Convert the given polar
coordinates into rectangular
coordinates.
(4,4)=([?],[√

Answer: 729

Step-by-step explanation:

3^2 is the same has 3 to the power of 2

9^2 is the same as 9 to the power of 2

When you see an expression like 3^2 x 9^2, it means you must raise 3 and 9 to the power of 2, multiply those numbers, and then do it again.

3 raised to the power of 2, often known as 3 times itself or 3 x 3, equals 9.

9 raised to the power of 2, often known as 9 times itself (9 x 9), equals 81.

As a result, when we change these values in the original expression, we obtain:

3^2 x 9^2 = 9 x 81

Now that we have these two integers, we can easily multiply them to obtain the result:

9 x 81 = 729

Therefore, 729 is the answer to the equation 3^2 x 9^2.

The emission of CO₂ after 14 years will be 52755 KT.

Given that, the emissions of CO₂ is 70,000 KL, will decrease at the rate of 2% per year for 14 years,

So,

Emission (E₀) for 14t year = 70,000 × (1-0.02)¹⁴

= 70000 × 0.75
= 52755

Hence, the emission of CO₂ after 14 years will be 52755 KT.

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These two events are independent. The action of Rafi downloading a song does not affect the probability of another customer in another city searching for a song on the same site.

The two events, Rafi downloading a song and a customer searching for a song, are independent because the occurrence of one event does not affect the probability of the other event occurring.

In other words, the actions of Rafi do not affect the actions of the customer in another city, and vice versa. The two events are unrelated and can occur simultaneously without affecting each other.

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The required value of probability P(B|A) is approximately 0.837.

As mentioned in the question,
P(A)=0.3, P(B)=0.57 and P(A and B)=0.251,

We can use the formula for conditional probability to find P(B|A):

P(B|A) = P(A and B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.251 / 0.3 = 0.83667

Rounding to the nearest thousandth, we get:

P(B|A) ≈ 0.837

Therefore, the value of P(B|A) is approximately 0.837.

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Answer: C) 15 cm, D) 10 cm

Step-by-step explanation:

Let's use the scale to convert the measurements on the drawing to real-life measurements in feet:

3 cm on the drawing = 4 feet in real life

To determine which lines on the drawing would be greater than 12 feet in real life, we need to find the lines on the drawing that correspond to more than 12 feet in real life.

For each line on the drawing, we can convert its length to feet using the scale:

A) 12 cm = (12/3) * 4 = 16 feet

B) 6 cm = (6/3) * 4 = 8 feet

C) 15 cm = (15/3) * 4 = 20 feet

D) 10 cm = (10/3) * 4 = 13.33 feet

Therefore, the lines that are greater than 12 feet in real life are C) 15 cm and D) 10 cm.

Answer:

C + D

Step-by-step explanation:

Answer:

2(3h^2+2)

Step-by-step explanation:

the given equation y = 2.81x² represents a non-proportional situation because the output variable y is not directly proportional to the input variable x.

HOW TO SOLVE THE QUESTION?

The given equation y = 2.81x² represents a non-proportional situation because the output variable y is not directly proportional to the input variable x. In a proportional relationship, when one variable increases or decreases, the other variable changes in direct proportion to it. However, in this equation, the output variable y increases at a non-linear rate as the input variable x increases.

A proportional relationship between two variables is characterized by a constant ratio between the two variables, which means that if one variable is doubled, the other variable is also doubled. In this case, the coefficient of x² is not a constant value, which indicates that the ratio between y and x² is not constant. Therefore, the given situation is not proportional.

Furthermore, a non-proportional relationship between two variables may exhibit a curved or nonlinear relationship between the variables, as in the case of this equation where y increases at an increasing rate as x increases. Therefore, the given situation can be categorized as non-proportional.

In conclusion, the given equation y = 2.81x² represents a non-proportional situation because the output variable y is not directly proportional to the input variable x.

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Answer:

Nicole pays 629 dollars per month.

Step-by-step explanation:

I think Nicole pays $629.29 per month

Step-by-step explanation:

An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

What is the slope-intercept form?

The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Here, we have

Given graph and we have to find the equation for the line shown in the given graph.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

Hence, an equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

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Therefore, the temperature at the summit of the 3,000-foot mountain on a sunny day is estimated to be 10.8 F°.

In mathematics, an equation is a statement that indicates the equality of two expressions. An equation typically contains one or more variables, which are placeholders for unknown values or quantities. The variables can take on different values, and the goal is often to find the values that satisfy the equation.

Here,

Let's start by calculating the rate of change of temperature with respect to elevation:

=-5.4 F° / 1,000 ft

This means that for every 1,000-foot increase in elevation, the temperature will decrease by 5.4 F°.

Next, we can calculate how much the temperature will decrease from the base of the mountain to the summit:

3,000 ft / 1,000 ft = 3

This means that the elevation difference between the base of the mountain and the summit is 3,000 - 0 = 3,000 ft.

So, the temperature decrease from the base to the summit is:

-5.4 F° / 1,000 ft * 3,000 ft = -16.2 F°

This means that the temperature at the summit will be:

27 F° - 16.2 F° = 10.8 F°

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Answer:

hi i can help you if you want just text

Answer:

15

Step-by-step explanation:

i got tHAT TEST TRUST ME

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After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.

To calculate the 90% confidence interval for the true mean income per month of a person who works from home in sales, we can use the following formula:

[tex]CI = X' ± Z\frac{a}{2}[/tex] * (σ/√n)

here:
X' = sample mean
Zα/2 = z-score that corresponds to the desired level of confidence (in this case, 90%)
σ = population standard deviation
n = sample size

Placing the  values

CI = 2350 ± 1.645 * (175 / √12)
= [2146.47, 2553.53]

After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
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Answer: 274 degrees.

Step-by-step explanation:

If the temperature in an oven increases by 8 degrees every minute, then in 3 minutes the temperature will increase by 8 x 3 = 24 degrees.

Therefore, the temperature in the oven after 3 minutes will be:

250 + 24 = 274 degrees.

A scatter plot is a graphical representation of a set of data points that displays the relationship between two variables.

How to solve the question?

The plot uses a Cartesian coordinate system, with one variable plotted on the x-axis and the other on the y-axis. Each data point is represented by a dot, with its location on the plot determined by its values for the two variables. The pattern of the dots on the plot gives insight into the relationship between the two variables.

Scatter plots are useful for visualizing the strength and direction of a relationship between two variables. A positive relationship between the variables means that as one variable increases, the other variable also increases. In contrast, a negative relationship means that as one variable increases, the other variable decreases. A scatter plot can also help to identify any outliers or unusual data points.

Scatter plots can be used to analyze many types of data, including scientific data, financial data, and social data. They can be used to identify trends, correlations, and patterns that might not be immediately apparent from a simple numerical analysis of the data. Scatter plots are a valuable tool for data analysis and visualization, and are widely used in scientific research, data analysis, and data-driven decision making.

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The sample points of events A, B, A ∩ B, A ∪ B and A' (complement of A) are given. The probability of event are 1/18, 11/36, 1/18, 7/18 and 17/18 respectively. The probability using additive rule of p(A ∩ B) is 1/36.  Events A and B are not mutually exclusive as they have a non-empty intersection.

Sample points in the events

A: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

B: {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (1, 4), (2, 4), (3, 4), (5, 4), (6, 4)}

A ∩ B: {(4, 3), (3, 4)}

A ∪ B: {(1, 4), (1, 6), (2, 4), (2, 5), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (6, 1), (6, 4)}

A' (complement of A): {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 3), (5, 5), (6, 2), (6, 3), (6, 5), (1, 5), (1, 6), (2, 6), (3, 5), (3, 6), (5, 6), (6, 6)}

The probability of event A is

p(A) = 2/36 = 1/18.

The probability of event B is

p(B) = 11/36.

The probability of event

A ∩ B (i.e., A and B) is p(A ∩ B) = 2/36 = 1/18.

The probability of event

A ∪ B (i.e., A or B) is p(A ∪ B) = 14/36 = 7/18.

The probability of event A' (i.e., not A) is p(A') = 17/18.

By the additive rule, we have p(A ∪ B) = p(A) + p(B) - p(A ∩ B). Therefore, p(A ∩ B) = p(A) + p(B) - p(A ∪ B) = (1/18) + (11/36) - (7/18) = 1/36. This inconsistent with the answer we obtained in above part.

The events A and B are not mutually exclusive because it is possible to roll a 4 and a 3 at the same time, which satisfies both events.

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The cost to paint the room with two coats of paint is $48, using paint that costs $8 per gallon and covers 300 square feet per gallon.

To determine how much it costs to paint the room if the paint costs $8 a gallon and each gallon covers 300 square feet of wall, we first need to determine how many gallons of paint we need. From problem #18, we know that the room has a total wall area of 800 square feet, and we need to apply two coats of paint.

The total wall area that needs to be covered by paint is:

800 square feet x 2 coats = 1600 square feet

To determine how many gallons of paint we need, we divide the total square footage by the coverage of one gallon of paint:

1600 square feet ÷ 300 square feet/gallon = 5.33 gallons (rounded up to the nearest gallon)

Therefore, we need 6 gallons of paint to complete the job (since we can't purchase a fractional amount of a gallon).

The cost of the paint can now be calculated by multiplying the number of gallons of paint by the cost per gallon

6 gallons x $8/gallon = $48

So it would cost $48 to paint the room.

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The piecewise function when represented on the graph based on each domain is added as an attachment

Given that

So, we have the following piecewlse function that represents the scenario

f(x) = 12 when 0 < x ≤ 2

     = 19 when 2 < x < 6

     = 25 when 6 ≤ x ≤ 14

Next, we plot the function on the graph based on each domain

See attachment for the graph

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Answer:

highest: $1,438

lowest: $1,062

Step-by-step explanation:

The highest and lowest points are adding $188 and subtracting $188 from her brother's amount.

So, to find the highest point, add $188 to $1,250, which is $1,438.

To find the lowest point, subtract $188 from $1,250, which is $1,062.

Hope this helps ;)

The median nerve and Klumpke's palsy are both related to nerve injuries in the arm, but they involve different nerve pathways and result in different symptoms.

The median nerve runs from the brachial plexus in the neck through the arm to the hand, and controls movement and sensation in the thumb, index, middle, and part of the ring fingers. Damage to the median nerve can result in symptoms such as weakness, numbness, and tingling in these fingers, as well as muscle wasting in the thumb.

Klumpke's palsy, on the other hand, involves damage to the lower brachial plexus nerves, specifically the C7, C8, and T1 nerve roots. This can result in weakness or paralysis in the hand and wrist, with symptoms such as a claw-like deformity, decreased grip strength, and loss of sensation in the affected areas.

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Answer:

To determine the number of sheets of cardboard in a stack, we need to use the information given in the problem.

We know that each sheet of cardboard is 1 inch thick, and 16 sheets are stacked on top of each other in packages. The height of each stack is 21 inches.

Using the model of a ruler, we can divide the height of the stack (21 inches) by the thickness of each sheet (1 inch) to find the number of sheets in the stack.

21 ÷ 1 = 21

So, there are 21 sheets of cardboard in a stack.

To write an expression that can be used to determine the number of sheets of cardboard in a stack, we can use:

Number of sheets = height of stack ÷ thickness of each sheet

Or, substituting the given values: Number of sheets = 21 ÷ 1 = 21

This expression is simply a representation of the model we used earlier. It shows that we can determine the number of sheets in a stack by dividing the height of the stack by the thickness of each sheet. In this case, the expression yields the same result as the model, which is 21 sheets.

Answer:

f≤ 12

Step-by-step explanation:

The cat can only eat up to 12 oz, but can also eat 12 oz, so we have to use the less than or equal to symbol to represent that.

So, option D is correct.

f≤ 12

The missing angles are sides are;

We can see that we would have to first apply the cosine rule here;

[tex]a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30[/tex]

a = 9.8

We can now apply the sine rule to obtain the angle B

[tex]a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)[/tex]

B = 60

Then;

C = 180 - (30 + 60)

C = 90 degrees

Thus the triangle in the problem have been solved.

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The value of x is 72°

An arc is any smooth curve joining two points. The length of an arc is known as its arc length.

A sector is the area bounded by two radii and an arc.

The measure of an arc is defined to be equal to the central angle of its sector.

Since the angle of the sector formed is 72° and it has been stated that the measure of an arc is defined to be equal the central angle of its sector, then we can say that the value of arc x is 72°.

Therefore the value of x is 72°.

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The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters

Area = length * width

Perimeter = 2(length + width)

Given the following:

Length of the rectangle = 5√7 + 2√3 meters

Width of the rectangle = 6√7 - 3√3 meters

a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)

10√7 + 4√3 + 12√7 - 6√3

22√7 - 2√3 meters

b. Area = (5√7 + 2√3)(6√7 - 3√3)

= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)

= 210 - 15√21 + 12√21 - 18

= 192 - 3√7

= 4√12 - 3√7 square meters

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Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be (c) 11.

The dot-plot displays a unimodal distribution with a moderate to large spread of the data.

The spread of the data is roughly from 0 to 40, with most of the dots being between 10 to 30.

The spread of the dots, it is unlikely that the standard deviation of the data is as small as 5 or 8.

Similarly.

It is unlikely that the standard deviation is as large as 20 or 15 as there are a significant number of data points that lie within the 20-30 range.

Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be around 11.

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Answer:

(i) Calculation:

1 GB = 1000 MB

Number of videos that could be stored = (1 GB / 100 MB) = 10

Therefore, William can store 10 videos on his computer if each video is 100MB in size.

(ii) Algorithm using pseudocode:

Ask the user to input the file size in megabytes.

Multiply the file size by 1,000,000 to convert it to bytes.

Print the result in a user-friendly format by dividing the bytes by 1,048,576 and rounding to two decimal places, and adding "MB" and "bytes" to the output.

Pseudocode:

Input file_size_in_mb

Set bytes = file_size_in_mb * 1000000

Set result = round((bytes / 1048576), 2)

Output "There are " + result + " MB " + bytes + " bytes".

In computer programming, variables are used to store and manipulate data. In this case, an int variable named strawsoncamel has been declared and assigned a value.

To increase the value of strawsoncamel by 1, you can use the increment operator (++). This operator adds 1 to the current value of the variable and assigns the result back to the variable.

For example, if strawsoncamel has a value of 5, the statement strawsoncamel++; would increase its value to 6. This can be useful in many scenarios, such as counting or iterating through a loop. It's important to note that the increment operator can also be used in other ways, such as ++strawsoncamel, which increments the value of the variable before it is used in an expression.

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To increase the value of the variable strawsoncamel by 1, you can use the increment operator "++". So the statement would be:
strawsoncamel++;

This will increment the value of strawsoncamel by 1. The increment operator is an example of an operator in programming, which performs a specific operation on a variable. In this case, it increases the value of the variable by 1, which is also known as an increment.
To increase the value of the integer variable `strawsoncamel` by 1 using the increment operator, follow this step:
Write the statement: `strawsoncamel++;`
This line of code will use the increment operator (`++`) to increase the value of the variable `strawsoncamel` by 1.

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