The surface area of the cylinder, with a radius of 39 inches and a height of 33 inches, is calculated using the formula for the surface area of a cylinder. It amounts to a total of 7386pi square inches, separating the calculation into the lateral surface area and the area of the bases for clarity.
Explanation:The question is about finding the surface area of a cylinder where the radius of the base is 39 inches and its height is 33 inches, all in terms of pi. To find the surface area of a cylinder, we use the formula: 2(pi)(r)(height) + 2(pi)(r)^2. Substituting the given values, we have 2(pi)(39)(33) for the surface area of the sides, and 2(pi)(39)^2 for the two circular ends.
Therefore, the total surface area in terms of pi is: 2(pi)(39)(33) + 2(pi)(39)^2. This simplifies to: 2562pi + 4824pi, resulting in a total surface area of 7386pi square inches.
This approach easily demonstrates the process of calculating the surface area of a cylinder by focusing on its geometrical components: the lateral surface area and the area of the two circular bases.
Find the average (mean) of the following test scores.
83, 92, 47, 78, 80
Ο Α. 76
Ο Β. 70
C. 72
Ο.
Ο
Answer:
The average (mean) of the test scores is
A. 76
To find the average (mean) of test scores, add them up and divide by the total number of scores. The average of these test scores is 76.
Explanation:To find the average (mean) of the test scores, you need to add up all the scores and then divide by the total number of scores. In this case, you have 5 test scores: 83, 92, 47, 78, and 80. Adding them all up, you get 83 + 92 + 47 + 78 + 80 = 380. Then, divide the sum by 5 (the total number of scores): 380 / 5 = 76. Therefore, the average of these test scores is 76.
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Solve for AD.
A) 12
B) 10
C) 8
D) 6
Answer: I believe the answer is C) 8
The pattern goes 0, 4, 8, 12
Inbetween them are 2, 6, 10
A graphic designer chose a base font size and represented it as 1 on the scale. She then listed some consecutive scale sizes. Two consecutive sizes were 2.744 and 3.8416.
What scale size came before 2.744?
Enter your answer, as a decimal, in the box.
The scale size that came before 2.744 is 1.92.
To find the scale size that came before 2.744, we need to understand the relationship between the consecutive scale sizes. Given that the base font size is represented as 1 on the scale, and we have two consecutive sizes as 2.744 and 3.8416, we can determine the common ratio of the geometric progression that these sizes follow.
Let's denote the common ratio as r. Then, we can write the following relationship:
[tex]\[ 2.744 \times r = 3.8416 \][/tex]
Now, we solve for r:
[tex]\[ r = \frac{3.8416}{2.744} \] \[ r = 1.4 \][/tex]
Now that we have the common ratio, we can find the scale size before 2.744 by dividing 2.744 by the common ratio:
[tex]\[ \text{Previous scale size} = \frac{2.744}{1.4} \] \[ \text{Previous scale size} = 1.92 \][/tex]
What is the equation of the parabola that has its vertex at (7,6) and contains the
point (6,8)?
C A) y = 2x2 - 28x + 52
C B) y= 2x2 - 14x + 104
C) y= 2x2 - 28x+ 104
r D) y = x2 - 144+52
The solution is Option C.
The equation of the parabola is y = 2x² - 28x + 104
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the vertex of the parabola be ( h , k ) = ( 7 , 6 )
Now , the point P ( 6 , 8 ) lies on the parabola
The equation of the parabola is given by
y = a ( x - h )² + k
Substituting the values in the equation , we get
y = a ( x - 7 )² + 6
8 = a ( 6 - 7 )² + 6
Subtracting 6 on both sides of the equation , we get
2 = a ( 1 )
So , the value of a = 2
Now , the equation of parabola is
y = 2 ( x - 7 )² + 6
On simplifying the equation , we get
y = 2 ( x² - 14x + 49 ) + 6
y = 2x² - 28x + 98 + 6
y = 2x² - 28x + 104
Hence , the equation of parabola is y = 2x² - 28x + 104
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What is the angle ACB?
Answer:
∠ ACB = 56°
Step-by-step explanation:
The angle subtended at the centre AOB is twice the angle on the circumference ACB , that is
∠ ACB = 0.5 × 112° = 56°
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries
Average Wind Speeds of Cities in Country A
Average Wind Speeds of Cities in Country B
Which statement compares the median wind speeds for the data in the two box plots?
The median wind speed for country A is greater than the median wind speed for country B.
The median wind speed for country B is greater than the median wind speed for country A
The median wind speed for country A is about 7 miles per hour, and the median wind speed for country B is about 9
miles phour
Answer:
B
Step-by-step explanation:
(y ^ 2 + 5y) ^ 2 + 10(y ^ 2 + 5y) + 24 = 0
Solve the equation by using substitution
Answer:
y=0
Step-by-step explanation:
if you mulitply all of thoughts with any other number you will get a huge number but anything *0 equals 0
Solve: 10 sin^2(X) - 3sin(X) - 1 = 0
Let u = sin(x).
The given equation is equivalent to
(2u - 1)(5u + 1) = 0
(10u + 1)(u - 1) = 0
(5u - 1 )(2u- 1) = 0
Answer:
(2u-1)(5u+1)=0
(2u-1), sin(x)= 1/2
(5u+1), sin(x)= -1/5
The solutions to the equation:
x=pi/6 + 2kpi
x=5pi/6 +2kpi
3.34+2kpi
-0.201+2kpi
Step-by-step explanation:
Correct on edge
[tex](2u-1)(5u+1)=0(2u-1), sin(x)= 1/2(5u+1), sin(x)= -1/5The solutions to the equation:x=pi/6 + 2kpix=5pi/6 +2kpi3.34+2kpi-0.201+2kpi[/tex]
How do you know if equations are equivalent?To solve this, you need to find "x" for each equation. If "x" is the same for both equations, then they are equivalent. If "x" is different (i.e., the equations have different roots), then the equations are not equivalent.
What is an example of an equivalent equations?
For example, if we take 3x + 12 = 7x - 2 and subtract 3x from both sides and add 2 to both sides, we get 14 = 4x. In doing this, we haven't changed the solution set, so 3x + 12 = 7x - 2 and 14 = 4x are equivalent.
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Please I need to get this right!!
Answer:
12.56
Step-by-step explanation:
The formula for circumference is:
Circumference = Pi x Diameter
In this case the diameter is 4.
So you can simplify Pi to just 3.14 and multiply that times 4 which gives you 12.56.
Hope this helped!
Answer::25.13
Answer:25.13
Step-by-step explanation: C=2πr=2·π·4≈25.13274
This is the correct answer to the question and thats the explanation
It wont let me turn it in for some reason
There are 20 students in speech class and five speeches are given each day. What is the probability that Maria is randomly selected on the first day?
A man has 12 coins in his pocket all of which are dimes and quarters if the total value of his change is 225 cents how many dimes and how many quarters does he have
Answer:
Quarters = 7
Dimes = 5
Step-by-step explanation:
Let d = dimes and q = quarters:
d+q = 12
10d+25q = 225
Solve for d:
d = 12-q
Substitute it into the second equation:
120+15q = 225
Subtract 120 from both sides:
15q = 105
Divide by 15 in both sides
q = 7
By setting up a system of linear equations based on the given conditions, we find that the solution involves having 9 dimes and 3 quarters. These numbers satisfy the conditions that there are 12 coins in total which combine to be worth 225 cents.
Explanation:This question is about solving a system of linear equations. Let's assign variable 'd' to the quantity of dimes and 'q' to quarters. We know from the problem that:
d + q = 12, which represents the total number of coins;10d + 25q = 225, with dimes worth 10 cents each, and quarters worth 25 cents each, their total value must be 225 cents.To solve for 'd' and 'q', we can use substitution or elimination method. In this case, let's isolate 'd' in the first equation: d = 12 - q. Then substitute 'd' into second equation: 10(12 - q) + 25q = 225. After simplifying, you will find q = 3. Subtituting q = 3 back into the first equation, we find d = 9. Thus, the man has 9 dimes and 3 quarters.
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need help with this problem
Answer:
¼
Step-by-step explanation:
m1 × m2 = -1
m2 = -1 ÷ -4
m2 = 1/4
Answer:
1/4
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other.
Perpendicular slope = [tex]\frac{-1}{m}[/tex]
The slope (m) of the green line is -4.
To solve the slope of the red line, substituted -4 into the equation:
[tex]\frac{-1}{-4}[/tex]
Solve:
[tex]\frac{-1}{-4}[/tex] which give you [tex]\frac{1}{4}[/tex]
If Maria travels at a rate of speed of 50 mph, How far does she go in an hour?
Answer:50 miles
Step-by-step explanation:
Answer:
50 miles
Step-by-step explanation:
If she goes 50 mph which is the same as 50 miles in a hour. That means that since she traveled for 1 hour she went 50 miles.
If r is an integer greater than 1, what is the value of (−1)^r +1 if r is an odd integer
Answer:
zero
Step-by-step explanation:
(−1)^r when r is an odd integer greater than 1 always equals -1 then -1 + 1 = zero
Answer:
0
Step-by-step explanation:
(−1)^r when r is an odd integer greater than 1 always equals -1,then -1 + 1 =0.
Hope this helps.
In the table above, x and y have a linear relationship. Which of the following expressions correctly gives y in terms
of x?
A: X+2
B. 3x
C. 2x+3
D. 2x+1
E. 4x-1
Answer:
The answer to this question is D, 2x+1.
estimate the square root of 82 to the nearest whole number
Answer:
The square root of 82 rounded to the nearest whole number is 9.
The square root of 82 is estimated to be 9, as it falls between the perfect squares 64 and 100, which have square roots 8 and 10 respectively, and it is closer to 64.
Explanation:The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8, because 8*8 equals 64. To estimate the square root of 82 to the nearest whole number, you should locate two perfect squares that 82 falls between. The perfect squares nearest to 82 are 64 (8^2) and 100 (10^2), so the square root of 82 must be between 8 and 10. As 82 is closer to 64 than to 100, the square root of 82 would be closer to 8. Therefore, we can estimate the square root of 82 to the nearest whole number as 9.
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Use the drop-down menus to justify Marlena's work in
each step of the process.
Step 1:
Step 2:
Step 3:
addition property of equality
multiplication property of equality
combined like terms
Answer: additional prop
subtraction prop
division prop
Step-by-step explanation:
Jason grew from 36 inches to 40 inches in 1 year. By percent did his growth increase? Round your answer off to the nearest tenths
The percentage increase in Jason's height is 11.1%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.
To find the percentage increase in Jason's height, we can use the following formula:
percent increase = (final value - initial value) / initial value x 100%
In this case, the initial value is 36 inches (Jason's height at the beginning of the year) and the final value is 40 inches (Jason's height at the end of the year). Plugging these values into the formula, we get:
percent increase = (40 - 36) / 36 x 100% = 4 / 36 x 100% = 11.11%
Rounded off to the nearest tenths, the percentage increase in Jason's height is 11.1%.
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A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Using the same ratio how many cups do they use with 20 tablespoons of honey?
Answer:
25 cups of flour
Step-by-step explanation:
we know that
A bakery uses 8 tablespoons of honey for every 10 cups of flour
so
using proportion
Find out how many cups they use with 20 tablespoons of honey
[tex]\frac{8}{10}=\frac{20}{x}\\\\x=10(20)/8\\\\x=25\ cups\ of\ flour[/tex]
There will be 25 cups of flour used for 20 table spoons of honey.
Number of teaspoonful of honey used:
8 spoons for 10 cups Let the Number of cups for 20 spoons = dWe can write the relation as :
8 = 1020 = d Cross multiply : 8 × d = 20 × 108d = 200Divide both sides by 8 to isolate dd = 200 ÷ 8 d = 25Hence, 25 cups of flour will be used for 20 teaspoonful of honey.
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Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).
A) y = 2x + 1
B) y = 2x + 3
C) y = 4x + 3
D) y
im to stupit plss help
Answer:
i believe 105ft
Step-by-step explanation:
5×5=25
8×5×.5×4=80
Answer:
105
Step-by-step explanation:
Write a ratio equivalent to 17/51
Answer:
I think it’s 17:51
Step-by-step explanation:
1. Which term best describes the angle below?
O A. Acute
O B. Straight
O C. Right
O D. Obtuse
A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
accompanying figure. Write the area of the sector. A as a function of
Answer:
[tex]A(\theta)=\frac{162 \theta}{(\theta+2)^2}[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Let
r ---> the radius of the sector
s ---> the arc length of sector
Find the radius r
we know that
[tex]2r+s=18[/tex]
[tex]s=r \theta[/tex]
[tex]2r+r \theta=18[/tex]
solve for r
[tex]r=\frac{18}{2+\theta}[/tex]
step 2
Find the value of s
[tex]s=r \theta[/tex]
substitute the value of r
[tex]s=\frac{18}{2+\theta}\theta[/tex]
step 3
we know that
The area of complete circle is equal to
[tex]A=\pi r^{2}[/tex]
The complete circle subtends a central angle of 2π radians
so
using proportion find the area of the sector by a central angle of angle theta
Let
A ---> the area of sector with central angle theta
[tex]\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}[/tex]
substitute the value of r
[tex]A=\frac{(\frac{18}{2+\theta})^2\theta}{2}[/tex]
[tex]A=\frac{162 \theta}{(\theta+2)^2}[/tex]
Convert to function notation
[tex]A(\theta)=\frac{162 \theta}{(\theta+2)^2}[/tex]
13. (09.06 LC) A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? (5 points) graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37 f(x), because an increasing quadratic function will eventually exceed an increasing exponential function g(x), because an increasing exponential function will eventually exceed an increasing quadratic function f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect g(x), because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect
Answer:
g(x), because an increasing exponential function will eventually exceed an increasing quadratic function
Step-by-step explanation:
From data, we know that for greater x values, g(x) is greater than f(x).
It is also known that exponential function has greater values than quadratic function for large enough x values.
Calculate the number in the middle of 2.7 and 9.5
Answer:
I got 6.1 as the answer!
Step-by-step explanation:
The required number in the middle of the numbers 2.7 and 9.5 is 6.1.
To determine the number in the middle of 2.7 and 9.5.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The middle number is evaluated as the sum of the numbers divided by 2,
= 2.7 + 9.5 / 2
= 12.2/2
= 6.1
Thus, the required number in the middle of the numbers 2.7 and 9.5 is 6.1.
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PLZZ HELP!!! A graphic designer chose a base font size and represented it as 1 on the scale. He then listed some consecutive scale sizes. Two consecutive sizes were 4.096 and 6.5536.
What scale size came before 4.096?
Enter your answer, as a decimal, in the box.
What is the median of Miguel's data
Answer:
Where is the data
Step-by-step explanation:
A kite was broken into two triangles.
A kite is broken into 2 triangles. Both triangles have a base of 16 centimeters and a height of 5 centimeters.
The height of the triangle h is
cm.
Step-by-step explanation:
A kite is broken into two triangles
Given the base of the traingle, b = 16 cm
Height of the triangle, h = 5 cm
Area of traingle = [tex]\frac{1}{2} (b.h)[/tex]
= [tex]\frac{1}{2} (16) (5)[/tex]
= 40 [tex]cm^{2}[/tex]
Area of the kite = area of triangle 1 + area of triangle 2
= 40 + 40
= 80 [tex]cm^{2}[/tex]
Answer:
its five
Step-by-step explanation:
Can someone please answer this
Answer:
Stairs come in many different forms, and while building a basic staircase may appear to be a simple task, there are actually a number of parameters, calculations, and building codes that must be considered. These range from the length, width, and height of specific parts of the stairs, to where doors are placed in relation to stairs; the arc of a door must be completely on the landing or floor and not be allowed to swing over steps. Below is a list of some of the most common terminology regarding stairs, as well as some commonly used building codes. Building codes or requirements can differ at a local level, and a person building a staircase should refer to the codes specific to their locations.
Run/Tread: The run or tread is the part of the stairway that a person steps on. Its length is measured from the outer edge of the step, which includes the nosing if it is present, to the vertical portion of the stair called the riser. Both nosing and riser are discussed below. When measuring total run of a staircase, the length of the tread above the last riser is not included in the measurement. Also, when nosing is present, total run is not simply the sum of tread length, since the overhang caused by the nosing must be subtracted from the total run.
Building codes generally suggest that the minimum length of a tread be 10 inches (25.4 cm).
Rise/Riser: The rise, or height of a step is measured from the top of one tread to the top of the next tread. It is not the physical height of the riser because this excludes the thickness of the tread. The number of risers, not the number of treads, is used to determine the number of steps that comprise a staircase.
Building codes generally suggest that the maximum height of a riser be 7.75 inches (19.7 cm)
Nosing: The nosing is the protrusion at the edge of a tread that hangs over the riser below. Not all steps have a nosing, but when present, the nosing is included in the length of the tread. The main purpose of a nosing is to improve safety by providing extra space on which a person can place their feet.
Common building codes generally suggest that the nosing have a minimum length of 0.75 inches (1.9 cm) and a maximum length of 1.25 inches (3.2 cm).
Headroom: Headroom is the height measured from the top of a tread to the ceiling above it. While building codes for headroom are primarily intended to ensure enough room for people to comfortably use the stairs, the codes typically require far more room than the average height of a person to allow for moving larger objects such as furniture.
Building codes generally suggest at least 6 ft. 8 inches (203.2 cm) of stair headroom.
Stair Width: Stair width is measured from edge to edge of each side of the tread, perpendicular to tread length. While measurements of length are conventionally longer than those of width when considering rectangles, in the case of steps, the width is usually the longer side. Stair width does not include handrails.
Building codes generally suggest that stairs be at least 36 inches (91.44 cm) wide.
Handrails & Guards/Guardrails: A handrail is a railing that runs up a stair incline for users to hold when ascending or descending a staircase. A guard is "a building component or a system of building components located near the open sides of elevated walking surfaces that minimizes the possibility of a fall from the walking surface to the lower level." Guards can include rails (guardrails), but can be any number of other constructions such as walls, half-walls, or even a bench.
Building codes generally require guards for stairs that have a total rise of more than 30 inches above the floor, and require that these guards be at least 34 inches (86.36 cm) in height measured from the top of the treads. Similarly, handrails must be between 34 and 38 (96.52) inches high measured from the top of the treads, with a diameter between 1.25 inches (3.18 cm) and 2.675 inches (6.79 cm).
Stringer: A stair stringer is a structural member that supports the treads and risers of a staircase. Typically, there are three in a staircase: one on each side, and one in the middle. Stringers are not always visible, but can be seen on stairs with open sides. The stringers can either be cut to the shape of each step, or in some cases are uncut and conceal the edges of the treads.
Step-by-step explanation:
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