The length of a rectangular prism is 5 more than twice the width w.
The volume of the prism is 2w³ + 7w² + 5w. What is a simplified expression
for the height of the prism?

The coordinates of K such that JK is 2/9 of JL are given as follows:

K(3, -4).

The coordinates of K are obtained applying the proportions in the context of the problem.

Considering that JK is 2/9 of JL, the equation is given as follows:

K - J = 2/9(L - J).

Hence the x-coordinate of K is obtained as follows:

x + 3 = 2/9(24 + 3)

x + 3 = 6

x = 3.

The y-coordinate of K is obtained as follows:

y - 4 = 2/9(-32 - 6)

y - 4 = -8

y = -4.

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The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

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The probability of the influenced voters, if The political scientist randomly surveyed 2509 voters, 709 said the advertisements did influence their vote, is 0.283.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.

Given:

The political scientist randomly surveyed 2509 voters, n = 2509,

709 said the advertisements did influence their vote, S = 709,

Calculate the probability of influenced voter as shown below,

\(Probability = S / n\)

Probability = 709 / 2509

Probability = 0.283

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Answer:

(d). 1/14

(e). -2 11/14

(f). -6.315

Step-by-step explanation:

Answer:

d). 1/14  e). -59/24  f). -6.315

Step-by-step explanation:

d). 1/14

e). -59/24

f). -6.315

We have to determine the exact values of the sine, cosine, and tangent of the angle 11π/12 using the identity pi/4 + 2pi/3. The angles that we'll be working with are 11π/12, pi/4, and 2π/3.

To solve the given problem, we first need to determine the values of sine, cosine, and tangent of pi/4 and 2π/3, which will help us in determining the exact values of these trigonometric functions for 11π/12. The angle 11π/12 can be expressed as pi/4 + 2π/3. Using the identity of pi/4 and 2π/3 we can easily determine the value of sin, cos, and tan of 11π/12.To find the value of sine of 11π/12, we first have to determine the sine values of pi/4 and 2π/3. The sine of pi/4 is √2/2, while the sine of 2π/3 is √3/2.

We can use these values to determine the sine of 11π/12. Similarly, we can use the cosine and tangent of pi/4 and 2π/3 to determine the cosine and tangent of 11π/12.Finally, the exact values of the sine, cosine, and tangent of 11π/12 are:Sin (11π/12) = (√6 - √2)/4 Cos (11π/12) ⇒ (√6 - √2)/4 Tan (11π/12) ⇒ 1

Therefore, we can conclude that the exact values of the sine, cosine, and tangent of the angle 11π/12 are (√6 - √2)/4, (√6 - √2)/4, and 1, respectively.

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The greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6.

This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6. This means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

To calculate the GCF, the prime factors of each number must be determined. The prime factors of 24 are 2 and 3 (2 x 2 x 2 x 3). The prime factors of 48 are 2 and 3 (2 x 2 x 2 x 2 x 3). The prime factors of 18 are 2 and 3 (2 x 3 x 3).

To determine the GCF, the highest power of each prime factor must be determined. In this case, the highest power of each prime factor is 3 (2 x 2 x 2 x 3). Therefore, the GCF of 24, 48, and 18 is 6. This means that the greatest number of baskets that can be made with the given items is 6.

In conclusion, the greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6. This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6, which means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

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Step-by-step explanation:

hope this helpsssssssss

Answer:

SSS (Or Side-Side-Side) is a theorem uses to proove congruency in triangles. In the following picture, we can tell that line AB = CD. We can also tell that line BC = AD. And because both triangles share the line BD, we can use the reflexive property and define line BD = BD. That is how we know that ΔABD + ΔCDB

(PLEASE MARK ME AS BRAINLIEST!)

Answer:

∠ ADB = 29°

Step-by-step explanation:

∠ ADB + ∠ BDC = ∠ ADC , that is

53° + ∠ BDC = 82° ( subtract 53° from both sides )

∠ BDC = 29°

Answer:

the value of BDC(angle on D) is 29

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Step-by-step explanation:

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Answer:

20 minutes

Step-by-step explanation:

Answer:

How  do I have the same problem as a high schooler when im in 6th grade

Step-by-step ex

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The average speed during the interval between 1 second and 2 seconds is most nearly 8 m/s, which corresponds to option (E).

To determine the average speed during the interval between 1 second and 2 seconds, we need to find the displacement of the object during that time interval and divide it by the duration.

Looking at the graph, we can observe that the object's position increases from approximately 0 meters at 1 second to approximately 8 meters at 2 seconds.

Therefore, the displacement is 8 meters - 0 meters = 8 meters.

The duration of the time interval is 2 seconds - 1 second = 1 second.

To calculate the average speed, we divide the displacement by the duration:

Average speed = Displacement / Duration = 8 meters / 1 second = 8 m/s.

Therefore, the average speed during the interval between 1 second and 2 seconds is most nearly 8 m/s, which corresponds to option (E).

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Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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Answer:

what? im hungry too..... and the photo is blurry

Answer:

Hungry too gonna go eat

Step-by-step explanation:

Continuous Loss Function: Uniform Distribution Given that the loss value (Y) follows the uniform distribution with a minimum value of $3K and a maximum value of $4K, i.e., U(3000, 4000). We have to find the VaR_a=0.9(Y) using the loss function.

Now, the probability distribution function of the uniform distribution is given by:$$f(x)=\frac{1}{b-a}$$$$f(x)=\frac{1}{4000-3000}$$$$f(x)=\frac{1}{1000}$$ Since VaR is the loss corresponding to a particular percentile, the first step is to find the percentile value. The percentile value for 0.9 is given by:$$p = L + \left(\frac{n}{100}\right)C$$where, L = Lower limit of the interval containing the percentile n C = Cumulative frequency of the class interval in which the percentile lies n = Total number of values

Let's calculate n C:$$nC = 0.9\times n = 0.9\times1=0.9$$ Since there is only one observation, we can say that the observation itself corresponds to the percentile for VaR_0.9. Therefore, VaR_0.9 is $4K$.Hence, the answer is: VaR_a=0.9(Y) = $4K$. We have given the loss function that is the uniform distribution, and we have to find VaR_a=0.9(Y). To solve the problem, first, we find the probability distribution function of the uniform distribution. Then we need to calculate the percentile value for 0.9. The percentile value is given by L + (n/100)C. After calculating nC, we get the value of 0.9. Since there is only one observation, the observation itself corresponds to the percentile for VaR_0.9. Therefore, VaR_0.9 is $4K. The concept of VaR or Value at Risk is commonly used in finance, risk management, and investing. It is defined as the loss level that is likely not to be exceeded in a given period of time with a certain level of confidence. VaR is expressed in monetary terms, and it indicates the potential loss amount beyond which the investors or financial institutions would not like to proceed.

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Answer:

Step-by-step explanation:

90

Based on the information, the value of the piano after 16 years is $140.74.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Using this formula to find the value of the piano, v, after t years.

CP = Principal(1-rate)\(^t\)

Where:

Principal=$5,000

Rate=20%

Number of year = 16 years

Let plug in the formula;

=5,000(1-0.20)^16

=5,000(.80)^16

=$140.737

= $140.74 (Approximately)

Hence, the value of the piano after 16 years is; $140.74.

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The new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

(a) The values of E(θ^1) and E(θ^2) are unknown without further information. Being unbiased estimators means that, on average, they provide estimates that are equal to the true population parameter θ. Therefore, we have:

E(θ^1) = θ

E(θ^2) = θ

(b) To find the expectation E(θ^3), we can use the linearity property of expectations:

E(θ^3) = E(aθ^1 + (1 - a)θ^2)

Since θ^1 and θ^2 are unbiased estimators, their expectations are equal to θ:

E(θ^3) = E(aθ^1 + (1 - a)θ^2) = aE(θ^1) + (1 - a)E(θ^2)

Using the values from part (a), we have:

E(θ^3) = aθ + (1 - a)θ = θ(a + 1 - a) = θ

Therefore, the new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

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Answer:

Mean: 33.3

SD: 32.8

Step-by-step explanation:

Answer:

$315

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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The angle between vectors A and B is approximately 89.78 degrees.

To find the angle between vectors A and B, we can use the dot product formula:

A · B = |A| |B| cos(θ)

Given that Ā· B = 4 and knowing the magnitudes of vectors A and B:

|A| = √(22² + 33²)

    = √(484 + 1089)

    = √(1573)

    ≈ 39.69

|B| = √((-1)² + 23² )

    = √(1 + 529)

    = √(530)

    ≈ 23.02

Substituting the values into the dot product formula:

4 = (39.69)(23.02) cos(θ)

Now, solve for cos(θ):

cos(θ) = 4 / (39.69)(23.02)

cos(θ) ≈ 0.0183

To find the angle θ, we take the inverse cosine (arccos) of 0.0183:

θ = arccos(0.0183)

θ ≈ 89.78 degrees

Therefore, the angle between vectors A and B is approximately 89.78 degrees.

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The probability that a junior is taking physics, given they are in Algebra II, is approximately 0.3846 or 38.46%.

1. First, let's find the number of juniors taking only Algebra II and not physics. We do this by subtracting the number of juniors taking both courses from the total number of juniors taking Algebra II:
  468 (Algebra II) - 180 (both courses) = 288 (only Algebra II)

2. Now, we have two groups of juniors enrolled in Algebra II:
  - 288 juniors taking only Algebra II
  - 180 juniors taking both Algebra II and physics

3. Since we want to find the probability that a junior is taking physics, given they are in Algebra II, we'll focus on the group taking both courses.

4. To calculate the probability, divide the number of juniors taking both courses by the total number of juniors taking Algebra II:
  Probability = (number of juniors taking both courses) / (total number of juniors in Algebra II)
  Probability = 180 / (288 + 180)
  Probability = 180 / 468
  Probability ≈ 0.3846 or 38.46%

So, if one of the 650 juniors was picked at random and we know they are in Algebra II, the probability that they are also taking physics is approximately 38.46%.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The lengths of the diagonals are 13.23 and 26.46 centimetres.

The area of rhombus is given by the formula -

Area of rhombus = product of diagonals/2

Let us assume one diagonal to be x centimetres. Then, the another diagonal will be 2x centimetres. Now keeping the values in formula to find the value of area of rhombus.

175 = (x × 2x)/2

Cancelled the number 2 and rearranging the equation

x² = 175

x = ✓175

Taking square root on Right Hand Side of the equation

x = 13.23 centimetres.

Length of second diagonal = 2 × 13.23

Length of second diagonal = 26.46 centimetres

Hence, the length of diagonals is 13.23 and 26.46 centimetres.

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Answer:

it should be 10x+3y=30 if im not mistaken

Step-by-step explanation:

you just add straight down with corresponding variables

The length of the instrument storage closet will be 15ft

Given the dimension of Mr. Miller’s band room is 50 ft wide and 75 ft long. In order to get an instrument storage closet that has the same proportions of length and width but is smaller, we can multiply the width and the length by a scale factor.

Using the scale factor of 1/5, the new dimension will be expressed as:

Hence the length of the instrument storage closet will be 15ft

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Answer:

j = -15/8

Step-by-step explanation:

Here, we want to find the value of j

-3/4j = 3/5 - 1/5

-3/4j = 2/5

4j * 2 = -3 * 5

8j = -15

j = -15/8

a

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Answer:

c as it is on a straight line

Answer:

C. 2x + 58 = 180

Step-by-step explanation:

Not 100% sure but I hope this helps you!