What is the slope of the line that contains the points (-1, 2) and (4, 3)?
A. -5
B. -1/5
C. 1/5
D. 5

Answer:

1.99 x 10 ^20 N

Step-by-step explanation:

Just substitute in the values given

F = (6.67x 10^-11) * (5.97x10^24)(7.36 x 10^22)  / ( 3.84 x 10^8) ^2

  = 1.99 x 10^20  N

Answer:

6x-24

Step-by-step explanation:

First, we must add x-12 to 2x. We will get 3x-12. Now, to get the perimeter, we must multiply that expression by 2. The answer is 6x-24.

Answer:

4

Step-by-step explanation:

a²+b²=c²

|BD|²+|AC|²=|AB|²

|BD|²+3²=5²

|BD|²+9=25

|BD|²=25-9

|BD|²=16

then you root both sides

therefore |BD|=4

The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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The limit of the fraction as x approaches 3 is 4.

We can use algebraic manipulation to simplify the fraction.

StartFraction x squared minus 12 Over x squared minus 3 x EndFraction

= StartFraction x squared minus 12 Over x squared minus 3 x EndFraction x squared

= StartFraction x squared minus 12 x squared Over x squared times x squared minus 3 x EndFraction

= StartFraction x squared times x squared minus 12 x squared Over x squared times x squared minus 3 x EndFraction

= StartFraction x to the fourth minus 12 x squared Over x squared times x squared minus 3 x EndFraction

Now we can plug in x = 3 to get the limit:

= StartFraction 3 to the fourth minus 12 x 3 squared Over 3 squared times 3 squared minus 3 x EndFraction

= StartFraction 81 - 36 Over 27 - 9 EndFraction

= StartFraction 45 Over 18 EndFraction

= 4

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The solution is, the simplification of 1-|0.2-(m-3)+1/4|=0 is m = 2.45.

We know that,

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

1-|0.2-(m-3)+1/4|=0

or, 1 = |0.2-(m-3)+1/4|

or, 1 - 1/4 = 0.2-(m-3)

or, 3/4 = 0.2-(m-3)

or, m-3 = -0.55

or, m = 2.45

Hence, The solution is, the simplification of 1-|0.2-(m-3)+1/4|=0 is m = 2.45.

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Answer:

distributive property

Step-by-step explanation:

3(2+7)=3(2)+3(7)

We are distributing the 3 to both terms in the parentheses so we are using the distributive property

Answer:

48 feet.

step-by-step explanation:

using Pythagoras theorem:

a² + b² = c²

h² + 55² = 73²

h² = 73² - 55²

h² = 5329-3025

h² = 2304

h = √2304

h = 48

Answer:

x = 48 ft

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for x:

⇒ x² + 55² = 73²

⇒ x² + 3025 = 5329

⇒ x² = 5329 - 3025

⇒ x² = 2304

⇒ x = ±√2304

⇒ x = ±48

Since distance is positive, x = 48 ft

Answer:

I think rotation and reflecting

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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Answer:

82.47

Step-by-step explanation:

.93n = 80

n = 80/.93

n = 82.47

the probability that if 3 donations are made, all of them can be safely used in a blood transfusion on someone with type A blood is 0.1373

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

The Three Kinds of Probability

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency

Given

49% type O blood

27% type A blood

20% type B blood

4% type AB blood

Then, the probability is:

(0.27)³ + (0.49)³ = 0.1373

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First let's review the area formula for a circle.

Area=π\(r^2\)

Now that we know the radius, r is 10. The area is

10*10*π=100π

I will approximate π to 3.14 although you could do it more precise or less precise. The final answer will be 100*3.14=314 squared centimeter.

Any question you have about this just ask in the comment of this answer :)

Answer:

\(\large\boxed{\mathtt{Exact = 100 \pi \ cm^{2}}}\)

\(\large\boxed{\mathtt{Approximate: 314.16cm^{2}}}\)

Step-by-step explanation:

\(\textsf{We are asked to identify the area of the circle with the given radius.}\)

\(\large\underline{\textsf{What is the Radius?}}\)

\(\textsf{The \underline{Radius} is a straight \underline{line segment} that covers the distance to the \underline{center} of the}\)

\(\textsf{circle, to the \underline{circumference}.}\)

\(\large\underline{\textsf{What is the Formula for Area?}}\)

\(\textsf{The formula we use for area is;} \mathtt{ \ Area = \pi(radius)^{2}.}\)

\(\textsf{Pi is used to help equal out the ratio of the formula. Mainly, it's helpful to find the area.}\)

\(\textsf{Now that we have the Radius, we can begin solving.}\)

\(\Large\underline{\textsf{Substitute:}}\)

\(\mathtt{Area = \pi(10)^{2}}\)

\(\mathtt{Area = 100 \pi}\)

\(\textsf{For our answer,} \ 100 \pi \ \textsf{is the \underline{exact answer} for the area of this circle.}\)

\(\Large\underline{\textsf{Evalulate 100 pi:}}\)

\(\mathtt{Area = 100 \pi \approx 314.16cm^{2}}\)

\(\textsf{314.16cm is the approximate area of this circle.}\)

Answer:

27

Step-by-step explanation:

Put this into numbers:

\(\frac{3^2*(2^3+4)}{2^2}\)

Use Order of Operations to simplify. First, you would do the stuff in parentheses which is:

\(2^3+4\)

Inside of those parentheses first simplify the exponents:

\(8 + 4\)

Now add

\(12\)

So the new equation is:

\(\frac{3^2*12}{2^2}\)

The next step is to simplify the exponents

\(\frac{9*12}{4}\)

Multiply out the top

\(\frac{108}{4}\)

Divide this

\(27\)

Answer:

first one is 4x

Step-by-step explanation:

Let me help. try doing what is in parenthesis first and then do the rest. for example, if u look at number 2, you have 8x - 6x + 4x. you have to solve whichever comes first. in this case, its 8x - 6x, which equals 2x. next you have +4x. 2x + 4x= 6x. hope this helped :)

Answer:

the first one is 4x

Answer:

Leons puppy weighs more

Step-by-step explanation

So first you have to add the weight of one puppy at a time with the weight each one gained

so jennys puppy would weigh 5.76 pounds

and leons puppy would weigh 5.79 pounds

therefore meaning that leons puppy currently weighs more.

The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."

The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.

Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find g[f(2)], we need to evaluate the composite function g[f(2)] by first finding f(2) and then substituting the result into g(x).

Let's start by finding f(2):

f(x) = 2x² - 3x

f(2) = 2(2)² - 3(2)

= 2(4) - 6

= 8 - 6

= 2

Now that we have the value of f(2) as 2, we can substitute it into g(x):

g(x) = 5x - 1

g[f(2)] = g(2)

= 5(2) - 1

= 10 - 1

= 9

Therefore, g[f(2)] is equal to 9.

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Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

The percent of net change for each corporation are:

The percent of net change is calculated using the formula given below as follows:

a. Berkshire Hathaway:

Percent of net change = (35 / 199740) x 100%

Percent of net change = 0.0175 x 100%

Percent of net change = 1.75%

b. Verizon:

Percent of net change = (0.04 / 51.19) x 100%

Percent of net change = 0.00078 x 100%

Percent of net change = 0.08%

c. McDonalds:

Percent of net change = (-1.13 / 116.34) x 100%

Percent of net change = -0.0097 x 100%

Percent of net change = -0.97%

d. Nike:

Percent of net change = (0.37 / 62.74) x 100%

Percent of net change= 0.0059 x 100%

Percent of net change = 0.59%

e. Delta Airlines:

Percent of net change = (-1.18 / 48.02) x 100%

Percent of net change = -0.0246 x 100%

Percent of net change = -2.46%

f. Toyota:

Percent of net change = (-0.15 / 105.42) x 100%

Percent of net change = -0.0014 x 100%

Percent of net change = -0.14%

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Complete question:

Berkshire Hathaway

Net change = +35

Last = 199740

VZ Verizon

Net change = +0.04

Last = 51.19

MCD McDonalds

Net change = -1.13

Last 116.34

NKE Nike

Net change = +0.37

Last = 62.74

DAL Delta Airlines

Net change = -1.18

Last = 48.02

TM Toyota

Net change = -0.15

Last = 105.42

use the information from exercise 5 to determine the percent of net change from april 21 to april 22 for each of the corporations listed in that question. round answers to the nearest tenth of a percent.

Answer:

Range{ -3,0,5,7,9}

Step-by-step explanation:

The range is the output values

In this case the y values

Range{ -3,0,5,7,9}

Answer:

-3,0,5,7,9

Step-by-step explanation:

The range is the list of all possible y values. Remember to sort them from least to greatest!

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

The most precise name of the quadrilateral will be rectangle .

Given,

Point A : (2,3) .

Here,

If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

So, graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

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Answer:

The sum of all 2 digit multiples of 6 is 810

Step-by-step explanation:

12+18+24+30+36+42+48+54+60+66+72+78+84+90+96 = 810

Answer:

810

Step-by-step explanation:

2 digit multiples of 6 are 12,18,24...90,96

You can just add them on your calculator.

Answer: 168 square feet

.44 x 300 = 132

Hes painted 132 square feet of the wall

Subtract that from our total to get how much is left (or 66% of the room)

300 - 132 = 168

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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