find a cartesian equation for the curve and identify it. r = 10 csc()

An acre is a unit of measurement used to quantify land area, and it is commonly used in the United States to measure the size of plots of land, farms, and estates. One acre is equal to 43,560 square feet.

To visualize an acre, imagine a rectangle that is approximately 208 feet by 209 feet, or a square that is approximately 209 feet on each side.

To convert acres to square feet, you can use the following formula:

1 acre = 43,560 square feet

Therefore, to convert acres to feet, you can simply multiply the acre value by 43,560. For example, if you want to convert 5 acres to square feet, you can use the following formula:

5 acres x 43,560 square feet per acre = 217,800 square feet

So 5 acres is equal to 217,800 square feet.

It's worth noting that the acre is a unit of measurement used primarily in the United States, and other countries may use different units of measurement to quantify land area. For example, in the metric system, the hectare is commonly used to measure land area, with 1 hectare equal to 10,000 square meters (about 2.47 acres).

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The given system of equations has solutions (-2, -1) and (-2, -1) respectively.

Calculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.

Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.

Given the system of equation below:

-2x² + y = -5

y = -3x² +5

Substitute equation 2 into 1 to have:

-2x² + (-3x+5) = -5

-2x²-3x² +5 = -5

-2x²-3x² +10=0
-5x² = -10

x²  = 10/5

x²  = 2

x = ±√2

If x = -√2

y = -3x² +5

y = -3(2) + 5

y = -1

If x = √2

y = -3x² +5

y = -3(2) + 5

y = -1

Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).

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We can change the negative sign into i instantly as sqrt-1 is i.

With this the problem simplifies to sqrt48*i.

Now sqrt48=sqrt4*sqrt4*sqrt3=2*2*sqrt3

So the final product is 4sqrt3*i=4isqrt3.

Thus choosing choice 3 :)

Answer:

10a²+5ab+2b²

Step-by-step explanation:

Start by combining like terms aka the ones that match:

Step 1: (4a²-5ab-6b²) + (10ab+6a²+8b²)

Step 2: (10a²-5ab-6b²) + (10ab+8b²)

Step 3: (10a²+5ab-6b²+8b²)

Final answer: 10a²+5ab+2b²

In step 1, I added the 4 and 6. In step 2, I added -5 and 10. In step 3, I added -6 and 8. For each I attached the proper ending (a², ab, and b²).

I hope this clears some confusion!

Radius of the semicircle is 8 km and diameter is 16 km.

What is area of the semicircle?

The area of the semicircle can be determined using the formula,\(A = 1/2 * \pi * r^2\)

The area of a semicircle is given by the formula:

\(A = 1/2 * \pi * r^2\)

where A is the area and r is the radius.

We are given that the area of the semicircle is 32π km². So, we can set up the equation:

\(32\pi = 1/2 * \pi * r^2\)

Simplifying this equation, we get:

r² = (2 × 32π) / π = 64

Taking the square root of both sides, we get:

r = 8 km

So, the radius of the semicircle is 8 km.

The diameter of the semicircle is twice the radius, so:

d = 2r = 2 × 8 km = 16 km

Therefore, the diameter of the semicircle is 16 km.

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Answer:

a)  median = 1,148 minutes

b)  IQR = 549.5

Step-by-step explanation:

Q1 = (952 + 866) / 2 = 909

Q3 = (1431 + 1486) / 2 = 1458.5

IQR = 1458.5 - 909.0 = 549.5

Answer:

c.  40.32%

Step-by-step explanation:

The condition that is satisfied in this case, which allows Clara to use the fundamental counting principle, is that the choices she needs to make (between Mexican or Italian food and between ordering online or over the phone) are independent of each other.

The fundamental counting principle states that if there are n ways to do one thing and m ways to do another thing, then there are n * m ways to do both things when the choices are independent.

In Clara's case, her decision to eat Mexican or Italian food does not affect her decision to order online or over the phone. These choices can be made independently of each other. Therefore, she can use the fundamental counting principle to determine the number of possible choices by multiplying the number of options for each decision together.

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Answer:

Yep! That looks right!

Step-by-step explanation:

The solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

The following are the solutions to determine RHP roots in the given polynomials in Control System:

Polynomial: \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)

To identify the number of RHP (Right Half Plane) roots of the given polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\), the number of sign changes in the coefficients of the polynomial's terms can be counted.

Using the Descartes rule of sign, the number of sign changes in the polynomial's coefficients will indicate the number of positive or RHP roots present in the polynomial.

Therefore, there is no change in the sign of coefficients in the polynomial p(S).Thus, the number of RHP roots of the polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)is zero.

Polynomial: \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\)

The given polynomial is \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\).

The coefficients of the polynomial are as follows:

a5 = 1, a4 = 1, a3 = 6, a2 = 6, a1 = 1, and a0 = 25.

According to the Routh-Hurwitz criterion, the RHP roots of the polynomial p(S) are given by the following conditions:

For the polynomial \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\), the Routh array can be written as:

1    6    25 0
1    6    25 0
6    155 0
5    25    0
25 0

Thus, the polynomial p(S) has no RHP roots since the Routh array contains no changes of sign.

Therefore, the given polynomial has no RHP roots.

Hence, the solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

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The Formula of Area of Obtuse Triangle is equal to ½ × b× h .

and by using Heron's formula,

A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2

A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.

Obtuse triangle: A type of triangle with the following properties:

Area formula of obtuse triangle :

Area of obtuse triangle = ½ × b × h

where b --> base of triangle

h ---> height of triangle.

The area of a triangle can also be found using Heron's formula.

A = √(S(S-a)(S-b)(S-c)),

where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.

the perimeter of the triangle = a + b + c cm then

S = (a + b + c)/2

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The probability that Amahle randomly selects a chocolate chip cookie from the bag, eats it, and then randomly selects an oatmeal cookie is 0.0068, rounded to 4 decimal places.

The probability that Amahle randomly selects a chocolate chip cookie and then an oatmeal cookie from a bag containing 7 chocolate chip cookies, 7 peanut butter cookies, 9 sugar cookies, and 8 oatmeal cookies can be calculated using the formula for conditional probability:

P(Oatmeal | Chocolate chip) = P(Chocolate chip and Oatmeal) / P(Chocolate chip)

The probability of selecting a chocolate chip cookie from the bag is 7/31, since there are 7 chocolate chip cookies in a bag of 31 total cookies. After Amahle selects and eats a chocolate chip cookie, there are 6 chocolate chip cookies and 30 total cookies remaining in the bag.

The probability of selecting an oatmeal cookie from the remaining cookies in the bag is 8/30, since there are 8 oatmeal cookies and 30 total cookies remaining.

Therefore, the probability of selecting a chocolate chip cookie and then an oatmeal cookie is:

P(Chocolate chip and Oatmeal) = (7/31) * (8/30) = 0.00678 (rounded to 4 decimal places)

The probability of selecting a chocolate chip cookie is 7/31, as mentioned earlier. Therefore, the probability of selecting an oatmeal cookie given that a chocolate chip cookie has been selected is:

P(Oatmeal | Chocolate chip) = (7/31) * (8/30) / (7/31) = 8/210 = 0.0381 (rounded to 4 decimal places)

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Answer:

2a+10 is your answer

Answer:

9 cups

Step-by-step explanation:

6 ÷ 2/3

6/1 ÷ 2/3

6/1 x 3/2 = 18/2 = 9/1 = 9

The polygon is translated five units to the right.

A translation does not alter the appearance of a shape; it merely shifts it up, down, or from side to side. A metamorphosis serves as an example of translation. A transformation is a method for changing a shape's size or placement. At each location, the shape is translated in the same direction by the same amount.

The polygon ABCD's vertices are provided to us as A (-1, -1); B (1, -5); C (5, -5) and D (3, -1)

Also, the vertices of second polygon A'B'C'D' are given as A' (4, -1); B' (6, -5); C' (10, -5) and D' (8, -1).

It is evident that neither polygon's y coordinates have changed.

A 5 increment is made to the x-coordinates.

The translation rule in use is therefore (x, y) → (x + 5, y)

As a result, the polygon is translated 5 units to the right.

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The complete question is:

Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1.

A second polygon A' B' C' D' with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1.

Determine the translation used to create the image.

1. 5 units to the right

2. 1 unit to the right

3. 5 units to the left

4. 1 unit to the left

Kierran's mother is employing the reward system when she tells him to play video games when he completes his chores, and she is employing the punishment system when she restricts video game play and only allows him to play if he does his chores then she is employing the negative reinforcement.

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The values οf the basic trigοnοmetric functiοns fοr an angle in standard pοsitiοn passing thrοugh (6,8) are:

\(\sin \theta &= 0.8\\\) \(\cos \theta &= 0.6\), etc.

Trigοnοmetry is a branch οf mathematics that deals with the study οf triangles and the relatiοnships between their sides and angles.

We can begin by finding the length οf the hypοtenuse οf the right triangle fοrmed by the given pοint and the οrigin. This will give us the value οf the trigοnοmetric functiοns sine, cοsine, and tangent.

The hypotenuse can be found using the Pythagorean theorem:

\(c^2 &= a^2 + b^2\)

\(&= 6^2 + 8^2\)

\(&= 36 + 64\)

\(&= 100\)

\(c &= \sqrt{100}\)

\(c &= 10\)

Therefore, the point (6,8) is 10 units away from the origin.

The sine of the angle can be found by dividing the opposite side (8) by the hypotenuse (10):

\(\sin \theta &= \frac{8}{10}\)

\(&= 0.8\)

The cosine of the angle can be found by dividing the adjacent side (6) by the hypotenuse (10):

\(\cos \theta &= \frac{6}{10}\)

\(&= 0.6\)

The tangent of the angle can be found by dividing the opposite side (8) by the adjacent side (6):

\(\tan \theta &= \frac{8}{6}\)

\(&= \frac{4}{3}\)

Therefore, the values of the basic trigonometric functions for an angle in standard position passing through (6,8) are:

\(\sin \theta &= 0.8\)

\(\cos \theta &= 0.6\)

\(\tan \theta &= \frac{4}{3}\)

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The statement is false because in a Poisson distribution, the probability of success does not vary from trial to trial.

The Poisson distribution is a discrete probability distribution that describes the number of times an event occurs in a fixed time interval or spatial region, given the average rate of occurrence and assuming that the events are independent and random.

The Poisson distribution has only one parameter, λ, which represents the average rate of occurrence of the event.

The probability of observing k events in the interval is given by the Poisson probability mass function:

P(k) = (e^(-λ) * λ^k) / k!

where e is the base of the natural logarithm, and k is a non-negative integer.

The Poisson distribution assumes that the probability of observing an event at any given point in time or space is constant, and that the events are independent of each other.

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The number of subjects who participated in the study is 20.

To determine the number of subjects who participated in the study, we need to understand the relationship between the degrees of freedom (df) and the sample size in a t-test.

In a matched-subjects experiment, participants are typically matched based on certain characteristics or variables to create pairs or groups. Each pair or group is then exposed to different conditions or treatments, and the differences within each pair or group are analyzed.

This type of design is often used to minimize individual differences and increase the precision of the study.

In a matched-subjects t-test, the degrees of freedom are calculated based on the difference scores between the pairs or groups. The formula to calculate the degrees of freedom is:

df = n - 1

Where 'n' represents the number of pairs or groups.

In a matched-subjects design, each pair contributes one degree of freedom.

Given that the t statistic has a df of 19, we can set up the equation:

19 = n - 1

Solving for 'n', we add 1 to both sides:

19 + 1 = n - 1 + 1

20 = n

In summary, based on the given information, there were 20 subjects who participated in the matched-subjects experiment.

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The total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

To determine this:

There are 10 options for the first digit (1-9) and 10 options for the last digit (2, 4, 6, 8). For the middle two digits, there are 10 options for each digit (1-9). Therefore, the total number of possible four-digit PINs is 10 x 10 x 10 x 10 = 10,000.

However, we must subtract the number of PINs that begin or end with a 0, which is 9 x 10 x 10 x 1 = 900. We must also subtract the number of PINs that are odd numbers, which is 9 x 10 x 10 x 5 = 4,500.

Therefore, the total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

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We have to find the equation of a line that pass through the point (4,3) and is perpendicular to the line:

This line, that is perpendicular, has a slope m=-9/11, as it is written in slope-point form.

The line we are looking for will have a slope that is the negative reciprocal of m=-9/11, so it will be:

Our line has a slope of m=11/9.

We can use the known point (4,3) to write the equation as:

If we want the equation in slope intercept form, we rearrange:

Answer: y-3=11/9*(x-4)

If covariance between two variables is near 0, it implies that the variables are not linearly related.

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Given

He bought 5/6 pound for $5

The price per pound can be calculated using the formula:

Hence, the price per pound is:

Answer:

price per pound : $6/ pound

The correct missing statement and the reason is NP = NO + OP by Segment Addition Property

Given: MONP

Prove: MN = OP

The Segment Addition Property states that,

When three locations A, B, and C are on the same line and point B is located between points A and C, the length of the line segment AC is equal to the sum of the lengths of the three line segments AB and BC.

In mathematical notation, this property can be represented as:

AB + BC = AC

Statements                                                  Reasons

1. MO = NP                                                     1. Given

2. MO = MN+ NO                                     2. Segment Addition Property

3. NP = NO + OP                                      3. Segment Addition Property

4. MN+NO = NO+ OP                              4. Substitution Property

5. MN = OP                                              5. Subtraction Property of Equality

Hence the correct option is 2nd.

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The relationship between the number of hot dogs eaten and time after

arrival is a linear relationship.

Reasons:

First question:

The given parameters are;

Number of hot dogs Uncle Blake has eaten after 3 minutes = 39 hot dogs

Number of hot dogs eaten after 5 minutes = 61 hot dogs

Therefore, we have that the points on a graph of hot dog eaten are;

(3, 39), and (5, 61)

Which gives;

\(The \ rate \ of \ hot \ dog \ eating = \dfrac{(61 - 39) \ hot \ dogs}{(5 - 3) \ minutes} = 11 \ hot \, dogs/minute\)

Second question;

From the given rate, we have the following equation;

n - 39 = 11·(t - 3)

n = 11·t - 33 + 39

n = 11·t + 6

The above equation for the number of hot dogs eaten is in the form, a straight line equation, y = m·x + c.

Where;

y = n = The number of hot dogs eaten

x = t = The time since arrival

c = 6 = The y-intercept

At the time of arrival, t = 0, therefore;

n = 11 × 0 + 6 = 6

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In the context of property variance, a variance refers to a legal authorization or exception granted to a property owner by the local governing authority. It allows the property owner to deviate from specific zoning regulations or land-use restrictions that would otherwise apply to their property.

The variance process is used when property owners believe that strict adherence to the existing regulations would cause undue hardship or prevent them from fully utilizing their property in a way that is reasonable and consistent with neighboring properties.

The purpose of property variances is to address unique circumstances or hardships that may exist for a particular property. Property variances typically involve submitting an application to the local zoning board or planning department, attending public hearings, and providing evidence or arguments to support the need for the variance.

The governing authority evaluates the application based on factors such as the impact on neighboring properties, public health and safety, and the intent of the zoning regulations. If approved, the property owner is granted permission to proceed with the proposed deviation from the regulations.

Overall, property variances provide flexibility in land-use regulations, allowing property owners to find reasonable solutions that meet their specific needs while still considering the broader community interests and objectives of zoning regulations.

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Answer:

B. -4y^17

Step-by-step explanation:

Answer:

2245

Step-by-step explanation:

2282-37=2245

2245 students are girls

Answer:

1304

Step-by-step explanation:

3/7 of students are boys

total students= 2282

girls are 1-3/7= 4/7 of all students

girls= 2282*4/7= 1304

Answer: 1.2 m

Step-by-step explanation:

Given

The length of the ramp to the building is 3.7 m

Distance from the beginning of the ramp to the base of the building is 3.5 m.

Suppose h is the height of the ramp

from the figure, we can write

\(\Rightarrow 3.7^2=3.5^2+h^2\\\Rightarrow 13.69-12.25=h^2\\\Rightarrow h^2=1.44\\\Rightarrow h=1.2\ m\)

So, the height of the ramp is 1.2 m