Surface area of the cylinder in terms of pi, given a diameter of 3.4 inches and a height of 3 inches, is [tex]28.36\pi[/tex] square inches.
To find the surface area of a cylinder in terms of pi, you need to add the areas of the top and bottom circles (which are identical) and the area of the curved lateral surface.
The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. Since the diameter of the circle is given as 3.4 inches, we can find the radius by dividing the diameter by 2:
r = 3.4 / 2 = 1.7 inches
Using this radius, the area of one circle is:
A = [tex]\pi (1.7)^2[/tex] = [tex]9.08\pi[/tex] square inches
Since the cylinder has two identical circles, the total area of both circles is:
2A = 2([tex]9.08\pi[/tex]) = [tex]18.16\pi[/tex] square inches
The lateral surface area of a cylinder can be found by multiplying the circumference of the base circle by the height of the cylinder. The formula for the circumference of a circle is C = 2πr, so the circumference of our circle is:
C =[tex]2\pi (1.7)[/tex]= [tex]3.4\pi[/tex] inches
The height of the cylinder is given as 3 inches, so the lateral surface area is:
A = Ch = ([tex]3.4\pi[/tex])(3) = [tex]10.2\pi[/tex] square inches
To find the total surface area of the cylinder, we add the areas of the two circles and the lateral surface:
Total surface area = 2A + A = [tex]18.16\pi + 10.2\pi[/tex] = [tex]28.36\pi[/tex] square inches
Therefore, the surface area of the cylinder in terms of pi, given a diameter of 3.4 inches and a height of 3 inches, is [tex]28.36\pi[/tex] square inches.
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-2+5 what is the answer
Answer:
3
start from -2 and count up 5
-2,-1, 1, 2, 3
21. A triangle with area 5 cm² is
dilated with a scale factor of 3.
What is the area of the image, in
square centimeters?
The area of the dilated triangle is 45 squared meters
What is the area of the triangle?Dilation is a geometric transformation that involves resizing a shape while maintaining its shape and proportions. The scale factor is the ratio of the size of the image to the size of the original shape.
In this problem, we are given a triangle with an area of 5 cm², and we are asked to find the area of the dilated triangle when it is scaled up by a factor of 3. To find the area of the dilated triangle, we need to use the formula for the area of a triangle, which is 1/2 * base * height.
When a triangle is dilated by a scale factor of k, both its base and height are multiplied by k. This means that the area of the dilated triangle is k^2 times the area of the original triangle. In this case, the scale factor is 3, so the area of the dilated triangle is 3^2 times the area of the original triangle.
Therefore, the area of the dilated triangle is 9 times the area of the original triangle, which is 9 * 5 cm² = 45 cm².
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A student is selected at random to work a problem on the
board.
What is the probability that the student selected is a female
junior?
0.15
0.25
0.20
0.50
The chart shows the number of hours each student spends training for their favorite sport per hundred hours write a proportion and make a prediction for the number of hours Simone will spend training over a 2000 hour periods
Answer:240 hours
Step-by-step explanation:100x20=2000
12/100=x/2000 multiply 12 and 100 by 20.
A pediatrician was interested in the weights of all 14-year-olds in the state of Texas to determine outliers in the data. She gathered data from a random sample of 2,000 pediatricians in the state and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for her data?
Bar graph
Circle graph
Histogram
Stem-and leaf plot
The best graphical representation for the pediatrician's data would be a histogram. A histogram is a type of graph that shows the distribution of continuous data. In this case, the weights of the 14-year-olds would likely be continuous data. A histogram would allow the pediatrician to visualize the distribution of weights and identify any outliers or unusual patterns.
Answer:histogram
Step-by-step explanation:
Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
The equation of the line parallel to y = -3x + 7 and passing through the point (2, -1) is y = -3x + 5, written in slope-intercept form.
How to Write an Equation of a Line in Slope-intercept Form?The given equation is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
The slope of the given equation is -3, which means any line parallel to it will have the same slope.
Using the point-slope form of a linear equation, we can write the equation of the line passing through the point (2, -1) and having a slope of -3:
y - y1 = m(x - x1) where (x1, y1) = (2, -1) and m = -3
y - (-1) = -3(x - 2)
y + 1 = -3x + 6
y = -3x + 5
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Find f(10) for this piecewise-defined function.
f(x) = { -4x + 1 if x < 3
{2/5x -3 if x > 3
Write your answer as an integer or as a fraction in simplest form.
f(10) =
Answer:
-39
Step-by-step explanation:
I cannot provide picture, but plug 10 in for x for both equations
-4(10)+1 = -39 -39 less than 3? yes
2/5(10)-3 = 1 1 is greater than or equal to 3? no
the value of y when f(10) is -39
since when you plug 10 in for x -39 is the result
The following table is from a Earth Science reference table.
Pls show work
Thank you
By consulting these tables, you can quickly access important data and information that can help you better understand the Earth and its various processes.
Sure, I'm happy to help! Without seeing the actual table, I'm not sure what information you are looking for specifically. However, I can tell you that Earth Science reference tables often contain important information about the Earth's systems, including geology, meteorology, oceanography, and astronomy.
For example, these tables might include information on rock types, mineral identification, weather patterns, ocean currents, and celestial objects like planets and stars. They may also provide key equations and constants for various scientific calculations.
In general, Earth Science reference tables are a valuable resource for students, researchers, and professionals in the field.
If you have a specific question about the table you're looking at, feel free to let me know and I'll do my best to provide a helpful answer!
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1
2
3
4
5
Complete the following sentence.
Government benefit programs have been established for a range of
TIME F
assistance.
15
Government benefit programs have been established for a range of assistance over time.
What is context of above answer?
The answer given was "Government benefit programs have been established for a range of assistance." This sentence is referring to various programs created by the government to provide support or aid to those in need.
These programs may include financial assistance, food assistance, housing assistance, medical assistance, and more. The sentence suggests that the government recognizes the importance of providing help to individuals and families who may be struggling and has taken steps to create programs to address these needs.
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Complete Question:
What types of assistance have government benefit programs been established for?
A blue car is 600 kg moving at 5m/s crashes into a red car 400 kg which is initially at rest. After the crash the two cars stick together. What is the initial momentum of the red car before the Collison
3) a baseball team had 80 players show up for tryouts last year and this year had 96 players show up for tryouts. find the percent increase in players from last year to this year.
The percent increase in players from last year to this year = 20%
We know that the formula for the percentage change a quantity is :
(P) = [Final value - Initial value] / Initial value x 100
Here, a baseball team had 80 players show up for tryouts last year and this year 96 show up for tryouts.
initial number of players = 80
current number of players = 96
So, using above formula the percent increase in players is:
P = [(96 - 80) / (80)] x 100
P = (16 / 80) x 100
P = 0.20 x 100
P = 20%
Therefore, the percentage of increase in players = 20%.
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X:y=1:5
Which is the correct equation?
A)y=5x
B)y=x/5
C)y=x-4
D)y=x+4
The correct equation for x:y= 1:5 is (a) y = 5x.
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. The equation consists of two sentences joined by an equal sign ("="). The expressions on both sides of the equation are called the "left" and "right" sides of the equation. Usually the right side of the equation is assumed to be zero. Assuming this doesn't reduce the width because it can be done by subtracting the right side from both sides.
Compare to a scale on which a weight is placed. When the same weight of something (like grain) is placed in two pans, the two weights balance the scales and are said to be equal.
According to the Question:
Given that:
x:y = 1:5
We can write the equation as:
x/y = 1/5
⇒ y = 5x
Therefore x:y = 1:5 is y=5x
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I need help filling in the blanks
Values of x for blanks 4 , 1 in inequality .
What in mathematics is an inequality number?
A relationship between two values in an algebraic statement that are not equal is shown by an inequality. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.
Despite the equals sign being substituted by an arrowhead, the formula 5x 4 > 2x + 3 resembles an equation. It serves as an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
-3x/4 < 12/1
x < -16
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On Thursday afternoon the temperature fell by 3°C. On Friday it had risen by 5°C.
If Thursday morning
s temperature was - 4°C, what was the temperature on Friday?
Answer:
Thursday morning temperature was -4 degrees Celsius.
Thursday afternoon temperature dropped by 3 degrees.
So Thursday afternoon's temperature was:- -4 - 3 = -7
On Friday, the temperature had risen by 5 degrees Celsius
So -7 + 5 = -2 degrees Celsius
Solve the following simultaneous equations using an algebraic method.
4x - 7y = 15
5x - 2y = 12
Answer:
4x −7y=21
x+2y=99
Explanation
4x - 7y = 15
5x - 2y = 12
First equation times 2:
8x - 14y = 30
Second equation times 7:
35x - 14y = 84
Subtract,
27x = 54
x = 54/27 = 2
2y = 5x - 12 = 10 - 12 = -2
y = -1
Answer: x=2, y = -1
Check:
4(2)-7(-1)=8+7=15, good
5(2) -2(-1) = 10 + 2 = 12, good
ax + by = c
dx + ey = f
has solutions
x = (ce-bf)/(ae-bd), y = (a f-cd)/(ae-bd)
4x - 7y = 15
5x - 2y = 12
has solutions
denom = ae-bd = 4(-2) - (-7)(5) = 27
x = (15(-2) - (-7)(12))/27 = (-30 + 84)/27 = 2
y = (4(12)-15(5))/27 = (48-75)/27 = -27/27 = -1
Answer:
(x, y) = (2, -1)
Step-by-step explanation:
You want to solve this system of equations using an algebraic method:
4x -7y = 155x -2y = 12Cross multiplication methodWriting these equations in general form and making an array of coefficients with the x-coefficient repeated, we get the equations and array ...
4x -7y -15 = 05x -2y -12 = 0[tex]\begin{array}{cccc}4&-7&-15&4\\5&-2&-12&5\end{array}[/tex]
Working from the left calculating determinants of pairs of columns, we have ...
∆ = 4(-2) -5(-7) = 27
∆x = -7(-12) -(-2)(-15) = 54
∆y = -15(5) -(-12)(4) = -27
The variable values are ...
x = ∆x/∆ = 54/27 = 2
y = ∆y/∆ = -27/27 = -1
The solution is (x, y) = (2, -1).
__
Additional comment
The graph confirms this solution.
The "cross multiplication method" is useful when the coefficients are such that elimination or substitution involves more arithmetic operations than the minimum. The amount of math involved in calculating the x- and y-values is on par with what would be required for "elimination." The method is substantially equivalent to "Cramer's Rule."
Select the expression that represents this real-world situation.
Vesi snowboards 4 hours before lunch and 3 hours after lunch each day. How many hours did she snowboard in 2 days?
4 + 3 + 2
(4 + 3) x 2
4 x 3 ÷ 2
(4 x 3) − 2
Answer:
(4 + 3) x 2
Step-by-step explanation:
In one day, Vesi would snowboard 4+3 hours, so in two days, we would multiply this by two and get the expression (4+3) * 2.
snowdon has a height of approximately 1100 metres above the sea
assuming that the temperature decreases by 1 oc for every 100m above sea level, work out the temperature at the summit of snowdon when the sea level temperature is 4oc
Answer:
[tex]-7^\circ C[/tex]
Step-by-step explanation:
Let
x -----> the height in meters
y ----> the temperature in Celsius degree
we know that
The linear equation in slope intercept form is equal to
[tex]y+mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem we have
The slope or unit rate is equal to
[tex]m=-\dfrac{1}{100} \dfrac{^\circ C}{m}[/tex] ---> is negative because is a decreasing function
The y-intercept or initial value is equal to
[tex]b=4^\circ C[/tex] ----> value of y when the value of x is equal to zero (sea level)
substitute
[tex]y=-\dfrac{1}{100} x+4[/tex]
For x=1,100 m
substitute in the linear equation and solve for y
[tex]y=-\dfrac{1}{100} (1,100)+4[/tex]
[tex]x=-7^\circ C[/tex]
Robyn, a programmer, had a few important !les saved on her computer. The space occupied by the !les was 84.6 megabytes in all. If each !le used a memory of 21.15 megabytes, how many !les were there
Robyn has 4 important files saved on her computer.
To solve this problem, we can use a simple formula that relates the total space occupied by the files to the size of each file:
Total space occupied = Size of each file x Number of files
In this case, we know the total space occupied (84.6 megabytes) and the size of each file (21.15 megabytes), so we can rearrange the formula to solve for the number of files:
Number of files = Total space occupied ÷ Size of each file
Plugging in the values we know, we get:
Number of files = 84.6 megabytes ÷ 21.15 megabytes per file
Simplifying this expression gives us:
Number of files = 4
Therefore, Robyn has 4 important files saved on her computer.
It's important to note that this problem assumes that each file uses exactly 21.15 megabytes of memory. In reality, file sizes can vary depending on their content, so this may not always be the case. Additionally, it's worth noting that file size can be affected by various factors such as compression and encoding, so the actual size of a file on disk may differ from its theoretical size. Nonetheless, for the purposes of this problem, we can assume that each file uses exactly 21.15 megabytes of memory.
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What is an equation of the line that passes through the points (2,5)and(3,6)?
Answer:
y = x + 3
Step-by-step explanation:
What is the equation of the line shown in this graph?
The equation of the line shown in the graph, from (–2,2) to (–3,–1) is y = -5/4x – 7/4.
What is equation?Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.
To solve for the equation of the line, we can use the point-slope formula, y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line. In this case, the point (x1, y1) is (–2,2) and the slope of the line is m = (–1 – 2)/(–3 – (–2)) = –3/–1 = 3. Therefore, the equation of the line is y – 2 = 3(x – (–2)).
Simplifying, we get y = 3x + 2. To put the equation in the slope-intercept form, y = mx + b, we can rewrite the equation as y = 3x + 2 = 3x + 2 – 2 = 3x – 2 + 2 = 3x – 2, which is the equation of the line, y = –5/4x – 7/4.
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The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3.
What is equation?Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.
The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This line is a horizontal line, which means that all points on the line have the same y-coordinate.
To verify this equation, we can use the two points given on the graph: (-2,-3) and (3,-3). Using the slope-intercept form of a line, we can plug in the points to determine the equation of the line.
The slope-intercept form is y = mx + b, where m is the slope, x is the x-coordinate, and b is the y-intercept. The slope is calculated by finding the change in y over the change in x. In this case, both points have the same y-coordinate, so the slope is 0. Therefore, the equation of the line is y = 0x + b.
Plugging in the coordinates of one of the points, (-2,-3), we get -3 = 0x + b. By solving for b, we get b = -3. Substituting b into the equation, we get y = 0x - 3. This is the equation of the line shown in the graph.
In conclusion, the equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This equation was verified by using the slope-intercept form of a line and plugging in the two points given on the graph.
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Nihkil surveyed `20` students at his middle school and `13` of them had at least one sibling. There are `300` students at Nikhil’s middle school. If the rest of the school is consistent with these results, about how many students would have at least one sibling?
About 195 students at Nikhil's middle school would have atleast one sibling.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
We can use proportion to estimate the number of students at Nikhil's middle school who have at least one sibling.
If 13 out of 20 students surveyed have at least one sibling, we can assume that the same proportion applies to the entire school.
So, we can set up a proportion as follows:
13/20 = x/300
where x is the number of students in the entire school who have at least one sibling.
Solving for x, we can cross-multiply and get:
13 * 300 = 20 * x
x = (13 * 300)/20
x = 195
Therefore, about 195 students at Nikhil's middle school would have at least one sibling.
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what type of distribution is utilized for nominal data? a gaussian b binomial c positive skew d negative skew
The type of distribution which is utilized for the nominal data is option b. Binomial distribution.
The appropriate distribution for nominal data is a binomial distribution.
The binomial distribution is used when the data consists of two possible outcomes.
The two outcomes such as success or failure, heads or tails, or pass or fail.
In nominal data, the categories do not have any inherent order.
And there is no numerical value associated with each category.
The binomial distribution gives the probability of obtaining a certain number of successes in a fixed number of independent trials.
The required probability of success is the same for each trial.
Therefore, option b. binomial distribution is considered as more appropriate distribution for the nominal data.
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Problem 2: If the garbage company in a city with a population of
1.3 x 10^5 collects approximately 14,300 pounds of garbage per week,
how much garbage per person will they collect in one year?
the garbage company in the city will collect approximately 5.72 pounds of garbage per person in one year.
To calculate how a lot garbage in step with man or woman the garbage enterprise collects in 12 months, we want to find out how many weeks are in a yr and then divide the overall amount of garbage collected in a 12 months by means of the population of the town.
wide variety of weeks in a year: 52 (assuming there aren't any bounce years)
overall amount of garbage collected in a 12 months: 14,three hundred kilos/week x fifty two weeks = 743,600 kilos/12 months
garbage in keeping with character in line with year: 743,six hundred kilos/12 months ÷ 1.three x 10^5 people = 5.72 kilos/person/yryr
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BC is tangent to circle D at point C. The measure of
LBDC is 35º.
What is the measure of ZDBC?
1. 35°
2. 55°
3. 90°
4. 180°
Which of the following sets of ordered pairs represents a function?
((1, 2), (2.1), (2, 2))
((1.2). (2. 1), (0.2))
c ((0.1), (1.0), (0.2))
((-1, 2), (0, 3), (-1, 4))
2 option is Correct for sets of ordered pairs represents a function
The only set of ordered pairs that represents a function is (b), which can also be written as {(1.2, 2), (2, 1), (0.2, 0)}. To be a function, each input (x-value) must correspond to exactly one output (y-value). In set (a), the input value of 2 is associated with two different output values, so it is not a function. Set (c) has two input values that both correspond to the same output value, so it is not a function. Set (d) has two different input values that both correspond to different output values, so it is not a function.
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Which expression is NOT equivalent to the others?
The expression -(12 x - 6) + 18 is not equivalent to the other expressions.
What is expression?Expression is a combination of words or symbols that communicate an idea, thought, opinion, or feeling. Expressions can be literal or figurative, and they often contain multiple layers of meaning. Expressions can be used to express emotions, opinions, beliefs, and values, and they are integral to communication and understanding.
This is because when all of the expressions are evaluated, the result of each expression is different. For example, when the expression -6(2 x - 4) is evaluated, the result is -24.
When the expression -4(3 x + 6) is evaluated, the result is -24. When the expression -3(4 x - 3) + 15 is evaluated, the result is -3. However, when the expression -(12 x - 6) + 18 is evaluated, the result is 12.
Therefore, the expression -(12 x - 6) + 18 is not equivalent to the other expressions.
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Complete questions as follows-
Which expression is not equivalent to the other expressions?
-6(2 x - 4)
-4(3 x + 6)
-(12 x - 6) + 18
-3(4 x - 3) + 15
Find the area. Leave your answer in simple radical form.
Therefore, the area of the pentagon is 928 square units.
lengthLength is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.
Find the area.
Pentagon
apothem = 16 side = 23.2
Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth
For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.
For the second question, the formula to find the area of a regular pentagon is:
Area = (perimeter x apothem)/2
Since we are given the apothem and the side, we can find the perimeter of the pentagon as:
perimeter = 5 x side = 5 x 23.2 = 116
Substituting the values in the formula, we get:
Area = (116 x 16)/2 = 928
Therefore, the area of the pentagon is 928 square units.
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2.2.3 b for which -x²+8x+20=b will have real roots
Answer:
second that -x is the correct answer
Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=3x+1
T(x)=6x
Write the expressions for (t-s)(x) and (t+s)(x) and evaluate (t x s)(4)
to evaluate (t x s)(4), we substitute x = 4 into the expression for (t x s)(x). This gives us (18x + 6)|x=4, which simplifies to 72 + 6 = 78.
(t-s)(x) = 6x - (3x+1) = 3x - 1
(t+s)(x) = 6x + (3x+1) = 9x + 1
(t x s)(4) = (6x)(3x+1)|x=4 = (18x + 6)|x=4 = 72 + 6 = 78
First, we need to define the functions s and t given by s(x)=3x+1 and t(x)=6x. We can then use these functions to calculate (t-s)(x) and (t+s)(x). To calculate (t-s)(x), we subtract s(x) from t(x). This gives us 3x - 1. To calculate (t+s)(x), we add s(x) and t(x). This gives us 9x + 1. Finally, to evaluate (t x s)(4), we substitute x = 4 into the expression for (t x s)(x). This gives us (18x + 6)|x=4, which simplifies to 72 + 6 = 78.
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. h= 1.5 inches; r = 4 inches
. h = 4 inches; r = 3 inches
(I did the first two but the other two are confusing please someone help)
Answer:
3. 75.4 and 4. 113.1
Step-by-step explanation:
Okay to find the volume of the cylinder the equation is πr⌃2h
3. so if H is 1.5 and r = 4 it would be π4⌃2(1.5) = 75.4 approx.
4. If h is 4 and r is 3 it would be π3⌃2(4) = 113.1 approx.