The number of ways six people can be placed in a line for a photo can be determined using the expression 6!. What is the value of 6!? Two of the six people are given responsibilities during the photo shoot. One person holds a sign and the other person points to the sign. The expression StartFraction 6 factorial Over (6 minus 2) factorial EndFraction represents the number of ways the two people can be chosen from the group of six. In how many ways can this happen? In the next photo, three of the people are asked to sit in front of the other people. The expression StartFraction 6 factorial Over (6 minus 3) factorial 3 factorial EndFraction represents the number of ways the group can be chosen. In how many ways can the group be chosen?.

Answer:

A

Step-by-step explanation:

when u see all the numbers after the point they all are not equal to or > 5 so we don't add any number.

\(-7\sqrt{3}\pi\)

Add similar elements

Answer:

A. \(-7\sqrt{3}\pi\)

Step-by-step explanation:

To find the simplified form of that expression, we have to combine like terms. To do this, we should remember that:

ab + cb = (a + c)b

\(\pi\sqrt{3}-8\pi\sqrt{3}=(\pi-8\pi)\sqrt{3}=((1-8)\pi)\sqrt{3}=-7\pi\sqrt{3}=-7\sqrt{3}\pi\)

So the simplified form would be \(-7\sqrt{3}\pi\).

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

-95

Step-by-step explanation:

(4 - m) / 9 = 11

Multiply both sides by 9:

4 - m = 99

Subtract both sides by 4:

-m = 95

Multiply both sides by -1:

m = -95

Answer:

-63

Step-by-step explanation:

4 - M = 11

---

9

Bring the 4 to the opposite side of the variable ( bring the 4 to the other side of the = sign where it shows 11 or a different number with no variable. basically if you get a question problem for math like this, and when you see a variable aka a letter, move it to the other side where it doesn't have a letter, move it with the = sign then add or subtract. if the number that your moving away from the variable is positive, you subtract making it negative... but if you have a negative number, do adding instead. )

4 - 11 = -7

subtract and then you muliply

M

--- = -7

9

once you mulipled -7 x 9

your answer should be

M = -63

( Have a good day! )

The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

Step-by-step explanation:

g(x)=3x−2

g(−2)= 3(-2) - 2 (after substituting -2 for x):  g(-2) = -6 - 2 = -8

g(0)=  3(0) - 2 = -2

g(5)=  3(5) - 2 = 13

Based on the distance that Pacman traveled for every 6 seconds, and the distance being proportional to time, the Constant of Proportionality is 3.

The Constant of Proportionality shows how the quantity of a variable increases of decreases as the quantity of another related variable increases or decreases as well.

In the distance traveled by Pacman, the constant of proportionality can be found by the formula:

= Distance traveled / Time traveled

= 18 feet / 6 seconds

= 3 feet per second

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Answer:

(-3,8) would NOT fit the table.

Answer: (-3,8)

Step-by-step explanation: click on the file

Answer:

4 miles in 1/3 hour

Step-by-step explanation:

A study of all the students at a small college showed a mean age of 20.4 and a standard deviation of 2.7 years.

(a) These numbers are statistics because they are based on a sample of students from a small college. They are not certain, but estimates.

(b) The mean age is labeled with the symbol x and the standard deviation with the symbol s. The sample size is not given, so we cannot use the symbol n to represent it.

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Answer:

y = 3x - 2

Step-by-step explanation:

There is no graph so I'll explain with the slope intercept form

slope is m so m = 3

y-intercept is -2 so b = -2

then y = 3x - 2

whichever graph has slope of 3 and y-intercept of -2 is the right answer

Answer:748cm^2

Step-by-step explanation:

Answer:

wut.

Step-by-step explanation:

Answer:

b =  2A

         h

Step-by-step explanation:

A=bh/2

2A = bh

b =  2A

          h

Answer:

b=(2a)/h

Step-by-step explanation:

Multiply both sides by 2

2A=bh

Divide both sides by h

(2a)/h=b

Answer:

Step-by-step explanation:

12%

Answer:

-21

Step-by-step explanation:

11. -4

21. -3

14. -20

Hope these answers are correct

The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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Question 1

Answer: C) First and last term

----------------

Explanation:

Recall that (a+b)^2 = a^2+2ab+b^2 when using the FOIL rule. To go in reverse, to factor, we would apply the square root to the a^2 to get 'a', and also apply the square root to b^2 to get b. This then helps form the a+b shown on the left side.

The next question will go over a specific example of what is going on. Note that in question 2, the use of the phrasing "root of the first term" and "root of the last term" which helps reinforce we have the correct answer for problem 1.

=========================================================

Question 2

Answers:

----------------

Explanation:

Apply the square root to the first term to get

sqrt(81v^2) = sqrt( (9v)^2 ) = 9v

Or you could note that (9v)^2 = (9v)*(9v) = 81v^2, from which we work in reverse when applying the square root.

Similarly, the square root of the last term is

sqrt(100) = sqrt(10^2) = 10

So that's why the answers are 9v and 10 for the blanks.

We can say:

(a+b)^2 = a^2 + 2ab + b^2

(9v+10)^2 = (9v)^2 + 2(9v)(10) + (10)^2

(9v+10)^2 = 81v^2 + 180v + 100

The vector z is (7/4, -5/4, -1/4).

To find the vector z, we need to isolate it in the given equation. First, we rearrange the equation to get:

4z = w + 2u

Then, we can substitute the given values for w and u:

4z = 5, -1, -5 + 2(-1, 2, 3)

Simplifying this gives:

4z = 7, -5, -1

Finally, we can solve for z by dividing both sides by 4:

z = 7/4, -5/4, -1/4


In summary, to find the vector z, we rearranged the given equation and substituted the values for w and u. We then solved for z by dividing both sides by 4. The resulting vector is (7/4, -5/4, -1/4).

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Answer:

The rate of change of the distance between the airplanes is approximately 316.760 kilometers.

Step-by-step explanation:

The distance between both airplanes (r), in kilometers, can be determined by the Pythagorean Theorem, that is:

\(r^{2} = x^{2}+y^{2}\) (1)

Where:

\(x\) - Distance of the westbound airplane from airport, in kilometers.

\(y\) - Distance of the southbound airplane from airport, in kilometers.

By Differential Calculus, we derive an expression for the rate of change of the distance between the airplanes (\(\dot r\)), in kilometers per hour:

\(2\cdot r\cdot \dot r = 2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y\)

\(\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}\) (2)

Where:

\(\dot x\) - Rate of change of the distance of the westbound airplane, in kilometers per hour.

\(\dot y\) - Rate of change of the distance of the southbound airplane, in kilometers per hour.

If we know that \(x = 17\,km\), \(y = 28\,km\), \(\dot x = -164\,\frac{km}{h}\) and \(\dot y = -271\,\frac{km}{h}\), then the rate of change of the distance between the airplanes is:

\(\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}\)

\(\dot r \approx -316.760\,km\)

The rate of change of the distance between the airplanes is approximately 316.760 kilometers.

We need the actual percentage of adults who do not work during summer vacation and additional information such as the sample size, specific values for x, or any other relevant details.

Let's solve the problem step by step:

a) To complete this part, we need the actual percentage of adults who do not work at all during summer vacation. Please provide that information.

b) Assuming the percentage of adults who do not work during summer vacation is p, we can express this as a probability. Let x represent the number of adults who do not work. Since it's a random sample, we can model x as a binomial random variable. The probability of an adult not working is p, so the probability mass function of x is given by:

P(x) = C(n, x) * p^x * (1-p)^(n-x)

Where n is the sample size. Since the question doesn't specify the sample size, we can't provide an exact probability.

c) Assuming you provide the value of p, we can calculate the probability for a specific sample size n and number of adults who do not work x using the formula from part b. For example, if p = 0.25, n = 100, and x = 30, we can substitute these values into the formula and calculate the probability.

d) To calculate the expected value of x, we multiply each possible value of x by its corresponding probability and sum them up. This can be expressed as:

E(x) = Σ(x * P(x))

e) The conclusion will depend on the specific values of p, n, and x, as well as the results obtained from the calculations in parts b, c, and d. Without the actual percentage or values for p, n, and x, it's not possible to draw a specific conclusion.

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Answer:

The function is missing in the question. The function is \($ C(x) = 0.8x^2 -544x +97410 $\)

The answer is 4930

Step-by-step explanation:

Unit cost of a car is given as

\($ C(x) = 0.8x^2 -544x +97410 $\)

Cost will be minimum when

x = -(-544)/ 2 x 0.8

  = 340

Therefore, minimum cost for unit car is

\($ C(x) = 0.8x^2 -544x +97410 $\)

\($ = 0.8(340)^2 -544(340) +97410 $\)

=  4930

the value of ∠C is 20°

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The answer is ∠C= 20 degree

We have given:

AB= 5

AC = 14

and we have to find ∠c to the nearest degree.

So,

We know that:

tan(C)= AB/AC

tan(C)= 5/14

tan(C)= 0.3571

C=20 degree

Thus the value of ∠C is 20°

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The probabilities are 1. 27/50, 2. 3/4, 3. 31/100, 4. 25/46, 5. 25/48

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item 1:

54 out of 100 people prefer bacon, hence:

P = 54/100

  = 27/50

Item 2:

Out of 100 people, 54 prefer bacon, 21 prefer sausage but pancakes, hence 54 + 21 = 75 desired outcomes, hence:

P = 75/100

  = 3/4

Item 3:

31 out of 100 people prefer bacon and pancakes, hence:

P = 31/100

Item 4:

Out of 46 people that prefer sausage, 25 prefer french toast, hence:

P = 46 / 25

Item 5:

Out of 48 people that prefer french toast, 25 prefer sausage, hence:

P = 48 / 25

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Answer:

p = 35

Step-by-step explanation:

the midsegment WY is half the measure of VZ , that is

WY = \(\frac{1}{2}\) VZ ( substitute values )

p - 21 = \(\frac{1}{2}\) (p - 7) ← multiply through by 2 to clear the fraction

2p - 42 = p - 7 ( subtract p from both sides )

p - 42 = - 7 ( add 42 to both sides )

p = 35

Answer:

hahahaha qiau181e81 8qy28e82

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

We have,

3.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees.

= 25

We add up all the dots above the numbers between 98.5 and 98.7.

We will not include the dots above 98.5 and 98.7.

4.

The dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population with a mean temperature of 98.6 degrees shows that the majority of the sample means are close to 98.6, and there are very few samples means that exceed 98.6, then it would be surprising to obtain a sample mean of 98.8 or greater from a different random sample.

Thus,

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

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These issues are the lack of technological innovation and the increasing competition in the global market. Addressing these issues is crucial for the organization's sustainability and growth.

The lack of technological innovation is an issue because it hinders International Industries from staying competitive and meeting changing market demands.

Without innovation, the organization may fall behind in terms of product development, process efficiency, and customer satisfaction.

To address this issue, the organization should prioritize research and development efforts, invest in new technologies, and foster a culture of innovation. This can involve collaborating with external partners, conducting market research, and providing training and incentives to employees.

The increasing competition in the global market is another significant issue. With globalization, companies from different countries are entering the market, creating intense competition for International Industries. This can impact market share, pricing, and profitability.

To tackle this issue, the organization should focus on strategic positioning and differentiation. This can be achieved through product diversification, expanding into new markets, improving marketing strategies, and enhancing customer relationships.

Additionally, the organization should constantly monitor and analyze the competitive landscape to identify opportunities and adapt accordingly.

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Answer:

The Answer is C

Step-by-step explanation:

To simplify the expression you will simply need to take the -7 and multiply it by each of the exponents. -7 times -3=21 and -7 times 3=-21

Hope this helps.

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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