Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
Mr.Rice students ran a 40 yard dash in the following times 6.8,7.3,7.1 ,7.0,7.2,7.3,7.0 how many race times are recorded
The number of race times recorded as portrayed by the number of data points is seven(7).
What is the number of race times recorded for the dash?From the task content;
It follows that the distance ran be Mr. Rice students was 40 yards.Additionally, it follows from the task content that the times recorded were; 6.8,7.3,7.1 ,7.0,7.2,7.3 and 7.0.
On this note, the number of race times recorded as portrayed by the number of data points is seven(7).
Read more on data points;
https://brainly.com/question/3514929
what variable will you use to represent the number of brochures
Answer: always “X”
Step-by-step explanation:
Answer:
i would use the variable b because b = brochures.
Step-by-step explanation:
i hope this helped heh
-23d + 81 <-98d + 1
Solve for d
Step-by-step explanation:
-23d + 81 < - 98d + 1
81 - 1 < - 98d + 23d
80 < - 75d
80/ - 75 < d
10/ - 3 < d
Please answer this correctly
Answer:
Chicken: 36%
Beef: 34%
Black Bean: 30%
Hope this helps!
Which of the following is not approximately equivalent to one of the metric units: 1 meter, 1 kilogram, or 1 liter
Answer:
A meter is not part of the metric system. It's part of the U.S. customary system.
Savings accounts are a reliable way to store money for the future
Answer:
true
Step-by-step explanation:
just took test
b. Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.) c. Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.) d. Find the expected value of X. (Round your answer to one decimal place.) e. Find the standard deviation of X. (Round your answer to three decimal places.)
Answer:
(a) Probability distribution is prepared below.
(b) The probability that two or fewer heads are observed in three tosses is 0.875.
(c) The probability that at least one head is observed in three tosses is 0.875.
(d) The expected value of X is 1.5.
(e) The standard deviation of X is 2.121.
Step-by-step explanation:
The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.
(a) Find the probability distribution of X.
(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)
(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)
(d) Find the expected value of X. (Round your answer to one decimal place.)
(e) Find the standard deviation of X. (Round your answer to three decimal places.)
Now, firstly the sample space obtained in three tosses of a fair coin is given as;
Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}
(a) The Probability distribution of X is given below;
Number of Heads (X) P(X) [tex]X \times P(X)[/tex] [tex]X^{2} \times P(X)[/tex]
0 [tex]\frac{1}{8}[/tex] = 0.125 0 0
1 [tex]\frac{3}{8}[/tex] = 0.375 0.375 0.375
2 [tex]\frac{3}{8}[/tex] = 0.375 0.75 3
3 [tex]\frac{1}{8}[/tex] = 0.125 0.375 3.375
Total 1.5 6.75
(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.125 + 0.375 + 0.375
= 0.875
(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.125
= 0.875
(d) The expected value of X = E(X) = [tex]\sum (X \times P(X))[/tex]
= 1.5
(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]
= [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]
= [tex]6.75 - 1.5^{2}[/tex] = 4.5
Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.121.
Really easy math question!
the answer is A: 146 ≤ 9c + 10
Please answer this correctly
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
------------
total 5
[tex]x = \frac{b + - \sqrt{{b}^{2} - 4ac } }{2a} [/tex]
O True
O False
If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative
The quadratic formula is
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
if the 5 numbers are different, the maximum difference is 64
Step-by-step explanation:
We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.
The mean will be:
M = (a + b + c + d + e)/5 = 15.
Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:
a = 1, b = 2, c = 3 and d = 4
M = (1 + 2 + 3 + 4 + d)/5 = 15
M = (10 + d)/5 = 15
10 + d = 15*5 = 75
d = 75 - 10 = 65
then the difference between a and d is = 65 - 1 = 64.
Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.
Suppose that the raw daily oxygen purities delivered by an air-products supplier have a standard deviation LaTeX: \sigma\approx.1 σ ≈ .1 (percent), and it is plausible to think of daily purites as independent random variables. Approximate the probability that the sample mean LaTeX: \frac{ }{X} X of n = 25 delivered purities falls within .03 (percent) of the raw daily purity mean, LaTeX: \mu μ .
Answer:
There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.
Step-by-step explanation:
We have a population standard deviation of σ ≈ 0.1.
We have a sample of size n=25.
Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:
[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{25}}=\dfrac{0.1}{5}=0.02[/tex]
Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{0.03}{0.02}=\dfrac{0.03}{0.02}=1.5[/tex]
Note: we considered that the margin is ±0.03.
Then, the probability is:
[tex]P(|X-\mu|<0.03\%)=P(|z|<1.5)=0.866[/tex]
DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime x-805 hours with a standard deviation s 158 hours. Using the hypotheses H0: μ = 904 vs Ha: μ < 904, find the P-value and state your conclusion. Use a significance level of 0.05.
1. P-value 0.039, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
3. P-value 0.079, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
4. P-value0.079, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: μ = 904
For the alternative hypothesis,
Ha: μ < 904
This is a left tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 10,
Degrees of freedom, df = n - 1 = 10 - 1 = 9
t = (x - µ)/(s/√n)
Where
x = sample mean = 805
µ = population mean = 904
s = samples standard deviation = 158
t = (805 - 904)/(158/√10) = - 1.98
We would determine the p value using the t test calculator. It becomes
p = 0.039
Since alpha, 0.05 > than the p value, 0.03953, then we would reject the null hypothesis. Therefore, the correct option is:
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
Which of the following is a subset of every set? * 1)Universal Set 2)Null Set 3)Both of these 4)None of these
Answer:
[tex]1[/tex]
Step-by-step explanation:
Universal set contains all elements and of which all other sets are subsets.
Consider the following quadratic equation: 25x2=36 Using the standard form ax2+bx+c=0 of the given quadratic equation, factor the left hand side of the equation into two linear factors.
Answer:
(5x -6)(5x +6) = 0
Step-by-step explanation:
Subtract 36 to put the equation in standard form. In this form, it looks like the difference of squares, so can be factored as such.
25x^2 -36 = 0
(5x)^2 -6^2 = 0
(5x -6)(5x +6) = 0
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards. A sample of 20 cards are selected from the lot without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least one defective card appears in the sample
Answer:
The probability that at least one defective card appears in the sample
P(D) = 0.9644 or 96.44%
Step-by-step explanation:
Given;
Total number of cards t = 140
Number of defective cards = 20
Number of non defective cards x = 140-20 = 120
The probability that at least one defective card = 1 - The probability that none none is defective
P(D) = 1 - P(N) ........1
For 20 selections; r = 20
-- 20 cards are selected from the lot without replacement for functional testing
The probability that none none is defective is;
P(N) = (xPr)/(tPr)
P(N) = (120P20)/(140P20)
P(N) = (120!/(120-20)!)/(140!/(140-20)!)
P(N) = (120!/100!)/(140!/120!) = 0.035618370821
P(N) = 0.0356
The probability that at least one defective card appears in the sample is;
P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644
P(D) = 0.9644 or 96.44%
Note: xPr = x permutation r
The base of a rectangular prism has an area of 24 square millimeters. The volume of the prism is 144 cubic millimeters. The shape is a cube. What is the height of the prism?
Answer:
height = 6 mm
Step-by-step explanation:
The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.
The height of the prism can be solved as follows.
Volume of the rectangular prism = Bh
where
B = base area
h = height
Volume = 144 mm³
B = 24 mm²
volume = Bh
144 = 24 × h
144 = 24h
divide both sides by 24
h = 144/24
h = 6 mm
Answer:
c
Step-by-step explanation:
edg 2022
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, and asymptotes. f(x)=-2cot x
Answer:
(See explanation below for further details)
Step-by-step explanation:
The domain of the function is:
[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]
The range of the function is:
[tex]f(x) \in \{-\infty, +\infty \}[/tex]
There are no absolute extrema and such function is not bounded.
Function is symmetric, whose period is π.
Lastly, the set of asymptotes is:
[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]
Answer:
Step-by-step explanation:
edge
The function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 0.2 inches. Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.2 inches to 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 5.5 inches to 5.6 inches.
Complete Question
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!
Answer:
(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)f(1.3)-f(0.2)
(d) f(5.6)-f(5.5)
Step-by-step explanation:
Let the Length of the paper =l (in inches)
Let the Width of the paper =w (in inches)
Let the length of the cutout square = x (in inches)
Base Length of the Box = l-2xBase Width of the box =w-2xHeight of the box =xVolume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]
(a)When the cutout length is 0.2 inches.
x=0.2
Volume of the box (in cubic inches) ,
[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)When the cutout length is 01.3 inches.
x=1.3
Volume of the box (in cubic inches) ,
[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)If the cutout length increases from 0.2 inches to 1.3 inches.
Change In volume (in cubic inches):
[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]
(d)If the cutout length increases from 5.5 inches to 5.6 inches.
Change In volume (in cubic inches):
[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]
Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?
Answer:
y = -2x + 5
slope = -2
y intercept = 5
Step-by-step explanation:
Slope intercept form of equation of line is given by y = mx + c
where m is the slope of line
c is the y intercept i.e point where given line intersect y axis.
________________________________________________
given equation 4x + 2y = 10
we have to re-write this equation in form y = mx + c
4x + 2y = 10
subtraction 4x from LHS and RHS
4x + 2y - 4x= 10 - 4x
2y = 10- 4x
we have to eliminate 2 from y for that we
divide LHS and RHS by 2 we
2y /2 = 10/2- 4x/2
y = 5 - 2x
rearranging it in y = mx+c form
y = -2x + 5
thus, m = -2 , c = 5
What degree of rotation about the origin will cause the triangle below to map
onto itself?
A. 90 degrees
B. 360 degrees
C. 180 degrees
D. 270 degrees
Answer: 360ᴼ
Step-by-step explanation:
If a figure goes 360ᴼ around the graph, it will be mapped onto itself.
360ᴼ is full circle (number of degrees in a circle), so the figure just went around in a circle, back into the same location before it rotated.
Answer:
360
Step-by-step explanation:
i took the text
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.
a. Level of significance, null and alternative hypothesis
b. What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
c. Find or estimate the P-value
d. Based on your answers to part a and c will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha?
e. Interpret your conclusion in the context of the application
Answer:
a) Level of significance α=0.05
Two-tailed test, with null and alternative hypothesis:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.
Test statistic t=-2.4
c) P-value = 0.018
d) Rejection of the null hypothesis.
The data is statistically significant.
e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that there is a significant difference in average off-schedule times for this bus lines.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.
The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.
The difference between sample means is Md=-7.
[tex]M_d=M_1-M_2=53-60=-7[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=51+60-2=109[/tex]
This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]
As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.
When a feasible region is bounded on all sides, where will the maximum and minimum values of the objective function occur?
at the center of the feasible region
at the top of the feasible region
anywhere within the feasible region
at the vertices of the feasible region
Answer:
Option 4: at the vertices of the feasible region.
I completed the quiz
Answer:
at the vertices of the feasible region
Step-by-step explanation:
this is the correct answer
hope i helped
Given the coordinates (0,0) and (4, 1), the distance is:
Answer:
[tex]\sqrt{17}[/tex] or ≈4.12
Step-by-step explanation:
Use the distance formula
d= √(x₂ - x₁) ² + (y₂-y₁) ²
d= √(4-0)² + (1-0)²
d= √16 + 1
d= √17
Use the area to find the radius. If you could include steps that’ll be very helpful :)
Answer:
Area = PI * radius^2
radius^2 = Area / PI
radius^2 = 169*PI/PI
radius^2 = 169
radius = 13
Step-by-step explanation:
leave answer in simplest radical form
Answer:
[tex]\dfrac{5\pm\sqrt{47}}{6}[/tex]
Step-by-step explanation:
Let's start by setting y to 0 to find the roots of the quadratic.
[tex]x=\dfrac{5\pm \sqrt{25+12}}{6}=\\\\\dfrac{5\pm\sqrt{47}}{6}[/tex]
Hope this helps!
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
the graph of f (x) shown below has the same shape as the graph of G (x) equals x ^ 4 but it is shifted 4 units to the right what is the equation
Answer:
D
Step-by-step explanation:
shifting 4 units to the right means that the new root = old root + 4
what that means is that the equation must have a transformation such that it equates to 0 with the root being 4 larger.
the root/vertex for x^4 is at x=0
we want the root to be at x=4
so that means we can subtract 4 from x
and get (x-4)^4
Find the values
Y = 3x - 7
Y = x - 1
X = Y =
Answer: Y=3x -7
Y=x-1
X=Y=
Step-by-step explanation: