Given the point (3,3√3). perform the following: a. find a polar coordinate (r.) of the point where r> 0 and 0 ≤ 0 <2n b. find a polar coordinate (r. 8) of the point where r <0 and 0 ≤ 8 <2n 2. Given the polar curve r² = 2 sin 20, obtain its equivalent Cartesian equation Convert the equation (x² + y²)² = 4x² - 4y² into a polar equation. 3. Locate the following points (2,4,-1) (-3.1.-2) O (7.-2.-6) O (-2.-3.-4) Let A(1, -5,2), B(3,2,-4) and C(-4.1.3). Find the midpoint of DC where D is the midpoint of AB a point in the z-axis that is equidistant to both A and B. the sphere centered at C, containing B. Define as the vector from (3, 1,-2) to (1,5,2). Find ||7 and its directional cosines. If u = (2,-3,1), 7= (1.0,-1) and = (-1,3,-2). find: O 20-V ou-v+w o - (0.5+1.57) Let ū=i-2j+k, v=4i+j-3k and w=2j-k. Find O 7-1 o uxi O xu ou-x w 。üxwxv A unit vector that lies in the xy-plane that is orthogonal to it. 2) Find an equation of the plane containing the point (2,1,3) and having 3i-4j+k as a normal vector. 3) Find the symmetric equation of the line that contains the points (3,4,1) and (-1.-2,5) 4) Find the point of intersection of the two lines. (₁:3=y= and (2: 2 x+3_5-y 3 =2+2

The error in the given equation is that the expression "cot(-x)" is incorrect. The correct expression should be "cot(x)" instead. With this correction, the equation would simplify to "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

In the given equation, the error lies in the term "cot(-x)". The cotangent function is an even function, meaning that cot(-x) is equal to cot(x). Therefore, the original equation simplifies to "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

The cotangent function, cot(x), is defined as the ratio of the adjacent side to the opposite side in a right triangle, where the angle is x. Since the cotangent function is the reciprocal of the tangent function, cot(x) is equivalent to 1/tan(x).

By substituting this equivalence into the equation, we can rewrite it as "1/tan(x) + 1/tan(x) = 2cot(x)". Simplifying further, we get "2/tan(x) = 2cot(x)". Canceling out the common factor of 2 on both sides of the equation, we arrive at "1/tan(x) = cot(x)". Therefore, the correct equation should be "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

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Answer:

d. How many animals weigh at least 15 pounds?

Step-by-step explanation:

The histogram displayed holds information about the number of animals who have a certain certain weight interval. Hence, answering questions about a point weight such as the number of animals whose weight is 4.9. This is a point value and such information given by the histogram.

Similarly, number of animals for intervals which aren't Cleary and explicly stated on the horizontal x - axis of the histogram cannot be determined by the histogram such as ; number of animals weighing less than 8 pounds and number of animals weighing between 5 and 10 pounds.

However, the number of animals weight less Than 15 pounds can be obtained from the histogram. This includes the sum give by the first, second and third bar. This is about (8 + 17 + 10) = 35 animals.

Answer:

17 meters

Step-by-step explanation:

Plug x=30 into the equation H(x) = 11 + 0.2x

H(30) = 11 + 0.2 * 30

H(30) = 11 + 6

H(30) = 17

Thus, the answer is 17 meters.

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

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Answer:

The area of the shaded region = (36·π - 72) cm²

The perimeter of the shaded region = (6·π  + 12·√2) cm

Step-by-step explanation:

The given figure is a sector of a circle and a segment of the circle is shaded

We have that since the arc AC subtends an angle 90° at the center of the circle, the sector is a quarter of a circle, which gives;

Area of sector = 1/4×π×r²

As seen the radius, r = AB = 12 cm

∴ Area of sector = 1/4×π×12² = 36·π cm²

The area of the segment AB = Area of sector ABC - Area of ΔABC

Area of ΔABC = 1/2×Base ×Height =

Since the base and the height = The radius of the circle = 12 cm, we have;

Area of ΔABC = 1/2×12×12 = 72 cm²

The area of the segment AB = 36·π cm² - 72 cm² = (36·π - 72) cm²

The area of the shaded region = The area of the segment AB = (36·π - 72) cm²

The perimeter of the shaded region = 1/4 perimeter of the circle with radius r + Line Segment AC

The perimeter of the shaded region =  1/4 × π × 2 × r + √(12² + 12²) = 1/4 × π × 2 × 12 + 12·√2 = (6·π  + 12·√2) cm

The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

It is given that:

14.2 cm correct 1 decimal place

14.2

Rounded to the nearest 0.1 or

the Tenths Place.

Rounded to the nearest tenth place. The 2 in the tenth place rounds down to 2 or stays the same because the digit to the right in the hundredth place is 14.2

Thus, the 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

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Answer:

no

Step-by-step explanation:

f(x) = x^3 has a domain of all real number and a range of all real numbers

f(x) = x^3 +k  just shifts the function up k units ( or down k units if k is negative)

It will not affect the domain or the range

Answer:

(x,y)--(-X, "): A' is at (5, -1)

Step-by-step explanat

Answer:

(x,y)→(−x,−y); A' is at (5, −1)

Step-by-step explanation:

Answer: The answer is 7/12

Step-by-step explanation:

First, multiply the denominators by each other (4*3) and you get 12. Then 12 is the main denomanator. Then multiply the numberators by the opposite numberator. (3*1 and 4*1). Then you will put (4/12+3/12) which you add the numberators together but keep the same denomerator and you will get (7/12)

The original number of dolls each girl owned is Linda = 8, Clare = 63, and Jane 45.

A ratio indicates the number of times one number contains another.

Given that, the total number of dolls is 116.

Let Linda, Clare, and jane have L, C, and J dolls respectively.

Now, Linda received 15 dolls from Clare, which can be represented as:

L + 15 and C - 15

Since Jane gave 13 dolls to Linda, the expression becomes:

L + 15 + 13, C - 15, J - 13

Or, L + 28, C - 15, J - 13

Now, the ratios are:

L + 28 : C - 15 = 3 : 4

J - 13 : C - 15 = 2 : 3

Rewrite the ratios after multiplying the first ratio by 3 and the second ratio by 4:

L + 28 : C - 15 = 9 : 12

J - 13 : C - 15 = 8 : 12

The ratio of all three is:

L + 28 : C - 15 : J - 13

  9      :     12   :    8

Note that the number of total dolls is still 116, therefore,

9 + 12 + 8 = 116

29 = 116

1 = 4

Hence, 1 unit is equivalent to 4 dolls.

The value of 9 is:

9 ×4 = 36

Hence,

L + 28 = 36

L = 8

Similarly,

C - 15 = 12 × 4

C - 15 = 48

C = 63

And,

J - 13 = 8×4

J - 13 = 32

J = 45

Hence, the original number of dolls each girl owned is Linda = 8, Clare = 63, and Jane 45.

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Answer:

its 3.

Step-by-step explanation:

Answer:

(3)

(1)

(4)

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

its 56 i think but tell me if its right or no Arigatōgo

Step-by-step explanation:

The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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Answer:

21 pounds

Step-by-step explanation:

Given that f varies inversely with l then the equation relating them is

f = \(\frac{k}{l}\) ← k is the constant of variation

To find k use the condition f = 15 when l = 7, then

15 = \(\frac{k}{7}\) ( multiply both sides by 7 )

105 = k

f = \(\frac{105}{l}\) ← equation of variation

When l = 5 , then

f = \(\frac{105}{5}\) = 21 pounds

Answer:

300

Step-by-step explanation:

50 x 6 gets your explanation.

Answer:

15 dollars

Step-by-step explanation:

2.50×6= 15

two dollars and fifty cent times the amount of days equals the amount of money Kasie has in here bank account

10 pounds of food each chicken eat last week.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

Each chicken eats the same amount of food, as per the question. Let's assume there is x number of chickens.

Therefore, if each chicken eats the same amount of food then the total food required for all chickens is, (x × x) = x² pound.

Again, Mrs. Rollins bought 100 pounds of chicken food.

Hence x² is equivalent to 100 pounds. We can generate an equation from this. Which is,

x² = 100

Or, √x² = √100         [ root both sides ]

Or, x = 10

Now, we can conclude that there are 10 chickens and each chicken eats 10 pounds of food in a week.

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The McNemar's Test can be thought of as the chi-square type equivalent to the paired t-test.

The McNemar's Test is a non-parametric statistical method used to analyze the differences between paired or matched categorical data, such as repeated measurements on a single group. Like the paired t-test, which is used to compare continuous data, the McNemar's Test evaluates the changes in the proportions of success or failure between the paired observations.

This test is particularly useful when dealing with small sample sizes or when the assumptions of normality and homogeneity of variances required for the paired t-test are not met. By using the chi-square distribution, McNemar's Test provides a way to determine the significance of the differences between paired categorical data, while accounting for the dependency between the observations.

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Answer:

Step-by-step explanation:

if x= -2, f(x)= -8

x= -1, y= -1

x=0, y=0

Answer:

I am pretty sure it’s either the first one or the last one

Step-by-step explanation:

Scores on one variable plotted against scores on a second variable.

The correct answer is (b)

Now, According to the question:

Let's know:

A scatterplot shows:

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

Hence, The correct answer is (b) i.e.,

Scores on one variable plotted against scores on a second variable.

Given,

In the question:

A scatterplot shows:

a. the average value of groups of data.

b. scores on one variable plotted against scores on a second variable.

c. the frequency with which values appear in the data

d. the proportion of data falling into different categories.

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Answer:

Independent.

Step-by-step explanation:

An independent event is an event that has no connection to another event's chances of happening. Then for a dice rolled three times, any of the events depends on the other. Hence, all three events are independent.

Answer:

5/12

Step-by-step explanation:

answers are in the picture above

A third-degree polynomial can have either one or three real roots, depending on whether it touches the x-axis at one or three distinct points.

To explain why a third-degree polynomial must have exactly one or three real roots. A third-degree polynomial is also known as a cubic polynomial, and it can be expressed in the form:

f(x) = ax³ + bx² + cx + d

To understand the number of real roots, we need to consider the possible combinations of x-intercepts.

The x-intercepts of a polynomial are the values of x for which f(x) equals zero.

Possibility 1: No real roots (all complex):

In this case, the cubic polynomial does not intersect the x-axis at any real point. Instead, all its roots are complex numbers.

This means that the polynomial would not cross or touch the x-axis, and it would remain above or below it.

Possibility 2: One real root: A cubic polynomial can have a single real root when it touches the x-axis at one point and then turns back. This means that the polynomial intersects the x-axis at a single point, creating only one real root.

Possibility 3: Three real roots: A cubic polynomial can have three real roots when it intersects the x-axis at three distinct points.

In this case, the polynomial crosses the x-axis at three different locations, creating three real roots.

Note that these possibilities are exhaustive, meaning there are no other options for the number of real roots of a third-degree polynomial.

This is a result of the Fundamental Theorem of Algebra, which states that a polynomial of degree n will have exactly n complex roots, counting multiplicities.

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Answer:

2

Step-by-step explanation:

Answer:

B: 9

Step-by-step explanation:

1/4(c^3 + d^2)

Plug in -4 for C and 10 for d

1/4((-4)^3 + (10)^2)

(-4)^3 = -64

10^2 = 100

1/4(-64 + 100)

-64 + 100 = 36

1/4(36)

= 36/4 = 9

9 is the final answer.

Step-by-step explanation:

Decrease in price = $50 - $20 = $30.

Percent of decrease = ($30/$50) * 100% = 60%. (A)

Based on the original price and the price the sweater decreased to, the percentage discount was 60%.

The percentage reduction can be found as:

= (Original price - Discount price) / Original price x 100%

Solving gives:

= (50 - 20) / 50 x 100%

= 60%

In conclusion, the correct answer is option A.

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False. The converse of the given conditional statement is "If a polygon has exactly three sides, then it is a triangle."

Logic statements that contain both the hypothesis and the conclusion are known as conditional statements. A statement is considered to be true when it is used as the hypothesis, but a statement is considered to be true when it is used as the conclusion. In a conditional statement, the conclusion can only be true if the hypothesis is accurate. For instance, "If it is raining, then the ground is wet" is a conditional statement, with "it is raining" serving as the hypothesis and "the ground is wet" as the conclusion. If the hypothesis is correct, the conclusion must likewise be correct. If the hypothesis is incorrect, the conclusion might be right or false.

How to solve?

The converse of the given conditional is false.

In general, the converse of a conditional statement is not always true.

In the given example, a polygon can have exactly three sides and still not be a triangle (e.g. an equilateral triangle).

Therefore, the converse of the given conditional is false.

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The quadratic equation is:

To find if the number of solutions, we use the discriminant of the equation. But first, we compare the given equation with the general quadratic equation:

By comparison, we find the values of a, b, and c:

Now, as we said previously, we have to use the discriminant to find the number of solutions. The discriminant is defined as follows:

• If the value of D results to be equal to 0, there will be 1 real solution.

• If the value of D results to be greater than 0, there will be 2 real solutions.

• And if the value of D results to be less than 0, there will be no real solutions.

We substitute a, b and c into the discriminant formula:

Solving the operations:

As we can see, the value of D is less than 0 (D<0) which indicates that there will be no real solutions for this quadratic equation.

Answer: No real solutions

The derivative of \(r\) with respect to \(\theta\) can be found using the chain rule. Let's proceed with the differentiation:

\frac{dr}{d\theta} = \frac{d}{d\theta}\left(\cos\left(\frac{\theta}{3}\right)\right)

To differentiate \(\cos\left(\frac{\theta}{3}\right)\), we treat \(\frac{\theta}{3}\) as the inner function and differentiate it using the chain rule. The derivative of \(\cos(u)\) with respect to \(u\) is \(-\sin(u)\), and the derivative of \(\frac{\theta}{3}\) with respect to \(\theta\) is \(\frac{1}{3}\). Applying the chain rule, we have:

\frac{dr}{d\theta} = -\sin\left(\frac{\theta}{3}\right) \cdot \frac{1}{3}

Now, let's evaluate this derivative at \(\theta = \pi\):

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\sin\left(\frac{\pi}{3}\right) \cdot \frac{1}{3}

The value of \(\sin\left(\frac{\pi}{3}\right)\) is \(\frac{\sqrt{3}}{2}\), so substituting this value, we have:

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\frac{\sqrt{3}}{2} \cdot \frac{1}{3} = -\frac{\sqrt{3}}{6}

Therefore, the slope of the tangent line to the polar curve \(r = \cos(\theta / 3)\) at the point specified by \(\theta = \pi\) is \(-\frac{\sqrt{3}}{6}.

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(a)There are 15,504 ways to select 5 students from the class of 20.

(b)There are 6,006 ways to select a group of 3 females and 2 males.

(c)The probability that of selecting 5 students that include 3 females is approximately 0.389 .

What is probability?

Probability provides a way to quantify uncertainty and make predictions about the likelihood of different outcomes in various situations.It is a numerical value between 0 and 1.

(a)To select 5 students from a class of 20, we can use the combination formula. The number of ways to select 5 students from 20 is given by:

\(C(20, 5) = \frac{20! } {5! * (20 - 5)!}\\\\ = \frac{20! }{5! * 15!} \\\\=\frac{ 20 * 19 * 18 * 17 * 16}{5 * 4 * 3 * 2 * 1}\\\\ = 15,504.\)

Therefore, we can select  the 5 students from the class of 20 in 15,504 ways.

(b)To select a group of 3 females and 2 males, we need to choose 3 females from the 13 available and 2 males from the 7 available.

\(C(13, 3) * C(7, 2) = \frac{13!}{3! * (13 - 3)!}* \frac{7!}{2! * (7 - 2)!}\\\\ = \frac{13!}{3! * 10!} *\frac{7! }{2! * 5!}\\\\=\frac{13 * 12 * 11}{3 * 2 * 1}* \frac{7 * 6}{2 * 1}\\\\ = 286 * 21 \\\\= 6,006.\)

Therefore,in 6,006 ways to select a group of 3 females and 2 males.

(c)To calculate the probability of selecting 5 students that include 3 females, we need to find the number of ways to select 3 females from the 13 available and 2 students (either males or females) from the remaining 7 students.

The total number of ways to select any 5 students from the class of 20 is given by C(20, 5) = 15,504 (as calculated in part (a)).

The number of ways to select 3 females from 13 females is given by C(13, 3) = 286 (as calculated in part (b)).

Therefore, the probability of selecting 5 students that include 3 females is:

P(3 females) = \(\frac{C(13, 3) * C(7, 2)}{C(20, 5)}\)

= \(\frac{286 * 21 }{15,504}\)

= 0.389.

Therefore, the probability that the selected 5 students include 3 females is approximately 0.389 or 38.9%.

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