Letters used in the word mathematics

The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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The value is 139027.81 dollar and the weight is 76,465.2955 lbs.

Given that, each penny weighs 4 grams.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To answer this question you need to convert each unit.

First, 1 dollar equal to 100 pennies. That mean the equation would be: 13902781 pennies × 1 dollar/100 pennies = 139027.81  dollar

Each penny weight 4 grams and 1 lb equal to 453.592grams.

Then the equation would be 13902781 pennies = 13902781/4 = 34,75,695.25 grams

Now, 34,75,6.9525 kg

34,75,6.9525×2.2=76,465.2955 lb

Therefore, the value is 139027.81 dollar and the weight is 76,465.2955 lbs.

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The amount that Yadira's friend will pay each month for rent and utilities is A.$472.00.

From the information, the monthly rent is $1,150.00, and monthly utilities will average $485.00.

The amount that the friend will pay will be:

= (1 - 80%) × Rent

= 20% × $1150

= 0.2 × $1150

= $230

The utilities to be paid will be:

= Utilities / 2

= $485 / 2

= $242

Total amount:

= Rent + Utility

= $230 + $242

= $472

The correct option is A.

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The type I error is assuming that cleaning terminals with petroleum jelly lowers the risk of developing a bad automobile battery when there is actually no discernible benefit. The type II error is assuming that cleaning terminals with petroleum jelly has no impact on the chances of developing a bad automobile battery when in fact it does. So the option B is correct.

A type I error is assuming that using petroleum jelly to clean terminals lowers the risk of having a malfunctioning automobile battery when, in fact, there is no difference between using petroleum jelly to clean terminals and not using it at all.

The conclusion that using petroleum jelly to clean terminals has no impact on the possibility of generating a defective automobile battery is a type II error, as using petroleum jelly to clean terminals actually lowers the possibility of doing so. So the option B is correct.

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The complete question is:

Consider a hypothesis test of the claim that using petroleum jelly to clean terminals reduces the likelihood of developing a faulty car battery.

Identify the type I and type II errors for this test.

A. A type 1 error is accepting that there was a significant relationship between using petroleum jelly to clean terminals and developing a faulty car battery. A type II error is accepting that there was not a significant relationship between using petroleum jelly to clean terminals and developing a faulty car battery.

B. A type I error is concluding that using petroleum jelly to clean terminals reduces the likelihood of developing a faulty car battery, when in reality, using petroleum jelly to clean terminals has no effect on the likelihood of developing a faulty car battery. A type II error is concluding that using petroleum jelly to clean terminals has no effect on the likelihood of developing a faulty car battery, when in reality, using petroleum jelly to clean terminals actually reduces the likelihood of developing a faulty car battery.

C. A type I error is concluding that using petroleum jelly to clean terminals has no effect on the likelihood of developing a faulty car battery, when in reality, using petroleum jelly to clean terminals reduces the likelihood of developing a faulty car battery. A type II error is concluding that using petroleum jelly to clean terminals effectively reduces the likelihood of developing a faulty car battery, when in reality, using petroleum jelly to clean terminals does not effect the likelihood of developing a faulty car battery.

D. A type I error is stating that the likelihood of using petroleum jelly to clean terminals is reduced by developing a faulty car battery. A type II error is stating that the likelihood of using petroleum jelly to clean terminals is not effect by the development of a faulty car battery.

Answer:

Ellipse

Step-by-step explanation:

Given

\(x = 7sin\theta\)

\(y= 2cos\theta\)

Required

The kind of shapes with such equations

This answer to this question is(B) Ellipse

The parametric equation of an ellipse is represented as:

\(x = asin(\theta)\) and \(y = bcos(\theta)\)

In this case:

\(a=7\ b = 2\)

So:

\(x = 7sin\theta\) and \(y= 2cos\theta\)

Answer:

x = - 0.5

\(x=-\frac{1}{2}\)

Step-by-step explanation:

2x + 5 = 4

2x + 5 - 5 = 4 - 5

2x = - 1

2x ÷ 2 = - 1 ÷ 2

x = - 0.5

When working with fractional readings, it is often necessary to convert them to a different format to ensure consistency and compatibility. One common conversion is to express the fractions as decimals or percentages.

This allows for easier comparison and calculation.

For example, if you have a fractional reading of 3/4, you can convert it to 0.75 or 75%. By converting the fraction, you bring the measurement into a standardized range, making it easier to work with and understand.

Converting fractions to decimals or percentages is a useful practice in various fields, including mathematics, engineering, and statistics, ensuring uniformity and facilitating data analysis.

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Answer:

15.94 meters

Step-by-step explanation:

11/0.69 = 15.942.......

Round it to get 15.94

Answer:

60 because I added all of them

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Answer:

since monomial means a one term expression...  A, D and E look good

Step-by-step explanation:

The mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

The average of a set of values is referred to as the mean. To calculate the mean of a dataset, add up all of the values and divide by the number of values.

We can calculate the mean of the given data set as follows:

Mean = (9 + 6 + 2 + 0 + 2 + 3 + 5 + 2 + 1 + 5)/10

Mean = 3.5

Variance:Variance is a measure of how much a set of data varies. In other words, variance tells us how far each value in the dataset is from the mean. The variance formula is as follows:

σ² = (Σ(x - μ)²) / N

Where σ² is the variance, Σ is the sum, x is each value in the data set, μ is the mean of the data set, and N is the number of values in the data set.

Using the above formula, we can calculate the variance for the given data as follows:

First, we need to calculate the mean of the data set.x f(x)

xf(x)4 1 45 3 15 6 4 24 7 4 28 8 2 16

Total 14 128

Mean (μ) = 128 / 14 = 9.14

σ² = (Σ(x - μ)²) / N

σ² = [1(4 - 9.14)² + 3(5 - 9.14)² + 4(6 - 9.14)² + 4(7 - 9.14)² + 2(8 - 9.14)²] / 14

σ² = 5.056

Approximating the Mean:

We can use the midpoint of each interval as an approximate value for the entire interval. We can calculate the approximate mean as follows:

Mean = Σ(midpoint × proportion of stocks)

Mean = (-0.80 × 0.03) + (-0.40 × 0.03) + (0.00 × 0.2) + (0.40 × 0.44) + (0.80 × 0.16) + (1.20 × 0.06) + (1.60 × 0.05) + (2.00 × 0.03)

Mean = 0.428

Therefore, the mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

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The volume of the resulting solid is 16623 when a circular hole of radius 5 has been bored through the center of a ball with a radius of 16.

Given that,

A circular hole of radius 5 has been bored through the center of a ball with a radius of 16.

We have to determine the resulting solid's volume.

We know that,

Volume of the original ball= 4/3πr³

Radius r=16

Volume v₁=4/3π(16)³ = 16384π/3

Volume of hole = 4/3πr³

Radius r=5

Volume v₂=4/3π(5)³ = 500π/3

Volume of the resulting solid = v₁-v₂

= 16384π/3 - 500π/3

= 15882π/3

= 16623

Therefore, The volume of the resulting solid is 16623 when a circular hole of radius 5 has been bored through the center of a ball with a radius of 16.

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a) The height of a baseball after 2 seconds = 480 ft

b)  The height of a baseball after 4 seconds = 384 ft

c) The time taken by the baseball to strike the ground = 7 seconds

Here, the height , h, of the baseball above the ground at any time, t, in seconds, is given by the equation,

h(t) = -16t² + 48t + 448.

a) the height after 2 seconds

substitute t = 2 in above equation,

h(2) = -16(2)² + 48(2) + 448

h(2) = 480 ft

b) in order to the height after 4 seconds:

substitute t = 24 in above equation,

h(4) = -16(4)² + 48(4) + 448

h(4) = 384 ft

c) To find the time taken by the baseball to strike the ground, substitute h(t) = 0

So, -16t² + 48t + 448 = 0

We solve above quadratic equation.

(t + 4)(t - 7) = 0

t = -4 OR t = 7

t = -4 is not possible

Therefore, the time to strike the ground would be 7 seconds

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The complete question is:

A baseball is projected upward from the top of a 448-ft-tall building with an initial velocity of 48 feet per second. The hieght, h, of the baseball above the ground at any time, t, in seconds, is given by the equation  h(t) = -16t² + 48t + 448.  a) Find the height after 2 seconds b) Find the height after 4 seconds c) Find the time it takes for the baseball to strike the ground.

Answer:

Below

Step-by-step explanation:

When we are talking about domain it is basically asking "are there any restrictions on the x's?". And range is basically asking "are there any restrictions on the y's?" So :

a) We can see that this graph extends from -3 to 3

Domain : { XeR | -3 < x < 3 }

Range : { YeR | -2 < y < 3 }

b) Because this graph has arrows, we know that the x and y coordinates will be infinite

Domain : { XeR }

Range : { YeR }

c) We can see that this graph extends from 0 - 4

Domain : { XeR | 0 < x < 4 }

Range : { YeR | -4 < y < 1 }

     * make sure you put a little dash under the < signs because they can be equal to these values as well! I didn't have the symbol unfortunately

Hope this helps! Best of luck <3

Answer:

yes clearly

Step-by-step explanation:

using rules of divisibility it is divisible

using your calculator it is divisible

the answer is 44

Step 2.1 code is given in the question. In step 2.2, we have to change the variables, m(t) and c(t) and plot the following equations:m(t) = 3cos(2π*700Hz*t)c(t) = 5cos(2π*11kHz*t)The modified code will be:Amplitude of message signal, Am = 3 Amplitude of carrier signal, Ac = 5 Frequency of message signal, fm = 700Hz Frequency of carrier signal, fc = 11kHz.

The amplitude modulation index is given as, mi = Am/Ac = 3/5 = 0.6The modulated signal is given as,s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t);The plot of the signals can be seen below:From the plots, we can see that the signal, s(t), faithfully represents the original message wave m(t). Hence, the correct option is (a) The signal, s(t), faithfully represents the original message wave m(t).

Step 2.3 requires us to plot the following equations:m(t) = 40cos(2π*300Hz*t)c(t) = 6cos(2π*11kHz*t)The modified code will be:Amplitude of message signal, Am = 40 Amplitude of carrier signal, Ac = 6 Frequency of message signal, fm = 300HzFrequency of carrier signal, fc = 11kHz The amplitude modulation index is given as, mi = Am/Ac = 40/6 > 1The modulated signal is given as,s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t);The plot of the signals can be seen below:From the plots, we can see that the signal, s(t), is distorted because the AM Index value is too high. Hence, the correct option is (a) The signal, s(t), is distorted because the AM Index value is too high.

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Answer:

the measure of angle sbt is 95 degrees

Step-by-step explanation:

50+35=85

180-85+95

Answer:

31.25 slides per hour.

Step-by-step explanation:

250 slides ÷ 8 hours = 31.25 slides per hour

You're welcome!

Answer:

You are trying to find how many slides they did per hour so the answer to that would be 31.25

Step-by-step explanation:

250 ÷ 8 = 31.25

With the help of the given graph, we know that Juan has read 10 books by day 12.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Create a graph by placing a series of bars on graph paper.

So, for path:
The curve line: y = kx + 5 which passes (4, 10)

10 = 4k + 5, k = 5/4

For Juan:

His reading rate same as Patti's.

Curve line: y = ax + b

a = 5/4

He has not read any book before 4th day.

So, when x = 4, y = 0.

0 = 4a + 5, 4 * 5/4 + b

b = -5

y = 5/4 * -5 (x > 4)

When x = 12, y = 5/4 * 12 - 5 = 15 - 5 = 10

Juan has read 10 books by day 12.

Therefore, with the help of the given graph, we know that Juan has read 10 books by day 12.

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With the help of the given graph, we know that Juan has read 10 books by day 12.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Create a graph by placing a series of bars on graph paper.

So, for path:
The curve line: y = kx + 5 which passes (4, 10)

10 = 4k + 5, k = 5/4

For Juan:

His reading rate same as Patti's.

Curve line: y = ax + b

a = 5/4

He has not read any book before 4th day.

So, when x = 4, y = 0.

0 = 4a + 5, 4 * 5/4 + b

b = -5

y = 5/4 * -5 (x > 4)

When x = 12, y = 5/4 * 12 - 5 = 15 - 5 = 10

Juan has read 10 books by day 12.

Therefore, with the help of the given graph, we know that Juan has read 10 books by day 12.

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As per given by the question,

There are given that a length of three sides of the triangle.

The length of sides are, 14cm, 22cm, and 30cm.

Now,

For finding the measure of the smallest angle,

The smallest angle in a triangle is always opposite the shortest side. and also the bigest angle is always opposite the longest side.

So,

Suppose length A is 14cm, B is 22 cm and C is 30cm.

Then,

From the law of cosines,

Let A be the smallest angle.

So,

Now,

Find the value of angle A,

Now,

Then,

Hence, the measure of the smallest angle is 25.84 degree.

Answer:

bro so i dont have an answer but i'm on the same thing rn lol

Step-by-step explanation:

Hey there! I'm happy to help!

Sum means to add. Let's call our number n.

n+6

We multiply this whole thing by 5.

5(n+6)

And this is 48.

5(n+6)=48

Have a wonderful day! :D

Answer:

pi?

me cemo jadumi elmoi numbe

The frequency distribution given shows the number of medical tests conducted on 32 randomly selected emergency room patients. It provides information on the number of tests performed and the corresponding number of patients for each test category.

To send this data to Excel, you can follow these steps:
1. Open Excel on your computer.
2. Create a new spreadsheet by selecting "Blank Workbook" or "New Workbook."
3. In the first column, enter the different categories of tests performed: 0, 1, 2, 3, and 4 or more.
4. In the second column, enter the corresponding number of patients for each test category: 14, 8, 4, 4, and 2.
5. Label the first column as "Number of Tests" and the second column as "Number of Patients."
6. Highlight the data in both columns.
7. Click on the "Insert" tab in the Excel menu.
8. From the "Charts" section, select the type of chart you want to create, such as a bar chart or column chart. This will visually represent the frequency distribution.
9. Customize the chart as desired by adding titles, adjusting colors, and modifying other formatting options.
10. Once you are satisfied with the chart, save the Excel file by clicking on "File" and then selecting "Save As." Choose a location on your computer to save the file, provide a name, and click "Save."

By following these steps, you will have successfully sent the data on the frequency distribution of medical tests to Excel and created a visual representation of the information using a chart.

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Answer: The answer is (B) 16.5%.

Step-by-step explanation:

There is 98% confidence that the true population mean falls within the range of $2782.11 and $3497.89 based on the provided sample data.

To construct a 98% confidence interval for the population mean,  use the following formula:

Confidence Interval = mean ± Z * (σ/√n)

where:

- Z is the critical value corresponding to the desired confidence level

- σ is the population standard deviation

- n is the sample size

Given the information provided:

(sample mean) = $3140

- σ (population standard deviation) = $686

- n (sample size) = 20

First, find the critical value Z for a 98% confidence level. The confidence level of 98% corresponds to a significance level (α) of 0.02.

Half of the significance level is distributed in each tail of the standard normal distribution.

Looking up the critical value for a significance level of 0.02/2 = 0.01 in a standard normal distribution table or using statistical software,  Z ≈ 2.33.

Substituting the values into the formula, calculate the confidence interval:

Confidence Interval = $3140 ± 2.33 * ($686/√20)

Calculating the expression inside the square root:

($686/√20) ≈ $153.45

Therefore, the confidence interval for the population mean is approximately:

Confidence Interval = $3140 ± 2.33 * $153.45

Confidence Interval ≈ $3140 ± $357.89

This can be expressed as:

Confidence Interval ≈ ($2782.11, $3497.89)

Thus, it is  98% confident that the true population mean falls within the range of $2782.11 and $3497.89 based on the provided sample data.

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The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

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