need help on this please

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

The probability that the team will win at most 4 out of 5 games is 8/9.

To calculate the probability of winning at most 4 out of 5 games, we need to find the probability of winning 0, 1, 2, 3, or 4 games.

The probability of winning exactly k games out of 5 is given by the binomial distribution formula:

P(X = k) = (5 choose k) * (2/3)^k * (1/3)^(5-k)

Where "n choose k" is the binomial coefficient, representing the number of ways to choose k items from a set of n items. In this case, it represents the number of ways to win k games out of 5.

Using this formula, we can calculate the individual probabilities:

P(X = 0) = (5 choose 0) * (2/3)^0 * (1/3)^5 = (1) * (1) * (1/243) = 1/243

P(X = 1) = (5 choose 1) * (2/3)^1 * (1/3)^4 = (5) * (2/3) * (1/81) = 10/243

P(X = 2) = (5 choose 2) * (2/3)^2 * (1/3)^3 = (10) * (4/9) * (1/27) = 40/243

P(X = 3) = (5 choose 3) * (2/3)^3 * (1/3)^2 = (10) * (8/27) * (1/9) = 80/243

P(X = 4) = (5 choose 4) * (2/3)^4 * (1/3)^1 = (5) * (16/81) * (1/3) = 80/243

To find the probability of winning at most 4 out of 5 games, we sum up these probabilities:

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = (1/243) + (10/243) + (40/243) + (80/243) + (80/243) = 8/9.

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The cubic feet of sand and cement are needed to make 160 cubic feet of concrete mix include 100 and 69 cubic feet respectively.

The mixture of concrete is made up of 62.5% sand and 37.5% cement.

In this case, 160 cubic feet of concrete mix is needed.

Sand will be:

= Percentage × Total mix

= 62.5% × 160

= 100 cubic feet

Cement will be:

= 37.5% × 160

= 60 feet

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Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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Answer:

x≤-8

Step-by-step explanation:

When solving 8x-8≤-72, first add 8 to both sides of the inequality.

This leaves you with 8x≤-64.

Divide both sides by 8: 8x/8 and -64/8

This leaves you with x≤-8 as your solution.

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F

and 014≤ 640 ≤ 2TT outward normal is

(r = 18) = √x² + y²+z2)

= F = ૪ 3

flux = [[Finds

. Rsing dodo = 83

(from put value of n

13 sind do do 23

2 TT, TT sing do do

R 11 R [["e. / sind dado (r= 171 = radius of ephare)

Π 2T ए [e" [" sind do do= ["- Casp" "do 0

[-(-1-1) do 2TT = 2x (2-0) 2 = do flux

flux = [[F·ñ-ds S = 4π

The flux is 411 and it depends on radius 'R'

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Answer:

2.291

Step-by-step explanation:

The area under the catenary between x = -6 and x = 6 is approximately 42.0754 square yards.

To find the area under the catenary modeled by the equation y = 12cosh(x/12) - 9 between x = -6 and x = 6, you can follow these steps:

Step 1: Understand the problem
You are given the equation of the catenary and the interval of interest, and you need to find the area under the curve.

Step 2: Set up the integral
To find the area under the curve, you need to integrate the given function with respect to x, from the lower limit (-6) to the upper limit (6). The integral is:
Area = ∫[-6, 6] (12cosh(x/12) - 9)dx

Step 3: Calculate the integral
Now, you need to find the antiderivative of the function inside the integral. The antiderivative of 12cosh(x/12) is 144sinh(x/12) and the antiderivative of -9 is -9x. So, the integral becomes:
Area = [144sinh(x/12) - 9x] evaluated from -6 to 6

Step 4: Evaluate the integral at the limits
Evaluate the antiderivative at the upper and lower limits and subtract the results:
Area = (144sinh(6/12) - 9(6)) - (144sinh(-6/12) - 9(-6))

Step 5: Simplify and calculate
Simplify the expression and calculate the result. Round the answer to four decimal places:

Area ≈ 42.0754 square yards

So, the area under the catenary between x = -6 and x = 6 is approximately 42.0754 square yards.

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Answer:

Step-by-step explanation:

Answer:

i think it would be 31.5 inches??

Step-by-step explanation:

If the diameter of the pool is 24ft, the area is 452.16 ft²

Here we have a circular pool and we want to find its area.

Remember that the area of a circle of radius R is given by:

A = pi*R²

Where pi = 3.14

Here we want to define the diameter as a value between 12 and 24 ft, so I will use 24 ft.

The radius is half of that, then we have:

R = 24ft/2 = 12ft

Then the area of the pool is:

A = 3.14*(12 ft)² = 452.16 ft²

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The equivalent form of 4x³y³ - 3x⁵y⁶ is ,

⇒      \(x^{3} y^{3}( 4 - 3x^{2}y^{3})\)

The given expression is.,

4x³y³ - 3x⁵y⁶

Here we have to write the equivalent form of the given expression by using exponent law,

Since we know that,

Exponent is defined as the method of expressing large numbers in terms of powers.

That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times,

i.e. 6 × 6 × 6 × 6.

This can be written as 64. Here, 4 is the exponent and 6 is the base. This can be read as 6 is raised to power 4.

Therefore,

Applying exponent law of product,

\(x^{a} x^{b} = x^{a+b}\)

So we can write the given expression as

⇒ \(4x^{3} y^{3} - 3x^{5} y^{6}\)

⇒ \(4x^{3} y^{3} - 3x^{3+2} y^{3+3}\)

⇒ \(4x^{3} y^{3} - 3x^{3} x^{2} y^{3}y^{3}\)

⇒ \(x^{3} y^{3}( 4 - 3x^{2}y^{3})\)

Hence the expression,

  \(x^{3} y^{3}( 4 - 3x^{2}y^{3})\) is equivalent to the given expression.

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As per the given probability, the estimated number of tosses in a single trial of the game is 7/11

Probability:

Basically, the term Probability refers the possibility of happening the particular event.

Given,

Here we have to simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. And consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing.

While we looking into the given question we have identified that, the total number possible events is 11.

And we have to find the single trial of the game that is 7.

So, the estimated number of tosses in a single trial of the game is written as,

=> 7/11

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Answer:

\( y = \frac{ - 3x}{4} + \frac{7}{4} \)

Step-by-step explanation:

First transpose 3x

you are having 3x+4y=7

by transposing you will get

4y=-3x+7

divide by 4 throughout by making y subject of the formula you will find your equation as y=mx+c.

Step 1; Complete the table

1. The number of engineers that like science are 266

2. The engineer surveyed the most is Electrical Engineers

3. Pr(mechanical Engineer) is

4. Pr(engineer who liked maths ) is

5. Pr( Engineer who like science or is a chemical engineer) is

Let Pr(engineer like science)=E and Pr(a chemical engineer)=S

The Pr( Engineer who like science or is a chemical engineer) is given as

Hence, we have

6. Pr( Electrical or chemical) is

7. Pr(Mechanical engineer who liked science) is given as

8. Pr(an engineer who liked maths and is an electrical engineer)

Subtract 4 from both sides of the equation, then subtract f from both sides and divide both sides by -7/2 to solve for f.

In order to solve for f, the equation must be manipulated to isolate it on one side of the equation. To do this, the equation must be manipulated algebraically. First, subtract 4 from both sides of the equation. This will move the constant part to the other side of the equation, leaving only the f on the left side. Then, subtract f from both sides, which will move the f to the other side and leave only the constant on the left side. Finally, divide both sides of the equation by -7/2. This will move the coefficient of f to the other side and will leave only f on one side of the equation, thus isolating it. The resulting answer is f=1. This process of manipulating the equation algebraically is called solving the equation for f.

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Answer:

20 minutes

Step-by-step explanation:

3 miles= 30 min

1 mile= 10 mins

2 miles= 10*2

2 miles= 20 min

It will take Stephanie 20 minutes to run 2 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Stephanie ran 3 miles in 30 minutes.

Therefore, Stephanie ran 1 mile in (30/3) = 10 minutes.

Hence, It will take Stephanie (2×10) = 20 minutes to run 2 miles.

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Answer:

10.5

Step-by-step explanation:

Unit test on edge 2021

The value of x from the figure is 10.5cm

Find the diagram attached

From the given diagram

tan 55 = 15/b

Given that tan 55 = 1.4281, hence;

1.4281 = 15/b

b = 15/1.4281

b  = 10.5cm

Hence the value of x from the figure is 10.5cm

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer:

(f+g)(x)=x²+2x-6

Step-by-step explanation:

(f+g)(x)=2x+1+x²-7

collect like terms

(f+g)(x)=x²+2x+1-7

according to mathematics x² is not a like term of 2x so don't add the them

(f+g)(x)= x²+2x-6

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

The time required for an investment of $5000 to grow to $6800 at an interest rate of 7.5% per year, compounded quarterly, is approximately 4.84 years.

To calculate the time required for an investment of $5000 to grow to $6800 at an interest rate of 7.5% per year, compounded quarterly, we can use the formula for compound interest:

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

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

In this case, we have:

P = $5000

A = $6800

r = 7.5% = 0.075 (decimal)

n = 4 (quarterly compounding)

Let's solve for t:

6800 = 5000(1 + 0.075/4)^(4t)

Divide both sides of the equation by 5000:

1.36 = (1 + 0.075/4)^(4t)

Take the natural logarithm of both sides:

ln(1.36) = ln[(1 + 0.075/4)^(4t)]

Using the logarithmic property, we can bring the exponent down:

ln(1.36) = 4t * ln(1 + 0.075/4)

Now we can solve for t by dividing both sides by 4 ln(1 + 0.075/4):

t = ln(1.36) / [4 * ln(1 + 0.075/4)]

Using a calculator, we find that t is approximately 4.84 years.

Therefore, it would take approximately 4.84 years for the investment to grow from $5000 to $6800 at an interest rate of 7.5% per year, compounded quarterly.

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The eigenspace associated with the eigenvalue -1 will consist of all vectors that are flipped or reversed under the reflection transformation.

In linear algebra, an eigenvalue is a scalar value that represents a special property of a square matrix. Eigenvalues are used to study the behavior of linear transformations and systems of linear equations.

In simpler terms, when we multiply the matrix A by its eigenvector v, the result is equal to the scalar multiplication of the eigenvector v by its eigenvalue λ. In other words, the matrix A only stretches or shrinks the eigenvector v without changing its direction.

The eigenvalues of a matrix A can be found by solving the characteristic equation, which is obtained by subtracting λI (λ times the identity matrix) from A and setting the determinant equal to zero. The characteristic equation helps find the eigenvalues associated with a given matrix.

To find an eigenvalue of matrix a for the linear transformation t that reflects points across some line through the origin, we can consider the following:

Since reflection across a line through the origin is an orthogonal transformation, the eigenvalues of matrix a will be ±1.

The eigenspace associated with the eigenvalue 1 will consist of all vectors that remain unchanged under the reflection transformation.

The eigenspace associated with the eigenvalue -1 will consist of all vectors that are flipped or reversed under the reflection transformation.

Please note that without additional information about the specific line of reflection, it is not possible to determine the exact eigenspace for matrix a.

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Hi there! :)

\(\large\boxed{x = 6, 10}\)

|x - 8| + 7 = 9

Subtract 7 from both sides:

|x - 8| = 2

Solve for both solutions by evaluating the expression as negative and positive:

x - 8 = 2

x = 10

-(x - 8) = 2

Divide both sides by -1:

x - 8 = -2

x = 6.

Therefore, the solutions are:

x = 6, 10

Answer:

x = [-b +- sqrt(b^2-4ac)]/2a

Step-by-step explanation: