assume a safety stock of 50 gallons.
Lead time demand = Product used per day * Lead time
Lead time demand = (Inventory / 30) * 6
Lead time demand = Inventory / 5
Reorder point = (Inventory / 5) + 50
We need to solve for the inventory level at which we should reorder. Let's assume the answer is X.
X / 5 + 50 = X
X - X/5 = 50
4X/5 = 50
X = (5/4) * 50
X = 62.5
So, the reorder point is 62.5 gallon. Therefore, the correct answer is "none of the above".
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1) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=e^(?x^2), y=0, x=0, and x=1 about the y -axis.
2) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=sqrt(x?1), y=0, x=5 about the line y=5
3) Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2 , y=8?x^2 and to the right of x=1.5 about the y -axis.
Answer: Number Question #1 - To find the volume generated by rotating the region bounded by y=e^(−x^2), y=0, x=0, and x=1 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be e^(−x^2).
Thus, the volume is given by:
V = ∫[0,1] 2πxe^(−x^2) dx
Using u-substitution with u=−x^2 and du/dx=−2x, we can rewrite this integral as:
V = ∫[0,−1] −πe^udu
Evaluating the integral, we get:
V = π/2(e^0 − e^(−1)) ≈ 0.436
Therefore, the volume generated by rotating the region about the y-axis is approximately 0.436 cubic units.
Number Question #2 - To find the volume of the solid obtained by rotating the region bounded by y=sqrt(x−1), y=0, x=5 about the line y=5, we can again use the method of cylindrical shells. In this case, the radius of each shell will be 5−y, and the height will be x−1.
Thus, the volume is given by:
V = ∫[0,4] 2π(5−y)(x−1)dy dx
Integrating with respect to y first, we get:
V = ∫[1,5] π(x−1)(5−y)^2 dx
Expanding and simplifying, we get:
V = 2π/3 [(5x−x^2−13)∣[1,5]]
Evaluating the integral, we get:
V = (32π/3)
Therefore, the volume of the solid obtained by rotating the region about y=5 is (32π/3) cubic units.
Number Question #3 - To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=x^2, y=8−x^2, and to the right of x=1.5 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be (8−x^2)−x^2=8−2x^2.
Thus, the volume is given by:
V = ∫[1.5,2] 2πx(8−2x^2)dx
Integrating, we get:
V = (32π/3) − (9π/2)
Therefore, the volume of the solid obtained by rotating the region about the y-axis is (32π/3) − (9π/2) cubic units.
A summary of two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metroplis, Ltd MTP 17.95 18.28 18.25
Suburbia, Inc SBR 5.63 5.88 4.98
Suppose you purchase 30 shares of Metropolis stock and 55 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks?
Day 2 is the best by $26.75.
Day 3 is the best by $26.75.
Day 2 is the best by $23.65.
Day 3 is the best by $23.65.
The best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day, option C is correct.
On Day 1, the total value of the 30 shares of Metropolis stock is:
30 shares x $17.95 per share = $538.50
And the total value of the 55 shares of Suburbia stock is:
55 shares x $5.63 per share = $309.65
So the total value of both stocks on Day 1 is:
$538.50 + $309.65 = $848.15
On Day 2, the total value of the shares of Metropolis stock is:
30 shares x $18.28 per share = $548.40
And the total value of the shares of Suburbia stock is:
55 shares x $5.88 per share = $323.40
The total value of both stocks on Day 2 is: $871.8
for Day 3, total value of both stocks on Day 3 is $$821.40
Therefore, we can see that the best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day:
$871.80 - $848.15 = $23.65
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In an arithmetic sequence, U2= 5 and U3= 11.
Find the common difference.
Find the first term.
Find the sum of the first 20 terms
The common difference is 6, and the sum of the first 20 terms for the arithmetic sequence 1120.
U2 = 5
U3 = 11
Finding the common difference (d)
U3 - U2
= 11 - 5
= 6
Finding the first term (U1):
U1 = U2 - (2 - 1) × d
= 5 - (2 - 1) × 6
= 5 - 6
= -1
Finding the sum of the first 20 terms:
Sn = n/2 × (2U1 + (n - 1)d)
Sn = 20/2 × (2 × -1 + (20 - 1) × 6)
= 10 × (-2 + 19 × 6)
= 10 × (-2 + 114)
= 10 × 112
= 1120
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Please solve this and I will give u brainlst.
A pipe at an amusement park sprays water onto visitors. A cross section of each pipe has the shape of a parallelogram. Answer parts (a)(c).
Answer:
a. The interior angles of Parallelogram B (Pipe B) are 30°, 150°, 150°, and 30°. Angle x measures 60° because the 120° angle and angle x are supplementary angles.
c. Correct answers, in order: 360, 360, 150, supplementary, 30, complementary, 60
represent -3/11 on the number line.
The number -3/11 on the number line is added as an attachment
Representing -3/11 on the number line.From the question, we have the following parameters that can be used in our computation:
Number = -3/11
To represent -3/11 on a number line, we use the following steps
Create an interval from -5 to 6 i.e. 11 spacesPlot -3/11 on point -3Using the above as a guide
The number line is added as an attachment
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The human resources department of the Mean Corporation would like to estimate the size of the annual salary that they should offer to university graduates. The CEO of the Mean Corporation has suggested that the salary offered (W) should be calculated based on the Grade Point Average (G) of a student. Based on a random sample of university graduates, the human resources department has calculated the mean salary offered to university graduates to be W and the mean Grade Point Average of university graduates to be G. The Mean Corporation will carry out a regression analysis to investigate the relationship between salary and Grade Point Average. Select the dependent variable in the regression analysis that will be conducted:___________
The dependent variable in the regression analysis that will be conducted is the salary offered (W) to university graduates.
It is considered the dependent variable because it is the variable that is predicted or explained by the Grade Point Average (G), which is the independent variable. The regression analysis will help to determine how much the salary offered varies with changes in the Grade Point Average, and the mathematical equation derived from the analysis will be used to predict the salary offered based on a given Grade Point Average.
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Need Help ASAP
10 points. please help
The length of the arc BC is given as follows:
Arc BC = 10π units.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
The radius in this problem is of 10 units, hence the length of the whole circumference is of:
C = 20π units.
The entire circumference is of 360º, hence arc BC is half the circumference, and it's length is given as follows:
Arc BC = 10π units.
Missing InformationThe problem asks for the length of arc BC.
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n/(sqrt(16n^2 5) find the limit of the following sequence or determine that the sequence diverges.
The expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is: Limit = 1/(sqrt(80))
To find the limit of the sequence n/(sqrt(16n^2 5)), we can simplify the expression by dividing both the numerator and denominator by n:
n/(sqrt(16n^2 5)) = 1/(sqrt(16*5/n^2)) = 1/(4sqrt(5/n^2))
As n approaches infinity, 5/n^2 approaches zero. Therefore, the denominator of the expression approaches infinity, and the whole expression approaches zero.
Therefore, the limit of the sequence is 0.
To find the limit of the given sequence n/(sqrt(16n^2 * 5)), we'll apply some algebraic simplification and use the properties of limits.
First, simplify the expression:
n/(sqrt(16n^2 * 5)) = n/(sqrt(80n^2))
Now, divide both the numerator and denominator by n:
n/(sqrt(80n^2)) = 1/(sqrt(80))
Since the expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is:
Limit = 1/(sqrt(80))
This is the final answer.
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Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between successive arrivals. The length of a phone call is distributed exponentially with mean 3 minutes. The probability that an arrival does not have to wait before service is A0.3B0.7C0.5D0.9
The probability that an arrival does not have to wait before service is 0.7 (Option B).
To calculate the probability that an arrival does not have to wait before service, we need to use the Poisson and exponential distributions.
First, we can calculate the average number of arrivals per hour:
60 minutes / 10 minutes per arrival = 6 arrivals per hour
Next, we can use the exponential distribution to calculate the probability that a phone call is less than or equal to 10 minutes (the time between arrivals):
P(call length ≤ 10 minutes) = 1 - e^(-10/3) ≈ 0.957
This means that there is a 95.7% chance that a phone call will end before the next arrival.
Finally, we can use the Poisson distribution to calculate the probability that there are no arrivals in the 10-minute window between the end of a phone call and the next arrival:
P(no arrivals in 10 minutes) = e^(-6) ≈ 0.002
So the probability that an arrival does not have to wait before service is:
P(no wait) = P(call length ≤ 10 minutes) * P(no arrivals in 10 minutes)
P(no wait) = 0.957 * 0.002
P(no wait) ≈ 0.002
Therefore, the answer is A) 0.3.
We're given that arrivals at a telephone booth follow a Poisson distribution with an average time of 10 minutes between arrivals, and the length of a phone call is exponentially distributed with a mean of 3 minutes. We need to find the probability that an arrival does not have to wait before service.
Step 1: Calculate the arrival rate (λ) and service rate (μ)
The average time between arrivals is 10 minutes, so the arrival rate λ is 1/10 arrivals per minute.
The average length of a phone call is 3 minutes, so the service rate μ is 1/3 calls per minute.
Step 2: Calculate the traffic intensity (ρ)
The traffic intensity ρ is the ratio of the arrival rate to the service rate.
ρ = λ/μ = (1/10) / (1/3) = 3/10 = 0.3
Step 3: Calculate the probability that an arrival does not have to wait (P_0)
For an M/M/1 queue (Poisson arrivals and exponential service times with a single server), the probability that an arrival does not have to wait before service is given by P_0 = 1 - ρ.
P_0 = 1 - 0.3 = 0.7
So, the probability that an arrival does not have to wait before service is 0.7 (Option B).
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PLEASE HELP I INCLUDED A WRITTEN VERSION OF MY PROBLEM I WROTE IT PLEASE HELP!!!
The expression x²-6x+9 is equal to the expression (x-3)², option A is correct.
The given expression is x²-6x+9
x is the variable in the expression
Plus and minus are the operators
We have to factor the expression
x²-6x+9
x²-3x-3x+9
x(x-3)-3(x-3)
(x-3)(x-3)
x²-6x+9 is equal to (x-3)²
(x-3)²
Hence, the expression x²-6x+9 is equal to the expression (x-3)², option A is correct.
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The line plot represents the wait time in line for a ride at a local fair.
A line plot titled Wait Time at the Fair. The horizontal line labeled Time in Minutes begins at 8, with every one unit labeled up to 20. There is one dot above 10, 11, 14, 16, and 17. There are two dots above 13. There are four dots above 12 and 15.
Which of the following best describes the shape of the data, and why?
The data is skewed and means that the wait times were less than 13 minutes for all the rides.
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutes long.
The data is symmetric and means that the wait times were around 13 minutes for all the rides.
The data is skewed and means that the wait times were over 13 minutes for all the rides.
The shape of the data of the line plot is best described by the option
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutesWhat is a line plot?A line plot is a graphical display of data as check marks showing the frequency of a data point above a number line.
The description of the line plot can be presented as follows;
The number of dota above the points marked 10, 11, 14, 16, and 17 = One dot each
The number of dots above the point marked 13 = Two dots
The number of dots above the points marked 12, and 15 = Four dots each
The above description of the line plot indicates;
The mode of the dataset are 12 and 15, therefore;
The data set is bimodalThe option that best describes the shape of the data, is therefore;
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suppose a random variable x is best described by a uniform probability distribution with range 2 to 5. Find the value of a that makes the following probability statements true.(a) P(x≤a)=0.24 A=?(b) P(x>a)=0.41 A=?(c) P(2.29≤x≤a)=0.36 A=?PART BIn a certain community, the probability that a family owns a dog is 35%. Given that a family owns a dog, the probability that they also own a cat is 20%. It is also known that 32% of all the families own a cat.What is the probability that a randomly selected family owns a dog?What is the conditional probability that a randomly selected family owns a dog given that it owns a cat?Hint: Write out each of the probabilities you've been given in probability notation, as well as the probabilities you need to find. You may need to find a joint probability ( P(A and B)) before you can answer the 2nd question. It may help to draw a Venn Diagram. Be sure to give your answers to at least 4 decimal places.
a) a = 2.72 makes the statement P(x ≤ a) = 0.24 true.
b)a = 3.77 makes the statement P(x > a) = 0.41 true.
c) a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.
Part A:
For a uniform probability distribution with range [2,5], the probability density function is:
f(x) = 1/(5-2) = 1/3 for 2 <= x <= 5
a) To find the value of a such that P(x ≤ a) = 0.24, we need to solve the following equation:
∫[2,a] f(x) dx = 0.24
Simplifying the equation, we get:
(a-2)/(5-2) = 0.24
a-2 = 0.72
a = 2.72
Therefore, a = 2.72 makes the statement P(x ≤ a) = 0.24 true.
b) To find the value of a such that P(x > a) = 0.41, we need to solve the following equation:
∫[a,5] f(x) dx = 0.41
Simplifying the equation, we get:
(5-a)/(5-2) = 0.41
5-a = 1.23
a = 3.77
Therefore, a = 3.77 makes the statement P(x > a) = 0.41 true.
c) To find the value of a such that P(2.29 ≤ x ≤ a) = 0.36, we need to solve the following equation:
∫[2.29,a] f(x) dx = 0.36
Simplifying the equation, we get:
(a-2.29)/(5-2) = 0.36
a-2.29 = 1.08
a = 3.37
Therefore, a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.
Part B:
Let D be the event that a family owns a dog, and let C be the event that a family owns a cat.
Given information:
P(D) = 0.35
P(C | D) = 0.20
P(C) = 0.32
We need to find:
P(D)
P(D | C)
Using Bayes' theorem, we can write:
P(D | C) = P(C | D) * P(D) / P(C)
Substituting the given values, we get:
P(D | C) = (0.20 * 0.35) / 0.32 = 0.21875
Therefore, the conditional probability that a randomly selected family owns a dog given that it owns a cat is 0.21875.
To find P(D), we can use the following formula:
P(D) = P(D | C) * P(C) + P(D | C') * P(C')
where C' represents the complement of C, i.e., the event that a family does not own a cat.
Since the probability of owning a cat or not owning a cat covers all possibilities, we have:
P(D) = P(D | C) * P(C) + P(D | C') * (1 - P(C))
Substituting the given values, we get:
P(D) = (0.20 * 0.35) + P(D | C') * (1 - 0.32)
We do not have enough information to directly calculate P(D | C'), so we need to use the fact that the probabilities must add up to 1. Thus:
P(D | C') = 1 - P(C' | D)
Using Bayes' theorem, we can write:
P(C' | D) = P(D | C') * P(C') / P
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(Chapter 13) Suppose f is twice continuously differentiable. At an in ection point of the curve y = f(x), the curvature is 0.
The curvature is zero at the origin, but f(x) is not twice continuously differentiable function at x = 0, because f''(x) does not exist at x = 0. Therefore, the statement is not necessarily true.
An inflection point is a point on a curve where the sign of the curvature changes. At an inflection point, the curvature may be zero, but it may also be undefined. Moreover, even if the curvature is defined and equal to zero at an inflection point, it does not necessarily imply that the function is twice continuously differentiable at that point.
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Jack is running a 5-mile race with Jill. Jack's run is represented by the function d = 0.05t,
where d is distance traveled in miles and t is the minutes run. Jill's run is represented by d
0.04t+ 0.5.
=
Part A
How do the graphs of Jack's representative function and Jill's representative function
compare to the graph of the linear parent function?
Part B
What do the effects of comparing Jack and Jill's functions to the linear parent function mean
in the real-world context?
When we compare functions we see that Jack and Jill have the smaller slopes
How to solve the problemJack's function: d = 0.05t
Slope (m1) = 0.05
Y-intercept (b1) = 0
Jill's function: d = 0.04t + 0.5
Slope (m2) = 0.04
Y-intercept (b2) = 0.5
Linear parent function: d = t
Slope (m0) = 1
Y-intercept (b0) = 0
When we compare functions we see that Jack and Jill have the smaller slopes
B. Given that they have smaller slopes this tells us that the pace with which they are running is smaller than that of the parent function
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43 cantaloupes at the farmers' market and had 25 left. Which equation could be used to find x, the number of cantaloupes Courtney had originally?
Answer: 43 - x =25
Step-by-step explanation:
43 - x = 25
so 43 - 25 = x
x = 18
Suppose a fair coin is tossed two times. Construct an equiprobable sample space for the experiment, and determine each of the following probabilities. (Enter your probabilities as fractions.) (a) Pr(0 heads) (b) Pr(1 head) (c) Pr(2 heads)
The probabilities of the possible outcomes obtained from tossing a fair coin two times are;
(a) Pr(0 heads) = 1/4
(b) Pr(1 head) = 1/2
(c) Pr(2 heads) = 1/4
What is the probability of an event?The probability of an event is the ratio of the number of required outcome to the number of possible outcomes.
The equiprobable sample space of tossing a fair coin two times is; {HH, HT, TH, TT}, where;
H = Heads
T = Tails
The sample space indicates that there are 4 possible outcomes
(a) The possibility of getting 0 heads, is to get TT, therefore, the probability of getting zero heads, Pr(0 heads) = TT = 1/4
(b) The possibility of getting 1 head is to get. HT or TH, therefore;
The probability of getting 1 head, Pr(1 heads) = 2/4 = 1/2
(c) The number of possibility of getting 2 heads, is to get HH = 1
Therefore, the probability of getting 2 heads, Pr(2 heads) = 1/4
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What is the value of X?
Answer: x = 2√381
Step-by-step explanation:
Call A the dotted line.
Using the Pythagorean theorem, we find that [tex]A^{2} + 16^{2}[/tex] [tex]= 22^{2}[/tex]
Simplifying gives:
[tex]A = \sqrt{16^2 + 22^2}\\A = \sqrt{740}\\A = 2\sqrt{185}[/tex]
Now we move to the other triangle we can call the sides: a, the dotted side, b the height, and x, the hypotenuse.
[tex]a = 2\sqrt{185}[/tex]
and
[tex]b = 44-16 = 28[/tex]
So,
[tex](2\sqrt{185})^{2} + 28^2 = x^2\\x = \sqrt{(2\sqrt{185})^2 +28^2 }\\x = \sqrt{740+784}\\x= \sqrt{1524}\\x= 2\sqrt{381}[/tex]
write 36 as a product of prime factors write the factors in order from smallest to largest
Answer:{2,2,3,3}
Step-by-step explanation:
six by six is 36 and 2 times three would give you six
Answer:
(2,2,3,3)
Step-by-step explanation:
Which word describes the "4" in this expression? 4h A term B product C sum D coefficient?
Answer:
coefficient
Step-by-step explanation:
the 4 is the coefficient
find the angle measures of trapezoid BCED
Answer:
BCDE= 100+ 80+100+80 = 360 degree
BAC = 20 degree
DBC = 100 degree
BDE = 80 degree
Step-by-step explanation:
Shows all is correct
We associate isosceles trapezoid in this question, this helps us prove with angle A in the triangle vertices how we can find one of the adjacent angles from the trapezoid by subtraction when all angles within one single trapezoid = 360 degrees. We can use 20 degree angle A to subtract and find each alternative angle easier.
Step-by-step explanation:
The semi circle shows 9 stones
Where angles are interior to the trapezoid
Where all 4 sided shapes add up to 360 degree
We draw a line of symmetry on BCED angle
To make midway points BC and DE = 90 degree
The two new formed shapes are still 4 sided and add up to 360 degree.
BC + DE = 180 degree
BDE = Triangle 180 -20/2 = 160/2 = 80
BCDE = Trapezoid = 360
Trapezoid angle DBC = 360-80-80/2 = 360-160/2 = 200/2 = 100 degree
Finding interior angle A (BAC)
BAC = 180/9 = 20 degree
BAC * (2) = 360 degree circle
BAC = 360/18 = 20 degree
Proves BAC = 20 degree
20 degree is used in BAC workings above in bold and proves all trapezoid angles are correct. We now know this is an isosceles trapezoid and that is why symmetry and midway points can help us find the angles without any given length.