For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.

Answer:

Below

Step-by-step explanation:

x^6 -16x^2   =   x^2 ( x^4 - 16 )    is one possibility

                                             ( you didn't include choices)

well, is really "x", which oddly enough is the 100%, but we also know that 4% of "x" is 1.48, hmmm what the heck is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.48& 4 \end{array} \implies \cfrac{x}{1.48}~~=~~\cfrac{100}{4} \implies \cfrac{ x }{ 1.48 } ~~=~~ 25\implies x=37[/tex]

Answer:

B

Step-by-step explanation: It is very simple. All you have to do is to do 350 000 divided by 700 which gives you 500. That's your answer!

Answer:

760ft

Step-by-step explanation:

Use the formula: πr^2h where r = radius(diameter/2) and h = height

radius: 11/2 = 5.5

pi: 3.14

Height: 8

3.14*5.5^2*8

= 759.88

Rounded: 760 ft

The solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.

Synthetic division, which is frequently used to determine a polynomial's zeros, is described as a streamlined method of dividing a polynomial with another polynomial equation of degree 1. Comparatively easier to calculate than the long division method, this division method is carried out manually.

we know that the volume of a rectangular prism as where V is volume ,A is area ,H is height

Now, we are given

V=[tex]2x^{3}+9x^{2} -8x-36[/tex]

h=x+2

now, we can find A

V=A*h

A=V/h

now, we can plug it

[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2}[/tex]

now, we can use synthetic division method

so, we can write it as

A=[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2} = 2x^{2} +5x-18[/tex]

So the area of base=[tex]2x^{2} +5x-18[/tex]

Therefore ,the solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.

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If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.

Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.

Sampling distribution of the sample mean:

using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.

The standard deviation of the population is σ = 3.1 and the sample size is n =103, people

The standard deviation σ/√n= 3.1/√103 =0.31.

As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.

x-bar ≈ N (216, 0.31)

μ_{x-bar}  = 216

σ_{x-bar}  =0.31

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(complete question)

Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.

The answer to the parts for the given standard deviation are 859, 629 , 308, 477.

What is standard deviation?

Standard Deviation may be a live that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists

Main body:

1 )

mean=5.6

sd=1.2

total number 1000 find number weight between 4 to 9 pounds

z=x-mue/sd

⇒ 4-5.6/1.2=-1.6/1.2 =-1.33

z value by table = 0.09176

⇒z=7-5.6/1.2=1.4/1.2 = 1.666

z value by table =0.95154

effective value  0.95154 -0.09176 = 0.8598

number of children =1000 x 0.8598=859.8

babies expect to weigh between 4 and 7 pounds are 859.

2)

less than 6 pounds

z=6-5.6/1.2=0.4/1.2=0.333

z value by table = 0.62930

number of children born less than 7 pounds =0.62930 x 1000=629.3

means 629 children less than 6 pounds

3)

more than 5 pounds

z=5-5.6/1.2= -0.6/1.2= -0.5

z value as per table -0.5 = 0.30854

number of children born 1000 x 0.30854=308.5

number of children born more than 5 pounds are 308

4)

weight between 5.6 to 8 pounds

z=5.6-5. 6/1.2=0/1.2 =0

value of z by table 0.5

z=8-5. 6/1.2=2.4/1.2 = 2

value of z by table 0.97725

0 value will be 0.97725-0.5000=0.4772

number of children born between 5.6 to 8 pounds=0.4772 x 1000 = 477.2 means 477.

Hence the value are as follows

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There are 1365 different committees that are possible if a group of 3 men refuses to serve together.

Given that,

From an 8 men, 7 woman group A committee made up of four men and three women will be created.

If all prerequisites are met, a total of committees could be formed.

⁸C₄ x ⁷C₅=  70 x  21= 1470

Three males now reject serving in unison.

As a result, in the event that they serve simultaneously, a combination is= ⁵C₄ x ⁷C₅= 5 x 21= 105

Therefore, a combination that could be used in the event that they don't work together is = 1470- 105= 1365

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The quadratic equation y = x² - x - 2 has a domain with all real numbers and a range with all values equal to or greater than - 9 / 4.

The domain of a function is the set of values of x that belongs to the functions and the range of the function corresponds to its set of values of y. In this case we find the definition of a quadratic equation, of which we must determine its domain and range. A brief manner to determine them is modifying the function by deriving its vertex form:

y - k = C · (x - h)²

Where:

First, write the quadratic equation:

y = x² - x - 2

Second, modify the equation into its vertex form:

y + 1 / 4 = x² - x + 1 / 4 - 2

y + 9 / 4 = x² - x + 1 / 4

y + 9 / 4 = (x - 1 / 2)²

The domain of all quadratic functions is all real numbers and the range of the quadratic function y = x² - x - 2 is y ≥ - 9 / 4 as the vertex constant is greater than zero.

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There are no solutions to linear equations of the following equation  

5-4x-7-10x=-8x-4-6x-10, because if they have the same variable term but different constant values on opposite sides of the equation.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation.

The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Given equation is ,

5-4x-7-10x=-8x-4-6x-10

-14x-2=-14x-14

If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.

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Answer:

Step-by-step explanation:

Given: AC = CB

CD Bisects AB 

Prove: ΔADC= ΔBDC

AC≅CB Given

AD ≅ DB are congruent because of the segment bisector theorem.

DC≅DC reflexive property

ΔADC≅ ΔBDC  SSS theorem

Answer:

8.24 + 7s + 1

Step-by-step explanation:

You negate everything in the parentheses, so --7s and --1, which turns into 7s and 1.

The irregular hexagon has an area of 147 square units. (Correct choice: A)

In this problem we have an irregular hexagon that is the result of subtracting a small rectangle from a great rectangle. Likewise, the area of this hexagon is the result of subtracting the area of the small rectangle from the area of the great rectangle. From geometry we know that the area formula for the rectangle is:

A = w · h

Where:

Now we proceed to determine the area of the irregular polygon:

A'' = A - A'

A'' = 13 · 12 - 3 · 3

A'' = 156 - 9

A'' = 147

The area of the irregular hexagon is equal to 147 square units.

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On tossing a fair coin 9 times, the probability of no more than 8 heads where at least one toss is heads would be 511/512.

The possibility of an event happening is gauged by probability. Many things are difficult to forecast with absolute confidence. We can only anticipate the likelihood of an event occurring using it. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

How to solve?

total number of possibilities on tossing a coin 9 times= 2^9

number of ways to get all heads = 1/2^9

number of getting at most 8 heads = number of ways of getting one tail

= 1 - 1/2^9

=511/512

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The fraction when five friends divide three bags of apples equally between them is 3/5.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Therefore, the fraction when five friends divide three bags of apples equally between them will be:

= Number of apple / Number of friends

= 3/5

The fraction is 3/5.

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The value of "-3" in the context of this situation is "tiger loses 3 balls each round".

The correct answer option is option A

y = -3x + 28

Where,

For instance, if the tigers played 8 rounds of golf,

The number of golf lost = - 3x

= -3(8)

= -24

Then,

The number of golf balls in tigers golf bag,

y = -3x + 28

= -3(8) + 28

= -24 + 28

= 4 golf balls.

Therefore, the situation can be solved using equation and determining the parameters of the equation.

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Answer:

Tiger begins with 3 balls in his golf bag.

Step-by-step explanation:

:)

Answer:

I think the values are :

Step-by-step explanation:

AC= -5

CB= -2

AB= -3

The equation that represents the predicted amount y that the store will make from sales of accessories and services x for the entire year is  y = 0.05x + 2500

As it is given that  Enrique can make extra money from the sales of services and accessories for computer products sold by his store and the store makes x dollars selling computer products,  he predicted to the store will make 0.05x dollars ($0.05) from selling accessories.we consider x to be dollars of selling computer products, in the month of January and February of this year, the stored made $2,500 from sales of accessories and services.

so the linear equation will be : y = 0.05x + 2500

If  sales from accessories and services for the entire year will be $5,000, then the  equation will be :

y = 0.05x + 5000

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The system of equations has no solutions, the correct option is A.

The system of equations is:

y = x^2 + x + 3

y = -2x -5

The system can be solved if we solve the equation:

-2x - 5 = x^2 + x + 3

So we need to solve that quadratic equation, we can rewrite it as:

x^2 + x + 3 + 2x + 5 = 0

x^2 + 3x + 8 = 0

Let's check the discriminant to see how many solutions we have:

D = (3)^2 - 4*1*8

D = 9 - 32 = -23

We have a negative discriminant, so we only have complex solutions, thus, the system of equations has no solutions.

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In this case, the standard error would be standard error = 2.50 / sqrt(41) = 0.342 and the z-score would be z = (5.61 - 5.00) / 0.342 = 1.71

A z-score value is the numerical measured value of the relationship of a value to the mean of a group of values and it is measured in the terms of standard deviations from mean value.

The z-score is measured by formula z=(x- μ)/ a where x is the raw score, μ is the population mean and a is the population standard deviation. So to calculate z-score, we subtract the population mean from the raw score and divide it by the population standard deviation.

standard error = population standard deviation / sqrt(sample size)

standard error = 2.50 / sqrt(41) = 0.342

Next, you would need to calculate the z-score for the observed mean wait time of 5.61 minutes.

z = (observed mean - population mean) / standard error

z = (5.61 - 5.00) / 0.342

z= 1.71

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8 ounce of yellow color required.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

if you mix 3 ounces of blue paint and 2 ounces of yellow paint.

So, we have the composition ratio as 2:3

Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.

Thus, yellow = 2/5 x 20= 8 ounce

Blue= 3/5 x20 = 12 ounce

Hence, 8 ounce of yellow color required.

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The temperature of the liquid at noon would be of:

-2.25ºC.

The linear function in this problem is defined in the slope-intercept format, as follows

y = mx + b.

In which the coefficients of the function are given as follows:

The values of these coefficients are given as follows:

m = -3/4, b = 0.

Then the function that gives the temperature in x hours after 9 A.M. is of:

y = -3/4x.

Noon is three hours after 9 A.M., hence the estimate is given as follows:

y = -3/4(3) = -9/4 = -2.25ºC.

The problem states that the initial temperature is of 0ºC at 9 A.M.

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Answer:

The equation is 15x + 2.50y = 800, where x is the number of care packages and y is the number of food satchels. Solving for y, we get y = 32. Therefore, each package contained 32 food satchels.

Step-by-step explanation:

Percentage of buyers who paid more than $155,000 is equal to 2.78%.

The standard deviation is a metric that reveals the degree of variation (such as spread, dispersion, and spread) from the mean. The standard deviation represents a "average" departure from the mean. Because it uses the original units of measurement from the data set, it is a well-liked measure of variability. Similar to variance, there is little variation when data points are close to the mean, but there is much variation when data points are widely scattered from the mean. The amount of departure from the average is determined by standard deviation. The most common measurement of dispersion, the standard deviation, is based on all values. Therefore, a change in even one value has an impact on the standard deviation's value. It is

Given:

Mean is $150,000, and

Standard deviation is $2500.

We need to determined the percentage of buyers who paid more than $1,55,000 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

z=    [tex]\frac{x-μ}{σ}[/tex]

As given in question sample mean i.e. X= 150,000

= [tex]\frac{1,55,000- 1,50,000}{2500}[/tex]

=2

By using standard normal distribution table,

P(X > 155000) = P( z > 2 )

= 1 - 0.9772

=0.0278

Hence, it is equal to 2.78%.

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A linear function with a rate of change of +5 is depicted in the table as m = 13 + 5 = 18.

A straight line on the coordinate plane is represented by a linear function.

As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).

We will discover what a linear function is in this article, along with information on its graph, domain, and range.

Additionally, we will learn how to recognize a linear function and how to calculate its inverse.

According to our question-

The graph in the table shows a linear function.

The linear function's general equation is y = ax+b, where a denotes slope and b denotes a constant.

Finding the equation of the linear function at x = 3 y = 13 and at x = 5 y = 23 13 = 3a+b by utilizing the first and third points from the table (1)

23 = 5a+b → (2) find a and b by resolving (1) and (2)

Consequently, a = 5 and b = -2; y = 5x – 2

After then, the equation of y = y = 5*4-2 = 18 was changed by substituting x = 4 in it.

m = 18

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Answer:

The answer is d: 24 square meters

Answer:

9/20

Step-by-step explanation:

(9/10)*(1/2)

(9/20) times

Answer: tis answer would be 9 over 20

Step-by-step explanation:

We know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).

So, we know that:

Each sheet is 1/2 inch thick.

The worker prepares a stack of 10 sheets.

Then, calculate the thickness of the tack as follows:

1/2 * 10

1 * 5

5 inches

Therefore, we know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.

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(a) The amount will be increasing by 83%.

(b)  Part B's account has a higher percentage change in money over the preceding year than Part A's account.

A part or quantity in every hundred is defined as a percentage. It's a fraction having a denominator of 100. The percentage difference is the change in the value of a quantity over time expressed as a percentage difference. Percentage Change is a term used to describe the growth or decrease in a quantity expressed in percentages.

Find:

Whether the amount is increasing or decreasing over the years and which is experiencing a greater change.

From the given equation,1.831>1 , this shows that money in account A is  83% more, compared to its previous year. The amount will be increasing by 83%.

Part B:

The change in each consecutive term is 94%. This shows that the consecutive term is multiplied by 94%  the previous year's amount. As a result, Part B's account has a higher percentage change in money over the preceding year than Part A's account.

Hence we get the required answer.

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660 or it may not be that because only said that theres 22 classrooms. So yeah ;)

30 x 22 = 660 its just multiplication