I can't do the open number line.

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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Answer:

The value of the discriminant tells you whether the quadratic has 2 solutions, 1 solution, or no real solutions. If b2 – 4ac simplifies into a positive number, then the quadratic has 2 solutions. If b2 – 4ac simplifies into a 0, then the quadratic has 1 solution.

Step-by-step explanation:

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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1. At an annual interest rate of 17.11%, an average family needs 74 months to settle $7,942 at a $175 monthly payment.

2. The total interest is $4,932.10.

The monthly payment is the amount paid each month to settle the loan within its maturity period.

The monthly payment can be computed using an online finance calculator.

We can also determine the period of payment using the same online finance calculator as below.

I/Y (Interest per year) = 17.11%

PV (Present Value) = $7,942

PMT (Periodic Payment) = $-175

FV (Future Value) = $0

Results:

N = 73.566

Sum of all periodic payments = $12,874.10

Total Interest = $4,932.10

Thus, while it will take 74 months for the average American family to pay off the loan of $7,942 with a monthly payment of $175 at 17.11% interest, the total interest paid is $4,932.10.

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

Step-by-step explanation:

A nonagon has nine sides.

The sum of exterior angles = 360°, so each exterior angle is 360°/9 = 40°.

Each interior angle = 180°-exterior angle = 140°.

13x + 10° = 140°

x = 10°

Answer:

possible outcomes:

hotdog + potato salad

hotdog + macaroni salad

hamburger + potato salad

hamburger + macaroni salad

total outcomes: 4

Step-by-step explanation:

To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5

A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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The radius of the cylinder is 7. 9 in

First, we need to know the formula for volume of a cylinder

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters of the formula are expressed as;

From the information given, we have that;

Substitute the values

196 = 3.14 × 1 × r²

Divide both sides by the values

r² = 62. 42

Find the square root of both sides

r = 7. 9 in

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Answer: 2/90 = 1/45

Step-by-step explanation:

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The 9th term of the given sequence is 78732.

The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:

aₙ = a₁rⁿ⁻¹

Here, a₁ = 12 and r = 3.

Therefore, the formula for the nth term becomes:

aₙ = 12(3)ⁿ⁻¹

Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:

a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732

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The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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Answer

Option C is correct.

The mean, median and mode are all within two minutes of each other.

Explanation

To know which statement is correct, we have to compute a number of the terms mentioned in these statements.

65, 45, 110, 90, 95, 90, 60, 88, 120, 125



The mean is the sum of variables divided by the number of variables

Mean = (Σx)/N

x = each variable

N = number of variables

Σx = 65 + 45 + 110 + 90 + 95 + 90 + 60 + 88 + 120 + 125 = 888

N = 10

Mean = (888/10) = 88.8

The median is the variable in the middle of the distribution when the variables are arranged in descending or ascending order.

45, 60, 65, 88, 90, 90, 95, 110, 120, 125

Since there are 10 variables, the median will be the average of the two numbers in the middle, the 5th and 6th variable.

Median = (90 + 90)/2 = 90

The mode is the variable that occurs the most number of times in the distribution.

For this data, all the variables except 90 occur only once. So,

Mode = 90

Range is the difference between the highest and the lowest variable.

Range = 125 - 45 = 80

Interquartile range is the difference between the third and first quartile.

Third quartile is the variable at the 3(N + 1)/4 position in the distribution.

3(10 + 1)/4 = (33/4) = 8.25th variable.

This will be between the 8th and 9th variable.

Third quartile = (110 + 120)/2 = 115

First quartile is the variable at the (N + 1)/4 position in the distribution.

(10 + 1)/4 = (11/4) = 2.75th variable.

This will be between the 2nd and 3rd variable.

First quartile = (60 + 65)/2 = 62.5

Interquartile range = (Third quartile) - (First quartile) = 115 - 62.5 = 52.5

Now checking the statements, one at a time,

A.) The interquartile range is half the mean.

Interquartile range = 52.5

Mean = 88.8

We can see that 52.5 isn't half of 88.

So, the interquartile range is not half of the mean.

Option A is not correct.



B.) The range of the data is twice the interquartile range.

Range = 80

Interquartile range = 52.5

We can see that 80 is not twice of 52.5.

So, the range is not twice the interquartile range.

Option B is not correct.



C.) The mean, median and mode are all within two minutes of each other.

Mean = 88.8

Median = 90

Mode = 90

88.8, 90 and 90 are all within 2 minutes of each other.

So, the mean, median and mode are within two minutes of one another.

Option C is correct.



D.) If the 3 students who studied the least each added 15 minutes of study time, the median would increase by 5.​

This is not true.

The 3 students with the least minutes will have 60, 75 and 80 minutes if 15 minutes is added to their times. And this doesn't touch the median at all.

Hope this Helps!!!

Answer: likely

Step-by-step explanation:

B) Likely

Step-by-step explanation:

i just just answered the question on e d g e n u i t y

i hope this helps <3

The statement indicates that when a set X is partitioned, each partition forms an  parity relation by grouping together  rudiments that are considered original within each subset, thereby creating distinct and non-overlapping subsets within the original setX.  

The statement" each partition P of X defines an  parity relation on X" means that when a set X is divided into non-overlapping subsets or partitions, each partition creates an  parity relation on the original set X.

An  parity relation is a relation that satisfies three  parcels reflexivity,  harmony, and transitivity.  In the  environment of partitions, when a set X is divided into subsets, each partition forms an  parity relation by grouping together  rudiments that partake a common characteristic or property.

Within each partition, the  rudiments are considered original or affiliated to each other, and they're distinct from  rudiments in other partitions.  The meaning of" each partition P of X" refers to every possible way of dividing the set X intonon-overlapping subsets.

It implies that different partitions may  live grounded on different criteria or conditions for grouping  rudiments.

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Given the equation:

2x - 3y = 7

Let's find the equation of a line passing through (-2, 2) which ic parallel to the given line.

Apply the slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

Rewrite the given equation in slope-intercept form.

• Subtract 2x from both sides:

• Divide all terms by -3:

Therefore, the slope of the given line is 2/3.

Parallel lines have equal slopes.

Hence, the slope of the parallel line will also be 2/3.

Now, we have:

Plug in the coordinates of the point (-2, 2) for x and y respectively to find the y-intercept of the parallel line, b.

We have:

Add 4/3 to both sides:

Therefore, the equation of the parallel line in slope-intercept form is:

ANSWER:

Answer:

B (3/4,5/4)

Step-by-step explanation:

y = 2- x

\( \frac{5}{4} = 2 - \frac{3}{4} \)

y = 3x - 1

\( \frac{5}{4} = 3 \times \frac{3}{4} - 1 \)

\( \frac{5}{4} = \frac{9}{4} - \frac{4}{4} \)

Hope this helps ^-^

Answer:

Step-by-step explanation:

d.

Therefore , the solution of the given problem of unitary method is Boat is travelling at a speed of 21.6 miles /hour.

The unit method is a way of problem-solving where you first calculate the worth of a single group, subsequently multiply that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint or reciprocal are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators)

Here,

A boat has a speed = 36 km/hour

a km is about 60% of a mile.

1 km = 60/100 mile = 0.6 mile

the boat has a speed = (0.6 × 36) mile/hour

                                   = 21.6 miles/ hour

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The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Answer:

so im not sure it can either be 33, 1.5 or 49.5

Step-by-step explanation:

Answer:

$33.48

Step-by-step explanation:

Answer:

Train A = 466

Train B = 60

Step-by-step explanation:

Answer:

The volume of her cube is \(15.625\ cm^3\).

Step-by-step explanation:

The formula V = s³, where s represents the side length of the cube.

Side length of Marie’s cube is \(2\dfrac{1}{2}\ cm=\dfrac{5}{2}\ cm\)

We need to find the volume of the cube. We can find the volume of the cube using the above formula as follows :

\(V=(\dfrac{5}{2})^3\ cm^3\\\\=\dfrac{125}{8}\ cm^3\\\\=15.625\ cm^3\)

So, the volume of her cube is \(15.625\ cm^3\).

Answer:

7.9

Step-by-step explanation:

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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