PLZZZZZ ANSWER ASAPPPPP 1. Calculate the unit rate: 324.8 meters in 28 seconds

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer:

A, B, C

Step-by-step explanation:

Assuming the choices are:

A. \((x-2)(x^{4}+3)\)

B. \(x^{2} -1\)

C. A+\(x^{4} +16\)

D. \(\frac{1}{x} +2\)

Put simply, a polynomial in this case will be a function that has at least one variable raised to a power greater than 1.

Choice A already has a variable raised to a power greater than 1 (\(x^{4}\)), so no additional manipulation is needed.

Choice B also has a term that is already raised to a power greater than 1 (\(x^{2}\)). It is the same for choice C (\(x^{4}\)).

Choice D does not have an obvious variable raised to a power greater than 1. When the equation is manipulated it becomes \(x^{-1} +2\). Since -1 is less than 1, choice D is not a polynomial.

Answer:

Option D

Step-by-step explanation:

\(\\ \sf\longmapsto \dfrac{1}{x}+2\)

Simplify

\(\\ \sf\longmapsto x^{-1}+2\)

Degree is less than 1 .It's not a polynomial

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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The probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

To solve this problem, we need to use the Poisson process and the exponential distribution.

Let X be the number of arrivals in a 3-minute interval. Since customers arrive at a rate of 25 per hour, the expected number of arrivals in a 3-minute interval is:

λ = (25/60) x 3 = 1.25

Thus, X is Poisson distributed with parameter λ = 1.25.

Let Y be the service time for a customer. Since Linda serves a customer, on average, in 1.5 minutes, Y is exponentially distributed with parameter μ = 1/1.5 = 0.6667.

Let Z be the waiting time for a customer in the line. Z is the sum of X independent service times, so Z is gamma distributed with parameters X and μ.

We want to find the probability that Z is between 3 and 6 minutes:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

where f(x,y) is the joint probability density function of X and Y:

f(x,y) = (λ^x / x!) e^(-λ) μ e^(-μy) = (1.25^x / x!) e^(-1.9167) e^(-0.6667y)

Now we can evaluate the double integral:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

= ∫∫ (1.25^x / x!) e^(-1.9167) e^(-0.6667y) dx dy

= ∫ e^(-0.6667y) e^(-1.9167) ∑ (1.25^x / x!) dx dy (x=0 to ∞)

= e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

The sum in the integral is the Taylor series expansion of e^1.25, which is equal to e^1.25 = 3.4903.

Using a table of integrals or a computer software, we can evaluate the integral:

∫ e^(-0.6667y) e^(1.25) dy = (1/0.6667) (e^(1.25) - e^(-0.6667(6))) = 3.7225

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is:

P(3 ≤ Z ≤ 6) = e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

= e^(-1.9167) (3.7225) (3.4903) = 0.1658 or about 16.58% (rounded to four decimal places).

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

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Answer:

9

Step-by-step explanation:

;)

Answer:

27

Step-by-step explanation:

First find the tax

25 *8%

25*.08

2

Add the tax to the cost of the book

25+2

27

Answer:

simple answer would be 27 dollars

Step-by-step explanation:

the more complicated answer would be:

25 times 0.08 on the calculator (or in your head) would be 2

25 added by 2 would equal 27 dollars

the first one is finding the sales tax total

the second one is subtracting the total cost of the book by the sales tax total to get 27 dollars or the NEW total

↝ g(x) + f(x) = (4x-2)+(x²+4x)

↝ g(x)+f(x) = 4x-2+x²+4x

↝ g(x)+f(x) = x²+8x-2

Therefore, g(x)+f(x) = x² + 8x - 2

Answer:

Step-by-step explanation:

We have the demand function: x = 600 - P - 3p P + 1.

Taking the partial derivative of x with respect to p, we get:

dx/dp = -4/(P+1)^2

Substituting p = 4, we get:

dx/dp | p=4 = -4/(4+1)^2 = -0.064

So the rate of change in the demand x for the price $4 is approximately -0.06 units per dollar.

Answer:

please see photo above for details

The length of each piece of wood is 0.725 feet.

We are given that the Length= 3.5feet

Now,

This is a word problem that can be solved by using algebra and arithmetic.

Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:

4x + 0.6 = 3.5

This is the equation that could be used to determine the length of each piece of wood.

Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.

Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:

4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725

Therefore, by the algebra the answer will be 0.725 feet.

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Answer:

24

Step-by-step explanation:

Answer

24!

Step-by-step explanation:

Person above me is correct :)

The polynomial representing the area inside the fence is \(2x^4\) - 6x² + 6x - 6.

To calculate the area within the fence, multiply the width by the length. The width is specified as (2x² + 3x - 3) and the length as (x² - 2x - 2). As a result, the area within the barrier is,

A = (2x² + 3x - 3) × (x² - 2x - 2)

When we expand the product, we get:

A = \(2x^4\) + x³ - 7x² - 3x² + 6x + 6x - 6

When we combine like words, we get:

A = \(2x^4\) - 6x² + 6x - 6

As a result, the polynomial describing the area within the fence is \(2x^4\) - 6x² + 6x - 6.

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The correct option is a. For every specific value of y, the value of x must be normally distributed about the regression line.

Regression is a statistical technique used in the fields of finance, investment, and other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (called independent variables).

Some key features of regression are-

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The complete question is-

The assumptions we use to determine the validity of predictions include which of the following?

a. For every specific value of y, the value of x must be normally distributed about the regression line.

b. The sample was collected carefully.

c. The standard deviation of each dependent variable must be the same for each independent variable.

d. All of the above

Answer:

some part of your question is missing below is the missing part

The graph represents the constraints on the number of cupcakes C and muffins M Sajid bakes.

M

20

18

16-

А

14-

12

10

8-

6+

B

41

2+

С

2

4 6

8

10 12 14

18 20

Sajid bakes 3 cupcakes. How many muffins can he bake to meet both his constraints?

answer : 13 ≥ muffins ≤ 16

Step-by-step explanation:

Sajid wants to bake a total of 16 cupcakes and muffins considering both constraints and the fact that he wants to make a total of at least 16 cupcakes and Muffin he would have to make a minimum of 13 muffins and at most 16 muffins

i.e. . 13 ≥ muffins ≤ 16

Answer:

\(y = 2.4^x \\ from \: intercepts \: using \: natural \: log( ln)\)

Answer:

2.4

Step-by-step explanation:

Using Pemdas rule

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.

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If marbles of the same color are indistinguishable, then we can treat each color as one "block" of marbles. Therefore, we have three blocks - one with 3 red marbles, one with 4 yellow marbles, and one with 4 green marbles.

The number of ways to arrange these blocks in a line is simply the number of ways to rearrange the 3 blocks. This is given by 3! which is equal to 6, Within each block, the marbles of the same color are indistinguishable, so we don't need to worry about arranging them.

Therefore, the total number of ways to arrange the marbles in a line is 6, Since marbles of the same color are indistinguishable, we will use the formula for permutations with indistinguishable items. The formula is:

Total permutations = n! / (n1! * n2! * n3! ... nk!) Using the formula, the number of ways to arrange the marbles in a line is:
Total permutations = 11! / (3! * 4! * 4!) = 39,916,800 / (6 * 24 * 24) = 13,860 So, the boy can arrange the marbles in 13,860 different ways if marbles of the same color are indistinguishable.

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It would take Jimbo 24 minutes to solve a 3-variable substitution problem alone.

Let's assume that Jimbo takes x minutes to solve a 3-variable substitution problem alone.

We know that Jimmy takes 8 minutes to solve the same problem alone, so his work rate is 1/8 of the problem solved per minute.

Together, Jimbo and Jim Bob can solve the same problem in 6 minutes. This means that their combined work rate is 1/6 of the problem solved per minute.

We can set up the following equation to represent the work rates:

1/8 + 1/x = 1/6

To solve for x, we can multiply both sides of the equation by 24x:

3x + 24 = 4x

x = 24

Therefore, it would take Jimbo 24 minutes to solve a 3-variable substitution problem alone.

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Answer:

3 scoops

Step-by-step explanation:

If the bird feeder holds 1/2 cup, and Maya is filling it with a scoop that holds 1/6 cup of birdseed, then Maya will need 3 scoops of the 1/6 cup scoop.

1/6 + 1/6 + 1/6

= 3/6

= 1/2

The distance of point from the axis of rotation of the second hand is 8.2 cm.

Here,

A point located on the second hand of a large clock has a radial acceleration of 0.09 cm/s2.

We have to find the distance of point from the axis of rotation of the second hand.

What is Rotation?

The circular motion of an object around the circle is called Rotation.

Now,

Let us consider the equation for the centripetal acceleration given by;

\(a_{c} = \frac{v^{2} }{r}\)

where, v is the velocity and r is the radius.

Now, the velocity can be expressed as;

\(v = wr = \frac{2\pi r}{T}\)

where, ω is the angular velocity and T is the period.

Solving for the radius using these equations given as;

\(a_{c} = \frac{v^{2} }{r}\\\\v^{2} = a_{c} r\\\\(\frac{2\pi r}{T} )^2 = a_{c} r\\\\\frac{4\pi ^{2}r^{2} }{T^{2} } = a_{c} r\\\\r = \frac{T^{2} a_{c} }{4\pi ^{2} } \\\\r = \frac{(60s)^2(0.09 cm/s^2)}{4\pi ^{2} } \\\\r = 8.2 cm\)

Hence, The distance of point from the axis of rotation of the second hand is 8.2 cm.

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The given equation, y = -1.7x + 8.5, is not in standard form with integer coefficients. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive.

To convert the given equation to standard form, we need to eliminate the decimal coefficient. We can do this by multiplying both sides of the equation by 10 to clear the decimal: 10y = -17x + 85 Next, we want the coefficient of x to be positive, so we can multiply both sides of the equation by -1: -10y = 17x - 85

Now, we can rearrange the terms to match the standard form: 17x - 10y = 85 So, the equation of the given line in standard form with integer coefficients is 17x - 10y = 85. To convert the given equation to standard form, we need to eliminate the decimal coefficient.

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The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.

The solution of the system of equations using Cramer's rule is calculated as follows;

The given equations are as follows;

9x - 2y = -9

-3x - 8y = 1

The determinant of the coefficient matrix is calculated as;

D = [9      -2]

      [-3     -8]

D = -8(9) - (-3 x - 2)

D = -72 - 6 = -78

The x coefficient is calculated as;

Dx = [-2      -9]

       [ -8       1]

Dx = -2(1) - (-8 x -9)

Dx = -2 - 72 = -74

The y coefficient is calculated as;

Dy = [9      -9]

       [ -3       1]

Dy = 9(1) - (-3 x -9)

Dy = 9 - 27 = -18

The x and y values is calculated as;

x = Dx/D  = -74/-78 = 74/78 = 37/39

y = Dy/D = -18/-78 = 18/78 = 9/39

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Step-by-step explanation:

-24+12d=2(d-3)+22

-24+12d=2d-6+22

12d-2d=-6+22+24

10d=40

10d/10=40/10

d=4

A person heart beats is 4.2 x 10∧7

there are 7,600,000,000= 7.6 x 10∧9

the heartbeats for all the people here on earth= 4.2 x 10∧7 x 7.6 x 10∧9

choosing like terms

4.2 ×7.6×10∧7×10∧9

31.92x10∧(7+9)

31.92×10∧16

a=31.92

b=16

Answer:

\(3.192*10^1^7\)

Step-by-step explanation:

To find this value, multiply the two values given:

4.2x10^7 = 4.2 x ( 10 x 10 x 10 x 10 x 10 x 10 x 10) = 42000000

42000000 x 7600000000 = 319200000000000000

Then convert 319200000000000000 into scientific notation:

319200000000000000 = 3.19200000000000000

Cut off all the zeroes and I moved the decimal 17 places to the left, so the exponent will be positive:

\(3.192*10^1^7\)

The limit of the given expression as x approaches 1 is 0.

To evaluate the limit of the given expression as x approaches 1, we can use L'Hopital's rule, which states that if the limit of a quotient of functions is of the form 0/0 or ±∞/±∞, then the limit can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the same point.

Using L'Hopital's rule on the given expression, we get:

lim x→1 [5x/(x-1) - 5/x] = lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)]

Plugging in x = 1 directly to this expression, we get:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = (5 - 10 + 5)/(1 - 1) = 0/0

Since the limit is still in an indeterminate form, we can apply L'Hopital's rule once again:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = lim x→1 [(10x - 10)/(2x - 1)] = 0

Therefore, the limit of the given expression as x approaches 1 is 0.

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(a) The probability of the flight being exactly 80% full is P(X = 8) = (11 choose 8) * (0.9)^8 * (0.1)^3. (b) The probability that there are enough seats for every passenger who shows up to get a seat on the plane is P(X ≤ 10) where X follows a binomial distribution with parameters n = 11 and p = 0.9. (c) The probability that there will be at least one empty seat (i.e., the flight is not full) is 1 - P(X = 10). (d) The probability that you and your partner will get a seat on the flight is P(Y ≥ 2) where Y follows a binomial distribution with parameters n = 10 and p = 0.9. (e) The probability of at most two passengers not showing up for the flight is P(Z ≤ 2) where Z follows a binomial distribution with parameters n = 11 and p = 0.1.

(a) The probability of the flight being exactly 80% full can be calculated using the binomial distribution. Let X be the number of passengers who show up for the flight. The probability of the flight being exactly 80% full is P(X = 8) = (11 choose 8) * (0.9)^8 * (0.1)^3.

(b) The probability that there are enough seats for every passenger who shows up to get a seat on the plane is the probability that the number of passengers who show up (X) is less than or equal to the number of seats available (10). This can be calculated as P(X ≤ 10) = P(X = 0) + P(X = 1) + ... + P(X = 10).

(c) The probability that there will be at least one empty seat (i.e., the flight is not full) is 1 minus the probability that the flight is full. This can be calculated as P(at least one empty seat) = 1 - P(X = 10).

(d) The probability that you and your partner will get a seat on the flight can be calculated using the binomial distribution. Let Y be the number of seats available after accounting for the passengers who have already purchased tickets. The probability that both of you get a seat is P(Y ≥ 2) = P(Y = 2) + P(Y = 3) + ... + P(Y = 10).

(e) The probability of at most two passengers not showing up for the flight can be calculated using the binomial distribution. Let Z be the number of passengers who do not show up for the flight. The probability of at most two passengers not showing up is P(Z ≤ 2) = P(Z = 0) + P(Z = 1) + P(Z = 2).

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Answer: b=2a/h-a

Step-by-step explanation:

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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