Which is equivalent to
^3*square root* 8^1/4x ?
pls hurry it’s a timed test

Answer: multiply by the right reciprocal.

NOTE//the reciprocal of an rational number is the Rational Number Obtained after interchanging the Numerator and Denominator is called Reciprocal of a Rational Number.

Step-by-step explanation:

To start, let's sketch the graph of the curve y = x from x = 0 to x = 20. This is simply a diagonal line that passes through the points (0,0) and (20,20), as shown below:

```
   |
20  |    *
   |   *  
   |  *  
   | *    
   |*    
0  --------------
  0   10   20
```

Now, we want to revolve this curve around the x-axis to create a solid shape. Specifically, we want to create a paraboloid, which is a three-dimensional shape that looks like an upside-down bowl.

To find the volume of this paraboloid, we need to use calculus. The basic idea is to slice the solid into very thin disks, and then add up the volumes of all the disks to get the total volume.

To do this, we'll use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the cylinder and h is its height. In our case, each disk is a cylinder with radius r and height h, where:

- r is equal to the y-value of the curve (i.e. r = y = x), since the disk extends from the x-axis to the curve.
- h is the thickness of the disk, which is a very small change in x. We can call this dx.

So, the volume of each disk is:

dV = πr^2dx
  = πx^2dx

To find the total volume of the paraboloid, we need to add up the volumes of all the disks. This is done using an integral:

V = ∫(from x=0 to x=20) dV
 = ∫(from x=0 to x=20) πx^2dx

Evaluating this integral gives us:

V = π/3 * 20^3
 = 8000π/3

So the exact volume of the paraboloid is 8000π/3.

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The given pair of functions, \(x = e^{-2t} + 3e^{6t}\) and \(y = -e^{-2t} + 5e^{6t}\), is a solution to the system of differential equations dx/dt = x + 3y and dy/dt = 5x + 3y on the interval (-∞, ∞).

To verify that the given functions\(x = e^{-2t} + 3e^{6t}\) and \(y = -e^{-2t} + 5e^{6t}\) are a solution to the system of differential equations dx/dt = x + 3y and dy/dt = 5x + 3y, we need to substitute these functions into the equations and check if they satisfy them.

Taking the derivative of \(x = e^{-2t} + 3e^{6t}\) with respect to t, we get \(dx/dt = -2e^{-2t} + 18e^{6t}\). Similarly, the derivative of \(y = -e^{-2t} + 5e^{6t}\) with respect to t is \(dy/dt = 2e^{-2t} + 30e^{6t}\).

Now, let's substitute x and y, as well as their derivatives, into the given system of differential equations. We have:

\(dx/dt = x + 3y\\-2e^{-2t} + 18e^{6t} = (e^{-2t} + 3e^{6t}) + 3(-e^{-2t} + 5e^{6t})\)

Simplifying the above equation, we can see that the left-hand side \((-2e^{-2t} + 18e^{6t})\) is equal to the right-hand side\((e^{-2t} + 3e^{6t} - 3e^{-2t} + 15e^{6t})\). Thus, the equation is satisfied.

Similarly, for the second equation dy/dt = 5x + 3y, we substitute the values:

\(2e^{-2t} + 30e^{6t} = 5(e^{-2t} + 3e^{6t}) + 3(-e^{-2t} + 5e^{6t})\)

By simplifying both sides of the equation, we can observe that the left-hand side\((2e^{-2t} + 30e^{6t})\) is equal to the right-hand side \((5e^{-2t} + 15e^{6t} - 3e^{-2t} + 15e^{6t})\). Thus, the equation is also satisfied.

Therefore, the given functions \(x = e^{-2t} + 3e^{6t}\) and \(y = -e^{-2t} + 5e^{6t}\) are indeed a solution to the system of differential equations dx/dt = x + 3y and dy/dt = 5x + 3y on the interval (-∞, ∞).

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer:

29

Step-by-step explanation:

69/2

To qualify for the second discount, the valuation must've been greater than $100, so 90% of 199.99 = 199.99/100*90 = $179.991. (Price after 1st discount) As well as, yes, you are good enough to qualify for a second discount.

Because the price following the initial discount is greater than $100, it qualifies for the second discount.

After the second 10% discount, the price is 179.991/100*90 = $161.9919.

Savings = 199.99 minus 161.9919 = 37.9981 = 38 dollars saved.

*Please keep in mind that you do not receive a -20% discount from the original price, as it states 10% after the first discount.

The following are five common discount strategies:

Discounts for frequent customers are known as loyalty discounts.

Discounts for buying and selling in a competing item are known as trade discounts.

Cash discounts are rewards for paying with cash rather than credit.

Quantity discounts are incentives to buy more of the same good or service.

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Since sin θ = -√6/2 and θ lies in quadrant IV, we know that cos θ > 0. Using the Pythagorean identity, we have cos^2 θ +\(sin^2\) θ = 1. Plugging in sin θ and solving for cos θ, we get:

cos θ = √(1 - \(sin^2\) θ) = √(1 - 6/4) = √(2/4) = √2/2 = 0.707

Using the identity \(sin^2\) θ +\(cos^2\) θ = 1, we can rewrite the left-hand side of the given identity as:

\(cos^2\) θ - \(sin^2\) θ = cos(2θ)

We can then solve for cos(2θ) by adding sin^2 θ to both sides and factoring:

cos(2θ) =\(cos^2\)θ - \(sin^2\)θ +\(sin^2\) θ

cos(2θ) = \(cos^2\)θ + \(sin^2\) θ

cos(2θ) = 1

Using the identity\(tan^2\) θ + 1 = \(sec^2\) θ, we can rewrite the left-hand side of the given identity as:

\(sin^2\) θ/\(cos^2\) θ + 1 = \(sec^2\) θ/sec^2\(sec^2\) θ

We can then multiply both sides by \(cos^2\)θ to get:

\(sin^2\) θ +\(cos^2\) θ = \(sec^2\) θ

1 = \(sec^2\)θ -\(tan^2\) θ

Since sin α = √6/4 and cos β = √3/2, we can use the identity cos(α + β) = cos α cos β - sin α sin β to get:

cos(α + β) = (√6/4)(√3/2) - (-1/2)(√6/4)

cos(α + β) = (√18 - √6)/8 + (1/8)√6

cos(α + β) = (√18 + √6)/8

Since cos α = -1/2 and sin β = -√3/2, we can use the identity tan(α + β) = (tan α + tan β)/(1 - tan α tan β) to get:

tan(α + β) = (tan α + tan β)/(1 - tan α tan β)

tan(α + β) = ((-1/2) + (-√3/2))/[1 - (-1/2)(-√3/2)]

tan(α + β) = (-√3 - 1)/[2 + √3]

Using the tangent double-angle identity, we have:

tan 2θ = (2 tan θ)/(1 - \(tan^2\)θ)

Since the given figure shows a right triangle with opposite side 2 and adjacent side 1, we have:

tan θ = opposite/adjacent = 2/1 = 2

Plugging this into the double-angle formula, we get:

tan 2θ = (2 tan θ)/(1 -\(tan^2\)θ) = (2(2))/(1 - \(2^2\)) = -8/3

This question was already answered in part 1, where we found that cos θ = √2/2.

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Full Question ;

Use the given information to find the exact value of the expression.

sin α =  5/13, α lies in quadrant II, and cos β =  15/17, β lies in quadrant I Find sin (α - β).

sin α = - 24/25, α lies in quadrant IV, and cos β = - (sqrt21)/5, β lies in quadrant III Find sin (α - β).

sin θ = 8/17, θ lies in quadrant II Find tan 2θ.

tan α =  5/12, α lies in quadrant III, and cos β = - 3/5, β lies in quadrant II Find sin (α + β).

tan θ =  5/12, θ lies in quadrant III Find sin 2θ.

 Express the sum or difference as a product.

cos 2x - cos 4x

sin 2x - sin 4x

Answer:

The watered area is approximately 3783 square feet.

Step-by-step explanation:

The area that is watered due to the rotation of the spankler is a circular section area (\(A\)), whose formula is:

\(A = \frac{\theta }{2}\times \frac{1}{360^{\circ}}\times 2\pi \times d^{2}\)

Where:

\(d\) - Water distance, measured in feet.

\(\theta\) - Rotation angle, measured in sexagesimal degrees.

Given that \(d = 85\,ft\) and \(\theta = 60^{\circ}\), the watered area is:

\(A = \frac{60^{\circ}}{2} \times \frac{1}{360^{\circ}}\times 2\pi \times (85\,ft)^{2}\)

\(A \approx 3783\,ft^{2}\)

The watered area is approximately 3783 square feet.

Answer:176

Step-by-step explanation:

6 times 29.33333333333333

The sewing kits bought by Ms, Clark is 17 in number.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.

Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17

Thus, the sewing kits bought by Ms, Clark is 17 in number.

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Answer:

1

Step-by-step explanation:

The slope can be found using the RISE/RUN equaton.

Looking at both graphs we see that they are parallel so that tells us that they have the same slope.

We can count how many boxes up and then how many boxes right this line goes to find the slope.

We also know that the slope is positive because the lines are increasing from left to right.

The marksman's velocity after firing the gun is about -0.63 m/s (in the opposite direction of the bullet's velocity), as calculated using the conservation of momentum principle.

The conservation of momentum principle can be used to resolve this issue. The initial momentum of the system (marksman plus gun) is zero, and the final momentum is also zero because the bullet and the marksman have equal and opposite momenta. Therefore, we can write:

initial momentum = final momentum

\(0 = (M + m) * V + m * v\)

where M is the mass of the gun, m is the mass of the bullet, V is the velocity of the gun after firing, and v is the velocity of the bullet after firing (which is 181 m/s in this case).

Solving for V, we get:

\(V = - m * v / (M + m)\)

= \(\frac{- 0.014 kg * 181 m/s}{(4.00 kg + 0.014 kg)}\) ≈ -0.63 m/s

Therefore, the marksman's velocity after firing the gun is about -0.63 m/s (in the opposite direction of the bullet's velocity).

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Answer:

144

Step-by-step explanation:

If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}  

If two indistinguishable dice are rolled, it is 3/36 or 1/12.

Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.

The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.

The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12

For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.

Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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To find E(X | Y = y), we need to use the formula for conditional expectation:

E(X | Y = y) = ∑x P(X = x | Y = y) * x

Since each girl sells an average of 30 boxes of cookies, the total number of boxes sold in the troop is Y * 30. We can assume that the number of boxes sold by each girl follows a Poisson distribution with parameter λ = 30. So, the probability of selling x boxes is given by:

P(X = x | Y = y) = e^(-λ) * λ^x / x!

Substituting λ = 30 and simplifying, we get:

P(X = x | Y = y) = e^(-30) * 30^x / x!

Now, we can plug this into the formula for conditional expectation:

E(X | Y = y) = ∑x P(X = x | Y = y) * x

= ∑x e^(-30) * 30^x / x! * x

= e^(-30) * 30 * ∑x (30^(x-1) / (x-1)!)

= e^(-30) * 30 * E(Y)

where E(Y) is the expected number of girls in the troop, which is equal to y. Therefore,

E(X | Y = y) = e^(-30) * 30 * y

This means that if there are y girls in the troop, we can expect to sell an average of 30y boxes of cookies.

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Answer: x= -197/77

Step-by-step explanation:

y=385x+985

substitute y=0

0=385x+985

move the variable to the left

-385x=985

divide both sides

x= -197/77

Answer:

x intercept: 385

y intercept: 958

Step-by-step explanation:

y=385x+985 -> y=mx+b

y = b

y = 985

Answer:

I got 5/16 as my answer

Step-by-step explanation:

I used a calculator to solve the equation :/

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

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Answer:

80,800

Step-by-step explanation:

Answer:

I think C

Step-by-step explanation:

The component form and magnitude of the vector is  < -6, -2>, √ 40, the correct option is A.

A vector is a quantity that needs both magnitude and direction for its representation.

A vector has origin (6, 2) and terminal point (0, 4).

The component of vectors is determined by the formula

<x,y> = < (x₂- x₁ ) , (y₂-y₁)>

<x,y> = < (0-6), (4-2)>

<x,y> = < -6, -2>

The magnitude of the vector is determined by

\(\rm |v| = \sqrt{x^2 +y^2\)

|v| = √ 40

The correct options are  

LeftAngleBracket negative 6, 2 RightAngleBracket and StartRoot 40 EndRoot LeftAngleBracket negative 6, 7 RightAngleBracket and 40 LeftAngleBracket negative 2,6 RightAngleBracket and StartRoot 47 EndRoot LeftAngleBracket negative 2, 6 RightAngleBracket and StartRoot 40

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Step-by-step explanation:

The square root of -1 is defined as i

\( \sqrt{ - 1} = i\)

Answer:

Step-by-step explanation:

The square root of -1 is undefined and has no solutions.

Its i

Answer:

11 units

Step-by-step explanation:

Given that t is on the line su , then

su = st + tu = 6 + 5 = 11

Answer:

it will be the third one 1.29x+1.35y<_12

Answer:  1.29x+1.35y<_12

Answer:

$254

$30 + $14x

Step-by-step explanation:

Jayden:

Guaranteed wage= $30

Tips per table = $14

Number of tables = 16

Total revenue = fixed revenue + variable revenue

Fixed revenue= $30

Variable revenue change with quantity= $14 × number of tables Jayden waits on

Total earnings of Jayden for the day = $30 + $14(16)

= $30 + $224

= $254

When Jayden waits on x number of tables

Total earnings of Jayden for the day = $30 + $14(x)

= $30 + $14x

Where x = number of tables Jayden waits on

Answer:

$254

30 + 14t

Step-by-step explanation:

Answer:

365/1,000 or .365

Step-by-step explanation:

HTH :)

Three hundred sixty five thousand in standard form is 365000.

The standard form of numbers is when we have to write the number in digits according to it's place and face value.

Word form of numbers is that when we have to write numbers given in numerical form to words by determining place and face value.

According to the given question we have to write  three thousand sixty five thousand in standard form.

We know thousand has three zeroes.Suppose we have to write one thousand in standard form which is 1000.

Given we have to write three hundred sixty five thousand in standard form which is 365000.

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