a cylinder is sliced such that the cross section is parallel to its bases. what is the shape of the cross section?a. circle
b. rectangle
c. trapezoid
d.triangle

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =300 \end{cases}\implies s=\cfrac{(300)\pi (3)}{180}\implies s=5\pi \implies s\approx 15.71~mm[/tex]

The area of the square according to the dimensions of base and height is 16 m².

The square is a shape with equal sides. Thus, the base and height of this shape is always equal. Now when we have the measurements of its side, we can calculate the area of the square. The formula for the same is -

Area = side²

Keep the value in formula to find the value of are of square

Area of square = 4²

Taking square on Right Hand Side of the equation

Area of square = 16 m²

Thus, the area of square is 16 m².

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Answer:

45.01

Step-by-step explanation:

You round to the nearest hundredth so since seven is big enough you add a 1 to the hundredth place

Answer:

Step-by-step explanation: (This is to show the equation of the Pythagorean Theorem.)

Remember the Pythagorean theorem is A^2 + B^2 = C^2. To find out a part of a right triangle using the Pythagorean theorem, you would find either A, B, or C. As an example, let us say that A is equal to 10, and B is equal to 8. How we find C^2, is we add A and B, but we square both numbers.

(10^2) + (8^2) = (C^2). We square 10 by itself, and we get 100 as our A. We also square 8 by itself as well, and we get 64 as our B. C does not have any number representing the variable, so we leave it as it is. 100 + 64 = 164 for C. We have to square root 164, since we're using exponents. (Please note that all my equations won't be a complete whole number, I'm using random numbers to show.) To find B or A, we find this equation. Let us keep our own variable, but C is equal to 15. To find B, we make the equation (10^2) + (B^2) = (15^2) or (A^2) + (8^2) = (15^2). To find B, We square 10 by itself to get 100, like from the last equation, but B doesn't have any number for the variable, so we keep it the same. We square 15 to get 225. After we get our 2 numbers, we subtract {100 + (B^2) = 225} ->

{(100 - 100) + (B^2) = (225 - 100)} -> {B^2 = 125}. We square root 125 to get our answer.

To find A, A doesn't have any number to fill in for the variable, We square 8 to get 64. We square 15 to get 225. After we get our 2 numbers, we subtract {(A^2) + 64 = 225} -> {A^2 + (64 - 64) = (225 - 64)} -> {B^2 = 161}. We square root 161 to get our answer. For the 3 sides: A and B, near the right triangle are both the "legs" of the triangle, while the slant of the triangle (C), is the hypotenuse.

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called factor analysis.

Statistical techniques are methods and procedures used in the collection, analysis, interpretation, and presentation of data. These techniques involve the use of mathematical and statistical models to draw meaningful insights and conclusions from data.

Some common statistical techniques include:

Descriptive statistics: These techniques are used to summarize and describe the key features of a dataset, such as central tendency, variability, and distribution.

Inferential statistics: These techniques are used to make inferences about a larger population based on a sample of data. This involves using probability theory to estimate population parameters and test hypotheses.

Regression analysis: This technique is used to model the relationship between one or more independent variables and a dependent variable.

Hypothesis testing: This technique is used to test the validity of a hypothesis or claim about a population using sample data.

Time series analysis: This technique is used to analyze data that varies over time, such as stock prices or weather patterns.

Cluster analysis: This technique is used to group similar observations together based on their characteristics.

Data mining: This technique involves the use of automated methods to discover patterns and relationships in large datasets.

Statistical techniques are widely used in many fields, including business, economics, social sciences, medicine, and engineering. They are used to make informed decisions, identify trends and patterns, and to understand complex systems.

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To find out how many oranges Cindy needs to make 7 cups of orange juice, we can use ratios and proportions.

First, let's find out how many oranges she needs to make 1 cup of orange juice:

2 1/2 oranges make 1/2 cup of orange juice

To make 1 cup of orange juice, she needs twice as many oranges: 2 1/2 * 2 = 5 oranges

So, Cindy needs 5 oranges to make 1 cup of orange juice.

Next, let's use this information to find out how many oranges she needs to make 7 cups of orange juice:

1 cup of orange juice requires 5 oranges

To make 7 cups of orange juice, she needs 7 times as many oranges: 5 * 7 = 35 oranges

Therefore, Cindy needs 35 oranges to make 7 cups of orange juice.

If Cindy used 2 1/2 oranges to make 1/2 cup of orange juice, Cindy will need 35 oranges to make 7 cups of orange juice.

To find out how many oranges Cindy will need to make 7 cups of orange juice, we can set up a proportion based on the information given.

First, we need to determine the ratio of oranges to orange juice. According to the given information, Cindy used 2 1/2 oranges to make 1/2 cup of orange juice. We can represent this as 2.5 oranges per 0.5 cups of juice.

To find the number of oranges needed for 7 cups of juice, we can set up a proportion:

2.5 oranges / 0.5 cups = x oranges / 7 cups

Now we can cross-multiply and solve for x:

(2.5 oranges) * (7 cups) = (0.5 cups) * (x oranges)

17.5 oranges = 0.5x

Divide both sides by 0.5:

17.5 / 0.5 = x

x = 35

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Answer:

115m

Step-by-step explanation:

Given

In TriangleXYZ

XZ = 23m

ZY = 19m

In TriangleXVW

WV = 95m

Solution

In Triangles XYZ and XVW

AngleWXV = AngleYXZ as they are Vertically Opposite Angles

AngleXWV = AngleXZY as they are Alternate Angles

Therefore TriangleXYZ and TriangleXVW are Similar Triangles

So,

XY/XV = YZ/VW = XZ/XW as they are Corresponding Sides of Similar Triangles

So,

XZ/XW = YZ/VW

or

23/XW = 19/95

23/XW = 1/5

XW = 23 × 5

XW = 115m

Therefore the distance WX is 115m

The equation solved for b is b = y/m

The equation y = m x b is a linear equation in slope-intercept form, which is commonly used to describe the relationship between two variables in a line. In this equation, the variable m is the slope of the line, and b is the y-intercept, or the point at which the line crosses the y-axis.

To solve this equation for b, we can rearrange it to isolate b on one side of the equation.

To do this, we can divide both sides of the equation by m, giving us y/m = b.

This is an equivalent equation that is solved for b, as b is on its own on the right side of the equation. Therefore, the equation solved for b is y/m = b

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68 kilograms is approximately equal to 149.91416 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

It is currently defined based on the fixed numerical value of the Planck constant, h,

Which is equal to 6.62607015 × 10-34 in the units of J·s.

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms.

To convert 68 kilograms to pounds,

We need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

68 kilograms multiplied by 2.20462 gives us:

68 kg x 2.20462 = 149.91416 pounds

(rounded to five decimal places)

So, 68 kilograms is approximately equal to 149.91416 pounds.

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The difference in total principal and interest payment between the 20-year loan versus the 15-year loan is B. $44,061.05.

The difference is obtained by computing the total payments for the Option B loan and comparing these to the total payments for Option A loan.

The total payments for Option B can be computed using an online finance calculator that determines also the monthly payments.

Mortgage loan = $167,800

Interest rate = 7.45%

Mortgage period = 240 (20 years x 12)

Total payment (Future Value) = $323,198.36

Monthly payment = $1,346.66 ($323,198.36/240)

N (# of periods) = 180 months (15 years x 12)

I/Y (Interest per year) = 7.45%

PV (Present Value) = $167,800

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $1,550.76

Sum of all periodic payments = $279,137.31

Total Interest = $111,337.31

Option A total payment = $323,198.36

Option B total payment = $279,137.31

Difference between the two options = $44,061.05 ($323,198.36 - $279,137.31)

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a) The point that is on both lines is given as follows: (4, 60).

b) They will have read the same number of pages on the 4th day, when they will have read 60 pages.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The equations for this problem are given as follows:

Then the ordered pair representing the solution is given as follows:

(5,60).

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25.44cm^2 is the area of the composite figure,

A composite shape is a shape that is made up of two or more figures.

The given shape is made up of circle and triangles. The area of the shaded region is expressed as:

Area = area of semicircle - area of triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.62 cm^2

For the triangle;

Area of triangle = 1/2absin60

For the value of a;

a/12 = cos60

a/12 = 1/2

a = 6

Area of triangle = 1/2(12)(6) sin60

Area of triangle = 31.17cm^2

Area of the shaded portion = 56.62 - 31.17

Area of the shaded portion = 25.44cm^2

Hence the area of the shaded portion is 25.44cm^2

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The total time of the guitar session will be 7¹/₂ hours.

A scatter plot is a plot mathematical chart or graph that depicts the relationships by the use of dots and shows the two numeric variables.

The dots are positioned on each horizontal and vertical value for an individual. They are used for observing the relationship between the variables. The graph shows are positive but nonlinear association.

The total time will be calculated as:-

T = ( 3) x ( 1 / 4 ) + (4) x (1 / 2 ) + ( 5 ) x ( 3 / 4 ) + 1

T = 3/4 + 4 / 2 + 15 / 4 + 1

T = 3 / 4 + 2 + 15 / 4 + 1

T = 18 / 4 + 3

T = 15 / 2

T = 7¹/₂ hours.

Therefore, the total time will be 7¹/₂  hours.

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The stage in Tuckman's Group Development Model in which members are socially cautious and overly polite is the Forming stage. thus option B is the answer.

Tuckman's Group Development Model is a structure for understanding the various stages that gatherings go through as they structure, create, and ultimately disband. The model incorporates four principal stages: forming, storming, norming, and performing with a potential fifth phase of dismissing. The framing stage is portrayed by individuals getting to know one another, being considerate, and attempting to lay out a feeling of direction for the gathering. They might be questionable about the gathering's objectives, jobs, and methodology. As the gathering advances through the stages, they will turn out to be more OK with one another and lay out a feeling of trust and union, prompting better execution.

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Answer:

Below

Step-by-step explanation:

Look for the letter that is between 1 and 2 ...very close to 2

=  1.85    <===== very close to '2'

In conclusion, it is not possible to determine with certainty who has what role.

Given by the solution:

Let's consider each statement one by one:

If Alice is the truth teller, then she is telling the truth, which means she can't be the truth teller, leading to a contradiction. So, Alice can't be the truth teller.

If Alice is the liar, then she is lying, which means she is the truth teller, leading to a contradiction. So, Alice can't be the liar.

If Alice is the spy, then she can either tell the truth or lie. If she tells the truth, then she can't be the truth teller, leading to a contradiction. If she lies, then she can't be the liar, leading to a contradiction. So, Alice can't be the spy.

Therefore, Alice can't have any of the roles.

If Bob is the truth teller, then he is telling the truth, which means he can't be the spy, leading to a contradiction. So, Bob can't be the truth teller.

If Bob is the liar, then he is lying, which means he could be the spy. Therefore, Bob can be the liar or the spy.

If Charlie is the truth teller, then he is telling the truth, which means he can't be the liar, leading to a contradiction. So, Charlie can't be the truth teller.

If Charlie is the liar, then he is lying, which means he could be the truth teller or the spy. Therefore, Charlie can be the liar, the truth teller or the spy.

Combining the results from the above statements, we get the following possibilities:

In conclusion, it is not possible to determine with certainty who has what role.

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The ramp will upward push to a top of about 18.8 inches at its maximum end.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given, The ramp has a length of 34 inches, The angle of elevation from the ground is 20 degrees.

We can use trigonometry to solve this problem.

The height of the ramp can be found using the following formula:

Height = Length x sin(θ)

where,

"Length" is the length of the ramp

"θ" is the angle of elevation in radians.

To convert the angle of elevation from degrees to radians,

angle in radians = (angle in degrees) x (pi/180)

Substituting the values we have, we get:

angle in radians = 20 x (pi/180) = 0.349 radians

Then, we can calculate the height of the ramp using the formula:

Height = 34 x sin(0.349)

= 18.8 inches (rounded to the nearest tenth)

Therefore, the ramp will rise to a height of approximately 18.8 inches at its highest end.

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The sum of the first 10 terms of the sequence -5, 15, 45, 135 is 295240.

We can use the following formula to determine the sum of a geometric sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

where an is the first term, r is the common ratio, and n is the total number of terms, S is the sum of the sequence.

We can see that the first term in the series -5, 15, 45, 135 is -5, and the common ratio is 3. (since each term is obtained by multiplying the previous term by 3). The series contains 4 terms, hence n is equal to 4. Adding these values to the formula yields the following results:

S = -5(1 - 3^4) / (1 - 3) (1 - 3)

S = -5(1 - 81) / (-2) (-2)

S = 5(80) (80)

S = 400

The total of the numbers 5, 15, 45, and 135 equals 400.

We may once more use the following formula to determine the sum of the first 10 entries in the same sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

Instead, we will use a = -5, r = 3, and n = 10 this time. By replacing these values, we obtain:

S = -5(1 - 3^10) / (1 - 3) (1 - 3)

S = -5(1 - 59049) / (-2) (-2)

S = 5(59048) (59048)

S = 295240

The result is 295240 for the first 10 terms in the series, which are -5, 15, 45, and 135.

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Answer:

Below

Step-by-step explanation:

See image.....the perpendicular slope was calculated incorrectly ....

Answer:

1) x=5, y=5sqrt(2)

2) x=14

3) 7sqrt(2)

Step-by-step explanation:

I will give you a quick lesson.

The formula is a² + b² = c²

The longest line(usually the bottom) is C

If something is squared, multiply it by itself, for example, 6² is 36, multiply 6 by 6(6 x 6).

Do the same thing with a and b.

Then add a and b after you square them.

To make the number smaller, square root it.

Then you will get your answer, don't forget the exponent.

Sorry for not giving you the answer, but I hope this quick lesson helped you, this is how I learned, I hope this makes it easier for you. Have a GOOD DAY!

This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

Here's an example Python function called count_characters that counts the number of times each character appears in a user-supplied string s:

def count_characters(s):

Given a string s, returns a dictionary containing the count of each character in the string.

char_count = {}

for char in s:

if char in char_count:

char_count[char] += 1

else

char_count[char] = 1

return char_count

This function creates an empty dictionary called char_count to store the counts of each character. It then loops through each character in the string s and checks if it's already in the char_count dictionary. If it is, it increments the count for that character. If it's not, it adds the character to the dictionary with a count of 1. Finally, the function returns the char_count dictionary.

You can call this function like this:

string = "hello world"

char_count = count_characters(string)

print(char_count)

Output:

python

{'h': 1, 'e': 1, 'l': 3, 'o': 2, ' ': 1, 'w': 1, 'r': 1, 'd': 1}

This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

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Answer:

here is how to solve the math problems with sales tax and discount:

a) To find the total bill, we need to add the purchase price and the sales tax. To find the sales tax, we need to multiply the purchase price by the sales tax rate. The purchase price is the sum of the prices of the two pairs of shoes, which is $37 + $42 = $79. The sales tax rate is 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 79 = $5.53. The total bill is 79 + 5.53 = $84.53.

b) To find the discounted price, we need to subtract the discount from the original price. To find the discount, we need to multiply the original price by the discount rate. The original price is the same as the purchase price in part a, which is $79. The discount rate is 25%, which as a decimal is 0.25. So, the discount is 0.25 x 79 = $19.75. The discounted price is 79 - 19.75 = $59.25. To find the total bill with the coupon, we need to add the sales tax to the discounted price. The sales tax rate is still 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 59.25 = $4.15. The total bill with the coupon is 59.25 + 4.15 = $63.40.

I hope this helps!

Step-by-step explanation:

The area of the rectangle will be 18a³b^6

The area of the circle will be 25x^6π

The area of the triangle will be 12a³c⁴

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area of the rectangle will be:

= Length × Width

= 6a²b⁴ × 3ab²

= 18a³b^6

The area of the circle will be:

= πr²

= π × (5x³)

= 25x^6π

The area of the triangle will be:

= 1/2 × base × height

= 1/2 × 4a²c × 6ac³

= 2a²c × 6ac³.

= 12a³c⁴

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The converted value of degrees Celsius to Fahrenheit which needs to convert  4 degrees Celsius equals to 39.2 degree Fahrenheit.

Scale factor which defines  the relation between Celsius and Fahrenheit is equal to :

(°C × 9/5) + 32 =°F

Now , to get the value of 4 degree Celsius and convert into Fahrenheit apply the above formula we have,

(4°Celsius × 9/5) + 32

= ( 36 / 5 ) + 32

= ( 7.2 ) + 32

= 39.2°Fahrenheit

Therefore, the converted value from degrees Celsius to Fahrenheit for the given temperature 4 degrees Celsius is equivalent to  39.2 Fahrenheit.

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Answer:

Step-by-step explanation:

You want the graphical solution to the set of inequalities that describes the numbers of games (x) and songs (y) that Staci can buy with $20, if a game costs $2 and a song costs $1, and Staci wants to buy at least 12 items.

The inequalities that describe the numbers are ...

  2x +y ≤ 20 . . . . . Staci has at most $20 to spend

  x + y ≥ 12 . . . . . . Staci wants to buy at least 12 items

Each of these inequalities has a solid boundary line on its solution space graph. The shading is below the line for the first inequality, and above the line for the second one. The vertices of the triangular solution space are ...

  (0, 12), (0, 20), (8, 4)

Possible numbers are the coordinates of any grid point within the triangle or on its boundaries.

The high - level design steps include :

High-level design steps refer to the early stages of the design process where the system is defined in general terms.

Defining system requirements and constraints involves collecting information about the system's desired features and capabilities. This information may come from various stakeholders, including customers, users, and subject matter experts.

Another important step involves identifying and addressing potential security risks and designing appropriate security measures.

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Options for this question include :

The commutative property of multiplication can be used to rewrite the given term as; 4g³h⁴.

The commutative property of multiplication simply postulates that changing the order of factors does not change the product. Hence; a × b = b × a.

Hence, since the given expression; 4gh³g²h can be written using the commutative property as;

4 • g • g² • h³ • h.

Consequently, the resulting form of the term is therefore; 4g³h⁴.

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Answer:

Angle 5 is 105 degrees.

Step-by-step explanation:

[tex]180-75[/tex]

[tex]105[/tex]

The missing information in the table is $290,000 for Firm 1 and $18,562,433 for Firm 2

The premium of a bond can be calculated by taking the coupon rate and subtracting the yield, and then multiplying the result by the face value of the bond.

For Firm 1, the premium is given by (7.00% - 8.00%) × $300,000 = -$10,000.

The proceeds of Firm 1 can then be calculated by

=> $300,000 – $10,000 = $290,000.

For Firm 2, the yield and coupon rate that is as interest are both given as 3.00%. This means that the bond will be sold at par value, so the face value and proceeds of the bond will be the same.

The face value of Firm 2 can be calculated by taking the proceeds given and dividing by the bond’s yield.

Thus, Firm 2’s face value is given by $556,853 / 3.00% = $18,562,433.

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Complete Question:

Complete the missing information in the table below. Assume that all bonds pay interest semiannually.

Do not use negative signs with answers.

Round percentages to one decimal place (ex. 0.0345 = 3.5%).

Round all other values to the nearest whole number.

Annual Years to Coupon  Issue

Yield Maturity Rate Face value Proceeds

Firm 1 8.00% 15 7.00% $300,000 $_______

Firm 2 3.00% 10 0.00% $_______ $556,853