The rubber track for a toy digger goes around four circular wheels of diameter 8 cm, as shown. (b) Calculate the length of the rubber track that goes around the four wheels. Give your answer correct to one decimal place.

Answer:

C. Translation 5 units left and 2 units down

Step-by-step explanation:

Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).

Look to see if this works for the other two points:

B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.

C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.

Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.

A picture will be shown below of a graph with the points in the table.

We only need to use (5, 2) and (0, 0) to solve this problem.

We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).

Therefore, the answer is [ C. Translation 5 units left and 2 units down ]

Best of Luck!

Answer:

56

Step-by-step explanation:

The mean is the average number of a data set.

To find the mean:

First, add all the numbers in the data set:

30 + 45 + 45 + 70 + 90 = 280

Next, divide the sum (280) by 5 (amount of values):

280 / 5 = 56

56 represents the mean of your data set.

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

<95141404393>

Answer:

4021.76

Step-by-step explanation:

v= πr^2h

3.142x8×8×20

Answer:

the answer in simplest form is 5/28

Answer:

5/28

Step-by-step explanation:

I just used a calculator but the denominator have to be the same. Then once the denominators are, make sure that how many times you multiplied to get the denominator you do to the top.

Answer:

Step-by-step explanation:

To calculate the probability that the number of heads is odd when flipping the coin 10 times, we can use the binomial probability formula.

The probability of getting exactly k successes (in this case, heads) in n trials (flips) is given by:

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

Where:

C(n, k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials and can be calculated as n! / (k! * (n - k)!)

p is the probability of success (getting a head on a single flip)

n is the number of trials (number of coin flips)

k is the number of successes (number of heads)

In this case, the probability of getting a head on a single flip is 0.1, and we want to calculate the probability of getting an odd number of heads in 10 flips.

Let's calculate the probability:

P(odd number of heads) = P(X = 1) + P(X = 3) + P(X = 5) + P(X = 7) + P(X = 9)

= C(10, 1) * 0.1^1 * (1 - 0.1)^(10 - 1) + C(10, 3) * 0.1^3 * (1 - 0.1)^(10 - 3) + C(10, 5) * 0.1^5 * (1 - 0.1)^(10 - 5) + C(10, 7) * 0.1^7 * (1 - 0.1)^(10 - 7) + C(10, 9) * 0.1^9 * (1 - 0.1)^(10 - 9)

Calculating the values:

P(odd number of heads) = 0.1 * 0.9^9 + 0.1176 * 0.1^3 * 0.9^7 + 0.136 * 0.1^5 * 0.9^5 + 0.1715 * 0.1^7 * 0.9^3 + 0.3874 * 0.1^9 * 0.9

P(odd number of heads) ≈ 0.056

Therefore, the probability of getting an odd number of heads when flipping the coin 10 times is approximately 0.056, rounded to three decimal places.

Hope this answer your question

Please rate the answer and

mark me ask Brainliest it helps a lot

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

The general term for the recurrence T(n) = 3T(n/2) + O(n) is O(nlog3). To get the answer, we should plug in k = log3. For the second recurrence, we cannot use the master theorem since it does not cover this case.

To solve this recurrence, we have to use the substitution method, where we guess a solution of the form T(n) = an^k and then prove that this is indeed a solution. This can be done by substituting the guessed solution back in to the recurrence. If the substitution works, then we have solved the recurrence. If not, we can try different values for a and k until the substitution works.

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To solve this problem, we need to use some basic math skills and conversion factors. We know that there are approximately $1.4 times 10^9$ cubic kilometers of water on earth, and that only about $2.5% $ of this water is freshwater.

To find out how much freshwater there is on earth, we can start by converting $2.5\%$ to a decimal by dividing it by 100. This gives us 0.025.
Next, we can multiply the total amount of water on earth by the decimal representing the percentage of freshwater:
$1.4\times10^9 \text{ km}^3 \times 0.025 = 3.5\times10^7 \text{ km}^3$
Therefore, there are approximately 3.5 million cubic kilometers of freshwater on earth. This may seem like a large amount, but it is actually a very small percentage of the total water on earth. It is important to conserve and protect this valuable resource for future generations.
In conclusion, problem solving requires understanding the given information, converting units and percentages, and performing simple calculations to arrive at a solution.

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Answer:

organaelles can i have brainlyest?

ik i didnt spell right

Step-by-step explanation:

If rp is 0.27ra, then a moon's orbital eccentricity is 0.57. Thus, option (a) is the correct answer.

Though the moon does not move around andra in a perfect ellipse, here, we assume that the moon's orbit is in the shape of an ellipse, we know that:

\(e = \frac{ra - rp}{ra + rp}\) ... (i)

where e ⇒ eccentricity of the ellipse

ra ⇒ apoapsis i.e., the longest distance between the moon and its planet

rp ⇒ periapsis i.e., the shortest distance between the moon and its planet

From the question, we know

rp = 0.27 ra

Putting this value in equation (i) we get:

\(e = \frac{ra-0.27ra}{ra+0.27ra}\\\)

\(e=\frac{0.73ra}{1.27ra}\)

e = 0.57

Hence, if rp is 0.27 of ra, the moon's orbital eccentricity is 0.57.

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The cost of 2 chairs is = $30

The cost of 1 table = $60

Step-by-step explanation:

Let a table represent x

A chair represents y

4x + 3y = 225.......eq 1

3x + 4y = 195........eq 2

Use elimination method

x - y = 30

x= 30 + y...... Eq 3

Substitute the value of x into equation 1

4(30+ y) + 3y= 225

120 + 4y + 3y= 225

7y + 120= 225

7y= 225-120

7y= 105

y= 15

Substitute the value of y in eq 2

3x + 15 = 195

3x= 195-15

3x= 180

x= 60

Therefore, the cost of 2 chairs is 15 * 2= $30

The cost of 1 table = $60

Answer:

65

Step-by-step explanation:

Branch and Bound method is an algorithmic technique used in the optimization problem, particularly in the mixed-integer programming problem. The primary purpose of this method is to cut the branches that do not provide any optimal solution to the problem.

The process involves two essential steps which are branching and bounding. Branching refers to dividing the initial problem into smaller subproblems that are easily solvable and then obtaining the upper and lower bound on the solutions of the subproblem. On the other hand, bounding is all about the process of checking the bounds so that the algorithm may run smoothly.

Given:

Max z = 3x₁ + x₂ s.t5x₁ + x₂ ≤ 122x₁ + x₂ ≤ 8X₁ ≥ 0, X₂ ≥ 0, x₁, x₂

integer We begin by drawing the feasible region in a graph. This involves identifying the points that satisfy all the given constraints. Below is the graph of the feasible region:Graph of feasible region From the graph, it's evident that the feasible region is a polygon with vertices (0, 0), (0, 12), (4, 4), and (8, 0).We then proceed with the Branch and Bound algorithm to solve the problem.Step 1: Formulate the initial problem and solve for its solution.Let the initial solution be x₁ = 0 and x₂ = 0. From the constraints, we obtain the equations:5x₁ + x₂ = 0; 2x₁ + x₂ = 0.Substituting the values of x₁ and x₂, we get the solution z = 0. Thus, z = 0 is the optimal solution to the problem.Step 2: Divide the problem into smaller subproblems.In this case, we divide the problem into two subproblems. In the first subproblem, we assume that x₁ = 0, while in the second subproblem, we set x₁ = 1.Step 3: Solve the subproblems and obtain their upper and lower bounds.Subproblem 1: If x₁ = 0, the problem becomes:max z = x₂s.t.x₂ ≤ 12; x₂ ≤ 8; x₂ ≥ 0The solution to this problem is z = 0. The upper bound for this subproblem is 0 (the optimal solution from the initial problem), while the lower bound is 0.Subproblem 2: If x₁ = 1, the problem becomes:max z = 3 + x₂s.t.5 + x₂ ≤ 12;2 + x₂ ≤ 8;x₂ ≥ 0The solution to this problem is z = 4. The upper bound for this subproblem is 4, while the lower bound is 3.Step 4: Select the subproblem with the highest lower bound.In this case, the subproblem with the highest lower bound is subproblem 2 with a lower bound of 3.Step 5: Repeat steps 2-4 until the optimal solution is obtained.In the next iteration, we divide subproblem 2 into two subproblems, one where x₂ = 0 and the other where x₂ = 1. We solve both subproblems to obtain their upper and lower bounds as follows:Subproblem 2.1: If x₁ = 1 and x₂ = 0, the problem becomes:max z = 3s.t.5 ≤ 12;2 ≤ 8;The solution to this problem is z = 3. The upper bound for this subproblem is 4, while the lower bound is 3.Subproblem 2.2: If x₁ = 1 and x₂ = 1, the problem becomes:max z = 4s.t.6 ≤ 12;3 ≤ 8;The solution to this problem is z = 4. The upper bound for this subproblem is 4, while the lower bound is 4.The subproblem with the highest lower bound is subproblem 2.1. We repeat the process until we obtain the optimal solution. After several iterations, we obtain the optimal solution z = 4 when x₁ = 2 and x₂ = 2. Thus, the optimal solution to the problem is x₁ = 2 and x₂ = 2 with a maximum value of z = 4.

In conclusion, the Branch and Bound method is a powerful algorithmic technique that is used to solve optimization problems, particularly mixed-integer programming problems. The method involves dividing the initial problem into smaller subproblems that are easily solvable and then obtaining the upper and lower bounds on the solutions of the subproblem. By applying the Branch and Bound algorithm to the problem Max z = 3x₁ + x₂ s.t. 5x₁ + x₂ ≤ 12; 2x₁ + x₂ ≤ 8; x₁ ≥ 0, x₂ ≥ 0, x₁, x₂ integer, we obtain the optimal solution x₁ = 2 and x₂ = 2 with a maximum value of z = 4.

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

0.3

Step-by-step explanation:

yushhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

0.3

Step-by-step explanation:

djdjwinqwp9dejnedm

To determine the Cartesian equation of the plane that contains the point A(2, 0, 2) and is perpendicular to the plane 2x - 3y + 4x + 5 = 0, we need to find the normal vector of the desired plane.

The given plane has the equation 2x - 3y + 4x + 5 = 0, which can be rewritten as 6x - 3y + 5 = 0. The coefficients of x, y, and z in this equation represent the components of the normal vector of the plane.

Therefore, the normal vector of the given plane is <6, -3, 0>.

Since the desired plane is perpendicular to the given plane, its normal vector should be perpendicular to the normal vector of the given plane. Thus, the normal vector of the desired plane can be found by taking the cross product of the normal vector of the given plane and the vector parallel to the z-axis, which is <0, 0, 1>:

<6, -3, 0> × <0, 0, 1> = <(-3)(1) - (0)(0), (6)(1) - (0)(0), (0)(0) - (-3)(0)> = <-3, 6, 0>.

Now we have the normal vector of the desired plane as <-3, 6, 0>. We can use this normal vector and the point A(2, 0, 2) to write the equation of the plane in Cartesian form using the formula:

Ax + By + Cz = D

where (A, B, C) is the normal vector of the plane, and D is the constant term.

Substituting the values, we have: (-3)(x - 2) + (6)(y - 0) + (0)(z - 2) = 0

Simplifying:

-3x + 6 + 6y + 0 + 0 = 0

-3x + 6y + 6 = 0

Therefore, the Cartesian equation of the plane that contains the point A(2, 0, 2) and is perpendicular to the plane 2x - 3y + 4x + 5 = 0 is -3x + 6y + 6 = 0.

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Answer:

the answer is 9 so yeah.....

Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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$7.50

The expected amount paid to the player is $7.50. This is calculated by taking the probability of each outcome multiplied by the amount paid for that outcome, and then summing them all together. The probabilities are as follows:

The expected amount paid is therefore: (0.75 x $5) + (0.0625 x $10) + (0.0039 x $20) + (0.0001 x $30) + (0.00001 x $50) = $7.50

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Answer:

62 degrees

Step-by-step explanation:

71 - 9

62

Hope this helps :)

Step-by-step explanation:

180 degrees ok.

height of the goal is 90

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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No, the simple digraph with 3 vertices and in-degrees 0, 1, 2, and out-degrees 0, 1, 2 respectively does not exist, while the simple digraph with 3 vertices and in-degrees 1, 1, 1, and out-degrees 1, 1, 1 does exist.

What is digraph?

A digraph is a directed graph where each edge has a direction associated with it. In-degrees refer to the number of edges pointing into a vertex, while out-degrees refer to the number of edges pointing out of a vertex.

For the first case, having in-degrees of 0, 1, 2, and out-degrees of 0, 1, 2 for the three vertices is not possible. The sum of in-degrees must equal the sum of out-degrees in a digraph. However, in this case, the sum of in-degrees is 3 while the sum of out-degrees is 3, which does not match. Therefore, such a digraph does not exist.

For the second case, a simple digraph with in-degrees of 1, 1, 1, and out-degrees of 1, 1, 1 is possible. Each vertex has exactly one incoming edge and one outgoing edge, forming a cycle among the three vertices. This configuration satisfies the condition of a simple digraph, where each vertex has the same in-degree and out-degree.

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Answer: Well we can look at whether or not cubes may or may not equal the same by using volume and surface area, where the volume can be used as x^3 and the surface area x^2, but the reason why polynomials can help us a great deal in world problems is whether or not measurements are accurate, or just in general for solving big math equations. Hope this helps.

The equation which will determine the number of pennies after the nth day will be an= 10+(n-1)2, since the situation is an arithmetic progression.

A series of numbers known as an arithmetic progression or arithmetic sequence (AP) has a constant difference between each subsequent term and its predecessor. The common difference of that arithmetic development is the constant difference.

The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression. An arithmetic series is the total of a finite math progression.

The total of all the words in a sequence can be used to very broadly define a series. All of the words in the sequence must, however, clearly relate to one another.

In this question,

Since Sam received 10 pennies,

a₁= 10

Everyday he receives 2 pennies,

d=2

As the common difference is the same throughout, it is an arithmetic progression. Therefore, the nth term will be,

aₙ= a₁+(n=1)d

Substituting the values, we get

aₙ= 10+(n-1)2

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