Convert the rectangular equation x ^ 2 + y ^2 = 2 y to polar form

Answer:

x < -3

Step-by-step explanation:

When two fair dice are rolled the probability that two sixes will appear is 1/36. The probability of at least one six appearing is 11/36.

(a) The probability that two sixes will appear when rolling two fair dice can be calculated by multiplying the probability of rolling one six by itself, since each die roll is independent of the other. The probability of rolling a six on one die is 1/6, so the probability of rolling two sixes is:(1/6) × (1/6) = 1/36.

Therefore, the probability that two sixes will appear is 1/36.(b) To calculate the probability of at least one six appearing when rolling two fair dice, we can find the probability of the complement event (no sixes appearing) and subtract it from

1. The probability of no sixes appearing is the probability of rolling any number other than six on the first die (5/6) multiplied by the probability of rolling any number other than six on the second die (5/6), since the dice rolls are independent:(5/6) × (5/6) = 25/36.

Therefore, the probability of at least one six appearing is:1 − 25/36 = 11/36Therefore, the probability of at least one six appearing is 11/36.

When two fair dice are rolled the probability that two sixes will appear is 1/36. The probability of at least one six appearing is 11/36.

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Answer:

\(15x^3-38x^2+9x+18\)

Step-by-step explanation:

\((5x-6)(3x^2-4x-3)\\(5x)(3x^2)+(5x)(-4x)+(5x)(-3)+(-6)(3x^2)+(-6)(-4x)+(-6)(-3)\\15x^3-20x^2-15x-18x^2+24x+18\\15x^3-38x^2+9x+18\)

Answer:

x=-7

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

5+3x-37=6x+23-8x

add like terms

-32+3x=-2x+23

add 2x to both sides

-32+3x+2x=23

add 32 to both sides

3x+2x=23+32

add like terms

5x=55

divide by 5 on both sides

x=11

The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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Therefore, Kim still owes $294.06 on her credit card account.

Addition is a basic mathematical operation that combines two or more numbers or quantities to give a total or a sum. In other words, it is the process of finding the total when two or more values are combined. It is denoted by the plus symbol (+). For example, in the expression 5 + 3, 5 and 3 are the addends, and the sum or total is 8. Addition is one of the four basic arithmetic operations, the others being subtraction, multiplication, and division. It is widely used in many areas of mathematics, as well as in everyday life situations such as counting objects or adding up a shopping bill.

Here,

Starting balance on the credit card account = $810.00

Return 1: $37.66

Return 2: $120.00

Total credits from returns = $37.66 + $120.00 = $157.66

Adjusted balance after returns = Starting balance - Total credits from returns

Adjusted balance after returns = $810.00 - $157.66 = $652.34

Purchase 1: $86.50

Purchase 2: $10.00

Purchase 3: $10.00

Total purchases = $86.50 + $10.00 + $10.00 = $106.50

Adjusted balance after purchases = Adjusted balance after returns + Total purchases

Adjusted balance after purchases = $652.34 + $106.50 = $758.84

Payment = $500.00

Adjusted balance after payment = Adjusted balance after purchases - Payment

Adjusted balance after payment = $758.84 - $500.00 = $258.84

Finance charge = $35.22

Total amount owed = Adjusted balance after payment + Finance charge

Total amount owed = $258.84 + $35.22 = $294.06

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True. The is subset() method is used to check if all elements of set1 are present in set2, which means set1 is a subset of set2 if the is subset() method returns true.

True. The "is subset()" method can be used to determine whether set1 is a subset of set2. If all elements of set 1 are present in set 2, then set 1 is considered a subset of set 2. The method returns `True` if set1 is a subset of set2 and `False` otherwise.
In mathematics, if all the elements of A are also elements of B, then the set A is one of the set B; then B is a superset of A. A and B may be equal; if they are not, A is a necessary condition of B. A relationship in which one group is one of the other is called existence (or sometimes existence). A is part of B, it can also indicate that B contains (or contains) A, or that A contains (or contains) B. A k-subset is a subset with k elements.

A linked subset defines the partial order of a set. In fact, intersection and union give intersection and intersection, with subsets of the given set being Boolean algebra in the relationship, and the link itself is a Boolean coverage relationship.
Example usage:
```python
set1 = {1, 2, 3}
set2 = {1, 2, 3, 4, 5}

result = set1.issubset(set2)
print(result) # Output: True
```

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The joint mass function of X1 and X2 is P(X1 = i, X2 = j) = (\(1-p)^(i+j) * [p + [(1-p)^(i+j+1) - 1] / p]\)

We need to find the joint mass function of X1 and X2, i.e., P(X1 = i, X2 = j) for i, j ≥ 0.

First, note that X1 and X2 are not independent. Specifically, we have:

P(X2 = j | X1 = i) = P(j failures between the (i+1)st and (i+j+1)st trials, given that the first i trials are failures and the (i+1)st trial is a success)

= \((1-p)^j * p\)

Now, we can use the law of total probability to find P(X1 = i, X2 = j) by considering all possible values of the first success:

P(X1 = i, X2 = j) = P(X1 = i, X2 = j | first success on trial 1) x P(first success on trial 1)

P(X1 = i, X2 = j | first success on trial 2) x P(first success on trial 2)

P(X1 = i, X2 = j | first success on trial 3) x P(first success on trial 3)

...

For the case where the first success occurs on trial k, where k ≥ 2, we have:

P(X1 = i, X2 = j | first success on trial k)

= P(i failures on trials 1 to k-1) x P(j failures on trials k to k+j-1) x P(success on trial k)

= (1-p)^(i+k-2) x (\(1-p)^j\)x p

For the case where the first success occurs on trial 1, we have:

P(X1 = i, X2 = j | first success on trial 1)

= P(i failures on trials 1 to 1) x P(j failures on trials 2 to j+1) x P(success on trial 2)

= (1-p)^i x (\(1-p)^j\) x p

Therefore, we have:

\(P(X1 = i, X2 = j) = (1-p)^i * (1-p)^j * p + Σ_{k=2}^{i+j+1} (1-p)^(i+k-2) * (1-p)^j * p= (1-p)^(i+j) * [p + Σ_{k=1}^{i+j} (1-p)^k]\)

We can simplify the expression in the brackets using the formula for the sum of a geometric series:

\(Σ_{k=1}^{i+j} (1-p)^k = [(1-p)^(i+j+1) - 1] / (1-(1-p))\)

\(= [(1-p)^(i+j+1) - 1] / p\)

Therefore, the joint mass function of X1 and X2 is:

P(X1 = i, X2 = j) = (1-p)^(i+j) x [p + [(1-p)^(i+j+1) - 1] / p]

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Answer:

15 inches

Step-by-step explanation:

you use Pythagorean Theorem

Answer:

width is 3m

Step-by-step explanation:

Length is x + 3

Width is x

Area of the remaining part is 2 * 6 = 12

Area of the whole floor is 12 + 6 = 18

\(area = l \times w \\ 18 =(x + 3) \times x \\ 18 = {x}^{2} +3x \\ { x}^{2} + 3x = 18 \\ {x}^{2} + 3x - 18 = 0 \\ {x}^{2} + 6x - 3x - 18 = 0 \\ (x - 3)(x + 6) = 0 \\ x - 3 = 0 \\ x = 3\)

The point when reflected across the y-axis is (0, -9)

From the question, we have the following parameters that can be used in our computation:

Point = (0, -9)

Transformation = Reflect the point across the y-axis:

The rule of reflection across the y-axis is represented as

(x, y) = (-x, y)

Substitute the known values in the above equation, so, we have the following representation

Image = (0, -9)

Hence, the image is (0, -9)

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Answer:

$15

Step-by-step explanation:

20-5= 15

Answer: The range is 15 because 20 is the highest and 5 is the lowest and when you subtract them you get 15.

Hope this helps :)

Answer:

26

Step-by-step explanation:

\(5^{2}\) = 5 · 5 = 25

then add 1

Answer:

26

Step-by-step explanation:

(5 x 5) + 1

25 + 1

26

Have an amazing day!!!

PLEASE RATE AND MARK BRAINLIEST!!!

Answer:

Simplifying -16t2 + 48t + 160 = 0

Reorder the terms: 160 + 48t + -16t2 = 0

Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0

Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.

hope it helps.

The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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Answer:

K and R      S and D

Step-by-step explanation: i hope this helps

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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wrong one -----/////

A-1 = (ATA)-1AT, and therefore ATA is also invertible.

If A is invertible, it means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. This means that A has an inverse, denoted by A-1.

Now, let's consider the matrix ATA. To show that it is also invertible, we need to find a matrix C such that (ATA)C = C(ATA) = I. We can do this by substituting B = A-1 into the equation and multiplying both sides by A:ATAA-1 = AIA-1 = AA-1 = I

This means that C = A-1 is the inverse of ATA, so (ATA)-1 = A-1. Now, let's substitute this back into the equation to find A-1:A-1 = (ATA)-1AT = A-1ATA-1AT = A-1IT = A-1

Thus, we have shown that A-1 = (ATA)-1AT, and therefore ATA is also invertible.

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Answer:

c

Step-by-step explanation:

The polynomial 2x^3 - 4x^2 + 3x - 7 has the remainder is -1, and the quotient is 2x^2 + 3.

To find the quotient and remainder of a polynomial, follow these steps:

Arrange the polynomials in descending order of degrees.

Divide the term with the highest degree of the dividend polynomial by the term with the highest degree of the divisor polynomial. This will be the first term of the quotient.

Multiply the divisor polynomial by the first term of the quotient and subtract the result from the dividend polynomial.

Bring down the next term from the dividend polynomial.

Repeat steps 2 to 4 until all the terms of the dividend polynomial are exhausted or the degree of the remaining polynomial is lower than the degree of the divisor polynomial.

The resulting polynomial after the division process is complete is the remainder.

The terms obtained during the division process form the quotient polynomial.

For example, let's divide the polynomial 2x^3 - 4x^2 + 3x - 7 by the polynomial x - 2.

The term with the highest degree in the dividend polynomial is 2x^3, and the term with the highest degree in the divisor polynomial is x.

Dividing 2x^3 by x gives 2x^2, which is the first term of the quotient.

Multiply (x - 2) by 2x^2, giving 2x^3 - 4x^2.

Subtracting 2x^3 - 4x^2 from the dividend polynomial gives 3x - 7.

Bring down the next term, which is 3x.

Dividing 3x by x gives 3, which is the next term of the quotient.

Multiply (x - 2) by 3, giving 3x - 6.

Subtracting 3x - 6 from the remaining polynomial gives -7 + 6 = -1.

Since the degree of -1 is lower than the degree of x - 2, the division process is complete.

The remainder is -1, and the quotient is 2x^2 + 3.

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The value of x as per the similarity of triangles is = 7.1.

If two triangles' sides have the same ratio or proportion and their angles are the same (corresponding angles), then the triangles will resemble one another (corresponding sides).

Similar triangles may have varied side lengths when compared individually, but they must all have the same ratio of their side lengths and equal angles.

Now in the figure, the triangles are similar.

So, sides of the triangles will be proportional to each other.

Now, 9/15 = 4.3/x

⇒ x = (4.3 × 15)/ 9

⇒ x = 7.1

Therefore, the value of x as per the similarity of triangles is = 7.1.

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Answer:

They need to wash 72 cars

Step-by-step explanation:

2000 - 1640 = 360

360/5 = 72

The correct answer is She have left $7.5 after buying the coat and skirt.

Step-by-step explanation

This question is incomplete, the complete question is:

Mary had $60 and spent 0.75 o 3/4 of it on a coat. She then bought a skirt with 50% of the money that she had left. How much money did she have left after buying the coat and skirt?

The answer is $7.50

Explanation:

To know how much money Mary has left after buying the coat we have to multiply $60 by 0.75 as this would help us know the price of the coat.

60 x 0.75 = 45 (price of the coat)

Then we have to subtract 45 from 60 to know how much money she have left after buying the coat.

60 -45 = 15 (Money left)

Then she bought a skirt with 50% of the money that she had left. To know how much money costs the skirt we have to multiply 15 by 0.50. The result of this operation is $7.5, and finally, we have to subtract again $7.5 that she spent on her skirt from $15 and the final result is $7.5

Answer:

4

Step-by-step explanation:

Step 1:

6x + 10 + 2x = 42          Equation

Step 2:

8x + 10 = 42     Combine Like Terms

Step 3:

8x = 32     Subtract 10 on both sides

Step 4:

x = 32 ÷ 8     Divide

Answer:

x = 4

Hope This Helps :)

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability.

The term "experiment" in the context of probability refers to a process or activity that involves observing or measuring an outcome that is subject to chance or uncertainty. The outcome of an experiment is not necessarily predictable with certainty, and it may depend on various factors such as the conditions under which the experiment is conducted and the randomness inherent in the process.

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability. An experiment is essentially a process that leads to one of several possible outcomes, and the probability of each outcome can be calculated or estimated based on the underlying assumptions and factors involved. Examples of experiments in probability include rolling a die, tossing a coin, drawing a card from a deck, or conducting a clinical trial to test a new drug.

Option b) is not an appropriate definition of an experiment because it suggests that the outcome can be predicted with certainty based on mathematical analysis, which is not always the case in experiments involving chance or uncertainty.

Option c) is also not an appropriate definition of an experiment because it suggests that an experiment is conducted to confirm a hypothesis, which may or may not be true. While experiments can be used to test hypotheses and provide evidence to support or refute them, the primary goal of an experiment in the context of probability is to observe or measure the outcome and calculate the probability of each possible outcome.

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Using the concept of Randomized Design ,we got 4 levels of treatment heave been done by farmer in this experiment.

1.Completely Randomized Design :-

A completely randomized design is basically the simplest experimental design, in terms of data analysis and convenience. With this design, subjects are randomly assigned to treatments.

This completely randomized design actually relies on randomization to control for the effects of extraneous variables. The experimenter actually assumes that, on average, extraneous factors will affect treatment conditions equally; so any relevant differences between conditions can fairly be attributed to the independent variable.

2.Double Blind Design :-

In an experiment, if subjects in the control group knows that they are receiving a placebo, the placebo effect will be reduced or will be eliminated; and the placebo will not serve its intended control purpose.

Blinding is basically the practice of not telling subjects whether they are receiving a placebo. In this way, subjects which are in the control and treatment groups experience the placebo effect equally. Often, knowledge of which groups receive placebos is also keep from analysts who evaluate the experiment. This practice is called double blinding. It prevents the analysts from "spilling the beans" to the subjects through subtle cues; and it assures that their evaluation is not tainted by the awareness of actual treatment conditions.

3.Matched Pairs Design :-

A matched pairs design is actually a special case of a randomized block design. It can be used when the experiment has basically only  two treatment conditions; and subjects can be grouped into pairs, on the basis of some blocking variable. Then, within each pair, subjects are randomly assigned to different treatments.

4.Randomized Block Design :-

With a randomized block design, the experimenter actually divides subjects into subgroups called blocks, such that the variability within blocks will become  less than the variability between blocks. Then, subjects within each block are randomly assigned to treatment conditions.

Hence, we got 4 levels of treatment have been done by farmer in this experiment.

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Given:

The volume of a cube = \((2+3p)^3\ \text{cm}^3\)

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

\(V=a^3\)            ...(i)

Where, a is the side length.

It is given that,

\(V=(2+3p)^3\ \text{cm}^3\)         ...(ii)

On comparing (i) and (ii), we get

\(a=2+3p\text{ cm}\)

Now, the total surface area of a cube is:

\(A=6a^2\)

Where, a is the side length.

Putting \(a=2+3p\), we get

\(A=6(2+3p)^2\)

Therefore, the total surface area of the cube in terms of p is \(6(2+3p)^2\ \text{cm}^2\).

Step-by-step explanation:

a) for the first part, you take your compass and stretch it more than halfway on to line UV. Place the fixed point at V and draw a curve. make sure you keep your compass the same size, put the fixed part of your compass on point U and draw a curve again. both curves should go both upward and downward. Now, your curves should meet at two points. use your straight edge to draw the line that meets at both points. I have drawn an example of what it should approximately look like. for the second part you are simply using your straight edge to draw a line from T down to the median M you previously found. I have drawn a second picture to show you.

b) now to check if they are perpendicular, we must find the slope of each line. I will not be able to do this accurately since I didn't use an exact method to find M, so you must follow my steps.

Step 1: find the slope of UV. To do so, we must take two points from the line. I will take points U and V because they are easiest to see. To find the slope, we can use the equation:

\(m = \frac{y2 - y1}{x2 - x1} \)

where m is the slope.

so, let's define our points.

Point V is (4,4), let's call this point one.

Point U is (14,6), let's call this point two.

So,

x1= 4

y1= 4

and

x2= 14

y2= 6

now, we can plug these into our slope equation.

\(m = \frac{6 - 4}{14 - 4} = \frac{2}{10} = \frac{1}{5} \)

You must then use the points T and M in order to solve the second slope. Where T is (2,12). I will keep M as (x1, y1) for now.

The equation should then look like:

\(m = \frac{2 - y1}{12 - x1} \)

now, in order for it to be perpendicular to our original slope, it must be the opposite reciprocal, which is the number flipped and made negative. The opposite reciprocal of 1/5 will be -5.

It should NOT be, as we have been told. So, we can state:

"I know that TM is not perpendicular to UV because the UV has a slope of 1/5 and TM has a slope of x, which is NOT the opposite reciprocal on 1/5."

Hope this helps! :)