hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?

The expression\(10x^5 + 4x^4 + 8x^3\) can be factored completely as \(2x^3(5x^2 + 2x + 4)\).

To factor the expression \(10x^5 + 4x^4 + 8x^3\), we first observe that all terms have a common factor of 2\(x^3\). Factoring out this common factor, we get:

\(10x^5 + 4x^4 + 8x^3 = 2x^3(5x^2 + 2x + 4)\).

Now, let's focus on factoring the quadratic term \(5x^2 + 2x + 4\) further. This quadratic cannot be factored using integer values, so we can apply the quadratic formula or complete the square to find its factors. However, in this case, the quadratic does not appear to have any rational factors.

Therefore, the factored form of the expression \(10x^5 + 4x^4 + 8x^3\) is \(2x^3(5x^2 + 2x + 4)\), where \(5x^2 + 2x + 4\) is the irreducible quadratic term that cannot be factored any further using integer values.

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Answer: 0.54166666666667 x 100 = 54.1667%

Step-by-step explanation:

Before we get started in the fraction to percentage conversion, let's go over some very quick fraction basics. Remember that a numerator is the number above the fraction line, and the denominator is the number below the fraction line.

When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form.

So, since our denominator in 13/24 is 24, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:

100 divided by 24 = 4.1666666666667

Once we have that, we can multiple both the numerator and denominator by this multiple:

13 times 4.1666666666667 over 24 times 4.1666666666667, equals 54.1666666666667 over a hundred.

Now we can see that our fraction is 54.166666666667/100, which means that 13/24 as a percentage is 54.1667%.

We can also work this out in a simpler way by first converting the fraction 13/24 to a decimal. To do that, we simply divide the numerator by the denominator:

13/24 = 0.54166666666667

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.54166666666667 x 100 = 54.1667%

Hope this helps ^^

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

The height of the pole anchored to a cable is 6.17 meters.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, The anchor cable is forming an angle of 51° angle with the ground attached to a pole and the distance between them is 5 meters.

So, We need height or the opposite side length with an adjacent length of 5 meters.

We know, tan = opposite/adjacent.

tan51° = opposite/5.

opposite = tan51°×5.

opposite = 1.235×5.

opposite = 6.17 meters.

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Answer:

x = -8.4 and -223.6

Step-by-step explanation:

I 'foiled' and simplied, then graphed; x-intercepts (listed above) were the x-intercepts

Answer:

Total number of people surveyed = 118

Number of people who own dogs = 78

Number of people who own cat = 44

Number of people who own both cats and dogs = 26

Number of people who only own dogs = 78 - 26 = 52

Number of people who own only cats = 44 - 26 = 18

Only dog owners + Only cat owners + Both + Neither = Total people surveyed

52 + 18 + 26 + Neither = 118

Neither = 22(answer)

Answer:

0.75x<9

Step-by-step explanation:

0.75x<9

0.75/0.75x < 9/0.75

x<12

The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

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Based on the equation y = 0.13x + 46, the correct statement is:

The equation indicates that for every additional unit (mile) in the independent variable (flight distance), the dependent variable (ticket price) increases by the coefficient 0.13, which represents 13 cents.

Therefore, the equation suggests a linear relationship between flight distance and ticket price, with a constant increase of 13 cents per mile.

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Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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There are four different ways to fold the square in half, however there are no different ways to fold the letter G.

A square has four symmetry lines.

Each symmetry line splits the square in half.

This indicates that the square can be folded into one half along any of its lines of symmetry.

As a result, there are four different methods to fold the square in half.

There is no symmetry line in the letter G.

This indicates the letter can't be folded such that the two parts are exactly aligned.

As a result, there are no methods to fold the letter G.

Answer:

x= 67

y=40

z=40

Step-by-step explanation:

 A=C        B=D

67=X    Y&?= Z&73

73+ x aka(67) = 140

180-140= y = 40

The equation that can be used to determine the price, in dollars, of any watermelon based on the number of pounds is p = 0.7w

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the price of a watermelon that weights 9.3 pounds is $6.51, the cost per pound of watermelon will be:

= $6.51 / 9.3

= $0.7

Therefore, the equation is p = (0.7 × w) = 0.7w

where P = price

w = pound of watermelon

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Answer:

y = -7 and x = -3

Step-by-step explanation:

Substitute x for y + 4 in the first equation and solve for y

4(y+4) - 2y = 2

4y + 16 - 2y = 2

16 + 2y = 2

2y = -14

y = -7

Then in order to find x, substitute y for -7 in the second equation

x = -7 + 4

x = -3

Answer:

x= -3, y= -7

Step-by-step explanation:

substitute x=y+4 in the first equation

4 (y+4) -2y =2 distribute

4y+16-2y=2 subtract both sides by 16

4y-2y=2-16 combine like terms

2y= -14 divide both sides by 2

y=-7

x=y+4 substitute y=-7

x= -7+4

x= -3

Answer: The relationship between map distance and real-world distance can be represented as a linear equation in the form y = mx, where m is the slope of the line. In this case, the slope is 6 kilometers per centimeter, since each centimeter on the map represents 6 kilometers of real-world distance. Therefore, the equation for the line is y = 6x.

To graph this line on the coordinate plane, we can plot two points and draw a straight line through them. One point that lies on the line is (0,0), since if there is no map distance, there is no real-world distance either. Another point that lies on the line is (1,6), since one centimeter on the map represents 6 kilometers of real-world distance.

Using these two points, we can draw the line y = 6x on the coordinate plane. Any point that lies on this line satisfies the relationship between map distance and real-world distance described in the problem.

To determine which of the given points lie on this line, we can substitute each point's x-coordinate into the equation y = 6x and check if it matches its y-coordinate.

Substituting (0.5,1), we get:

y = 6x

y = 6(0.5)

y = 3

Therefore, (0.5,1) does not lie on the line.

Substituting (1,6), we get:

y = 6x

y = 6(1)

y = 6

Therefore, (1,6) lies on the line.

Substituting (1.5,9), we get:

y = 6x

y = 6(1.5)

y = 9

Therefore, (1.5,9) lies on the line.

Substituting (2,12), we get:

y = 6x

y = 6(2)

y = 12

Therefore, (2,12) lies on the line.

Substituting (2.5,13), we get:

y = 6x

y = 6(2.5)

y = 15

Therefore, (2.5,13) does not lie on the line.

Therefore, the points that lie on the line described above are (1,6), (1.5,9), and (2,12).

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The probability that a student who has a brother also has a sister is 2/7 or approximately 0.2857.

To find the probability that a student who has a brother also has a sister, we need to use the concept of conditional probability.

Let's first find the probability of a student having both a brother and a sister. According to the problem, there are 2 students who have both a brother and a sister. Therefore, the probability of a student having both a brother and a sister is:

P(Brother and Sister) = 2/23

Now, let's find the probability of a student having a brother:

P(Brother) = 7/23

Using the formula for conditional probability, we can find the probability that a student who has a brother also has a sister:

P(Sister|Brother) = P(Brother and Sister) / P(Brother)

Substituting the values we found, we get:

P(Sister|Brother) = (2/23) / (7/23) = 2/7

This means that if we randomly select a student who has a brother, the probability that they also have a sister is about 0.2857.

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Answer: To make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.

Step-by-step explanation:We want the total mixture to be 310mL so: F + S = 310

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(310)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310     [substitute answer for S back into original equation]

F = 186

sinx

cosx

tanx

The solution to the initial-value problem is x(t) = 3 cos(3t) - (1/9)t sin(3t), where x(0) = 3 and x'(0) = 0.

To determine the initial-value problem, we'll use the method of undetermined coefficients.

The complementary solution (or homogeneous solution) is obtained by setting the right-hand side of the differential equation to zero:

d²x/dt² + 9x = 0

The characteristic equation for this homogeneous equation is:

r² + 9 = 0

Solving this quadratic equation gives us complex roots: r = ±3i. The general solution for the homogeneous equation is:

x_c(t) = C₁ cos(3t) + C₂ sin(3t)

where C₁ and C₂ are constants determined by the initial conditions.

Now, let's find the particular solution for the non-homogeneous equation:

d²x/dt² + 9x = 5sin(3t)

Since the right-hand side contains sin(3t), we assume a particular solution of the form:

x_p(t) = A sin(3t) + B cos(3t)

where A and B are the undetermined coefficients to be determined.

Taking the derivatives, we have:

dx_p/dt = 3A cos(3t) - 3B sin(3t)

d²x_p/dt² = -9A sin(3t) - 9B cos(3t)

Substituting these derivatives back into the differential equation:

(-9A sin(3t) - 9B cos(3t)) + 9(A sin(3t) + B cos(3t)) = 5 sin(3t)

Simplifying, we get:

(-9A + 9A) sin(3t) + (-9B + 9B) cos(3t) = 5 sin(3t)

This equation reduces to:

0 = 5 sin(3t)

Since this equation must hold for all t, we have:

0 = 5

This is not possible, so there is no particular solution of the form A sin(3t) + B cos(3t) that satisfies the non-homogeneous equation.

However, we can modify the particular solution and assume a particular solution of the form:

x_p(t) = At cos(3t) + Bt sin(3t)

Taking the derivatives, we have:

dx_p/dt = A cos(3t) - 3At sin(3t) + B sin(3t) + 3Bt cos(3t)

d²x_p/dt² = -6At cos(3t) - 6Bt sin(3t) - 9A sin(3t) + 9B cos(3t)

Substituting these derivatives back into the differential equation:

(-6At cos(3t) - 6Bt sin(3t) - 9A sin(3t) + 9B cos(3t)) + 9(At cos(3t) + Bt sin(3t)) = 5 sin(3t)

Simplifying, we get:

(3A + 9B) cos(3t) + (-3B + 9A) sin(3t) = 5 sin(3t)

Comparing the coefficients of cos(3t) and sin(3t), we get the following equations:

3A + 9B = 0

-3B + 9A = 5

Solving these equations simultaneously, we find:

A = 1/3

B = -1/9

Therefore, the particular solution is:

x_p(t) = (1/3)t cos(3t) - (1/9)t sin

(3t)

Now, the general solution to the non-homogeneous equation is the sum of the complementary and particular solutions:

x(t) = x_c(t) + x_p(t)

    = C₁ cos(3t) + C₂ sin(3t) + (1/3)t cos(3t) - (1/9)t sin(3t)

To determine the values of C₁ and C₂, we'll use the initial conditions:

x(0) = 3

x'(0) = 0

Substituting t = 0 into the general solution:

x(0) = C₁ cos(0) + C₂ sin(0) + (1/3)(0) cos(0) - (1/9)(0) sin(0)

     = C₁

Since x(0) = 3, we have:

C₁ = 3

Differentiating the general solution with respect to t:

dx/dt = -3C₁ sin(3t) + 3C₂ cos(3t) + (1/3)cos(3t) - (1/9)sin(3t)

Substituting t = 0:

x'(0) = -3C₁ sin(0) + 3C₂ cos(0) + (1/3)cos(0) - (1/9)sin(0)

      = 3C₂ + (1/3)

Since x'(0) = 0, we have:

3C₂ + (1/3) = 0

C₂ = -1/9

Therefore, the solution to the initial-value problem is:

x(t) = 3 cos(3t) - (1/9)t sin(3t)

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Answer:

1, 0, 2, 3

Step-by-step explanation:

Answer:

1, 0, 2, 3

Step-by-step explanation:

360 degrees equals a circle. A circle can be divided into more manageable pieces. A circle's circumference is referred to as an arc, and an arc is given a name based on its angle.

Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry. The shape of a car tire, a wall clock that indicates the time, and a lollipops are a few objects that are circular in nature. The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.

The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles. A curved line forms a circle, a two-dimensional shape. The curving line's tips are evenly spaced apart from the center since it is a sphere.

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Answer:

$780

Step-by-step explanation:

According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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Answer:

If y = x then when x = -1 then y = -1

Step-by-step explanation:

The total deposit made by Shannon Kelley is $194.16 using arithmetic operations.

The two main arithmetic operations that we learn to add and subtract two or more numbers or other mathematical values are addition and subtraction. To add, one must sum two or more numbers or values to get a new number. To subtract is to reduce from another value in order to obtain the desired value. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). 

Given that Shannon Kelley makes a deposit in her cheque account and she has cheques for $178.16 and $36.0.

This means that the total deposit amount will be obtained by adding both the cheques.

Hence, total deposit amount = 178.16+36.0

= $214.16

Now, it is also given that she gets back $20.00 in cash which is that this amount is reduced from her cheque deposit.

Hence, the remaining amount is obtained by subtracting $20.00 from the total cheque deposit amount.

That is, 214.16 - 20.00 = $194.16.

Therefore, the total deposit is $194.16.

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