Answers
Answer:
[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]
Explanation-
As,
[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]
and
[tex]a^{-n}=1/a^n[/tex]
Related Questions
An bus station has determined that the relationship between the number of passengers on a bus and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=118+14x. Predict the weight of luggage for a flight with 142 passengers.
Answers
Answer:
The weight of luggage for a flight with 142 passengers is 2,106
Step-by-step explanation:
The total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation:
y=118+14*x
where y is the total weight of luggage stored in the luggage compartment and x is the number of passengers on a bus.
If you want to predict the weight of luggage for a flight with 142 passengers, this means that x must have a value of 142. So, replacing in the expression:
y=118+14*142
you get:
y=118+1,988
y=2,106
The weight of luggage for a flight with 142 passengers is 2,106
last month you had an outstanding check of $87.90 that had not yet been cashed, so it did not show up on your statement. This month, you wrote checks totaling $379.42. You made one deposit of $100, and you withdrew $60 from an ATM. If the check from last month was cashed and recorded on your statement, and if the bank paid $0.23 in interest, then by how much did your account balance change this month?
Answers
Answer:
Step-by-step explanation:
Deposit made = + $ 100 . 00
withdrawal made = - $ 60 .00
check of last month encashed = - $ 87 . 90
interest paid by bank = + $ 00 . 23
-----------------------------------------------------------------------
Net effect = - $ 47.67
the account balance reduces by amount = $ 47.67
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Answers
Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z = \frac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y = 9 + \frac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]
Calculating:
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]
[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5
The volume of the tetrahedon is 1087.5 cubic units.
The tripple integration will be [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5
What is triple integration?The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.
To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z=\dfrac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y=9+\dfrac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
Calculating:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]
[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]
The volume of the tetrahedron is 1087.5 cubic units.
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20+2x=x+56 solve for x
Answers
Answer:
Rearrange the numbers to their like terms.
which is 2x-x=56-20.
x=36.
The solution to the equation is x = 36.
To solve the equation 20 + 2x = x + 56 for the variable x, you can follow these steps:
Step 1: Move all terms containing x to one side of the equation by subtracting x from both sides:
20 + 2x - x = x + 56 - x
20 + x = 56
Step 2: Subtract 20 from both sides to isolate the x term:
20 + x - 20 = 56 - 20
x = 36
Therefore, the solution to the equation is x = 36.
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13 The diagram shows nine identical squares inside a rectangle.
The length of the rectangle is 12 cm.
Work out the width of the rectangle
Answers
Answer:
5...is the width of the rectangle .
Point u is on line segment tv given tv = x + 10, tu =3x-8, and Uv = 10 determine the numerical length of tv
Answers
Answer:
[tex]|tv = 14[/tex]
Step-by-step explanation:
Given
[tex]|tv = x + 10[/tex]
[tex]|tu = 3x - 8[/tex]
[tex]|uv = 10[/tex]
Required
Determine length of tv
Length tv is calculated by adding lengths tu and uv.
In other words
[tex]tv = tu + uv[/tex]
Substitute values for tv, tu and uv
[tex]x + 10 = 3x-8+10[/tex]
Collect like terms
[tex]x - 3x = -8+10 -10[/tex]
[tex]-2x = -8[/tex]
Divide both sides by -2
[tex]x = 4[/tex]
Recall that [tex]|tv = x + 10[/tex]
Substitute 4 for x
[tex]|tv = 4 + 10[/tex]
[tex]|tv = 14[/tex]
Hence, the length of line segment tv is 14
A rectangular cake has a length of 25in, a width of 18in, and a height of 4in. Each container of frosting can cover 200 square inches.
Answers
Answer:
9 containers of frosting
Step-by-step explanation:
25 x 18 x 4, gives you 1800 square inches, divide 1800 by 200 and you get 9
Solve 1 over 36 = 6x−3.
Answers
Answer:
x = 109/216
Step-by-step explanation:
Solve for x:
1/36 = 6 x - 3
Hint: | Reverse the equality in 1/36 = 6 x - 3 in order to isolate x to the left hand side.
1/36 = 6 x - 3 is equivalent to 6 x - 3 = 1/36:
6 x - 3 = 1/36
Hint: | Isolate terms with x to the left hand side.
Add 3 to both sides:
6 x + (3 - 3) = 3 + 1/36
Hint: | Look for the difference of two identical terms.
3 - 3 = 0:
6 x = 1/36 + 3
Hint: | Put the fractions in 1/36 + 3 over a common denominator.
Put 1/36 + 3 over the common denominator 36. 1/36 + 3 = 1/36 + (36×3)/36:
6 x = 1/36 + (36×3)/36
Hint: | Multiply 36 and 3 together.
36×3 = 108:
6 x = 1/36 + 108/36
Hint: | Add the fractions over a common denominator to a single fraction.
1/36 + 108/36 = (1 + 108)/36:
6 x = (1 + 108)/36
Hint: | Evaluate 1 + 108.
1 + 108 = 109:
6 x = 109/36
Hint: | Solve for x.
Divide both sides by 6:
x = (109/6)/36
Hint: | Multiply 36 and 6 together.
36×6 = 216:
Answer: x = 109/216
Answer:
x = 109/216
Step-by-step explanation:
Add 3, divide by 6.
[tex]\dfrac{1}{36}=6x-3\\\\3+\dfrac{1}{36}=6x\\\\\dfrac{109}{(36)(6)}=\boxed{x=\dfrac{109}{216}}[/tex]
Use the figure to find the Total Area. 48 sq. units 84 sq. units 96 sq. units
Answers
Answer:
84 sq. units
Step-by-step explanation:
Total area is:
6*6 + 4*1/2*6*√(5² - (6/2)²) = 36 + 12*√16= 36 + 48 =84 sq. unitsIn a certain year, 23% of all teenagers in the United States had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account. (a) If TeenChex selects a random sample of 1,000 teenagers, what number of teenagers without checking accounts can it expect to find? teenagers What is the standard deviation σ of this number? (Round the standard deviation to one decimal place.)
Answers
Answer:
1. 770
2. 13.31
Step-by-step explanation:
n = 1000
P (probability of those with account) = 23% = 0.23
q(probability of those without account) = 1-p = 0.77
a. We are expected to find the expected number of those without checking account
= n * q
= 1000 * 0.77
= 770
b. Standard deviation
= √n*p*t
= √1000x0.77x0.23
= √177.1
= 13.31
Are the ray AB and BA the same? if yes why and if no why
Answers
Answer:
No,the ray AB and BA are not same because the ray AB denotes the ray(light) is coming from the direction through A while the ray BA denotes the ray is coming from the direction through B.
NASA is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before launch, and has a diameter of 4.7 feet, what is the total weight in pounds of the satellite on Earth? Use π = 3.14.
Answers
Answer:
774 lb
Step-by-step explanation:
weight = volume * density
radius = diameter/2
volume = (4/3)πr^3
volume = (4/3)(3.14)(4.7/2 ft)^3
weight = (4/3)(3.14)(4.7/2 ft)^3 * 14.25 lb/ft^3
weight = 774 lb
If 15 oranges cost Rs. 70,how much do 39 oranges cost ?
Answers
Answer:
firstly divide 70 by 15 and when the product came multiply it with 39Step-by-step explanation:
70 ÷ 15 = 4.66
4.66 × 39 = 181.974
HELP ASAP
8^2 – 10x - 3
NEED ALL STEPS PLZZZZ
Answers
Answer:
hope this attachment will help you
10) The perimeter of a rectangular yard is 60 meters. What is its length if its width
is twice its length?
*
A 10 meters
B 18 meters
C 20 meters
D 24 meters
Answers
Answer:
Length = 20 metres
Width = 10 mteres
Step-by-step explanation:
Let the width be x metres
Let the length be 2x metres
Perimeter = 60 metres
therefore, by the problem ,
2(length+breadth)= perimeter
=>2(2x+x)=60
=>2 *3x=60
=>6x=60
=>x=10
length = 20 metres
width = 10 mteres
What is the probability of getting a 10 or a jack from a deck of poker cards (52 cards)?
Answers
Answer:
15.38%
Step-by-step explanation:
there are four 10 cards and four jack cards.
4+4=8
you want to get one from 52 cards, so it's 8 out of 52. 8/52
to calculate the percentage, you multiply 8 by 100, then divide by 52.
8*100/52=15.38 (rounded answer)
The equivalent resistance of R1 = 1000 ohms and R2 = 1500 ohms connected in parallel is _____ ohms.
Answers
Answer:
600 Ω see attachement
Step-by-step explanation:
what is onetenth for 19,548
Answers
Step-by-step explanation:
one-tenth of 19,548 is 1954.8
Convert 2 centimeters into feet. Round your answer to the nearest hundredth.
Answers
.066
1 Centimeter = 0.03280839895 Feet
The conversion of 2 centimeters into feet would be 0.066 feet.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
We have to determine the conversion of 2 centimeters into feet.
Since one centimeter = 0.03280839895 feet
Therefore two centimeters = 2×0.03280839895 feet
⇒ two centimeters = 0.0656167
Round the answer to the nearest hundredth.
⇒ two centimeters = 0.066
Therefore, the conversion of 2 centimeters into feet would be 0.066 feet.
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How can you create a cone and a cylinder using this tool? Describe the shapes and the specific axes of rotation that produce a cone and a cylinder. If there is more than one polygon that can generate the same cone or cylinder, state each shape in the table.
Answers
Answer:
The answer is in the image.
Step-by-step explanation:
Answer:
Cone- 1 isosceles triangle revolved 180° about its height
2 isosceles triangle revolved 180° about its height
cylinder 1 rectangle revolved 180° about either axis of symmetry
2 revolved 360° about any side
Step-by-step explanation: plato edmentum
Which fraction below is NOT equivalent to 1/3 2/6 3/9 4/12 5/13
Answers
Answer:
5/13 (irreducible)
Step-by-step explanation:
1/3=2/6=3/9=4/12 are all thirds of the total.
40% of the cost was tax. if the taxes paid were $15,000, what was the total cost of the car?
Answers
Answer:
$37500
Step-by-step explanation:
For this we can simply create a proportion of the percentages.
.4 / 1 == 15000 / x
Now we solve for x:
x = 15000/.4
x = 37500
Thus, the cost of the car was $37,500.
Cheers.
A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.
Answers
Answer:
The question is incomplete. The complete table is:
Score in percent (X): 80, 75, 70, 90, 95, 100, 75, 60, 75, 95
Time in minute (Y) : 45, 48, 40, 50, 40, 30, 30, 39, 38, 55
The answer is 0.55 %
Step-by-step explanation:
ΣX = 815
ΣY = 425
ΣX x Y = 34565
Σ = 67925
Σ[tex]$Y^2$[/tex] = 18699
So, correlation coefficient, b
[tex]$b= \frac{n \Sigma XY- \Sigma X \Sigma Y}{\sqrt{n \Sigma X^2-( \Sigma X)^2} \times \sqrt{(n \Sigma Y^2 -(\Sigma Y)^2}}$[/tex]
[tex]$b = \frac{(10 \times 34565)-(815 \times 425)}{\sqrt{(10 \times 67925)-(815)^2} \times \sqrt{(10 \times 10699)-(425)^2}}$[/tex]
[tex]$b= -\frac{725}{9779 \times 2702}$[/tex]
b = -0.0741
Correlation Determination:
[tex]$B^2 = (-0.0741)^2$[/tex]
= = 0.0055 = 0.55%
Therefore, 0.55 percentage of the variation in y can be explained by x variable.
x = 2, w = -1, y = 6, z = 4 x²+4w - 2y
Answers
Answer:
-12Step-by-step explanation:
[tex]x = 2\\ w = -1\\ y = 6\\ z = 4\\x^2+4w-2y\\[/tex]
[tex](2)^2 +4(-1) -2(6)\\4 -4 -12\\0-12\\\\=-12[/tex]
Answer:
4x² + 4w - 2y
4(2)² + 4(-1) - 2(6)
4×4 + (-4) - 12
16 - 4 - 12
12 - 12
0 is the answer
7-7 im gonna post 7 more please helppp!
Answers
Transposing -18 to RHS
= p = 18 + 3
p = 21
Verification
21-18=3
= 3=3
Hence, RHS = LHS
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------
Answer: p = 21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]p - 18 = 3[/tex]
Add 18 to both sides.
[tex]p = 3 + 18[/tex]
Add 3 and 18 to get, you guessed it, 21!If 8 people can pick the apples from trees in 6 days, how long will it take12 people?
Answers
If it takes 6 days for 8 people to pick apples then it must take 48 days for 1 person to do it because 6•8=48.
So then it must take 12 people
48/12 days which is 4 to pick apples from trees.
A researcher examines the records of all registered voters in one city and finds that 43% are registered democrats. Is the evaluated group a population or a sample?
Answers
Answer: Population
Step-by-step explanation: Population is refers to the whole or entire members or of a given set. This is different from a sample which is used to refer to members of a subset (a subset is a certain portion or fraction of an entire set). In the scenario above, since the evaluation was based on the entire number of registered voters in the country, this means we are referring to a population. The inference about the percentage of democratic voters was drawn from a pool of all the entire number of registered voters available in the country and not from a certain subset or portion of registered voters. Hence, the evaluated group is a population.
ustin's hair is 3 1/4 inches long. How long will it be in 2 months if it grows 1/2 inch each month? Which method will NOT give the correct number of inches?
Answers
Answer:
3 1/2
Step-by-step explanation:
1/4 + 1/4
(1x4) + (1x4)
=_________
4x4
=8/16
8÷8
=_________
16÷8
=3 1/2
Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately. Explain why these particular equations can be graphed immediately.
Answers
i hope this helps <3
The equations can be graphed immediately because the slopes and the y-intercepts are known
The system of equations is given as:
y = 3x + 2y = -2/3x - 4The equations in the system are linear equations, and they are represented as:
[tex]y = mx + b[/tex]
Where:
m represents the slopeb represents the y-interceptFrom the given system, we can find the slopes and the y-intercepts of both functions easily
Hence, the equations can be graphed immediately because the slopes and the y-intercepts are known
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the fourth term of an arithmetic
progression is one less than twice the
second term If the sixth term is 7,
find the first term
Answers
Answer:
2
Step-by-step explanation:
Given AP where:
a₄ = 2a₂ - 1a₆ = 7To find
a₁ = ?Since
a₄ = a₁ + 3da₂ = a₁ + da₆ = a₁ + 5dInitial equations will change as:
a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1a₁ + 5d = 7 ⇒ a₁ = 7 - 5dComparing the above:
d + 1 = 7 - 5d6d = 6d = 1Then:
a₁ = d + 1 = 1 + 1 = 2a₁ = 2The first term is 2