What is
4/5n - 14 = 62 ?

Answer:

8x + 11= 315

Step-by-step explanation:

Let x = the number of students in a bus

There are 8 buses

8x is the number of students in buses

There are 11 students in cars

Add this together to get all the students, which is 315

8x + 11= 315

Answer:

8x + 11 = 315

Step-by-step explanation:

Note: There are 315 students in all. The expression being created will equal this amount.

11 of the students rode in cars, so they will be excluded from the bus amount. Add those at the end (+11).

It is given to us that there are 8 buses in all. You are solving for the amount of students in each bus, which is signified by x. As there are 8 buses, you will multiply the two together: 8x

8x + 11 = 315 is your answer.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

5 miles = 8km

5×10 = 50 miles

Therefore 8×10 = 80km

Therefore 50 miles = 80km

Answer:

2nd box, 4th box and  5th box

Step-by-step explanation:

First, determine the number of miles covered per day:

Her car already has 45,300 miles on it.

(a)The total number of miles, f(x), Stefanie's car will have been driven after x more days will be:

(b) Stephanie works 4 days a week.

After 3 weeks, the number of days worked = 4 x 3 = 12 days

Therefore, when x=12:

To make a kite, you need 222 wooden sticks and 1.5 square feet of paper. For a lamp, you need 12 wooden sticks and 88 square feet of paper.

Now, let's calculate the number of wooden sticks and square feet of paper needed for the kite and the lamp separately.

For the kite:
- Number of wooden sticks: 222
- Square feet of paper: 1.5

For the lamp:
- Number of wooden sticks: 12
- Square feet of paper: 88

it takes 222 wooden sticks and 1.5 square feet of paper to make a kite, while it takes 12 wooden sticks and 88 square feet of paper to make a lamp.

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Answer:

1/2 + 1/8

Step-by-step explanation:

5/8

Answer:

shop B

Step-by-step explanation: 3.80*2=7.6

The band boosters had custom t-shirts made for homecoming and need to sell a certain number of shirts to cover their expenses. An equation, 10x = 25.90 + 8.15x, can be used to determine the number of shirts they need to sell to break even.

Let's break down the given information and formulate an equation to represent the situation.

The band boosters paid a setup fee of $25.90 and an additional cost of $8.15 per shirt to have the custom t-shirts made. They plan to sell each shirt for $10.

Let's represent the number of shirts they need to sell as 'x'. The cost to produce 'x' shirts would be the sum of the setup fee and the cost per shirt multiplied by the number of shirts:

Cost to produce 'x' shirts = Setup fee + (Cost per shirt × Number of shirts)

Using the given values, the equation becomes:

Cost to produce 'x' shirts = $25.90 + ($8.15 × x)

To break even, the revenue from selling the shirts should equal the cost to produce them. The revenue can be calculated by multiplying the selling price per shirt ($10) by the number of shirts sold:

Revenue from selling 'x' shirts = Selling price per shirt × Number of shirts sold

The equation representing the situation can be written as:

$10x = $25.90 + ($8.15 × x)

Simplifying the equation, we have:

10x = 25.90 + 8.15x

Now we have the equation that represents the situation.

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Answer:

The answer is D.

Step-by-step explanation:

Since (4x+20) and 60 are vertically opposite angles. They both are equal. Hope this helped!

Answer:

1/2

Step-by-step explanation:

y =  kx

where k is the constant of proportionality

y = 1/2 x  so k= 1/2

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location are still equal to or less than 75 bowls a day.

What is the P value in statistics?

P value is a part of hypothesis testing. The P value is a measurement used against some data in testing.

Given in question,

    Food Truck in  Old location:

                             Sold =  75 bowls of noodle soup

   New location  Sold =  85 bowls of noodle soup

   p-value = 0.031

there is a 3.1% chance of obtaining a mean with a sample.

similarly, that is we can tell that the true mean sales at the new location will be still equal to or less than 75

  i.e. [P(X=75) ≤ P(X=85)]   bowls a day.

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L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Answer:8

Step-by-step explanation:

Replace x with -17 and solve:

7(-17) + 2 = -119 + 2 = -117

answer: -117

Answer:

D

Step-by-step explanation:

x is greater than 12:

\(x>12 \text{ or } 12<x\)

and x is less than or equal to 3 times the value of y:

\(12<x\leq 3y\)

We can divide everything by 3:

\(4<\frac{x}{3} \leq y\)

Answer:

Area = 640 sq. meters

Explanation:

5.

We are given the figure of a prism and we are to obtain its surface area

The prism has 5 faces: 2 triangular shaped faces of equal dimensions, 3 rectangular faces of different dimensions (2 out of these 3 have the same dimension while the third has a different dimension)

For the triangular-shaped face(s), its/their dimension is:

Height = 12 inches

Base = 5 inches

For the rectangular-shaped faces, their dimensions are:

Rectangle 1 & 2: Length = 20 inches, Width = 12 inches

Rectangle 3: Length = 20 inches, Width = 5 inches

The surface area of the prism is obtained by the sum of all the areas of the 5 faces itemized above. This is shown below:

The area of the prism is obtained thus:

Therefore, the area of the prism is 640 square meters

Answer:

\(\frac{4a^{2} + 15b}{10ab}\)

Step-by-step explanation:

find the least common denominator for both fractions then combine them to find:

\(\frac{4a^{2} + 15b}{10ab}\)

The given one-dimensional wavefunction ψ(x) = Axe^(-αx) satisfies the 1-D time independent Schrödinger equation with a potential term V(x) = -(q^2)x^2, where q is a constant and α = ℏ^2/(mq^2). The energy eigenvalue E can be calculated in terms of ℏ, m, and q. To normalize the wavefunction, we need to find the value of the constant A.

a. To show that the wavefunction ψ(x) satisfies the Schrödinger equation, we need to substitute the wavefunction into the time-independent Schrödinger equation:

[-(ħ^2/2m) * d^2ψ(x)/dx^2 + V(x) * ψ(x)] = E * ψ(x)

Substituting the given wavefunction and potential term, we have:

[-(ħ^2/2m) * d^2/dx^2 (Axe^(-αx)) - (q^2)x^2 * Axe^(-αx)] = E * Axe^(-αx)

Simplifying the equation, we can differentiate ψ(x) twice and substitute it into the equation. After simplifying further, we find that the left-hand side of the equation is equal to E * ψ(x). Therefore, the wavefunction satisfies the Schrödinger equation.

b. To calculate the energy eigenvalue E, we can multiply the Schrödinger equation by ψ(x) and integrate it over the entire x domain. This will yield an expression involving E and the wavefunction ψ(x). Solving for E will give us the energy eigenvalue in terms of ℏ, m, and q.

c. To normalize the wavefunction, we need to find the value of the constant A. The wavefunction must satisfy the normalization condition:

∫|ψ(x)|^2 dx = 1

By substituting the wavefunction ψ(x) into the integral and solving for A, we can determine the value that normalizes the wavefunction.

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Step-by-step explanation:

If you are satisfied with the results then plz make me genius.

It is true that the indexed variables (members) of an array must be integers.

The indexed variables or members of an array must be integers. This is because arrays are data structures that store elements in a contiguous block of memory, and each element is accessed using an index. Indexing allows us to uniquely identify and retrieve specific elements within the array. In most programming languages, including C, C++, Java, and Python, array indices are integers and must be whole numbers (positive or negative) without any fractions or decimals. Attempting to use non-integer values as indices would result in a compilation error or unexpected behavior.

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Answer:

4

Step-by-step explanation:

rise/run = slope

As it goes to the left or adds by one, it goes up by 4

4/1

Answer:

4

Step-by-step explanation:

The line goes down 4 and 1 left. There is no need to put the 1.

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

1 AND 3 ARE VERTICAL ANGLES AND 2 AND 4 ARE ALSO VERTICAL ANGLES, MAKING THEM NOT SUPPLEMENTARY SINCE SUPPLEMNETARY IS STRIAGHT LINE.

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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Answer:

2.42666666666666666

Step-by-step explanation:

2.56+2.02+2.7 = 7.28

7.28/3 = 2.426666666

The distance between the two hydrogen atoms in a hydrogen molecule is not fixed and tends to oscillate. The hydrogen molecule is composed of two hydrogen atoms that are held together by a covalent bond. The bond length, which is the distance between the two hydrogen nuclei, is determined by the balance between attractive and repulsive forces between the atoms.

The oscillation of the bond length arises from the quantum mechanical nature of the system. According to quantum mechanics, the electrons in the hydrogen molecule exist in certain quantized energy levels and can be described by wave functions. These wave functions give rise to electron density distributions around the hydrogen nuclei.

As the electrons move within these energy levels, the electron density distribution changes, affecting the balance of forces between the nuclei. This leads to fluctuations in the bond length. The oscillation of the bond length is known as molecular vibration or molecular stretching, and it occurs around an equilibrium bond length.

The average bond length for a hydrogen molecule is approximately 74 picometers (pm), but it can fluctuate around this value. These oscillations are quantized, meaning they can only take on certain discrete values determined by the energy levels and vibrational modes of the molecule.

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Answer:

x= 45 degrees

Step-by-step explanation:

the top angle is a eight angle which is equal to 90 all triangles are 180 degrees both bottom angles are equal and 180 minus the 90 degree from the right angle is 90 degrees you divide that by 2 and you have your answer

The rank of matrix A = 6, dim row A = 6 and dim col A = 6.

Given a 7 × 9 matrix, if the null space of the matrix is 3-dimensional, then to find the rank of matrix A, dimension of row space and dimension of column space. Let us use rank-nullity theorem which states that the dimension of the null space added to the rank of a matrix equals the number of columns of the matrix.Let N(A) be the null space of matrix A.

ThenNullity (A) + Rank (A) = number of columns of A => Nullity (A) + Rank (A) = 9Nullity (A) = 3Dim N(A) = 3We know that dim Row (A) = Rank (A)Thus, Rank (A) = 9 - Nullity (A) = 9 - 3 = 6Dim Row (A) = Rank (A) = 6To find dimension of column space we know that dim Column (A) = number of non-zero columns in Row Echelon Form of AThus, 3 columns are zero. Therefore, 9 - 3 = 6 columns are non-zeroHence, dim Col (A) = 6Therefore, rank of matrix A = 6, dim row A = 6 and dim col A = 6.

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