Answer:
1.33333 hours
Step-by-step explanation:
Given :
Time taken by Libby = 2 hours
Time taken by Ethan = 4 hours
rate = 1 / time taken
Libby's rate = 1 /2
Ethan's rate = 1/4
Combined rate = Libby's rate + Ethan's rate
Combined rate = 1/2 + 1/4 = 3/4
Time taken = 1 / combined rate
Time taken = 1 / (3/4)
Time taken = 4 /3
Time taken = 1.33333 hours
divide 3x2 − 11x − 4 by x − 4. (2 points) x 1 x − 23 3x 1 3x − 23
Dividing 3x^2 - 11x - 4 by x - 4 results in the quotient of 3x + 1 and a remainder of -23.
To divide 3x^2 - 11x - 4 by x - 4, we can use long division.
First, we divide the highest degree term of the dividend by the divisor. In this case, (3x^2) / (x) gives us 3x as the first term of the quotient.
Next, we multiply the divisor (x - 4) by the first term of the quotient (3x) to obtain (3x)(x - 4) = 3x^2 - 12x.
We subtract this result from the dividend (3x^2 - 11x - 4) to get a new polynomial: (3x^2 - 11x - 4) - (3x^2 - 12x) = x + 8x - 4.
Now, we repeat the process with the new polynomial (x + 8x - 4). We divide the highest degree term (x) by the divisor (x - 4), which gives us the second term of the quotient, 8.
Multiplying the divisor (x - 4) by the second term of the quotient (8) gives us (8)(x - 4) = 8x - 32.
Subtracting this from the new polynomial (x + 8x - 4) - (8x - 32) = 40, we obtain the remainder.
Therefore, the division of 3x^2 - 11x - 4 by x - 4 gives the quotient 3x + 1 and the remainder -23.
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Connor has a box of 100 T-shirts in different sizes that he will be throwing to fans in the stands at the Greenville Township Allstars baseball game. Since the T-shirts are all mixed together, he's curious about how many of each shirt size is in the box. So, he randomly checks 10 shirts from different parts of the box. Here are the sizes of those shirts: large, small, extra large, medium, small, extra large, large, small, medium, small Based on the data, estimate how many small T-shirts are in the box.
The Sample, we estimate that there are approximately 40 small T-shirts in the box.
The number of small T-shirts in the box, sampling and assume that the proportion of small T-shirts in the sample is representative of the proportion in the entire box.
In the given sample of 10 shirts, we have the following sizes: large, small, extra large, medium, small, extra large, large, small, medium, small.
Out of the 10 shirts, 4 of them are small. To estimate the number of small T-shirts in the entire box, we can set up a proportion:
Small shirts in sample / Total shirts in sample = Small shirts in box / Total shirts in box
Plugging in the values we have:
4 / 10 = x / 100
Cross-multiplying:
4 * 100 = 10 * x
400 = 10x
Dividing both sides by 10:
x = 400 / 10
x = 40
Based on the sample, we estimate that there are approximately 40 small T-shirts in the box.
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Arecipe calls for 12 ounces of molasses. The cook gets out a volume measuring container and measures out 12 fluid ounces of molasses a) What assumption did the cook make that was incorrect? b) How much more molasses did the cook add than should have been added?
The cook added 6 ounces more molasses than should have been added since the assumption was wrong.
a) The assumption the cook made that was incorrect was that the volume of molasses is the same as its weight. The cook measured 12 fluid ounces of molasses instead of 12 ounces of molasses by weight. It is assumed that weight and volume are the same, but this is not always the case because the density of different substances varies.
b) The amount of molasses the cook added than should have been added can be calculated by converting 12 fluid ounces of molasses to weight ounces. We can use the density of molasses to calculate the weight. Let's assume the density of molasses is 1.5 ounces per fluid ounce.
Then, the weight of 12 fluid ounces of molasses = 12 fluid ounces × 1.5 ounces/fluid ounce = 18 ounces
The cook added 6 ounces more of molasses than should have been added because:
12 fluid ounces - 12 weight ounces = 6 ounces
Therefore, the cook added 6 ounces more molasses than should have been added.
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Della is renting a car for the day. The rental
fee (y) is $30 plus $0.25 per mile (m).
Which of the following equations represents
this cost?
(A) y = 0.30m + 25
(B) y = 30m + 0.25
(C) y = 0.25m + 30
(D) y = m(0.25 +30)
Answer: C) y = 0.25m + 30
Step-by-step explanation:
Since the rental fee (y) of the car is $30 plus $0.25 per mile (m), then the cost will be:
= $30 + $0.25(m)
= 30 + 0.25m
For example, to calculate the cost of someone who rented the car and used 20 miles will be:
= 30 + 0.25m
= 30 + 0.25(20)
= 35
help plz plz plz plz plzzz brainliest
Answer: About 4
Step-by-step explanation:
16 divided by 3 2/3 is 4. decimal so round that and about 4 is you’re answer.
Answer:
4 dress will be the max
Step-by-step explanation:
it is a division question
16 yards on a roll ÷ 3⅔ yards of fabric
16÷3⅔
16÷ 11/3
16*3/11
48/11
4.3636.
SOMEONE HELPPPP PLEASEEEEEEEEEEEEEEEE
Answer:
No, Collin didn't reach his goal. He got a 81% on his test.
Step-by-step explanation:
Gradient methods are used to find local optima of functions. Apply the Method of Steepest Descent to the function f(x1, x2) = 3xí + 2xż starting from the initial point Xo = (2, 1) (you should only perform the first 2 iterations of the algorithm). e) If the initial start point xo is changed to a different position, how might this affect the operation of the algorithm?
The first two iterations of the Method of Steepest Descent algorithm starting from the initial point Xo = (2, 1) for the function f(x1, x2) = 3x1 + 2x2 are as follows:
Iteration 1:
1. Compute the gradient at the current point Xo: ∇f(Xo) = [∂f/∂x1, ∂f/∂x2] = [3, 2].
2. Choose a step size (learning rate) α.
3. Update the current point Xo using the gradient and step size: X1 = Xo - α * ∇f(Xo).
Iteration 2:
1. Compute the gradient at the current point X1: ∇f(X1) = [∂f/∂x1, ∂f/∂x2].
2. Choose a step size (learning rate) α.
3. Update the current point X1 using the gradient and step size: X2 = X1 - α * ∇f(X1).
In the given function f(x1, x2) = 3x1 + 2x2, the partial derivatives with respect to x1 and x2 are 3 and 2, respectively. These represent the gradients in the x1 and x2 directions at any given point (x1, x2).
The Method of Steepest Descent is an iterative optimization algorithm that aims to minimize a function by moving in the direction of the steepest descent (negative gradient) at each iteration.
It starts from an initial point Xo and updates the current point by taking steps in the opposite direction of the gradient, multiplied by a step size or learning rate α.
In the first iteration, we compute the gradient at the initial point Xo = (2, 1), which is ∇f(Xo) = [∂f/∂x1, ∂f/∂x2] = [3, 2]. Let's assume we choose a learning rate α of 0.1.
Using the gradient and learning rate, we update Xo to X1:
X1 = Xo - α * ∇f(Xo) = (2, 1) - 0.1 * [3, 2] = (2, 1) - [0.3, 0.2] = (1.7, 0.8).
In the second iteration, we compute the gradient at the current point X1 = (1.7, 0.8), which is ∇f(X1) = [∂f/∂x1, ∂f/∂x2]. Let's assume we again choose a learning rate α of 0.1.
Using the gradient and learning rate, we update X1 to X2:
X2 = X1 - α * ∇f(X1) = (1.7, 0.8) - 0.1 * [∂f/∂x1, ∂f/∂x2] = (1.7, 0.8) - [0.1 * ∂f/∂x1, 0.1 * ∂f/∂x2].
The above calculations provide the values of X1 and X2 after the first two iterations of the Method of Steepest Descent algorithm for the given function.
Now, let's move on to the second part of your question.
If the initial start point Xo is changed to a different position, it can significantly affect the operation of the algorithm. The Method of Stee
pest Descent aims to find a local optimum of the function, and the starting point plays a crucial role in determining the convergence behavior.
If the new initial point is closer to a local optimum, the algorithm may converge faster as it takes smaller steps towards the optimal point. However, if the new initial point is far from any local optima, the algorithm may take longer to converge or even converge to a different suboptimal point.
The choice of learning rate α also affects the algorithm's performance. A larger learning rate may lead to faster convergence but can also cause overshooting and instability. On the other hand, a smaller learning rate may lead to slower convergence but better stability.
In summary, changing the initial start point xo can affect the convergence behavior and the final solution obtained by the Method of Steepest Descent algorithm. It is crucial to choose an appropriate initial point and learning rate to achieve the desired optimization outcome.
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Crystal reads 25 pages in 1 hour. Write an equation to represent the 2
relationship between the number of pages Crystal reads and how much time she spends reading. Let p = number of pages and t = number of hours.
Answer:
she read 25 pages in 60 minutes
Step-by-step explanation:
hey besties i need sum help with this pls
16Acos(x)-Bsin(x)-2Asin(x)+19Bcos(x)=65cos(x) can someone helps me to find the exactly value of A and B ?
The exact values of A and B that satisfy the equation are A = -65/22 and B = 65/11.
To find the exact values of A and B in the equation 16Acos(x) - Bsin(x) - 2Asin(x) + 19Bcos(x) = 65cos(x), we need to equate the coefficients of the corresponding trigonometric functions on both sides of the equation.
Comparing the coefficients of cos(x) on both sides:
16A + 19B = 65 (Equation 1)
Comparing the coefficients of sin(x) on both sides:
-2A - B = 0 (Equation 2)
We now have a system of two equations with two unknowns (A and B). We can solve this system to find the values of A and B.
Let's solve the system of equations:
From Equation 2, we can express B in terms of A:
B = -2A
Substituting this expression for B in Equation 1:
16A + 19(-2A) = 65
16A - 38A = 65
-22A = 65
A = -65/22
Substituting the value of A back into the expression for B:
B = -2A
B = -2(-65/22)
B = 65/11
Therefore, the exact values of A and B that satisfy the equation are:
A = -65/22
B = 65/11
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Evaluate the double integral where R is the region enclosed by y = x² and y = 9. Answer: I =
Given that R is the region enclosed by y = x² and y = 9. The value of the double integral over the region is I =81.
We are given the region R that is enclosed by y = x² and y = 9.
The x values range from -3 to 3.
The y values range from x² to 9.
We thus evaluate the double integral as follows:
I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dA
I= [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
We integrate the integral with respect to y from x² to 9, and then integrate that expression with respect to x from -3 to 3.
We get: I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
I= [tex]\int_{(-3)}^ {(3)[/tex] (9 - x²) dx
= [tex]\int_{(-3)}^ {(3)} 9 dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[tex]\int_{(0)}^ {(3)} x dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[(3²/2) - (0²/2)] - [(3³/3) - (-3³/3)]
= 18(9/2) - 54
= 81
Answer: I = 81.
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Find the value of the variables in the image above
Answer:
x = 8[tex]\sqrt{3}[/tex] , y = 8
Step-by-step explanation:
Using the sine and cosine ratios in the right triangle and the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 16[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 8[tex]\sqrt{3}[/tex]
----------------------------------------------------------
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{16}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 16 ( divide both sides by 2 )
y = 8
The cartesian product of two sets P and Q can be written as
Answer:
P x Q
Step-by-step explanation:
The Cartesian product of two sets P and Q can be written as,
P × Q.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given:
P and Q are the two sets.
The Cartesian product of two sets P and Q can be written as,
P × Q.
For example,
if A = {1, 2} and B = {3, 4},
then the Cartesian Product of A and B is {(1, 3), (1, 4), (2, 3), (2,4)}.
Therefore, P × Q is the required expression.
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write solutions to the systems of inequalities that should lie on the double- shade region
Answer:
(1,1) (2,2) (1,2) (1,5) (4,4) (4,5)
there are a lot more but those are some.
Step-by-step explanation:
Express 0.80 as a fraction in its simplest form.
Answer:
4/5
Step-by-step explanation:
Answer:
4/5
Step-by-step explanation:
0.8
=8/10
=4/5
What is the MAXIMUM amount of a lien that can be claimed by a subcontractor who notifies the lien agent for a two-family residential property on August 1 that the subcontractor first provided labor and materials on the project on May 1? The subcontractor billed the general contractor for $4,000 per month, through September 30, and was never paid.
The maximum amount of a lien that can be claimed by a subcontractor in thisscenario would be $16,000.
Why is this so ?Since the subcontractor first provided labor and materials on May 1 and continued billing the general contractor until September 30 at a rate of $4,000 per month,the total unpaid amount would be $16,000.
This unpaid amount represents the maximum lien claim that the subcontractor can make against the two family residential property.
A lien is a legal claim or right that allows a creditor tohold property as collateral until a debt is paid.
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5.) What is the mean of the data?
3, 3, 5, 5, 5, 7, 7, 8, 15, 15
Answer:
How to Find the Mean. The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
An archer hits a target 50% of the time. Design and use a simulation to find the experimental probability that the archer hits the target exactly four of the next five times.
MARK AS BRAINLEST FOR THE CORRECT ANSWER
Given:
An archer hits a target 50% of the time.
To find:
The experimental probability that the archer hits the target exactly four of the next five times.
Solution:
It is given that an archer hits a target 50% of the time. It means the probability of hitting the target is
[tex]p=\dfrac{50}{100}[/tex]
[tex]p=0.5[/tex]
The probability of not hitting the target is
[tex]q=1-p[/tex]
[tex]q=1-0.5[/tex]
[tex]q=0.5[/tex]
Binomial distribution formula:
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
We need to find the probability that the archer hits the target exactly four of the next five times. So, [tex]n=5,r=4,p=0.5,q=0.5[/tex].
[tex]P(x=4)=^5C_4(0.5)^4(0.5)^{5-4}[/tex]
[tex]P(x=4)=\dfrac{5!}{4!(5-4)!}(0.5)^4(0.5)^{1}[/tex]
[tex]P(x=4)=5(0.5)^{5}[/tex]
[tex]P(x=4)=0.15625[/tex]
Therefore, the experimental probability that the archer hits the target exactly four of the next five times is 0.15625.
Find the area of the figure below, round your answer to the nearest hundredth. (use
3.14 for 7)
15 ft
25 ft
Step-by-step explanation:
[tex]\pi \times {7}^{2} = 3.14 \times 49 = 153.86 \\ 15 \times 25 = 375 \\ 153.86 + 375 = 523.86 \: {ft}^{2} [/tex]
Which function would be produced by a horizontal stretch of the graph of y = sqrt(x) followed by a reflection in the x - axis ?
Answer:
the answer is the first one
Step-by-step explanation:
Explanation: be im smart
Function transformation involves changing the form of a function
A function that could represent the transformed function is function (c) [tex]f(x) = -\sqrt{\frac 12 x}[/tex]
The equation of the function is given as:
[tex]f(x) = \sqrt x[/tex]
The rule of horizontal stretch is:
[tex](x,y) \to (ax,y)[/tex]
Where:
[tex]0 < a < 1[/tex]
Take for instance:
[tex]a = \frac 12[/tex]
So, we have:
[tex]f(x) = \sqrt{\frac 12 x}[/tex]
Next, the function is reflected in across the x-axis.
The rule of this transformation is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]f(x) = -\sqrt{\frac 12 x}[/tex]
Hence, a function that could represent the transformed function is function (c)
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Ms. Contento buys a BMW with an initial value of $45,000. Yearly, the car's
value depreciates by 5%. How much will the car be worth after 8 yours?
Find the correlation coefficient between x and y
X 57 58 59 59 60 61 62 64
Y 77 78 75 78 82 82 79 81
Answer:
0.603
Step-by-step explanation:
Given the data:
X 57 58 59 59 60 61 62 64
Y 77 78 75 78 82 82 79 81
The Correlation Coefficient, R value gives a measure of the degree of correlation between two variables, the dependent and independent variable. The correlation Coefficient value ranges from - 1 to 1. With negative values depicting a negative relationship and positive values meaning a positive relationship. The closer the R value is to + or - 1, the higher the strength of the relationship. With a value of 0 meaning 'no correlation'.
The correlation Coefficient value of the data above is 0.603, this gives a fairly strong positive correlation
Plzz its urgent answer my question
Answer:
the answer is option (b)
good day mate
find the square root of 8.1 x 10^15
Answer:
9x10^7 is your scienctific notation, which is also 90000000 in expanded form
Order form least to greatest
0.777, 9/11, 5/9, 65%, 0.714, 83.3%, 0.583, 0.5, 0.75, 4/9
Answer:
4/9, 0.5, 0.583, 5/9, 65%, 0.714, 0.75, 0.777, 9/11, 83.3%!
Step-by-step explanation:
Hope this helps
Given –9x2 + 4y2 – 18x + 16y – 29 ≤ 0, which graph represents the inequality?
edge2021
Answer:
C.
Step-by-step explanation:
Edge2021
The graph of the answer is plotted and attached.
What is Inequality?Inequality is the mathematical statement formed when two expressions are joined by an inequality operator.
The inequality is –9x² + 4y² – 18x + 16y – 29 ≤ 0,
The inequality represents a hyperbolic inequality.
The graph of inequality is plotted and attached with the answer.
The shaded portion is the representation of inequality.
The shaded portion shows that the graph is a graph of a hyperbola.
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Sams gym charges a one time fee of $60 plus $32 per Session for a personal trainer. the new gym in town a membership fee of $350 plus $20 for each session with a trainer. which inequality would be used to determine X the number of sessions with a personal trainer where is the new gym is the better deal?
Answer: i think $35
Step-by-step explanation: have a great day
Setup a double integral that represents the surface area of the part of the x2 + y2 + z2 = 8z that lies inside the paraboloid z = x2 + y2
The double integral should be integrated in terms of dr d(theta).
The bounds for the d(theta) integral are from 0 to 2pi.
I know the lower bound for dr is 0 but I cannot get the upper bound.
Please show all work, especially the equation in r and theta being integrated. Thank you!!
The surface area of the part of the x2 + y2 + z2 = 8z that lies inside the paraboloid z = x2 + y2, using the cylindrical coordinates is given as below:
The integral to find the surface area in the cylindrical coordinates, we can write as,
∫∫ dS = ∫∫ r dθ dr The given surface is x2 + y2 + z2 = 8z and the paraboloid is z = x2 + y2
By substituting the value of z from the paraboloid to the first equation,
we get,x2 + y2 + (x2 + y2)2 = 8(x2 + y2) Simplify it by expanding the square term as,
x2 + y2 + x4 + 2x2y2 + y4 = 8x2 + 8y2Now,
re-write the equation as,
x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = 0On
solving this equation, we get
x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0
The equation of the paraboloid is given as, z = x2 + y2Hence,
the integral to find the surface area of the given surface in cylindrical coordinates,
∫∫ dS = ∫∫ r dθ dr Bounds of the integral to find the surface area are 0 ≤ θ ≤ 2π and r1 ≤ r ≤ r2,
where r1 and r2 are the radii of the cylinder.
Solve this equation and get the values of r1 and r2,r2 = 2r1
On solving the quadratic equation of (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0,
we get,
x2 + y2 - 4x - 4y + 4 = 0
The equation of the circle is given as
,x2 + y2 = 4x + 4y - 4 Solve for x and y to get,
x = 2 + cos θ y = 2 + sin θ
The radius of the circle is given as,
√(42 + 42) = √32 Thus,
the limits of integration of r are r1 = 0 and r2 = √32.
Integrating over the limits,
∫0^2π ∫0^√32 r dr dθ= 1/2(32) (2π)= 16πTherefore,
the surface area of the given surface is 16π.
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Write 4^3 using repeated multiplication. Then find the value of 4^3
Susan paints a stack of 30 blocks in a pattern. Starting from the bottom, she paints every 3rd block red and every 5th block green. Wherever red and green land on the same block, she paints that block yellow.
The 3rd block from the bottom that is painted green is how many blocks up from the bottom?
Answer:
20 blocks
Step-by-step explanation: