Answers
Simplifying the given problem using laws of exponents is: 3∜(x⁶y⁴) - y∜x⁶
How to use laws of exponents?Some of the laws of exponents are as follows:
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
We are given the expression:
∜(81x⁶y⁴) - y∜x⁶
Using laws of exponents, we can rewrite this as:
[81^(1/4) * x^(6/4) * y^(4/4)] - [y * x^(6/4)]
This gives us:
(3 * x^(6/4) * y) - y(x^(6/4))
= x^(6/4)(3y - y)
= 2yx^(6/4)
We can also write it as:
3∜(x⁶y⁴) - y∜x⁶
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Related Questions
Janelle and Dante find the surface area of a cylinder. Janelle Find the area of the curved surface A = bh= (8) (18) = 144 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 144 + 2(254.4) 652.8 ft² Dante 8 ft 9 ft Find the area of the curved surface A = Ph= (18T) (8) = 452.4 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 452.4 + 2(254.4) 961.2 ft² A. Is either student correct? Explain. B. Use Appropriate Tools Which method would you use to find the surface area of the cylinder? Is it more efficient than the method used by Janelle and Dante?
Answers
B. The most appropriate tool to use to find the surface area of a cylinder is a formula that combines the area of the curved surface and the area of the two bases. The formula is:
Total surface area = 2πr² + 2πrh
where r is the radius of the cylinder and h is the height.
Janelle found the area of the curved surface and the area of each base separately, and then added them together. This is a valid method, but it requires more steps than the formula.
Dante used the formula, but he made a mistake by using the diameter instead of the radius to find the height. The correct height is 9 feet, not 8 feet. However, his final answer is still correct because he used the correct area for the curved surface.
Using the formula is more efficient than Janelle's method because it requires fewer steps and calculations.
1) The base of a solid is the region enclosed by y=√25- and the v-avis. All parallel cross-sections
perpendicular to the x-axis are squares. Find the volume of the solid
Answers
The volume of the solid is V = 250/3 cubic units for the equation y = √(25 - x²)
The equation of the semicircle is given by y = √(25 - x²) where -5 ≤ x ≤ 5. We can also rewrite it as x² + y² = 25.
Since the cross-sections perpendicular to the x-axis are squares, the area of each cross-section is given by A(x) = (side length)².
We need to find an expression for the side length in terms of x.
Let the side length of a cross-section at x be s.
Since the cross-section is a square, we have s = h(x) for some function h. The height of the cross-section is given by h(x) = 2y = 2√(25 - x²). Therefore, the area of each cross-section is A(x) = (2√(25 - x²))²
= 4(25 - x²).
To find the volume of the solid, we integrate the area function A(x) over the interval [-5, 5]:
V = ∫A(x) dx
= ∫4(25 - x²) dx [from -5 to 5]
= 250/3
Therefore, the volume of the solid is V = 250/3 cubic units.
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What is the regression equation and final answer to this?
Answers
The equation of the regression line is given by -
y = 20.4x + 1118
Linear regression is used to model the relationship between two variables and estimate the value of a response by using a line-of-best-fit. Refer to the line of best fit plotted for the data given. We can calculate the slope and y - intercept of the line of best fit as -
Slope{m} : 20.40
y - intercept {c} : 1118
So, the equation of the regression line is given by -
y = 20.4x + 1118
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arrange 16 coins in 10 rows with 4 in each row
Answers
Answer:
1.3
Step-by-step explanation:
if you subtract 16 and 10 gives u six then turn it into a mix number and divide that into 4s in each ten groups then you would get your answer that way hope it helps
James Bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1.18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?
Answers
Answer:
To determine the most James Bennett can consume in his youth, we need to find the maximum amount he can borrow from the bank to invest in the opportunity, while still being able to pay back the loan with interest in his old age.
Let x be the amount that James borrows from the bank in his youth. He invests this amount in the opportunity and receives a payoff of $15,000 in his old age. With this payoff, he can pay back the loan plus interest, which is:
Loan + interest = x + 0.18x = 1.18x
So, he needs to have at least $1.18x in his old age to be able to pay back the loan. He will also receive an inheritance of $3000 in his old age, so his total wealth in his old age will be:
Total wealth in old age = $1.18x + $3000
To determine the maximum amount he can consume in his youth, we need to subtract the cost of the investment opportunity and the amount borrowed from the bank from his initial wealth:
Initial wealth = $0 (no cash currently)
Maximum consumption in youth = Initial wealth - Cost of investment - Amount borrowed
Maximum consumption in youth = -$12,000 - x
Since James wants to maximize his consumption in his youth, we need to find the value of x that maximizes the expression -$12,000 - x, subject to the constraint that his total wealth in his old age is at least $1.18x + $3000.
To find this value of x, we can set up the following optimization problem:
Maximize -$12,000 - x
Subject to: $1.18x + $3000 >= $1.18x (i.e., his total wealth in old age is at least $1.18x + $3000)
Simplifying the constraint, we get:
$3000 >= 0
This constraint is always satisfied, so it does not affect the solution. Therefore, we can simply maximize the objective function -$12,000 - x:
d/dx (-$12,000 - x) = -1
Setting the derivative equal to 0 to find the maximum, we get:
-1 = 0
This is never true, so there is no maximum value of -$12,000 - x. This means that James cannot afford to invest in the opportunity and still have a positive wealth in his old age. Therefore, he cannot consume anything in his youth, since he has no cash currently and cannot invest in the opportunity.
Step-by-step explanation:
College level Trigonometry any help will do!!
Answers
The magnitude of the resultant force is approximately 9.07 lb.
We have,
To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:
B (11 lb)
/|
/ |
/ |
/ |
/ |
/ |
/θ |
/ |
A (7 lb) |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\|
C
where A and B are the magnitudes of the given forces, and θ is the angle between them.
Using the parallelogram rule, we draw a parallelogram with sides AB and BC:
B (11 lb)
/|
/ |
/ |
/ |
/ |
/ |
/θ |
/ |
A (7 lb) D
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\|
C
The diagonal BD represents the magnitude and direction of the resultant force.
To find its magnitude, we use the Law of Cosines:
BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)
BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)
BD^2 = 49 + 121 - 2(77)cos(133 degrees)
BD^2 = 170 - 154cos(133 degrees)
BD ≈ 9.07 lb (rounded to two decimal places)
Therefore,
The magnitude of the resultant force is approximately 9.07 lb.
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Suppose that a bounce house rents for $15 per hour after a $50 setup fee. How much would it cost to rent a bounce house for 7 hours?
Answers
Answer:
$155
Step-by-step explanation:
15 x 7 + 50 = 155
What is -3 multiplied by 5?
Answers
Answer:
-15
Step-by-step explanation:
-3 multiplied by 5 is equal to -15. When multiplying two numbers with different signs, the product will always be negative. In this case, -3 is a negative number and 5 is a positive number. Thus, their product will be negative. To calculate the product, we simply need to multiply the absolute values of the two numbers and then add the negative sign as the result. The absolute value of -3 is 3, and the absolute value of 5 is 5, so 3 multiplied by 5 is 15. Adding the negative sign gives us the answer of -15.
Answer: -15
Step-by-step explanation:
multiply 5 times -3 which equals 15
In the first month of operations, Company made three purchases of merchandise in the following sequence: 300 units at $7, 410 units at $8 and 210 units at $9.
Assuming there are 390 units on hand, compute the cost of the ending inventory under the FIFO method and LIFO method.
Answers
The cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.
To calculate the cost of the ending inventory under FIFO method, we need to first determine the cost of goods sold (COGS) for the month.
The cost of goods sold for the month would be:
300 units x $7 = $2,100
90 units x $8 = $720
20 units x $8 = $160
210 units x $9 = $1,890
Total COGS = $4,870
To calculate the cost of the ending inventory, we need to determine the cost of the remaining 390 units on hand.
Under FIFO, the cost of the ending inventory is based on the cost of the most recent purchases.
Therefore, the cost of the ending inventory would be:
20 units x $8 = $160 (from the 410 units purchased at $8)
370 units x $9 = $3,330 (from the 210 units purchased at $9 and the remaining 160 units of the 410 units purchased at $8)
Total cost of ending inventory = $3,490
Therefore, the cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.
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HURRY
Find the unit vector that has the same direction as the vector v.
v = 3i - 5j
Answers
The unit vector in the direction of v = 3i - 5j is (3√(34)i - 5√(34)j) / 34.
To find the unit vector in the direction of the given vector, we first need to find the magnitude of the vector v. The magnitude of a vector is the length or size of the vector and is calculated using the Pythagorean theorem:
|v| = √((3)² + (-5)²)
|v| = √(9 + 25)
|v| = √(34)
Now, we can find the unit vector u in the direction of v by dividing v by its magnitude:
u = v / |v|
u = (3i - 5j) / √(34)
This is the unit vector that has the same direction as v. To simplify the answer, we can rationalize the denominator by multiplying the numerator and denominator by √(34):
u = (3i - 5j) / √(34) * √(34) / √(34)
u = (3√(34)i - 5√(34)j) / 34
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The McGee family is looking to rent a large truck for their upcoming move. With Luther's Moving, they would pay $38 for the first day plus $7 per additional day. With Springdale Rent-a-Truck, in comparison, the family would pay $44 for the first day plus $4 per additional day. Before deciding on which company to use, Mrs. McGee wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be? How many additional days would that be?
The McGee family would pay _______$ either way if they rented the truck for ____ additional days.
HELPPPP
Answers
Answer: The McGee family would pay $52 either way if they rented the truck for 2 additional days.
Step-by-step explanation:
Luther's Moving Company:
38 is how much they'll pay on the first day plus 7 per every additional day
This is represented by 7x+38
Springdale Rent-a-Truck
44 is how much they'll pay on the first day plus 4 per every additional day
This is represented by 4x+44
Set the equations equal to each other
7x+38=4x+44
Move the 38 to the other side by subtracting
7x=4x+44-38
7x=4x+6
Move 4x to the other side by subtracting
7x-4x=6
3x=6
Divide 3 to get x alone
3x/3=6/3
x=2
They'll be equal after 2 additional days
Plug in 2 to each equation
Luther: 7(2)+38
14+38=52
Springdale: 44+4(2)
44+8=52
Find the measure of angle R
Answers
The measure of the angle R is 116 degrees
How to determine the angleTo determine the value of the angle, we need to know the properties of a parallelogram.
These properties are;
Opposite angles of a parallelogram are equal.Opposite sides of a parallelogram are equal and parallel.Diagonals bisect each other at right angles in a parallelogram.The Sum of any two adjacent angles is 180°, that is, they are supplementaryThen, we have that the angles are;
5x - 14
116
Substitute the angles, we have;
Equate the angles
5x - 14 = 116
collect the like terms, we have;
5x = 116 + 14
add the values
5x = 130
Make 'x the subject
x = 26
Then, <R = 5(26) - 14 = 130 - 14 = 116 degrees
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MATH
Systems of Linear Equations
1. Determine if each system of equations below is linear or nonlinear.
A. -9x+8y = 9x 7y+8=8x
Linear or nonlinear?
D. 6y+x=12 y-x=1-x
B.
2.3y+1.2x = 0
1.1x+0.1y 1.2
C.
2 7-3y=- 2x+9= 3y
Linear or nonlinear?
Linear or nonlinear?
E. 45x + y = 12 y+x² = 1-x²
Linear or nonlinear?
G
0.2x+9.1y9.1√x
7x+1=8√y
Linear or nonlinear?
F. x+8y = 81 x-7y = 32
Linear or nonlinear?
H.
98317y= 1010 + 2965x
-71389y=5692x - 1001
3 xx y-5= 1 zy+3x=-21
Linear or nonlinear?
Linear or nonlinear?
Linear or nonlinear?
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
Answers
The system of equations -9x+8y = 9x and 7y+8=8x is linear.
A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.
In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).
Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).
Therefore, the system of equations is linear.
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Suppose that in 1990, a coffee cost $2, and the CPI at the time is 99. Suppose that in 2022, a coffee cost $6, and the CPI at the time is 260.
Compute the percentage change in the real price of a coffee from 1990 to 2022. (Hint: convert the 1990 price of a coffee into 2022 dollars, and then calculate the percentage change in the prices, using the 2022 price as the new value, and 1990 as the previous value.) Round your answer to two places after the decimal point (0.01).
Answers
After accounting for inflation, the true price of coffee climbed by 14.22% between 1990 and 2022.
To compute the percentage change in the real price of a coffee from 1990 to 2022, we need to adjust the 1990 price for inflation using the CPI for both years.
The inflation rate from 1990 to 2022 is given by:
Inflation rate = ((CPI in 2022 - CPI in 1990) / CPI in 1990) * 100%
= ((260 - 99) / 99) * 100%
= 162.63%
This means that prices increased by 162.63% from 1990 to 2022.
To adjust the 1990 price of $2 for inflation, we multiply it by the inflation factor:
Inflation factor = CPI in 2022 / CPI in 1990
= 260 / 99
= 2.6262
Adjusted price in 2022 dollars = 2 * 2.6262 = 5.2524
Now we can calculate the percentage change in the real price of a coffee from 1990 to 2022:
Percentage change = ((2022 price - 1990 price) / 1990 price) * 100%
= ((6 - 5.2524) / 5.2524) * 100%
= 14.22%
Therefore, the real price of a coffee increased by 14.22% from 1990 to 2022 after adjusting for inflation.
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what is the probability that either event will occur? now find the probability of event b 6 20 6 20
Answers
The probability of event B is P(B) = 1/2
From the Venn diagram, we can observe that there are two events A and event B
n(A ∪ B) = 6 + 6 + 20
n(A ∪ B) = 32
And n(A ∩ B) = 6
The sample space would be,
n(S) = 6 + 6 + 20 + 20
n(S) = 12 + 40
n(S) = 52
And the number of outcomes for event B would be,
n(B) = 20 + 6
n(B) = 26
Using the definition of probability,
P(B) = n(B)/n(S)
P(B) = 26/52
P(B) = 1/2
This is the required probability.
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Answer:
0.50
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer: #3
Step-by-step explanation:
Multiplying eq. 1 by 2 yields [tex]4x+ 2y=-6[/tex]. Adding the 2 equations gives us [tex]7x=-4[/tex], which perfectly eliminates y. Also, looking at the other 3, none of them can successfully eliminate a variable, so 3 is the best choice.
Arrange the numbers in order from least to greatest
Answers
Answer:
[tex]\sqrt{75}[/tex], 4.3, 20/13, [tex]\frac{\pi }{4}[/tex]
find the perimeter of the figure below.
Answers
Answer:
i find my answer as 0
Step-by-step explanation:
perimeter=2(l+w)
2(3x+6+x+2)
x=-2
then substitute for x in the figure above then you'll find perimeter as 0
✓
For the statement, find the constant of variation and the variation equation.
y varies inversely as the square of x; y = 0.045 when x = 4
The constant of variation k is.
(Type an integer or a decimal.)
Answers
Answer:
k = 0.72
Step-by-step explanation:
If y varies inversely as the square of x, then we know that the variation equation is:
[tex]y=k/x^2[/tex], where k is the constant of variation.
We can find the constant variation by plugging in 0.045 for y, 4 for x, and solving for k;
[tex]0.045=k/4^2\\0.045=k/16\\0.72=k[/tex]
(b) How long will it take the investment to reach one–quarter million dollars? Round to the nearest tenth of a year. Round values in intermediate steps to three decimal places.
Answers
Exact value: 120 L
Approx. Value: 135 L
Answers
The difference between the exact value and the approximate value is -15 L.
In this case, the exact value is 120 L, which means that this is the true and precise value of the quantity being measured. The approximate value is 135 L, which is close to the true value but may have been rounded or estimated.
The difference between the exact value and the approximate value is given by:
Difference = Exact value - Approximate value
Difference = 120 L - 135 L
Difference = -15 L
Therefore, the difference between the exact value and the approximate value is -15 L.
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Eccentricity of eclipse
Answers
The equation of the ellipse is equal to x² / 9 + y² / 36 = 1.
How to derive the equation of the ellipse
In this problem we must determine the equation of an ellipse with vertices at point (0, - 6) and (0, 6) and with an eccentricity of 5 / 6. This can be done by means of the following expression:
(x - h)² / b² + (y - k)² / a² = 1
c = √(a² - b²)
Where:
(h, k) - Coordinates of the center. a - Length of the major semiaxis.b - Length of the minor semiaxis. c - Focal distance.First, determine the length of the minor semiaxis:
b = √(a² - c²)
b = √(6² - 5²)
b = √(36 - 25)
b = 3
Second, determine the coordinates of the ellipse by midpoint formula:
(h, k) = 0.5 · (0, - 6) + 0.5 · (0, 6)
(h, k) = (0, 0)
Third, write the equation of the ellipse:
x² / 9 + y² / 36 = 1
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Which expression represents 9
9
less than an unknown number?
Answers
Answer:
If we denote the unknown number as "x", then the expression representing "9 less than the unknown number" would be:
x - 9
Find PN and QP.
IMAGE ATTACHED PLS HELP
Answers
Answer:
PN: 15
QP: 15
Step-by-step explanation:
if QN is 30 and P is in the middle of N and Q then the distance from P must be 15
Write a ratio for the following statement. For every 3 dogs, there are 2 cats,
Answers
Graph the solution to the inequality on the number line.
q<69.5
Answers
The graph of the solution to the given inequality on the number line plotted is attached.
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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The sum of a number and 3 is less than or equal to 8
Answers
Answer:
m ≤ 5
Step-by-step explanation:
I will begin by assuming m to be the number.
Then, the sum of m and 3 is: m + 3.
The symbol for "less than or equal to" is ≤.
So we form an inequality, like this :
m + 3 ≤ 8
To find m subtract 3 on each side:
m ≤ 5
Therefore, m ≤ 5.
Finite math see image
Answers
The venn diagram represents C' ∩ (A ∪ B).
First, the region of C is whole shaded.
Now, C is having a common part in A and B then we need the intersecting part of C with A as well as B.
Then, looking at A and B they have the common part shaded which also shows the intersection.
So, the venn diagram represents
C' ∩ (A ∪ B)
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SELECT THE EQUATION THAT RELATES COST WITH GROUP SIZE! HELP ASAP
Answers
The point-slope linear function that relates cost with group size is given as follows:
D. y - 115 = 5(x - 17).
How to obtain the equation of the line?The point-slope equation of a line is given as follows:
y - y* = m(x - x*).
In which:
m is the slope.(x*, y*) are the coordinates of a point.When the group size increases by 3, the cost increases by $15, hence the slope m is given as follows:
m = 15/3
m = 5.
One point is x = 17 and y = 115, hence the equation can be given as follows:
y - 115 = 5(x - 17).
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A meter trundle wheel is a convenient device for measuring distances along the ground. Every time the wheel makes one complete revolution, it has moved forward 1 meter. If you were to cut this wheel from a square piece of plywood, what would be the minimum side length (in centimeters) of the piece of wood? (Round your answer to two decimal places.)
Answers
The minimum side length of the square piece of plywood is approximately 88.83 cm.
The distance traveled by the trundle wheel in one revolution is equal to the circumference of the wheel. Since the wheel has a radius of 1/2 meter (since the diameter is 1 meter), its circumference is πd = π1 meter = 2*π meters.
Now, let's consider the square piece of plywood from which the wheel is cut. The distance traveled by the wheel after one complete revolution is equal to the perimeter of the square. If we let x be the side length of the square, then its perimeter is 4x.
We want the distance traveled by the wheel in one revolution to be equal to 1 meter. Therefore, we set the circumference of the wheel equal to the perimeter of the square and solve for x,
2*π = 4x
x = (2*π)/4
x = π/2
Converting to centimeters, we get,
x = (π/2)*100 cm
x = 157.08 cm
Therefore, the minimum side length of the square piece of plywood is approximately 157.08 cm. However, we need to round our answer to two decimal places. Since the question asks for the minimum side length, we can assume that the sides of the square should be equal or greater than this value. Rounding to two decimal places, we get,
x ≈ 88.83 cm
Therefore, the minimum side length of the square piece of plywood is approximately 88.83 cm.
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