Convert the polar equation r
4 = 2 sin θ cos θ into an equation in Cartesian (rectangular) coordinates.

Jenny earns $36 in interest in one year in her savings account.

To calculate the interest that Jenny earns in one year on her savings account, we can use the formula for simple interest:

I = P x r x t

where I is the interest earned, P is the principal amount (in this case, $1200), r is the interest rate (in decimal form), and t is the time period (in years).

In this case, the interest rate is 3% per year, which can be written as 0.03 in decimal form. The time period is one year. So we have:

I = 1200 x 0.03 x 1

I = $36

Therefore, Jenny earns $36 in interest in one year in her savings account.

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The volume of the prism in cubic inches is 4/9 cubic in if each cube in the prism measures 1/3 inch on one side.

Hence, the correct option is A.

If each cube in the prism measures 1/3 inch on one side, then the volume of one cube is (1/3)³ = 1/27 cubic inches.

To find the volume of the prism, we need to know how many cubes are in the prism. Let's assume the prism has dimensions of length L, width W, and height H, all measured in units of cubes. Then, the total number of cubes in the prism is L × W × H.

Therefore, the volume of the prism in cubic inches is

Volume = (L × W × H) × (1/27) cubic inches

From the given figure, we can find

L = 3 inch

W = 2 inch

H = 2 inch

Substitute the values in formula to find the volume

= (3 × 2 × 2) × (1/27) cubic inches

= 4/9 cubic inches

Hence, the correct option is A.

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The complete table for the time it takes to empty the barrel for the given rates is attached below. The value of constant k is 60.

To solve the problem, we can use the formula for inverse variation

time = k/leaking rate

where k is a constant of proportionality. We can find k by using the information given in the problem

30 = k/2

Solving for k, we get:

k = 60

Now we can use this value of k to fill in the table

Leaking rate (gallons per minute)                Time to empty (minutes)

      2                                                                           30

      1                                                                            60

      0.5                                                                        120

      0.25                                                                     240

      0.1                                                                        600

As the leaking rate decreases, the time to empty the barrel increases, because the liquid is leaking out more slowly.

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Answer:

254.3 ft^2

Step-by-step explanation:

First, let’s find the area of the entire circle. The area for a circle is 3.14 * radius^2

3.14*18^2 = 1017.36

Now, notice how the angle marked is 90 degrees, that means that this section of the circle is 90/360 (360 is the angle of a circle), or 1/4 of a whole circle. Now we can multiply 1/4 by the area to find 1/4 of the whole circle.

1017.36*1/4 = 254.34

Round to nearest tenth:

254.3 ft^2

Answer:

Step-by-step explanation: its c

The probability distribution for X is given below:

Probability of no even number, (X = 0)= 1/2

Probability of one even number, (X = 1) = 1/2

Probability of two even numbers, (X = 2) = 1/8

The probability distribution for X is found as follows:

The probability that an even number is not selected i.e. X = O

P(X = 0) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 0) = 1/2

The probability that an even number is selected once i.e. X = 1

P(X = 1) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 1) = 1/2

The probability that an even number is selected twice i.e. X = 2

P(X = 2) = 2/4 * 2/4

P(X = 2) = 1/8

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Answer: The slope of the ramp is defined as the rise over the run, where the rise is the height of the step (2 feet) and the run is the horizontal distance from the bottom of the ramp to the step (7.0 feet). However, since the ramp is not straight but inclined, we need to use the length of the ramp (7.3 feet) to calculate the actual horizontal distance it covers.

Therefore, the run of the ramp is the square root of the difference between the length of the ramp squared and the height of the step squared:

run = sqrt(7.3^2 - 2^2) = sqrt(52.29 - 4) = sqrt(48.29) ≈ 6.95 feet

Now we can calculate the slope of the ramp:

slope = rise / run = 2 / 6.95 = 0.2885 ≈ 2/7

Therefore, the slope of the ramp is approximately 2/7.

Answer: this is hard

Step-by-step explanation:

The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

Answer:(−1,−4π/3)

Step-by-step explanation:Note that the point is on the circle whose radius is labeled 1, so r=1 or r=−1. Of the choices available, only an angle of −4π3, drawn from the negative x axis plots at the point Q.  So θ=−4π3, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−1,−4π3).

The equation of each of the line are as follows;

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Since the equation of this line is parallel to the line x + 2y = 4, the slope is given by;

Slope, m = -0.5

y - y₁ = m(x - x₁)

y + 3.5 = -0.5(x - 1)

y = -0.5x - 3

Since the equation of this line is perpendicular to the line 5x + 2y + 2 = 0, the slope is given by;

Slope, m = -5/2

m₁ × m₂ = -1

-5/2 × m₂ = -1

Slope, m₂ = 2/5

y - y₁ = m(x - x₁)

y - 2 = 2/5(x + 5)

y = 2x/5 + 4

Since the equation of this line passes through the origin (0, 0) and parallel to the line 4x - 5y = 10, the slope is given by;

Slope, m = 4/5

y - y₁ = m(x - x₁)

y - 0 = 4/5(x - 0)

y = 4x/5

Since the equation of this line is perpendicular to the line 3x - y = 4 and cuts the x-axis at -1, the slope is given by;

Slope, m = 3

m₁ × m₂ = -1

3 × m₂ = -1

Slope, m₂ = -1/3

y - y₁ = m(x - x₁)

y - 0 = -1/3(x + 1)

y = -1/3(x) - 1/3

Since the line is perpendicular to the y-axis and passes through the point (-3, 5), the equation is given by;

y = 5.

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In the equation c + a = d + r, a = d + r - c

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question:

c + a = d + r

To solve for a in the equation c + a = d + r, we need to isolate a on one side of the equation by performing the same operation on both sides of the equation.

c + a = d + r

First, we can simplify the right side of the equation by subtracting c from both sides of the equation:

c + a = d + r

c + a - c  = d + r - c

Simplify

a + c - c  = d + r - c

a = d + r - c

Therefore, the solving for a as the subject of the formula is a = d + r - c.

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The surface area of the square pyramid using given dimensions is given by option a.  3,456m².

In the square pyramid,

Using Pythagoras theorem,

Height of the square pyramid is equal to,

In a right angled triangle,

Base = 18m

Hypotenuse = 30m

Height = √ Hypotenuse ² - base ²

Substitute the values we have,

⇒ height = √ 30² - 18²

⇒ height = √576

⇒ height =  24m

Dimensions of square pyramid are,

Base edge 'b' = 36m

height of the pyramid 'h' = 24m

Surface area of square Pyramid = b² + 2b√(b²/4) + h²

Substitute the values we have,

⇒Surface area of square Pyramid

= 36² + 2(36)√((36)²/4) + (24)²

= 1296 + 72√324 + 576

= 1296 + 2160

= 3,456m²

Therefore, the surface area of square Pyramid is equal to option a.  3,456m².

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Answer: (B)

Step-by-step explanation:

To determine which point is a solution to the system of inequalities, we must test each point to see if it satisfies both inequalities. Starting from point A, we plug in its coordinates (2, 9) into both inequalities. However, it does not satisfy y < 1 over 2x − 2. We then move on to point B, which has coordinates (3, 0). Plugging this into both inequalities, we find that it satisfies both of them. Therefore, the point that is a solution to the system of inequalities is point B.

Answer:

We can solve this inequality for x as follows:

3 - 3x ≤ 4x + 7

Subtract 4x from both sides:

3 - 7x ≤ 7

Subtract 3 from both sides:

-7x ≤ 4

Divide both sides by -7, remembering to reverse the inequality since we are dividing by a negative number:

x ≥ -4/7

Therefore, the solution to the inequality is:

x ≥ -4/7

The mean is approximately 9, the median is 9, the mode is 8, and the range is 7.

To find the mean, we add up all the numbers in the data set and divide by the total number of numbers:

Mean = (7 + 6 + 8 + 12 + 9 + 13 + 8) / 7 = 63 / 7 ≈ 9

So the mean is approximately 9.

To find the median, we need to arrange the numbers in order from smallest to largest:

6, 7, 8, 8, 9, 12, 13

Since there are an odd number of values in the data set, the median is the middle value, which is 9.

To find the mode, we need to look for the value that occurs most frequently in the data set. In this case, 8 occurs twice, which is more than any other value, so the mode is 8.

To find the range, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value = 13 - 6 = 7

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The sequence of steps that translates figure W to figure X are -

Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -

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The values that make the inequality true are given as follows:

-4, -3, -2, -1,  0.

The equivalent inequality is given as follows:

b ≥ -4.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The inequality for this problem is given as follows:

b/2 ≥ -2.

b ≥ -4.

Which is composed by numbers that are greater than or equal to -4.

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The solution is:

(a) A (20, 60), B = (0, 0) and C = (80, 0).

(b) The values of x and y that maximize the objective function are

(20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

We have,

The set of all possible points of an optimization problem that satisfy the problem's constraints—which may include inequalities, equalities, and integer constraints—is referred to in mathematics as a feasible region, feasible set, search space, or solution space.

Given,

x ≥0, y ≥ 0

x + y ≤ 80

y ≤ 3x

Objective function: z = 250x + 300y

(a) For the given constraints the feasible region is attached below.

The feasible region is ABC.

where, A (20, 60), B = (0, 0) and C = (80, 0).

(b) Now to find the values of x and y which maximize the objective function.

z = 250x + 300y

At A = (20, 60)

z = 250(20) + 300(60) = 5000 + 18000 = 23000

At B = (0, 0)

z = 250(0) + 300(0) = 0

At C(80, 0)

z = 250(80) + 300(0) = 2000 + 0 = 2000

Therefore, the values of x and y that maximize the objective function are (20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

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The visual that can help you in  creating a  3D structure using rectangular prism and others is given in the image attached.

3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.

In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure  will see and work within the real world.

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See text below



1. Start by creating a rectangular prism

as the base of your structure. This will

be the main structure that includes

the walls and interior rooms.

2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.

3. Add another cylindrical tower to the opposite corner of the rectangular

prism. Again, adjust the size and

height to your liking.

4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-

shaped roof to the other cylindrical tower.

5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.

6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.

7. Add a rectangular prism

perpendicular to the main structure,

creating an L-shape. This can be a

separate building or an extension of

the main structure.

8. Add a pyramid-shaped roof to the new

rectangular prism, and a cone-shaped roof to the cylindrical tower on the

opposite side of the main structure. 9. Finally, add spheres as decorative

elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,

pyramids, or cones, as long as you have at least 2 of each of the 5

required shapes.

Being male and preferring Brand A are independent, as:

P(male|Brand A) = P(male).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the table, we are already given the relative frequencies, hence the probability of being male is given as follows:

0.5 + 0.15 = 0.65.

The conditional probability of being male, given that the person prefers brand A, is given as follows:

P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 =  0.625.

As the probabilities are equal, the events are independent.

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The method that results in a random sample of the population is D) randomly selecting 100 residents paying real estate taxes, using the town's list of taxpayers and a random number generator.

A random sample is one in which each member of the population has an equal chance of being selected for the survey. Option D satisfies this requirement because it uses a random selection process and targets the specific population of interest (residents paying real estate taxes).

Option A does not result in a random sample because it only includes people who happen to enter Town Hall over the course of one month, which may not be representative of the entire population.

Option B only targets parents of soccer players and may not be representative of the entire population.

Option C also does not result in a random sample because it only includes people entering a specific supermarket on the east side of town, which may not be representative of the entire population.

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The graph of the inequality is on the image at the end.

To graph this, we need to do a solid graph of the linear equation:

y = -(7/2)x + 4

And because the symbol ≥  (and that is why we will use a solid line instead of a dashed line) is used, we need to shade all the region above that line graph.

Then the graph of the inequality will be something like the one of the graph at the end.

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Hello!

For this you would just need to multiple straight across. Here's how you would set it up:

3/4 ·1/8

Then you would multiple 3 x 1 = 3

And 4 x 8 =32

Your answer should be 3/32, it cannot be simplified so that is the final answer :).

Answer:

C

Step-by-step explanation:

To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:

(2x-1)/(7x+x+2) + (x-2)/(8x-2)

Simplifying the denominators, we get:

(2x-1)/(8x+2) + (x-2)/(8x-2)

Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:

[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)

Simplifying the numerator, we get:

[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)

Combining like terms, we get:

(24x²-2) / (64x²-4)

Factoring out a 2 from the numerator and denominator, we get:

2(12x²-1) / 2(32x²-2)

Simplifying further, we get:

(12x²-1) / (16x²-1)

Therefore, the sum of the rational expressions is:

12x²-1

-----------

16x²-1

So, the answer is option C.

Being Male and driving to work are independent events.

P(Drive | Male) = P(Drive)

Hence, Blank 1 is 'independent event' and Blank 2 is '='.

Probability of being male is,

P(Being male) = 0.54

Probability of driving to work is,

P(Driving to work) = 0.5

Probability of being male and driving to work is,

P(Being male and driving work) = 0.27

And P(Being Male)*P(Driving to work) = 0.54*0.5 = 0.27

Since, P(Being male and driving work) = P(Being male)*P(Driving to work)

Hence, Being Male and Driving to work are independent event.

P(Drive | Male) = P(Male and Drive)/P(Male) = 0.27/0.54 = 0.5

Since, P(Drive) = 0.5

Hence, P(Drive | Male) = P(Drive)

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Assuming the Social Security contribution rate is 6.2% of the wage, Ted's contribution to Social Security can be calculated as follows:

Ted's total wage for the month = 160 hours * $10/hour = $1600

Social Security contribution = 6.2% * $1600 = $99.20

Therefore, the answer is option C. $99.20.

Answer: 5:9

Step-by-step explanation:

Hope this helps! :)