g The tangent plane to z=f(x,y) at the point (1,2) is z=5x+2y−10. (a) Find fx(1,2) and fy(1,2). fx(1,2)= Number fy(1,2)= Number (b) What is f(1,2)? f(1,2)= Number (c) Approximate f(1.1,1.9). f(1.1,1.9)= Number
Answers
Answer:
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Approximation at points (1.1,1.9) is 0.7
Step-by-step explanation:
Given:
Tangent plane to a surface z=5x+2y-10 as the function at point (1,2)
To find :
f(x,y) at (1,2)
partial derivatives of function w.r.t. (x and y) and value of that function at given points.
Solution:(refer the attachment also)
Now we know that
the equation of tangent plane at given points to the surface is given by,
f(x1,y1,z1) and z=f(x,y)
z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)
here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.
now
taking partial derivative w.r.t. x we get
Fx(x1`,y1)=[tex]\frac{d}{dx} (5x+2y-10)[/tex]
=5.
Then w.r.t y we get
Fy(x1,y1)=
[tex]\frac{d}{dy}(5x+2y-10)[/tex]
=2.
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Using the Linearization or linear approximation we get
L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)
=-1+5(x-1)+2(y-2)
=5x+2y-10
Approximation at F(1.1,1.9)
=5(1.1)+2(1.9)-10
=5.5+3.8-10
=0.7
Approximation at points (1.1,1.9) is 0.7
Final answer:
The partial derivatives of f(x, y) at (1, 2) are fx(1,2) = 5 and fy(1,2) = 2. The function value f(1,2) is 0. An approximation for f(1.1, 1.9) using the tangent plane is 0.5.
Explanation:
The question concerns the computation of partial derivatives and the evaluation of a function f(x, y) given its tangent plane at a specific point. Given the tangent plane to z=f(x,y) at the point (1, 2), which is z=5x+2y−10, we have:
fx(1,2) is the partial derivative of z with respect to x at the point (1,2), equivalent to the coefficient of x in the tangent plane equation, which is 5.
fy(1,2) is the partial derivative of z with respect to y at the point (1,2), equivalent to the coefficient of y in the tangent plane equation, which is 2.
To find f(1,2), we substitute x=1 and y=2 into the tangent plane equation to get z = 5(1) + 2(2) − 10 = 0.
The value f(1.1,1.9) can be approximated by using the tangent plane equation. By plugging x=1.1 and y=1.9 into the equation, we obtain z = 5(1.1) + 2(1.9) - 10 = 0.5, for an approximate value of f(1.1, 1.9).
Summary of Answers:
fx(1,2) = 5
fy(1,2) = 2
f(1,2) = 0
f(1.1,1.9) ≈ 0.5
Related Questions
Can someone help me please
Answers
Answer:
1 unit
Step-by-step explanation:
If the circumference is 6, then the arc measured by a 60 degree angle, which is 1/6 of 360, represents 1/6 of the total circumference. Thus the answer is 1.
2. a) Find the break - even points for company X, which sells all it produces, if the
variable cost per unit is $3, fixed costs are $2 and Yrr = 5/9, where q is the number
of thousands of units of output produced.
b) Graph the total revenue curve and the total cost curve in the same plane.
c) Use your answer in (a) to report the quantity interval in which maximum profit
occurs.
Show all steps to get full credit. Solve it Algebraically
Answers
Find the solution in the attachments
In this exercise we have to use the knowledge of finance and thus plot a graph, this way we have that it corresponds to:
A)[tex]q= 0 \ or \ q=1[/tex]
B) The graph bellow.
C) The points of the grapg bellow.
Knowing that:
[tex]total \ cost = (variable \ cost \ per \ unit + final \ cost \ per \ unit * produced)[/tex]
The data that was informed is;
Variable cost por unit: 3Linear cost per unit: 2Units produced : 9A) The result is:
[tex]T= (3+2)*9\\T= 59[/tex]
Break even points one the points at which total cost are equal to :
[tex]T(q)= Y_T(9)\\5q= 5\sqrt{9}\\q=\sqrt{9}\\ q= 0 or q=1[/tex]
B) One plot of total cost are total revenue are ploted below. The blue curve is of total revenue and real graph is of total cost.
C) With the graph, it's closes that from q=0 ot q=1. Total revenue dominantes total cost and beyond a=1 the total cost dominands total revenue.
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Estimate the solution to the system of equations, y = 4x-2 and y = x+3.
Answers
Answer:
x = 1.67 about and y = 4.67 about
Step-by-step explanation:
y = 4x-2 and y = x+3
4x - 2 = x + 3
3x = 5
x = 5/3 = 1.67 about
y = 5/3 + 3 = 5/3 + 9/3 = 14/3 = 4.667
What are the roots of y=x2-3x-10
Answers
Answer:
x = 5 and -2
Step-by-step explanation:
This question wants the roots, which are when y = 0.
Set the equation equal to 0:
y=x2-3x-10
0=x2-3x-10
Now we can factor this (or use our calculators).
0=(x-5)(x+2)
Separate these by the Zero Product Property.
0 = x-5
x = 5
0 = x+2
x = -2
Answer:
-2 and 5
b on edu 2020
Step-by-step explanation:
edu 2020
The lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours. What is the probability that a battery will last more than 19 hours?
Answers
Answer:
Probability that a battery will last more than 19 hours is 0.0668.
Step-by-step explanation:
We are given that the lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.
Let X = lifetime of a battery in a certain application
So, X ~ N([tex]\mu=16,\sigma^{2} =2^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean lifetime = 16 hours
[tex]\sigma[/tex] = standard deviation = 2 hours
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, the probability that a battery will last more than 19 hours is given by = P(X > 19 hours)
P(X > 19) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{19-16}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
Hence, the probability that a battery will last more than 19 hours is 0.0668.
The probability that a battery with a mean lifetime of 16 hours and a standard deviation of 2 hours will last more than 19 hours is approximately 6.68%, calculated using the z-score for a normal distribution.
Explanation:Probability of Battery Lasting More Than 19 Hours
The question asks about the probability that a battery with a normal distribution will last more than 19 hours, given a mean μ = 16 hours and standard deviation σ = 2 hours. To find this probability, we calculate the z-score using the formula:
[tex]Z = (X - \mu) / \sigma[/tex]
For X = 19 hours:
[tex]Z = (19 - 16) / 2 = 1.5[/tex]
Next, we use a standard normal distribution table or a calculator to find the probability associated with this z-score. The area to the right of Z = 1.5 represents the probability that a battery lasts more than 19 hours. Assuming we've looked up the value in the standard normal distribution table:
[tex]P(X > 19) = 1 - P(Z \leq 1.5) = 1 - 0.9332 = 0.0668[/tex]
Thus, the probability that a battery will last more than 19 hours is approximately 6.68%.
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At what point does the line given by the following equation cross the x-axis?
y = -x + 7
Answers
Answer:
(7,0)
Step-by-step explanation:
you can 0 in for Y in order to find the x-axis
0=-x+7
-7=-x
x=7
Answer:
(7, 0)
Step-by-step explanation:
We are trying to find the location that the equation crosses the x-axis.
This location is also known as the x-intercept.
To find the x-intercept, you can just set y in the equation to 0 and then solve for x.
0 = -x + 7
-x = -7
x = 7
So, the x-intercept is 7.
X-intercepts always have a y of 0 by definition, so it can be found at the point (7, 0)
What are the solutions 3(x-4)(2x-3)=0
Answers
3 doesn’t have an x so you don’t set it equal to zero hope this helped
Evaluate 2x for x = 7
Answers
Answer:
Step-by-step explanation:
x = 7
so 2x is 2 x 7
The answer is 14
Answer:
14
Step-by-step explanation:
when x is 7 then 2x is 7*2
7*2=14
A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 264264 trials, the touch therapists were correct 105105 times. Use a 0.050.05 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?
Answers
To test the effectiveness of touch therapists, a hypothesis test can be conducted using a significance level of 0.05. The test statistic is calculated by comparing the observed success rate to the expected success rate under the null hypothesis. If the test statistic falls within the critical region, the null hypothesis can be rejected and it can be concluded that the touch therapists are effective.
Explanation:To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted using a significance level of 0.05. In this case, the null hypothesis would state that the therapists' success rate is no better than random chance, while the alternative hypothesis would state that the therapists are effective. The test statistic can be calculated using the observed success rate and the expected success rate under the null hypothesis. If the test statistic falls within the critical region, which is determined by the significance level, then the null hypothesis can be rejected, suggesting that the touch therapists are indeed effective.
First, let's calculate the expected success rate under the null hypothesis. Since the therapists are guessing randomly, the probability of guessing correctly is 0.5. Therefore, the expected success rate can be calculated by multiplying the total number of trials by the probability of guessing correctly:
Expected success rate = 0.5 * 264 = 132
Next, we can calculate the test statistic using the observed success rate and the expected success rate:
Test statistic = (observed success rate - expected success rate) / sqrt(expected success rate * (1 - expected success rate) / number of trials)
Substituting the values into the formula:
Test statistic = (105 - 132) / sqrt(132 * (1 - 132/264) / 264) = -3.181
Finally, we can compare the test statistic to the critical value. The critical value can be obtained from the Z-table or using statistical software. If the test statistic falls within the critical region (i.e., if it is less than the negative critical value), then we can reject the null hypothesis and conclude that the touch therapists are effective.
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To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted. The data provided is used to calculate the p-value, which is found to be less than 0.05. This suggests that touch therapists are effective.
Explanation:To test the claim that touch therapists use a method equivalent to random guesses, we can use a hypothesis test. The null hypothesis is that the therapists' accuracy is due to random chance, while the alternative hypothesis is that they are effective. We can use a binomial hypothesis test with a significance level of 0.05. Using the given data, the therapists were correct in 105 out of 264 trials. Calculating the p-value, we find that it is less than 0.05, which means we reject the null hypothesis. Therefore, the results suggest that touch therapists are effective.
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Which object shown below could we slice perpendicular to its base/face to create a cross-section whose shape has two edges, one straight and one curved?
A- Cone
B-Cube
C-Cylinder
D-Sphere
Answers
The cone is the correct answer.
What is cone ?A cone is the shape that could be slice perpendicular to its base/face to create a cross-section whose shape has two edges, one straight and one curved.
cone, in mathematics, the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).
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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years. He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.
Assuming that the laptop replacement times have a mean of 3.8 years and a standard deviation of 0.4 years, find the probability that 44 randomly selected laptops will have a mean replacement time of 3.6 years or less.
P(¯¯¯X≤3.6 years)P(X¯≤3.6 years) = Round to 4 decimal places.
NOTE: Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?
No. The probability of obtaining this data is greater than 5%, high enough to have been a chance occurrence.
Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
Answers
Answer:
Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is 0.0092.
Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
Step-by-step explanation:
We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years.
He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.
Let [tex]\bar X[/tex] = sample mean replacement time
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean replacement time = 3.8 years
[tex]\sigma[/tex] = standard deviation = 0.4 years
n = sample of laptops = 44
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years)
P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{3.6-3.8}{\frac{0.4}{\sqrt{44} } }} }[/tex] ) = P(Z [tex]\leq[/tex] -3.32) = 1 - P(Z < 3.32)
= 1 - 0.99955 = 0.0005 or 0.05%
So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.32 in the z table which has an area of 0.99955.
Hence, the required probability is 0.0005 or 0.05%.
Now, based on the result above; Yes, the computer store has been given laptops of lower than average quality because the probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
Is the pie of 34 rational are in rational
Answers
Answer:
34 would be a Rational number
Step-by-step explanation:
it's clean number and not sloppy like 0.888883
A person places $934 in an investment account earning an annual rate of 6.1%, compounded continuously. Using the formula V = P n r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
Answers
To find the total amount in an investment account after 13 years with continuous compounding, use the formula for continuous compound interest. Substitute the given values into the formula and compute.
Explanation:The question deals with the concept of continuous compound interest. The formula for this is given by the equation V=P * e^{rt}, where V is the total value of the investment after time t, P is the principal amount, r is the rate of interest, and e is the base of the natural logarithm.
Plug these values into the equation: V = $934 * e^{0.061 * 13} . Using the value of e, which is approximately 2.71828, compute to get V. Therefore the total amount in the account after 13 years, when rounded to the nearest cent, will be V.
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The amount of money in an account with continuously compounded interest, substitute the given principal, interest rate, and time values in the formula V = Pert. Convert the interest rate to a decimal before using. Calculate the exponent using a scientific calculator or similar tool.
Explanation:You're looking to calculate the future value of an investment using the formula for continuous compounding, V = Pert. In this case, P = $934, r = 6.1%, and t = 13 years.
First, convert the percent interest rate to a decimal by dividing by 100, which gives r = 0.061.
Then, substitute the given values into the formula:
V = $934 * e(0.061 * 13).
Calculator the exponent to find the value V. Round the final answer to the nearest cent.
In summary, computing the amount of money in a continuously compounded account involves substituting the given values into the proper formula and calculating using an appropriate method such as a scientific calculator or algorithm.
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5 inches
What is the approximate length of the radius, r? Use 3 14
for w. Round to the nearest inch.
12 inches
24 inches
38 inches
46 inches
Answers
Answer:
The answer is 24 inches
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
8 – 6 ∙ 4 + 10 ÷ 2 =
Answers
Answer:
-11
Step-by-step explanation:
I got it wrong, sorry! T-T
convert 11 pi /6 radians to degrees
Answers
Answer:
330 degrees.
Step-by-step explanation:
π radians / 180 degrees = 1
(11 π)/6 radians * 180 / π = 11 * 180 / 6 = 11 * 30 = 330 degrees.
After converting into degree we get;
⇒ 11 pi /6 radians = 330 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
The expression is,
⇒ 11 pi /6 radians
Now, To change into degree we can multiply by 180 / π in the given expression as;
⇒ 11 pi /6 radians
⇒ 11 π /6 × 180 / π degree
⇒ 330 degree
Thus, After converting into degree we get;
⇒ 11 pi /6 radians = 330 degree
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The rectangle below has a length of 4x+3 and a width of 3x.
a) Find the perimeter
b) Find the area
c) Find the perimeter and area if x = 8
Answers
Just add al the sides up like normal
Area- 12x^2+9x
Multiply the length and width
C)
Perimeter- 118
Area- 840
I’m pretty sure these are right
A survey of 1060 randomly selected US teens ages 13 to 17 found that 605 of them say they have made a new friend online
Answers
The question discusses a survey of US teens and their online interaction. It's emphasizing on the statistical data that shows approximately 57% of surveyed teens reported making new friends online. Other data are also relevant to highlight various aspects of teens internet usage.
Explanation:The question is about a survey conducted on US teens, where 1060 were randomly selected and it was found that 605 of them have made a new friend online. This is relevant to statistics, a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
To calculate the percentage of teens making friends online, it is calculated as follows: (Number of teens reporting making new friends online / Total number of teens surveyed) * 100 = (605/1060) * 100 = 57.08%. This implies that approximately 57% of the surveyed teens reported making new friends online.
The other data provided discuss various aspects of teen internet usage, including use of social media, smartphone adoption, and experiences with digital relationships. The given data can be used to set up and test various statistical hypotheses about teen behavior relating to internet use.
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if each slice of pizza is 1/16 of the pizza what is the decimal form of 8 slices of pizza
Answers
Answer:
0.5
Step-by-step explanation:
8 slices of a pizza cut into 16 pieces is a half of the pizza. A half is 0.5
Mr. Jackson filled up his 15-gallon gas tank for $37.50. What was the price 10
of gas per gallon?
Answers
Answer:
[tex]Unit Price =\$2.5 \:per\: gallon[/tex]
Step-by-step explanation:
15 Gallon of Gas costs $37.50
To determine the Unit Price, we divide the Total Cost by the number of gallons of gas bought.
Unit Price
[tex]=\dfrac{\$37.50}{15gallons}\\Unit Price =\$2.5 \:per\: gallon[/tex]
Answer:
Price per gallon = $2.5 per gallon
Step-by-step explanation:
Given;
Price of 15 gallons = $37.50
Number of gallons = 15
Price per gallon = 37.50/15 = $2.5
Simplify the expression 4×3+4×x
Answers
Answer:
12+4x
Step-by-step explanation:
What is the expression for the quotient of z and 4
Answers
Answer:
[tex]\dfrac{z}{4}\text{ or }z/4\text{ or }z\div 4[/tex]
Step-by-step explanation:
"The quotient of z and 4" means "z divided by 4." That can be written several ways, as shown above.
LetA,B,CandDbe the following sets:A={red, blue, green, purple}B={red, red, green}C={red,{green}, red,{red, green},{green, green, red}}D={blue, blue, blue, green, green, purple}Let the universal set forA,B,C,Dbe defined by:U={red, blue, purple, green}⋃P({red, blue, purple, green})Provide the answer to the following questions about the above sets. Justify your answers unless otherwisespecified.9(a) IsB⊆A? g
Answers
Answer:
No it is not
Step-by-step explanation:
B is a subset of A but not all the elements in Set A are in B hence they don't contain equal elements
Based on information below (2 countries x 2 products), if US has comparative advantage in producing Rice, what can you say about X? (note: figures represent production or output.)Please assume that X is a positive number.Rice CarUS 7 6Korea 9 XX < 4X > 54/7X < 63/7X < 7
Answers
Answer:
Check the explanation
Step-by-step explanation:
US has a comparative advantage in producing rice.
This means US's opportunity cost of producing rice is less than that of Korea.
Korea's opportunity cost of producing rice will be given as:
For producing 9 units of Rice, Korea gives up 5 cars.
For producing 1 unit of rice's, Korea will give up 5/9 units of car.
Kindly check the image below.
If the U.S. has a comparative advantage in producing rice, then [tex]\( X > \frac{54}{7} \).[/tex]
The correct answer is option B.
Comparative advantage in the context of international trade is determined by the opportunity cost of producing one good over another. If the U.S. has a comparative advantage in producing rice, it implies that the U.S. can produce rice at a lower opportunity cost compared to Korea. To analyze the situation, let's consider the production figures provided:
In the U.S., the opportunity cost of producing one unit of rice is 6/7 units of cars. In Korea, the opportunity cost of producing one unit of rice is X/9 units of cars. Since the U.S. has the comparative advantage in rice production, X/9 (opportunity cost for Korea) should be greater than 6/7 (opportunity cost for the U.S.).
Mathematically, this can be expressed as:
[tex]\[ \frac{X}{9} > \frac{6}{7} \][/tex]
To simplify the comparison, multiply both sides of the inequality by 9 to get:
[tex]\[ X > \frac{54}{7} \][/tex]
Therefore, the correct statement is [tex]\( X > \frac{54}{7} \)[/tex] making option B the correct option.
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i need help with my math
Answers
Number 6 is true
Number 9 is D
Number 5 is B
Number 4 is B
Number 7 the x int is (2,0) the y int is (2,0)
Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actual weight of the chocolate has a uniform distribution ranging from 31.8 to 32.6 ounces. a. Define a probability density function for the weight of the box of chocolate. b. What is the probability that a box weighs (1) exactly 32 ounces; (2) more than 32.3 ounces; (3) less than 31.8 ounces? c. The government requires that at least 60% of all products sold weigh at least as much as stated weight. Does Delicious Candy violate government regulation?
Answers
Answer:
a. [tex]f(x)= 1.25\ \ \ \ , \ for \ 31.8\leq x\leq 32.6[/tex]
[tex]b. \ P(X=32)=0\\P(X>32.3)=0.375\\P(X<31.8)=0[/tex]
c. No. Delicious Candy isn't violating any government regulations
Step-by-step explanation:
a.
-A uniform distribution is given by the formula:
[tex]f(x)=\frac{1}{b-a} \ \ \ for \ \ \ a\leq x\leq b[/tex]
#we substitute our values in the formula above to determine the distribution:
[tex]f(x)=\frac{1}{b-a}\\\\=\frac{1}{32.6-31.8}\\\\=1.25\\\\\therefore f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]
Hence, the probability density function for the box's weight is given as: [tex]f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]
b. The probability of the box's weight being exactly 32 ounces is obtained by integrating f(x) over a=b=32:
[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32}_{32} {1.25} \, dx \\\\\\=[1.25x]\limits^{32}_{32}\\\\\\=1.25[32.0-32.0]\\\\\\=0[/tex]
Hence, the probability that a box weighs exactly 32 ounces is 0.000
ii.The probability that a box weighs more than 32.3 is obtained by integrating f(x) over the limits 32.3 to 32.6 :
[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32.6}_{32.3} {1.25} \, dx \\\\\\=[1.25x]\limits^{32.6}_{32.3}\\\\\\=1.25[32.6-32.3]\\\\\\=0.375[/tex]
Hence, the probability that a box weighs more than 32.3 ounces is 0.3750
iii. The probability that a box weighs less than 31.8 is 0.000 since the weight limits are [tex]31.8\leq x\leq 32.6[/tex].
-Any value above or below these limits have a probability of 0.000
c. Let 32 ounces be the government's stated weight.
[tex]1.25(32.6-32)=0.75\\\\0.75>0.60[/tex]
Hence, Delicious Candy isn't violating any government's regulations.
(a): The required probability density function for the weight of the box of chocolate is 1.25
(b): The probability that a box weighs (1) exactly 32 ounces is 0
and (2) more than 32.3 ounces is 0.375
(c): Therefore, Delicious Candy does not violate government regulation.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in from 0 to 1.
Given that,
The uniform distribution between [tex]a = 31.8[/tex] ounce and [tex]b = 32.6[/tex] ounce
Part(a):
The probability density function for the weight of the box of chocolate is,
[tex]\frac{1}{b-a}=\frac{1}{32.6-31.8} \\=1.25[/tex]
Part(b):
(1) P(exactly 32 ounces) = 0, because this is a continuous distribution.
(2) P(more than 32.3 ounces) =[tex]1.25\times (32.6-32.3)=0.375[/tex]
Part(c):
The stated weight of Delicious Candy = 2 pounds
That is, [tex]2\times 16=32[/tex] ounces
P(a candy weigh at least as much as stated) = P(at least 32)
[tex]1.25\times (32.6-32)=0.75[/tex]
So, 75% of candies weigh at least as much as stated.
Learn more about the topic of Probability:
https://brainly.com/question/6649771
A research company desires to know the mean consumption of milk per week among males over age 25. A sample of 715 males over age 25 was drawn and the mean milk consumption was 2.9 liters. Assume that the population standard deviation is known to be 1.2 liters. Construct the 90% confidence interval for the mean consumption of milk among males over age 25. Round your answers to one decimal place.
Answers
Answer:
The 90% confidence interval for the mean consumption of milk among males over age 25 is (2.8 lt, 3.0 lt).
Step-by-step explanation:
The (1 - α) % confidence interval for population mean is:
[tex]CI=\bar x\pm z_{\alpha /2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=715\\\bar x=2.9\ \text{lt}\\\sigma=1.2\ \text{lt}[/tex]
Confidence level = 90%
Then, α = 10%
Compute the critical value of z for α = 10% as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
*Use a z-table.
Compute the 90% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha /2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]=2.9\pm 1.645\times \frac{1.2}{\sqrt{715}}\\\\=2.9\pm 0.074\\\\=(2.826, 2.974)\\\\\approx (2.8\ \text{lt}, 3.0\ \text{lt})[/tex]
Thus, the 90% confidence interval for the mean consumption of milk among males over age 25 is (2.8 lt, 3.0 lt).
see attachment and answer for extra points
Answers
Answer:
2x
Step-by-step explanation:
[8x² - 4x] ÷ [4x - 2]
[4x(x - 2)] ÷ [2(x - 2)]
[2x × 2(x - 2)] ÷ [2(x - 2)]
2x
What is 11/12 minus 7/9
Answers
Answer:
5/36
Step-by-step explanation:
This is in fractions so that's what i did and its simplified as well
Which equation can be used to find the volume of this solid?
Answers
Answer: the first one
Step-by-step explanation: base×width×height
Answer:
The first choices.
Step-by-step explanation:
The solid is a rectangular prism which means V=l × w × h