My guys got me right? I’m giving brainliest

Answer:

908.967

Step-by-step explanation:

i hope this helps :)

There are 720 different ways can a race with 6 runners be completed.

What is a combination?

The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.

Here, we have

The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.

So the total number of possible results can be calculated as:

n = 6×5×4×3×2×1= 6!

= 720

Hence, there are 720 different ways can a race with 6 runners be completed.

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Hi there! Hopefully this helps!

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First we need to substitute the value of the variable into the expression and simplify.

b-(b+a×4c÷4) = 1 - (1 + -6 × 4(2) ÷ 4).

Now we need to solve 1 - (1 + -6 × 4(2) ÷ 4).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 - (1 + -6 × 4(2) ÷ 4)

|

|  First, we cancel out 4 and 4.

\/

1 - (1 - 6 × 2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Next, we multiply -6 and 2 to get -12.

1 - (1 - 12)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Then we subtract 12 from 1 to get -11.

1 - (-11)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The opposite of -11 is 11.

1 + 11.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

Answer: 12

Hope this helps

The greatest common divisor (GCD) of 735 and 504 is 21. Using the Euclidean algorithm, we find that the GCD can be expressed as 735x + 504y, where x = 11 and y = -5.

(a) To compute the GCD using the Euclidean algorithm, we start by dividing the larger number (735) by the smaller number (504):  \(735 = 504 * 1 + 231\)

Next, we divide the previous divisor (504) by the remainder (231):

\(504 = 231 * 2 + 42\)

We continue dividing the previous divisor by the remainder until we reach a remainder of 0:

\(231 = 42 * 5 + 21\\42 = 21 * 2 + 0\)

The last non-zero remainder is 21, which is the GCD of 735 and 504.

(b) To find integers x and y such that the GCD of 735 and 504 can be written in form 735x + 504y, we can use the extended Euclidean algorithm.

Starting with the last two equations from part (a):

\(21 = 231 - 42 * 5\\21 = 231 - (504 - 231 * 2) * 5\)

To simplifying, we have:

\(21 = 11 * 231 - 5 * 504\)

Therefore, we can write the GCD of 735 and 504 as:

\(21 = 11 * 735 - 5 * 504\)

So, x = 11 and y = -5 satisfy the equation 735x + 504y = 21, with x and y being integers.

In conclusion, the GCD of 735 and 504 is 21, and it can be expressed as 735x + 504y, where x = 11 and y = -5.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

In this case, we have:

dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)

So,

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]

Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)

Therefore, the length of the curve is:

L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2

So the length of the curve is 7√2/2.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

it will be c

Step-by-step explanation:

Answer:

  16.6°

Step-by-step explanation:

The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.

__

We choose to use a=10, b=4, C=29°.

  c² = a² +b² -2ab·cos(C) . . . . . law of cosines

  c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304

  c ≈ √46.0304 ≈ 6.78457

Then angle B (opposite side b) is ...

  sin(B)/b = sin(C)/c . . . . . . . . . law of sines

  sin(B)/4 = sin(29°)/6.78457

  B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°

The missing acute angle is about 16.6°.

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

Answer: -1

Step-by-step explanation:

The Polynomial Remainder Theorem

It states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).

We have the polynomial:

\(f(x)=x^3+x^2+x+1\)

And we need to determine if x=1 and/or x=-1 are zeros of the polynomial.

Considering the polynomial remainder theorem, if we try any value for x, and the remainder is zero, then that value of x is a root or zero of the polynomial.

Find:

\(f(1)=1^3+1^2+1+1\)

f(1)=4

Thus, x=1 is not a zero of f(x)

Now, find:

\(f(-1)=(-1)^3+(-1)^2+(-1)+1\)

\(f(1)=-1+1-1+1=0\)

Thus, x=-1 is a zero of f(x)

Answer: -1

Answer:

152.68 in²

Step-by-step explanation:

The question asks us to calculate the amount of paper required to wrap around a paint can with a radius of 2.7 inches and a height of 9 inches. To do this we must calculate the curved surface area of the cylindrical paint can using the following formula:

\(\boxed{\mathrm{A = 2\pi r h}}\),

where:

A ⇒ curved surface area of cylinder

r ⇒ radius of cylinder

h ⇒ height of cylinder.

Substituting the information above into the formula, we can calculate the amount of paper needed:

A = 2 × π × 2.7 × 9

  = 2 × π × 2.7 × 81

  = 152.681 in²

  = 152.68 in²   (rounded to the nearest hundredth)

Therefore, the company will need 152.68 in² of paper to create a label to go around the can.

The probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

To solve this problem using the direct method, we can use the fact that 22% of TV sets were tuned to the game. This means that the probability of a randomly selected TV set being tuned to the game is 0.22.

To find the probability that at least one of the 33 households surveyed had their TV set tuned to the game, we can use the complement method. The complement of the event "at least one household has their TV set tuned to the game" is "none of the households have their TV set tuned to the game".

Using the complement method, we can find the probability of this event by taking the probability that no households have their TV set tuned to the game, which is (1-0.22)^33.

So, the probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

If I had to do this by hand, I would use the complement method, as it involves simpler calculations.

To find the probability that at least one TV set among the 33 households surveyed is tuned to NBC Sunday Night Football, we can use either the direct method or the complement method.

1. Direct Method:
The direct method requires calculating the probabilities of 1, 2, 3, ..., 33 households watching the game, and then summing up these probabilities. This method can be tedious and time-consuming, especially when done by hand.

2. Complement Method:
The complement method is generally easier and quicker, as it involves calculating the probability that none of the 33 households is watching the game and then subtracting this probability from 1.

Given that 22% (0.22) of the TV sets in use were tuned to the game, the probability that a household is not watching the game is 1 - 0.22 = 0.78.

For all 33 households not to be watching the game, the probability is (0.78)^33 ≈ 0.00038.

Now, to find the probability that at least one household is watching the game, we subtract this probability from 1:

1 - 0.00038 ≈ 0.99962.

So, the probability that at least one of the 33 households is tuned to NBC Sunday Night Football is approximately 0.99962.

If you had to do this by hand, the complement method would be the preferred approach, as it requires fewer calculations and is more straightforward.

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Answer: 1/7 of a cup

Step-by-step explanation:

7x=1 x=food per day

divide 7 from both sides

7 / 7x = 1 /7

x = 1/7

a. The initial amount of money deposited into the account is $1575.

b. The annual interest rate being paid on the account is 4.5%.

c. The amount of money in the account after 15 years is approximately $2946.27.

d. It will take approximately 20 years for the account to reach a balance of at least $4000.

To answer these questions, let's analyze the given equation:

A(1) = 1575 * (1.045)^t

a. The initial amount of money deposited into the account is $1575. This is evident from the equation, where A(1) represents the amount of money after 1 year.

b. To determine the annual interest rate, we can compare the given equation with the general formula for compound interest:

A = P * (1 + r)^t

Comparing the two equations, we can see that the interest rate in the given equation is 4.5% (0.045) since (1 + r) is equal to 1.045.

c. To find the amount of money in the account after 15 years, we can substitute t = 15 into the equation and calculate the result:

A(15) = 1575 * (1.045)^15 ≈ $2946.27 (rounded to the nearest dollar)

Therefore, after 15 years, the amount of money in the account will be approximately $2946.

d. To find the number of years it will take for the account to have at least $4000, we need to solve the equation for t. Let's set up the equation and solve for t:

4000 = 1575 * (1.045)^t

To solve this equation, we can take the logarithm of both sides (with base 1.045):

log(4000) = log(1575 * (1.045)^t)

Using logarithm properties, we can simplify the equation:

log(4000) = log(1575) + log((1.045)^t)

log(4000) = log(1575) + t * log(1.045)

Now, we can isolate t by subtracting log(1575) from both sides and then dividing by log(1.045):

t = (log(4000) - log(1575)) / log(1.045)

Calculating this expression, we find:

t ≈ 19.56 (rounded to two decimal places)

Therefore, it will take approximately 20 years (rounded to the nearest whole year) for the account to have at least $4000.

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This statement is false. The y-intercept is (0, 1), not (0, 1).So, the correct statements are:A. y is a function of x.

The data provided can be used to deduce the equation 4(3x) = y, where y is the output and x is the input.

Let's examine each statement separately:

The assertion that y is a function of x is true. B. The relationship is addressed by a line on the chart. In a capability, each info (x) compares to a particular result (y), and in this occasion, the condition characterizes y as a component of x.

This affirmation is misdirecting. The equation's exponentiation (4(3x)) indicates that the relationship is not linear. This relationship's chart won't be a straight line yet rather a bend.

C. The conclusion is 4 when the information is minus 3.

Since 4(3x) = y, we can use x = - 3 to solve the following problem:

Since 4(3(- 3)) = 4(- 9) = 1/49 = 1/262144, this declaration is misleading. At the point when the information is - 3, the result isn't 4.

D. Right when the data is - 2, the outcome is 3.

We can alter the condition by subbing x = - 2:

This is false because 4(3(-2) = 4(-6) = 1/46 = 1/4096. The output is not 3 when the input is -2.

E. The relationship has a y-block of 0.

We insert x = 0 into the following circumstance to locate the y-block:

This statement is false because 4(3(0)) = 40 = 1. The y-intercept is instead of (0, 1), so the statements that are true are:

A. y is a part of x.

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S" > 0 indicates that the rate of change of sales is increasing.

What is rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity, typically expressed as a ratio.

The derivative of a function represents its rate of change at a particular point. In this case, S represents the monthly sales of Bluetooth headphones, and its derivative S' represents the rate of change of sales. If S' is increasing, it means that the rate of change of sales is getting larger over time.

Mathematically, this means that the second derivative S" (which represents the rate of change of the rate of change) is positive, since an increasing slope of the original function (S') corresponds to a positive value for the second derivative.

Therefore, S" > 0 indicates that the rate of change of sales is increasing.

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The statement is true.

When dummy coding qualitative variables, the base variable is assigned a value of 1. This statement is true. Dummy coding or binary coding is a technique for converting a categorical variable into a numerical variable that can be used in regression analysis. It is used when data has categorical variables, and we need to convert them into a numerical format. It is a method of coding data into numerical data.



Dummy coding is a process that assigns binary variables to each category of a nominal or ordinal variable. It converts the categorical variable into a numerical variable that can be used in regression analysis. The most commonly used method is to define one of the categories as the baseline (reference group) and assign it a value of 1. All the other categories are assigned 0.

For example, suppose we have a categorical variable called "Fruit" with three categories: apples, oranges, and bananas. We can assign binary variables to each category. If we define apples as the base variable, then we will assign it a value of 1 and assign oranges and bananas 0. If we define oranges as the base variable, then we will assign it a value of 1 and assign apples and bananas 0.



When dummy coding qualitative variables, the base variable is assigned a value of 1. This is because the base variable represents the reference group, and all other variables are compared to it. The dummy variable is an essential tool for analyzing categorical data, as it helps to create a numerical format for data analysis.

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The total amount that Avion paid (including taxes) is:

dollars, and the total amount that Brandon paid (including taxes) is:

dollars.

Then, the difference in the amount Avion and Brandon paid is:

Answer: $32.70.

Answer:

x=5

Step-by-step explanation:

I took the test. Hope this helps

The solution of the given equation is when the x = 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the equation 1/4x−3/4=1/2, also the replacement set {−1, 1, 5}

First, substitute the values from the given set;

When x = -1

1/4x−3/4=1/2

1/4(-1) − 3/4 = 1/2

-1/4 - 3/4 = 1/2

-4/4 = 1/2

-1= 1/2

This is not the solution to the given equation.

When x = 1

1/4x−3/4=1/2

1/4(1) − 3/4 = 1/2

1/4 - 3/4 = 1/2

-2/4 = 1/2

-1/2 = 1/2

This is not the solution to the given equation.

When x = 5

1/4x−3/4=1/2

1/4(5) − 3/4 = 1/2

5/4 - 3/4 = 1/2

2/4 = 1/2

1/2 = 1/2

This is the solution to the given equation.

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Answer:

− 3

Step-by-step explanation:

We can rewrite the equation as: y = − 3 x + 0 This equation is now in the slope-intercept form. The slope-intercept form of a linear equation is: y = m x + b Where m is the slope and b is the y-intercept value. For: y = − 3 x + 0 the slope is: m = − 3

Answer:

2

Step-by-step explanation:

Taylor: x

Jim: x + 18

Andre: 2x

Sum: x + (x + 18) + 2x = 26 ↔ x = 2

Answer:

180 feet

Step-by-step explanation:

85+95=180 because depth + depth.

The total deep 180 feet from the surface was the coral.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that diver found the school of fish 85 feet below the surface of the ocean. Which he found coral 95 feet deeper than the fish.

The total deep from the surface was the coral.

Therefore, it could be;

depth + depth.

85 + 95 = 180

Hence, the total deep 180 feet from the surface was the coral.

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Answer:

Circumference ~ 233.7

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is about 37.2. Plug 37.2 into the formula 2(pi)r to find the Circumference. The answer is 233.7 rounded to the nearest tenth.

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. There are 108 college students who do not like any of the three vegetables.

It may also include exponents, radicals, and parentheses to indicate the order of operations.

Algebraic expressions are used to represent relationships, describe patterns, and solve problems in algebra. They can be as simple as a single variable or involve multiple variables and complex operations.

To find the number of college students who do not like any of the three vegetables, we need to subtract the total number of students who like at least one of the vegetables from the total number of students surveyed.

First, let's calculate the total number of students who like at least one vegetable:

- Number of students who like brussels sprouts = 70
- Number of students who like broccoli = 90
- Number of students who like cauliflower = 59

Now, let's calculate the number of students who like two vegetables:

- Number of students who like both brussels sprouts and broccoli = 30
- Number of students who like both brussels sprouts and cauliflower = 25
- Number of students who like both broccoli and cauliflower = 24

To avoid double-counting, we need to subtract the number of students who like all three vegetables:

- Number of students who like all three vegetables = 15

Now, we can calculate the total number of students who like at least one vegetable:

70 + 90 + 59 - (30 + 25 + 24) + 15 = 155

Finally, to find the number of students who do not like any of the three vegetables, we subtract the number of students who like at least one vegetable from the total number of students surveyed:

263 - 155 = 108

Therefore, there are 108 college students who do not like any of the three vegetables.

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