It looks like you're asked to compute
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz[/tex]
where C is parameterized by ⟨t, t, t⟩ with 0 ≤ t ≤ 1.
In other words, x = y = z = t, so dx = dy = dz = dt, and the integral reduces to
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz = \int_0^1 t\,\mathrm dt + t\,\mathrm dt + t\,\mathrm dt \\\\ = 3 \int_0^1 t\,\mathrm dt \\\\ =\frac32t^2\bigg|_{t=0}^{t=1} \\\\ =\boxed{\frac32}[/tex]
What integer is equal to 5!×2!?
Answer:
240
Step-by-step explanation:
! means factorial or to multiply by the previous number down to one so 5!=5*4*3*2*1=120 120*2=240.
Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a. .4 × .15 = .060 b. 0.40 + .15 = .55 c. 1 − (.40 + .15) = .45 d. 1 − (.6 × .85) = .490
Answer: a. 0.4 × 0.15 = 0.060
Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.
For P(A):
P(A') = 1 - 0.6
P(A') = 0.4
For P(B):
P(B') = 1 - 0.85
P(B') = 0.15
To determine probability of A' and B':
P(A' and B') = P(A')*P(B')
P(A' and B') = 0.4*0.15
P(A' and B') = 0.06
Probability of the complement of the event is 0.060
Ahmed bought a TV for his room in 2016 for AED 1,500. he decided to sell it in 2020 for AED 900. what is the rate of depreciation when he bought the TV and when he sold it
Answer:
40% depreciation over the 4 years
10% depreciation per year
Step-by-step explanation:
The number of years between buying and selling is:
2020 - 2016 = 4
4 years
The amount of depreciation in the 4 years is:
AED 1,500 - AED 900 = AED 600
The percent depreciation for the 4 years is:
(1500 - 900)/1500 * 100% = 40%
The percent depreciation per year is:
40%/4 = 10%
Please help me. I don't understand fractions here is my problem.
Add:
5/24+9/20
Answer:
79/120
Step-by-step explanation:
5/24+9/20
to add the fractions the denominator (bottom part) has to be the same. ex you can add one third and one third to make two thirds. but you wont know what 1/2 + 1/3 is.
convert to same denominator. to do this, the fractions themselves need to stay the same value but the bottom number needs to change. ex 1/2=2/4 and 1/3= 2/6. when you multiply and divide the top and bottom part of the fraction by the same number, the value of the fraction stays the same. ex 3/6 divide both parts by 3 you get 1/3. so 3/6=1/3
to get the common denominator we have to find the least common multiple, or LCM (since 5 and 9 dont share any common factors.)
24 and 20 LCM
=120
convert both 5/24+9/20 to x/120 and y/120
5/24 multiply by 5 on top and bottom
=25/120
9/20 multiply by 6 on top and bottom
=54/120
25/120+54/120
=(25+54)/120
=79/120
pls help me asap !!!!!!
9514 1404 393
Answer:
(-2.5, 1)
Step-by-step explanation:
The desired point is the weighted average of the end points, where the weight of each point is the fraction of distance from the opposite end.
P = 5/8(-1, 7) +3/8(-5, -9) = (-5-15, 35-27)/8 = (-2.5, 1)
The desired point is (-2.5, 1).
Next, the students at the Pearson Cooking Academy are assigned a take-home written exam to assess their knowledge of all things culinary. Historically, students scores on this exam had a N(68, 36) distribution. However, these days, there is an company called Charred Egg that offers to help students on tasks whether or not the exercises are for homework or for exams. In a cohort of 19 students, what is the probability that their average score will be at least 70?
Answer:
The probability is [tex]P( \= X \ge 70 ) = 0.07311[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 68[/tex]
The standard deviation is [tex]\sigma = \sqrt{36} = 6[/tex]
The sample size is [tex]n = 19[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{6 }{\sqrt{19} }[/tex]
=> [tex]\sigma_{\= x } = 1.3765[/tex]
Generally the probability that their average score will be at least 70 is mathematically represented as
[tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(\frac{ \= X - \mu }{\sigma_{\= x}} < \frac{70 - 68}{ 1.3765} )[/tex]
Generally [tex]\frac{ \= X - \mu }{\sigma_{\= x}} = z(The \ z-score \ of \ \= X )[/tex]
So
[tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(Z <1.453 )[/tex]
From the z-table
[tex]P(Z <1.453 ) = 0.92689[/tex]
=> [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - 0.92689[/tex]
=> [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 0.07311[/tex]
=> [tex]P( \= X \ge 70 ) = 0.07311[/tex]
How many solutions does the following equation have? -14(z-5)=-14x+70
Answer:
Infinite amount of solutions
Step-by-step explanation:
Parallel lines have no solution
Same lines have infinite solutions
Intersecting lines have 1 solution
Step 1: Write out equation
-14(x - 5) = -14x + 70
Step 2: Distribute -14
-14x + 70 = -14x + 70
Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.
Alternatively, we can plug in any number x and it would work. So then we would have infinite amount of solutions as well.
Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. Compare the two curves. The two curves will have ▼ the same line different lines of symmetry. The curve with the larger standard deviation will be ▼ more less spread out than the curve with the smaller standard deviation.
Answer:
The same mean ⇒ the same symmetry axis
Bigger standard deviation major spread
Step-by-step explanation: See Annex
The annex shows two different normal curves:
1.- N (μ₀ ; σ₁ )
2.- N (μ₀ ; σ₂ )
Where σ₁ > σ₂
They both have the same symmetry axis ( they have the same mean and both curves have to be symmetrically related to the mean )
Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation. Standard deviation is a measure of the spread of the curve.
Whenever deviation is high, the data is more dispersed than when deviation is low.
Let the mean be 2.
Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.
Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.
For more information, refer this link:
https://brainly.com/question/12421652
URGENT! WILL GIVE BRAINLIEST (PICTURE INCLUDED)
9514 1404 393
Answer:
x > -1 and x ≠ 3
Step-by-step explanation:
The function value will be positive when there are an even number of negative factors. The factors change sign at x = -1, are zero at x = 3. The expression is positive for ...
x > -1 and x ≠ 3
I will rate you brainliest/ / / Tonicha is creating two triangular gardens in her backyard. The total area of each triangle varies jointly with the length of the triangle's base and the height. The area of the smaller triangle is 16 square feet. It has a base that is 8 feet in length and the height is 4 feet. What is the area of the larger triangle when its base is 12 feet in length and its height is 8 feet?
Answer:
The area of larger triangle is 48 ft².
Step-by-step explanation:
Assuming that the area of triangle formula is A = 1/2 × base × height. Then, you have to substitute the following values :
[tex]area = \frac{1}{2} \times b \times h[/tex]
[tex]let \: b = 12,h = 8[/tex]
[tex]area = \frac{1}{2} \times 12 \times 8[/tex]
[tex]area = \frac{1}{2} \times 96[/tex]
[tex]area = 48 \: {feet}^{2} [/tex]
Given that;
A∞bh
A=kbh. where k is a constant
For smaller triangle
A=kbh
16=8(4)k
16=32k
k=½
For bigger triangle
A=kbh
Where k=½ , b= 12 and h=8
A=½(12)8
A=48 square feet
How many more cherry pies have 60 to 89 cherries than 90 to 119 cherries?
Answer:
6 pies
Step-by-step explanation:
For 60 - 89 cherries there are 10 pies
For 90 -119 cherries there are 4 pies
10 -4 = 6
There are 6 more pies in the 60 -89 cherries category than in the 90-119 category
Which of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7
Answer:
f(x) = 7
Step-by-step explanation:
f(x) = f(-x) it is even
-f(x)=f(-x) it is odd
f(x) = (x – 1)^2 neither even nor odd
f(x) = 8x this is a line odd functions
f(x) = x^2 – x neither even nor odd
f(x) = 7 constant this is an even function
Answer:
answer is f(x)= 7
Step-by-step explanation:
just took edge2020 test
Solve the system 2x + 3y = 3 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system? (2 points) (−3, 3) (−1, −7) (1, −4) (3, −1)
Answer:
(3,-1)
Step-by-step explanation:
Graph boths functions (picture below)
given point (-6, -3) and a slope of 4, write an equation in point-slope form
Answer:
y = 4x + 21
Step-by-step explanation:
Hello!
Point-slope form is y - y1 = m(x - x1)
y1 is the y point
x1 is the x point
m is the slope
Put in what you know
y - -3 = 4(x - -6)
Subtracting a negative is the same as adding
y + 3 = 4(x + 6)
Distribute the 4
y + 3 = 4x + 24
Subtract 3 from both sides
y = 4x + 21
The answer is y = 4x + 21
Hope this helps!
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
[tex](y - 1) log_{10}(4?) = log_{10}(16?) [/tex]
find the value of y
Answer:
3Step-by-step explanation:
Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;
[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]
Open the bracket
[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]
Hence the value of y is 3
What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
Step-by-step explanation:
(5+(-4))/2 = 1/2 or 0.5
(-7 + 6)/2 = -1/2 or -0.5
the solution is D
(0.5, -0.5)
What is the slope of the line that passes through (2, 12) and (4, 20)?On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?
Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.
The value of the y-intercept is 9.
Step-by-step explanation:
Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]
[tex]=\dfrac{8}{2}=4[/tex]
So, the slope of the line that passes through (2, 12) and (4, 20) is 4.
To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).
[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]
By comparison, c= 9
Hence, the value of the y-intercept is 9.
Which expressions are equivalent to 6 + 12x?
A.
5(1 + 2x) + 1 + 2x
B.
7(1 + 2x) + 2x - 1
C.
3(2 + 6x) + 2x
D.
7(1 + 2x) - 2x - 1
E.
3(2 + 4x)
Answer:
A. 5(1 + 2x) + 1 + 2x
D. 7(1 + 2x) - 2x - 1
E. 3(2 + 4x)
What would the equation be if I multiplied each side by 12
Answer:
It's option a. 36 + 6x^2 = 28x
Step-by-step explanation:
please Help with my area math question. I don't remember how to do it. multiply or add? and what is the answer to this?
Answer:
100 inches^3
Step-by-step explanation:
The volume of the back rectangle is
V = l*w*h
V = 8*5*1 = 40 inches ^3
The volume of the front rectangle is
V = 6*2*5 = 60 inches^3
Add the volumes
40+60 = 100 inches^3
If a faucet drips 2ml of water every second, how much water will it spill waste in 2 days?
Answer:
[tex]\boxed{345,600 mL}[/tex]
Step-by-step explanation:
Hey there!
Well first we need to find the amount of seconds in a day,
24hrs in a day * 60 min in an hour
= 1440 minutes in a day
1440 min • 60 secs in a minute
= 86,400 seconds in a day
So now we do 2*86400 = 172800
172800 mL in a day
172800 * 2
= 345600 mL in 2 days
Hope this helps :)
The area of a square is 64 cm2 then find it's perimeter.
Answer:
32cm
Step-by-step explanation:
The area of sqaure is a^2
Side will be
underroot of 64 =8
Premeter of sqaure is 4a = 4×8 = 32cm
first we need to find length.
here.
Area= 64cm^2
or, 64= l^2
using formula area = length × length
therefore solving we get ,
length = 8 cm.
now,
perimeter = 4l
= 4 × 8 cm.
= 32 cm..........
Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 2.
Answer:
[tex]\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
Construct a polynomial function with the following properties...
... fifth degree
It means that the polynomial can be written as below.
[tex]a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}[/tex]
... 4 is a zero of multiplicity 3
We can write the polynomial as below.
[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)[/tex]
... −2 is the only other zero
Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.
[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2[/tex]
... leading coefficient is 2.
Finally, it means that k = 2 and then the polynomial function is:
[tex]\large \boxed{2(x-4)^3(x+2)^2}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Nina skated for 2 hours and 14 min she stop at 8:24 pm when did Nina start skating
Answer:
6:10 pm
Step-by-step explanation:
she skate for 2 h and 14 min so,
8:24- 2:14
=6:10 pm
Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2
Answer:
[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]
I hope I helped you^_^
If the diameter of a hockey rink is 250 ft what is the surface area of the sphere?
Answer:
62,500 pi
Step-by-step explanation:
diameter = radius + radius
d = 2r
r = d/2
A = 4pi r^2
= 4 pi (d/2)^2
= 4pi d^2/4
= 4pi* 250^2/4
= 4pi * 62,500/4
= 4pi * 15625
= 62,500 pi
9.) Ezri earns $10 per day plus $25 for every lawn she mows. How many lawns does she need to mow today to earn $135? First, write the equation that fits this model. Let x be the amount of yards she mows. Hurry please
Answer:
5 lawns
Step-by-step explanation:
Firstly, the equation is 25x + 10 = 135
Ezri makes $25 for every lawn she mows (25x) and has an automatic $10 per day (10). In order to make $135 we take what she makes each day and set it equal to 135.
To solve, we subtract 10 from both sides to create 25x = 125. We then divide 25 from both sides to get x=5. This means that Ezri needs to mow 5 lawns in order to make $135.
I hope this is helpful to you!
**To anyone out there seeing this - let me know if you think I made a mistake and I will fix it.**
Ernie Rolph borrowed $6700 at 4% annual simple interest. If exactly 1 year later he was able to repay the loan without penalty, how much interest would he owe? Ernie will owe $___ in interest.
Ernie will owe an interest of $268