took a random sample of markers from the bucket and counted 12 1212 yellow markers, 37 3737 blue markers, and 1 11 red marker. use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. input your answers as fractions or as decimals rounded to the nearest hundredth.

In this case, the standard deviation is 3.7, so the variance is 3.7², or 13.69. This means that the data points in the data set are, on average, 13.69 units away from the mean.

The variance of a data set is a measure of how the data points are distributed around the mean. It is calculated by squaring the standard deviation, which is the average distance of the data points from the mean.

Variance is a useful measure for quantifying the spread and variability of the data points in a data set. By knowing the variance, it is possible to make predictions about how likely it is that a given data point will fall within a certain range from the mean.

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Answer:

-1.1

Step-by-step explanation:

3.1 - 1.3 = t + 2.9

t = 3.1 - 1.3 - 2.9

t = -1.1

Answer:

t = -1.1

Step-by-step explanation:

\(3.1 - 1.3 = t + 2.9 \\ 1.8 = t + 2.9 \\ 1.8 - 2.9 = t \\ - 1.1 = t \)

Answer:

-6, 7

Step-by-step explanation:

Answer: B(-6,7)

Step-by-step explanation:

M(-5, 1)      A(-4,-5)       B(x,y)=?

\(\displaystyle\\M_x=\frac{x_A+x_B}{2} \\\\-5=\frac{-4+x_B}{2}\\\\\)

Multiply both parts of the equation by 2:

\(-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6\)

\(\displaystyle\\\\\\1=\frac{-5+y_B}{2} \\\\\)

Multiply both parts of the equation by 2:

\(1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7\)

For the shown figure:

Given:

We will prove:

The proof will be as follows:

Statement Reason

1. PQ ≅ RS Given

2. QR ≅ SP Given

3. PR ≅ RP Reflexive property

4. ΔPQR ≅ RSP Congruent by SSS postuelate

Given:

13 is the final answer.

The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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Answer:

Independent- Miles traveled, Dependent- cost

Step-by-step explanation:

3dg3nuity

Answer:

I did it :D

Step-by-step explanation:

Answer:

I select b, 1,3, or 9 photos as my answer.

A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = \(x^2\) * h = 8500

Solving for h, we get:

h = 8500 / \(x^2\)

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = \(2x^2\) + 4x(8500 / \(x^2\)) = 2\(x^2\)+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/\(x^2\) = 0

Multiplying both sides by \(x^2\) and solving for x, we get:

x = (8500/2\()^(1/3)\) ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / \(x^2\) ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = \(X^2 + 34000/X\)

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

\(X^{2Y} = 8500\)

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = \(X^2 + 4XY\)

We can substitute the value of Y from the equation for volume, giving:

Surface Area = \(X^2 + 4X(8500/X^2)\)

Surface Area = \(X^2 + 34000/X\)

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = \(20.5^2 + 4(20.5)(8500/20.5^2)\)= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

\(X^2Y = 8500\)

\((20.5)^2 Y = 8500\)

\(Y = 8500/(20.5)^2 = 16.87\) inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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The thickness of the tharsan thir is approximately 0.06 mm when expressed in two decimal places.

To convert micrometers (μm) to millimeters (mm), we need to divide the value in micrometers by 1000 since there are 1000 micrometers in a millimeter.

Given that the thickness is 60 μm, we can perform the conversion as follows:

60 μm / 1000 = 0.06 mm

Therefore, the thickness of the tharsan thir is approximately 0.06 mm when expressed in two decimal places.

Millimeters and micrometers are both units of length, with millimeters being the larger unit. Micrometers are often used to represent very small measurements, such as the thickness of thin materials or microscopic objects. In this case, the tharsan thir has a thickness of 60 micrometers, which is equivalent to 0.06 millimeters.

Converting between micrometers and millimeters is a simple process involving the division by 1000. This conversion is necessary when dealing with different scales or when using units that are more convenient for a specific application.

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A tharsan thir has a thicknoss of about 60μm. What is this in millimeters? Express your answer in two decimal places

The first octant refers to the space where all coordinates are positive. Therefore, the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6 is: V = 3 x 1.5 x 2.5 = 11.25 cubic units.

The three faces in the coordinate planes means that three sides of the rectangular box are parallel to the x-axis, y-axis, and z-axis. Finally, one vertex in the plane x + 2y + 3z = 6 means that one corner of the rectangular box is on this plane.
To find the volume of the largest rectangular box in this scenario, we can use optimization techniques. Let's call the length, width, and height of the box L, W, and H respectively. Since we know that three faces of the box are in the coordinate planes, we can say that:
L + 2W = 6 (from the equation of the plane)
L, W, H > 0
We want to maximize the volume of the box, which is given by:
V = LWH
We can use the equation L + 2W = 6 to solve for L in terms of W:
L = 6 - 2W
Now we can substitute this into the equation for V:
V = (6 - 2W)(W)(H)
V = 6WH - 2W^2H
To maximize V, we need to find the critical point(s) of this function. We can do this by taking partial derivatives with respect to W and H and setting them equal to 0:
dV/dW = -4WH + 6H = 0
dV/dH = -2W^2 + 6W = 0
Solving these equations gives us W = 1.5 and H = 2.5. We can plug these values back into the equation for L to find that L = 3. This means that the maximum volume occurs when the rectangular box has dimensions 3 x 1.5 x 2.5.
To check that this is indeed the maximum volume, we can use the second partial derivative test. The second partial derivatives are:
d^2V/dW^2 = -4H < 0
d^2V/dH^2 = -4W < 0
Since both of these are negative, we know that the critical point we found is a maximum.
Therefore, the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6 is: V = 3 x 1.5 x 2.5 = 11.25 cubic units.

To find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6, follow these steps:
Step 1: Identify the coordinates of the vertex in the plane.
Since the rectangular box has faces in the coordinate planes, one vertex will have coordinates (x, y, z) such that x + 2y + 3z = 6.
Step 2: Find the volume of the rectangular box.
The volume of a rectangular box can be found by multiplying its dimensions, which are the lengths of its sides. In this case, the dimensions are x, y, and z. So, the volume V can be expressed as V = xyz.
Step 3: Express volume in terms of a single variable.
To find the largest volume, we need to express the volume in terms of a single variable. From the given equation, x = 6 - 2y - 3z. Substitute this expression into the volume equation:
V = (6 - 2y - 3z)yz
Step 4: Find the critical points.
To find the largest volume, differentiate the volume equation with respect to both y and z, and set both derivatives equal to zero. This will give us the critical points, where the maximum volume might occur.
∂V/∂y = z(6 - 2y - 3z) - 2yz = 0
∂V/∂z = y(6 - 2y - 3z) - 3yz = 0
Step 5: Solve the system of equations.
Solve the system of equations obtained in Step 4 to find the values of y and z. Then, use the original equation (x + 2y + 3z = 6) to find the value of x.
Step 6: Calculate the maximum volume.
Using the values of x, y, and z obtained in Step 5, calculate the maximum volume V = xyz.
In conclusion, the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6 can be found by following these steps and solving the corresponding equations.

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Answer:

\((x+2)(x+3)\)

Step-by-step explanation:

⭐What does factorisation mean?

⭐What are factors?

Thus, we have to write \(x^2+5x+6\) in terms of its factors.

I have a picture attached to this response to show you how factorisation works, but I will also explain it here.

How to factorise:

The picture of factorisation is attached to this response.

⭐ if this response helped you, please mark it the "brainliest"!⭐

Answer:

3,6,9,12,15,18

Step-by-step explanation:

how i came up with this ordered pair is taking the multiples of three

this relation is a function because it is asking to list six ordered pairs showing the output of the thickness of the paper that he folds and the way that i came up with the ordered pairs in Part A is because you have to take the multiples of three or you could just take 6 and multiple it by 3 and you would get the same answer

Answer:

First dropbox: 7h + 43 = 64

Second dropbox: $3

Step-by-step explanation:

Here's what we know about the question so far:

$43 is the initial fee

The rototiller worked for 7 hours

$64 is the total cost (including initial fee)

h = hourly fee

The answer should be 7h + 43 = 64 because:

- It includes the initial fee of $43

- It sets the equation equal to $64, which is the total cost

- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )

For the 2nd drop box, we will use basic algebra to solve for h:

7h + 43 = 64

(subtract both sides by 43)

7h = 21

(divide both sides by 7)

h = 3

There's your 2 answers!

Hope it helps (●'◡'●)

Answer:

I hope this helpfull.

Step-by-step explanation:

But if it not,im so sorry

Answer:

10

Step-by-step explanation:

Answer:

12                                        

Step-by-step explanation: 60

Answer:

it's going to be d.

Answer: c

Step-by-step explanation:

2*6=12

12+3=15

15 is not less than 10

2*4=8

8+3=11

11 is not less than 10

2*2=4

4+3=7

7 is less than 10

10*2=20

20+3=23

23 is not less than 10

In a binary tree with leaves l1, l2, ..., lM at depths d1, d2, ..., dM respectively, the sum of \(2^-^d^_i\) for all leaves is always less than or equal to 1: Σ  \(2^-^d^_i\) <= 1.

In a binary tree, each leaf node is reached by following a unique path from the root. Since it is a binary tree, each internal node has two child nodes.

Consider a full binary tree, where all leaves have the maximum number of nodes at each depth. For a full binary tree, the total number of leaves is  \(2^d\) , where d is the depth.

Each leaf node contributes \(2^-^d\) to the sum. Thus, the sum for a full binary tree is Σ  \(2^-^d\) = (2⁰ + 2⁰ + ... + 2⁰) = \(2^d\) * \(2^-^d\)  = 1. Now, if we remove any node from the full binary tree, the sum can only decrease, as we are reducing the number of terms in the sum. Hence, for any binary tree, the sum Σ \(2^-^d^_i\)  will always be less than or equal to 1.

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The simplification of the given expression using laws of exponents is; (3⁴)⁻¹/3³ = 3⁻⁷

We want to simplify the indices expression which is;

(3⁴)⁻¹/3³

Now, according to Laws of Exponents, we know that;

Applying the above Laws of Exponents, we can solve our expression;

(3⁴)⁻¹/3³ = (3⁴*⁻¹)/3³

⇒ 3⁻⁴/3³

Lastly;

3⁻⁴/3³ =  3⁽⁻⁴ ⁻ ³⁾

⇒ 3⁻⁷

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The slope of the line is given as -2/3.

We are also given the point (1, 1) in which this line passes through.

Before we can plot the graph of the line, we need to know the equation of the line first.

The values given are more than enough to find the equation of the line.

The formula used to get the equation of the line is given below:

Now, with this formula, let us find the equation of the line.

Thus, the equation of the line is:

Now, using a graph calculator, let us plot this equation.

After doing this, the following is the result:

Answer:

Step-by-step explanation:

1. Isolate Y by subtracting 13x from both sides

2. Divide the whole equation by the coefficient of y (-11)

Final Equation

y = 13x/-11 + 12/11

Hope this helps! :)

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

20 cm

Step-by-step explanation:

We can use ratios to solve

We know x = 7 since they are of equal length

x          x+7

----- = -------

10         y

7          7+7

----- = -------

10         y

Using cross products

7y = 14*10

7y = 140

Divide by 7

7y/7 = 140/7

y = 20

Answer:

2,292/3 = x/12

Step-by-step explanation:

if you were to solve

2,292/3 finds you how many people per hour

and multiply that by 12 to find how many people for 12 hours.

Step-by-step explanation:

\(\frac{2292}{3} =\frac{x}{12}\)  

cross multiply divide.

x=9168

Answer:

Total is 3

Step-by-step explanation:

AI-generated answer

Let's start by finding out how many marbles John had initially. We can do this by using the information given in the problem.

Let the original number of marbles be x.

John gave away 3/4 of his marbles, which means he has 1/4 of the original number of marbles left. We can express this as:

1/4 x = the number of marbles John has left

If we solve for x, we get:

4/1 * 1/4 x = 4/1 * the number of marbles John has left

x = 4 * the number of marbles John has left

Now we know that John had 4 times the number of marbles he has left.

Next, John receives another bag of marbles containing 2/4 (which is the same as 1/2) of the original number of marbles.

We can express this as:

1/2 x = the number of marbles in the new bag

To find the total number of marbles John has now, we can add the number of marbles he has left to the number of marbles in the new bag:

Total number of marbles = the number of marbles John has left + the number of marbles in the new bag

Total number of marbles = 1/4 x + 1/2 x

Total number of marbles = (1/4 + 1/2) x

Total number of marbles = (3/4) x

We know that x = 4 times the number of marbles John has left, so we can substitute this into the equation:

Total number of marbles = (3/4) * 4 * the number of marbles John has left

Total number of marbles = 3 * the number of marbles John has left

Therefore, the total number of marbles John has now is 3 times the number of marbles he has left.

Tell me in the commets if you didn't understand a word or something in the equation. :)

The probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

To determine the probability that a basketball player hits all 4 shots during a game, when the player hits three-point shots 41% of the time, we have to apply binomial probability distribution.

Let X be the number of successful shots when taking 4 shots, the probability of success in each trial, p = 0.41 and the number of trials, n = 4.

Therefore, we can use the binomial probability distribution as given below: `P(X = k) = (n choose k) × p^k × q^(n-k)

`Where q = 1 - p = 1 - 0.41 = 0.59 is the probability of failure.In this case, k = 4, and we can calculate P(X = 4) as follows:`P(X = 4) = (4 choose 4) × 0.41^4 × 0.59^(4-4)`= (1) × (0.41)^4 × (0.59)^0= 0.0416

Therefore, the probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

Note: A probability is a number between 0 and 1, and it can be represented as a fraction, decimal or percentage. In this case, we have represented the answer in percentage format.

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Answer:

Data handling refers to the process of collecting, storing, manipulating, and analyzing data. This can include tasks such as inputting data into a computer system, organizing and storing data in a database, cleaning and preprocessing data to make it usable, and performing statistical or other types of analysis on the data. It also includes visualization of data to make it more understandable. Data handling is an important aspect of many fields, such as business, science, and technology, as it allows for the efficient management and analysis of large amounts of information.

Answer:

Data handling is the process of ensuring that research data is stored, archived or disposed off in a safe and secure manner during and after the conclusion of a research project. This includes the development of policies and procedures to manage data handled electronically as well as through non-electronic means .

Answer:

It’s (-2,0) and (0,2)

Step-by-step explanation:

The required interval where a local maximum and a local minimum lie is (-2, 0) and (0,2).

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
For a function, the local minimum is defined as at a point the left and right-hand limit should be greater than of the point, while for a local maximum the left and right-hand limit should be lower.
So, while observing the table,
The graph between the interval (-2,0) is increasing, and decreasing so between this interval a local maximum is located,
while between the interval (0,2) graph of the function is decreasing than increasing, so a local minimum is located between the interval.

Thus, the required interval where a local maximum and a local minimum lie is (-2, 0) and (0,2).

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