The volume of a rectangular prism is 6,142.5 cm3. If the height is 16.25 cm and the length is 28 cm, what is the value of the width?

13.125 cm
13.25 cm
13.5 cm
13.75 cm

The derivative of U with respect to x is A1 x/(x²+y²).

In order to find the value of dU/dx, we need to differentiate U with respect to x.

As A0 and A1 are constants, they will remain the same after differentiation.

Therefore, dU/dx = d/dx (A1 ln (√x²+y²))

Here, we will use the chain rule.

So, the derivative of ln(√x²+y²) is (1/√x²+y²) d/dx (√x²+y²).

Applying chain rule, d/dx (√x²+y²) = (1/2) (x²+y²)^(-1/2) .

2x = x/(√x²+y²)

Therefore, dU/dx

= d/dx (A1 ln (√x²+y²))

= A1 (1/√x²+y²) d/dx (√x²+y²)

= A1 (1/√x²+y²) . (x/(√x²+y²))

= A1 x/(x²+y²)

Learn more about chain rule here:

https://brainly.com/question/28972262

#SPJ11

Since the distribution of number of heads in 100 flips is a binomial distribution, it is not practical to create a histogram with 100 bars. However, we can use the Normal approximation to the binomial distribution because n=100 is a large value. We know that the mean of the binomial distribution is μ = np = 100 * 0.5 = 50, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(100 * 0.5 * 0.5) = 5.

To find the probability of getting between 40 and 60 heads, we can use the Normal distribution and standardize the values. Let X be the number of heads in 100 flips, then we can write:

P(40 ≤ X ≤ 60) = P((40 - μ)/σ ≤ (X - μ)/σ ≤ (60 - μ)/σ)

= P(-2 ≤ Z ≤ 2), where Z is a standard Normal random variable

Using a Normal distribution table or calculator, we find that the probability of Z being between -2 and 2 is approximately 0.9544. Therefore,

P(40 ≤ X ≤ 60) = P(-2 ≤ Z ≤ 2) ≈ 0.9544

So the probability of getting between 40 and 60 heads is approximately 0.9544.

Answer:

25+3x simplified

Step-by-step explanation:

HOPE THIS HELPS YOU OUT! BE THE FIRST TO COMMENT /FREE ON THESE COMMENTS TO GET A FREE BRAINLIY AWARD! PLZ ALSO CONDISER MARKING ME BRAINLIEST AND THANKS! MY JOURNEY HAS JUST BEGAN ON BRAINLY SO ASK ME IF U HAVE ANY QUESTIONS! -BEACHVIBES23

The new coordinates after a reduced scale factor of 0.77 with the origin will be equal to (−10, 10), (20, 40), (30, 30). Hence, option B is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the data given in the question,

We will combine the x and y dimensions even by scale factors to shrink the picture by a multiplier of 0.77 with both the origins as that of the center of dilatation because the figure's vertices are (-13, 13), (26, 52), and (39, 39).

So, the first point is (-13, 13)

-13 × 0.77 = -10 and,

13 × 0.77 = 10

So, the new point is (-10, 10).

The second point is (26, 52).

26 × 0.77 = 20

52 × 0.77 = 40

So, the new point is (20, 40)

The third point is (39, 39)

39 × 0.77 = 30

39 × 0.77 = 30

So, the new point is (30, 30).

To know more about Graph:

https://brainly.com/question/17267403

#SPJ1

Answer:

y=-1x-6

Step-by-step explanation:

do you need a explanation aswell?

Answer: a rotation about point A

Step-by-step explanation:

The rigid transformation would map ΔAQR to ΔAKP is rotation about point A.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have to transform ΔAQR to ΔAKP.

We know that,

Point A is invariant, so we that it cannot be rotation about point R.

Also, the orientation is same then reflection is not happening here.

So, there is rotation about the point A.

Learn more about Transformation here:

https://brainly.com/question/11990146

#SPJ5

Answer:

its easy

use this formula

the right one is the solution of question number 1

Step-by-step explanation:

At first, we will change the root fourth to an exponent 1/4

Each term inside the bracket will take the exponent 1/4

567 = 81 . 7

We will multiply the exponents of x and the exponent of y

1st step: 3rd one

2nd step: 1st one

3rd step: 6th one

4th step: 2nd one

5th step: 5th one

6th step: 8th one

7th step: 7th one

8th step: 4th one

The greater principal is there for Account A as $400.

Simple interest can be defined as a type of interest where the rate is applied on the same principal.

Given that,

The interest for Account A is $15.75 and Account B is  $28.

The total time for interest is 21 months.

Rate of interest for Account A is  3% and Account B is 4%.

Now, the time period can be written in years as,

21 months = 21 / 12 years

                  = 7 / 4

Suppose the principal for Account A and Account B is P₁ and P₂ respectively.

The formula for simple interest is given as,

(P × r × t) / 100

Substitute the respective values for both the accounts to get,

For Account A,

15.75 = (P × 3 × 7 / 4) / 100

⇒ P = (1575 × 4) / (3 × 7)

⇒ P = 300

For Account B,

28 = (P × 4 × 7 / 4) / 100

⇒ P = 2800 / 7

⇒ P = 400

Hence, Account B had greater principal.

To know more about simple interest click on,

https://brainly.com/question/25845758

#SPJ1

Answer:

B-a population growth of 3% each year

Step-by-step explanation:

The 1.03 would mean that the exponential function is increasing by 3% every year because it is 0.03 units above 1.

The sum of the perimeters of all squares is 80 ft.

What is perimeter?

Perimeter is the distance around the outer boundary of a two-dimensional shape, such as a rectangle, square, triangle, or circle. It is the total length of all the sides of the shape.

Starting with a square with a perimeter of 40 ft, we can find the length of one side by dividing the perimeter by 4:

\(\frac{40ft}{4} = 10ft\)

So, the original square has a side length of 10 ft.

Connecting the midpoints of the sides of this square creates a new square with half the side length of the original square. Each side of this new square is the hypotenuse of a right triangle with legs equal to half the side length of the original square (i.e., 5 ft).

Using the Pythagorean theorem, we can find the length of each side of the new square:

\(s^2 = (5 ft)^2 + (5 ft)^2\)

\(s^2 = 50 ft^2\)

\(s = \sqrt{50}ft\)

So, the second square has a side length of \(\sqrt{50}ft\), which is approximately 7.07 ft.

Continuing this process, each subsequent square will have half the side length of the previous square. Therefore, the side length of the third square will be half the side length of the second square, which is:

\(\frac{1}{2}\) * \(\sqrt{50}ft\) = \(\sqrt{25}ft\) = 5 ft.

The side length of the fourth square will be half the side length of the third square, which is: \(\frac{1}{2}\) * 5 ft = 2.5 ft. And so on.

The perimeters of the squares are:

The perimeter of the first square is 40 ft.

The perimeter of the second square is 4 * \(\sqrt{50}ft\), which is approximately 28.28 ft.

The perimeter of the third square is 4 * 5 ft = 20 ft.

The perimeter of the fourth square is 4 * 2.5 ft = 10 ft.

We can see that the perimeter of each subsequent square is half the perimeter of the previous square. So, the series for the perimeters of the squares is a geometric series with a first term of 40 ft and a common ratio of 1/2.

Using the formula for the sum of an infinite geometric series, we can find the sum of the perimeters of all squares:

S = a / (1 - r)

where a is the first term (40 ft) and r is the common ratio (1/2). Plugging in these values, we get:

S = 40 ft / (1 - 1/2)

S = 80 ft

Therefore, the sum of the perimeters of all squares is 80 ft.

To learn more about perimeter visit:

https://brainly.com/question/25092270

#SPJ1

False. A homogeneous system of equations is a system of equations that contain only one variable and all terms are the same. If the system has a solution, it will be consistent.

A homogeneous system of equations is a system of equations where all the equations contain only one variable and all the terms are the same. For example, the system of equations 2x + 3y = 0 and 4x + 6y = 0 is an example of a homogeneous system. In order for a system of equations to have a solution, it must be consistent. A consistent system of equations means that when the equations are solved, all the variables will have a unique solution. If the system of equations is inconsistent, this means that there is no solution for all the variables. An inconsistent homogeneous system of equations means that there is no solution for the equations, regardless of how many equations there are in the system. An example of an inconsistent homogeneous system of equations is 2x + 3y = 0 and 4x + 6y = 1. As there is no solution for both equations, the system is considered to be inconsistent. Therefore, it is false that a homogeneous system of equations can be inconsistent.

Learn more about variable here

brainly.com/question/29583350

#SPJ4

This inequality means that the sum of "d" and "c" must be greater than or equal to 12.

What is algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's represent the number of drinks Olivia buys as "d", and the number of candies as "c".

We know that Olivia must buy no less than 12 drinks and candies altogether. This means that the total number of drinks and candies purchased, d + c, must be greater than or equal to 12.

So the inequality that represents the possible values for the number of drinks purchased and the number of candies purchased is:

d + c ≥ 12

This inequality means that the sum of "d" and "c" must be greater than or equal to 12. For example, Olivia could buy 8 drinks and 4 candies, or 6 drinks and 6 candies, or 10 drinks and 2 candies, and so on, as long as the total number of drinks and candies is 12 or more.

Therefore, This inequality means that the sum of "d" and "c" must be greater than or equal to 12.

To learn more about Algebraic expression from given link.

https://brainly.com/question/953809

#SPJ1

Answer:

Step-by-step explanation:

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint. In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0.

Answer:

slope = - \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (8, - 8 ) ← 2 ordered pairs from the table

note that any 2 ordered pairs may be used to calculate m

m = \(\frac{-8-1}{8-2}\) = \(\frac{-9}{6}\) = - \(\frac{3}{2}\)

The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

To know more about prism visit: brainly.com/question/21308574

#SPJ4

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

-6 is the slope of the line

Answer:

1.5/2 or 75%

Step-by-step explanation:

3/2=1.5

4/2=2

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

To learn more about harmonic oscillator click here: brainly.com/question/13152216

#SPJ11

x = 65

y = 71

z = 44

x is 65 because the two angles are vertices.

z is 44 because the unknown angle beside z and the vertice of x are corresponding angles.

So the unknown angle is 65

therefore, 180 - 71 - 65 = 44

finding y is easy now because two angles of the triangle are already figured out

180 - x - z = y

180 - 65 - 44 = y

y= 71

Hope this helps, I suck at explaining and also bad at English cuz I'm asian.

The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

Learn more about finding relationship between variables here:

https://brainly.com/question/4219149

#SPJ1

The probability of a randomly selected student being tall but not very tall is 41/104. This can be solved by the concept of Probability.

To find the probability of a randomly selected student being tall but not very tall, we need to first determine the total number of students and then calculate the probability.

Determine the total number of students
Add up the number of students in each category:
Very short: 45
Short: 60
Tall: 82
Very tall: 21

Total students = 45 + 60 + 82 + 21 = 208

Calculate the probability
Now, we need to find the probability of selecting a tall student who is not very tall. This means we will focus on the 'tall' category, which has 82 students.

Probability = (number of tall students) / (total number of students) = 82/208

Simplify the probability
Divide both the numerator and the denominator by their greatest common divisor to simplify the fraction:

Probability = 82/208 = 41/104

So, the probability of a randomly selected student being tall but not very tall is 41/104.

To learn more about probability here:

brainly.com/question/30034780#

#SPJ11

Answer:

-25

Step-by-step explanation:

Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

x= 6 x= 1

Step-by-step explanation:

hope this helps..........

(a)  n = 10, p = 1/4, and x = 5. Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)

(b) P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)

Here n = 10, p = 1/4, and x = 5.Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)

Find P(More than 3)For this, we need to calculate P(4), P(5), P(6),...,P(10) and add them.Using the formula of binomial probability function,P(4) = 10C4 * (1/4)^4 * (3/4)^6 = 0.2503 (rounded to three decimal places)P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)P(6) = 10C6 * (1/4)^6 * (3/4)^4≈ 0.0014 (rounded to three decimal places)P(7) = 10C7 * (1/4)^7 * (3/4)^3≈ 0.0001 (rounded to three decimal places)P(8) = 10C8 * (1/4)^8 * (3/4)^2≈ 0.0000 (rounded to three decimal places)P(9) = 10C9 * (1/4)^9 * (3/4)^1≈ 0.0000 (rounded to three decimal places)P(10) = 10C10 * (1/4)^10 * (3/4)^0≈ 0.0000 (rounded to three decimal places)P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)

Learn more about Binomial probability

brainly.com/question/29350029

#SPJ11

Answer:

If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.

Step-by-step explanation:

yw;)

Answer:

40

Step-by-step explanation:

No. Of Meal=Budget/price of Meal

=800/ 20

=40

Answer: 55°

Step-by-step explanation:

∠YAZ + ∠YAX = 180° because they are linear pairs

∠YAZ + ∠YAX = 180°

∠YAZ + 125 = 180

Subtract both sides by 125

∠YAZ = 55°

Hope that helped!

Answer:

it would be 10

Step-by-step explanation: