find the area of the region enclosed by one loop of the curve. r = 3 cos(5)

Answer:

it should be y= -4x + 10

Step-by-step explanation:

hope this helps.

Answer:

3.7

Step-by-step explanation:

2-5=3 and 3- -4=7

Answer:

What are the items?

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

a: 3

b: -1

c: -2

3 - - 1 = 3 + 1 = 4

4 - - 2 = 4 + 2 = 6

Your answer is 6

The simplification of the expression when a = 3 b = -1 and c = -2 will be; 6.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as; |a-b-c|

Now substituting  a = 3 b = -1 and c = -2

|a-b-c|

|3 - (-1) - (-2)|

Solving the equation;

|3 + 1 + 2| = 6

Hence, the answer is 6

The simplification of the expression when a = 3 b = -1 and c = -2 will be; 6.

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Answer:

60 feets

Step-by-step explanation:

Given that :

Using Pythagoras rule :

Hypotenus = sqrt(Adjacent^2 + opposite^2)

From the attached picture :

x² = 87^2 - 63^2

x^2 = 7569 - 3969

X^2 = 3600

Take the square root of both sides :

X = sqrt(3600)

X = 60 feets

Hence, Katy and Tony are 60 feets apart

Answer:

-x^2-15xy-50y^2+14y

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

Using the converse of the Side Opposite 30° Theorem, we find that ∠X is 30°.

Hope this helps :)

Answer:  \(2\frac{1}{12}\)  acre

Step-by-step explanation:

Total acres of lawn mowed by Stephen = \(\frac{1}{4}\) + \(\frac{1}{2}\) + \(1\frac{1}{3}\)

                                                                  =  \(\frac{1}{4}\) + \(\frac{1}{2}\) + \(\frac{4}{3}\)

                                        LCM of 4, 2, and 3 is 12

                                                                  =  \(\frac{3+6+(4*4)}{12}\)

                                                                  =  \(\frac{25}{12}\)

                                                                  =  \(2\frac{1}{12}\)  

Answer:

y = -3 and x = -3

Step-by-step explanation:

See attachment for math work and answer.

The probability of the employee arriving between 8:05 a.m. and 8:30 a.m. is 0.625 or 62.5% when rounded to the nearest tenth.

The probability of the employee arriving between 8:05 a.m. and 8:30 a.m. is the same as the probability of selecting a random time between 8:05 a.m. and 8:30 a.m. out of all possible arrival times between 8:00 a.m. and 8:40 a.m.

The total possible arrival times between 8:00 a.m. and 8:40 a.m. is 40 minutes, and the total possible arrival times between 8:05 a.m. and 8:30 a.m. is 25 minutes.

Therefore, the probability of the employee arriving between 8:05 a.m. and 8:30 a.m. is:

P(arrival between 8:05 a.m. and 8:30 a.m.) = (number of arrival times between 8:05 a.m. and 8:30 a.m.) / (total number of possible arrival times.

P(arrival between 8:05 a.m. and 8:30 a.m.) = 25 / 40

P(arrival between 8:05 a.m. and 8:30 a.m.) = 0.625.

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The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Here, we want to use the imaginary number to rewrite the given expression as a complex number

Mathematically, the complex number can be written as;

Thus, we have;

Answer:

Jonah only added two sides together instead of all four sides

Perimeter = 12 \(\frac{1}{2}\)x - 6

Step-by-step explanation:

P = 2(6x - 5) + 2(1/4x + 2)

P = 12x - 10 + 1/2x + 4

P = 12 1/2x - 6

Answer:

10x = 75 100 ft X = 7.5 3.

Step-by-step explanation:

The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

In this question,

The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.

The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.

From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.

Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

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Answer:

C is correct

Step-by-step explanation:

I just know this from having previously learned it, I'm not sure how to explain it but hope the answer helps!

Answer:

71.1%

Step-by-step explanation:

V=πr²h

Container A=

424.12

Container B=301.59

Container A had 424.12 and it lost 301.59.  Since the volume empty is 301.59, we can divide that by 424.12 and get 0.7111, or 71.1%.

Hence , equation of the line that is perpendicular to the line y = 6 and passes through the point (-4,-3) is x = -4 which is option (a) .

The line y = 6 could be a horizontal line through the purpose (0,6) on the coordinate axis. A line perpendicular thereto are vertical and thru the coordinate axis. this suggests its equation are x = a wherever a is that the x-coordinate. Since it should experience the purpose (-4,-3) then the equation is x =  -4.

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The correct statement is "Since the data is variable and available, the given question is a statistical question." Therefore, option B is correct.

The question "How many times do Jack Nursing Home residents search the Internet each day?" is a statistical question because it is a variable that varies from person to person and from day to day. The purpose of the question was to collect data on Internet searches, indicating an interest in understanding the distribution and patterns of residents' search behavior.

Additionally, in the question he states that web search data is available. This means there is an opportunity to collect and analyze data to generate meaningful insights. This question is therefore a statistical question that takes into account the variability and availability of the data. 

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The value of b in the function f(x) = 5x² - bx + 8 when (2, 8) is on the graph is 10

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 5x² - bx + 8

Also, we have the point

(2, 8)

This means that x = 2 and f(x) = 8

Substitute the known values in the above equation, so, we have the following representation

5(2)² - b(2) + 8 = 8

So, we have

5(2)² - b(2) = 0

Divide through by 2

5(2) - b = 0

This means that

b = 5(2)

Evaluate

b = 10

Hence, the value of b is 10

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Complete question

In the xy-plane, the point (2, 8) lies on the graph of the function f(x) = 5x² - bx+8. What is the value of b ?

The expression that represents the cost of m tickets is simply 2m.

To write an algebraic expression, follow these steps:

If the cost of a single raffle ticket is $2, then the cost of m tickets would be:

2m

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The estimation of the function f() allows us to utilize the available data to make informed decisions, gain insights, and understand the behavior of the system or phenomenon we are studying.

1. Prediction: One common reason for estimating a function f() is to make predictions or forecast future values based on available data.

By understanding the relationship between input variables and the corresponding output values, we can estimate the function f() and use it to predict the output for new or unseen input values.

This is particularly useful in various fields such as finance, weather forecasting, sales forecasting, and stock market analysis, where accurate predictions can be valuable for decision-making.

2. Inference: Another reason for estimating a function f() is to gain insights and understand the underlying relationship between the input variables and the output.

By estimating the function, we can examine the effect of different inputs on the output and draw conclusions about the factors influencing the phenomenon we are studying.

This is commonly used in scientific research, social sciences, and data analysis to understand the causal or associative relationships between variables and to uncover patterns or trends in the data.

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B. This quantity might be the optimal order quantity, but we also need to consider the company’s attitude toward risk.

Simulation models are useful tools for predicting the outcomes of different scenarios, but they are not always accurate representations of reality. Running a simulation model several times with different order quantities can give an indication of the order quantity that maximizes the output, but it does not guarantee that this is the optimal order quantity.

There are many factors that can affect the outcome of a simulation model, such as the model's assumptions, limitations, and inputs. Additionally, simulation models are subject to randomness and variability, so the results of different runs may vary.

For this reason, it is important to consider other factors, such as the company's attitude toward risk, when making decisions based on the results of a simulation model. The company's attitude toward risk can influence the choice of order quantity and affect the overall outcome of the simulation.

Therefore, while the order quantity that maximizes the output in a simulation model might be a good starting point, it is not necessarily the optimal order quantity. Further analysis and consideration of other factors is necessary to determine the best order quantity for the company.

A ratio is a mathematical expression that compares the relative size of two or more values. It is a way of expressing the relationship between two or more quantities in terms of their relative size.

A ratio can be expressed in different ways, such as a fraction, decimal, or percentage. For example, the ratio of 2 to 4 can be expressed as 2/4, 0.5, or 50%.

Ratios are used in many areas of mathematics and science, such as finance, economics, engineering, and physics, to describe and analyze relationships between quantities. For example, in finance, ratios are used to measure a company's financial performance, such as its profitability, liquidity, and debt-to-equity ratios. In engineering, ratios are used to describe the relationship between the size and power of a machine, such as the gear ratio in a car's transmission.

In general, ratios are useful for comparing quantities and understanding the relationships between them, and they play a key role in many aspects of mathematics and science.

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Given that the periodic function f(t) is explained with the alternative Fourier coefficients.  A1∠θ1= 3∠5°, A4∠θ4= 4∠4° and the frequency, ωo = 1000radHz.We know that a periodic function can be expressed as the sum of sine and cosine waves.

The Fourier series represents a periodic function as a sum of an infinite series of sines and cosines. This representation can be expressed mathematically as,

f(t) = a0 + Σ[an cos(nω0t) + bn sin(nω0t)]Here, ωo is the angular frequency of the waveform. a0, an, and bn are the Fourier coefficients and are expressed as follows; a0 = (1/T) ∫T₀f(t) dt an = (2/T) ∫T₀f(t)cos(nω₀t) dt bn = (2/T) ∫T₀f(t)sin(nω₀t) dt

where T₀ is the period of the waveform, and

T

= n T₀ is the interval over which the Fourier series is to be computed. In this case, the values of a1 and a4 have been given, A1∠θ1

= 3∠5° and

A4∠θ4

= 4∠4°. Hence the expression of the function is,  f(t)

=  a0 + 3cos(ω0t + 5°) + 4cos(4ω0t + 4°) where,

ω0 = 1000 rad/s. This is the required expression of the function f(t).

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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The equation of straight line having

(a) gradient -4 and coordinates (-2,1) is  4x + y \(=\) -7

(b) gradient 0 and coordinates (-1,21) is y = 21 .

In the question ,

the gradient and coordinates of the point on the line is given .

we have to find the equation of the straight line .

Part(a)

the gradient of the line \(=\) -4 ,

the coordinates of a point on the line = (-2,1)

So , the equation of the line is

(y - 1) = (-4)*(x -(-2))

y - 1 = -4(x + 2)

y - 1 = -4x - 8

4x + y = -8 + 1

4x + y = -7

the equation is 4x + y = -7  .

Part(b)

the gradient of the line = 0 ,

the coordinates of a point on the line = (-1 , 21)

So , the equation of the line is

(y - 21) = 0(x-(-1))

y - 21 = 0

y = 21

the equation of the line is y = 21  .

Therefore , The equation of straight line having  (a) gradient -4 and coordinates (-2,1) is 4x + y \(=\) -7  and (b) gradient 0 and coordinates (-1,21) is  y = 21  .

The given question is incomplete , the complete question is

Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

(a) -4, (-2 , 1)

(b) 0, (-1, 21)

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Null Hypothesis (H₀): The mean amount of time statistics students spend doing homework each night is greater than or equal to one hour.

Alternative Hypothesis (H₁): The mean amount of time statistics students spend doing homework each night is less than one hour.

The appropriate hypotheses for this scenario can be stated as follows:

Null Hypothesis (H₀): The true mean amount of time that statistics students spend doing statistics homework each night is equal to or greater than one hour.

Alternative Hypothesis (H₁): The true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.

In symbols:

H₀: μ ≥ 1

H₁: μ < 1

Here, μ represents the population mean amount of time spent doing statistics homework each night by statistics students.

The student wants to investigate if the data provide convincing statistical evidence to reject the null hypothesis and support the alternative hypothesis, suggesting that the true mean amount of time spent is less than one hour.

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A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.

In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.

To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.

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