Answers
Answer:
9.38
Step-by-step explanation:
I did the math
The length of circumference of this circle is 21.9911 inches.
The area of this circle is, approximately, 38.4845 (in²).
Step-by-step explanation:For the circumference.1. Formula.The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:
[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.
The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.
Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.
2. Rewrite the formula.So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:
[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]
3. Calculate.We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:
[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].
Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.
The length of circumference of this circle is 21.9911 inches.
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For the area.1. Formula.These are the most commonly used formulas for the area of circles:
[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.
Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.
2. Calculate.Let's use the area formula that directly involves diameter to avoid any conversions.
Substitute letter "d" by the length of the diameter (7 inches).
[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]
Therefore, the area of this circle is, approximately, 38.4845 (in²).
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Related Questions
Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
73
%, Worksheets =
79
%, and Quizzes =
84
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
Answers
The minimum grade you need to get a B in the course is given as follows:
x = 80.625.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The grades and their percentages are given as follows:
73 worth 15%.79 worth 20%.84 worth 25%.x worth 40%.You want a grade of 80, hence the minimum test average is obtained as follows:
0.15 x 73 + 0.2 x 79 + 0.25 x 84 + 0.4x = 80
47.75 + 0.4x = 80
x = (80 - 47.75)/0.4
x = 80.625.
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Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base?
Answers
The polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base include :
B. SquareC. RectangleE. CircleHow to find the polygons ?If a plane intersects three distinct vertices of the cube while bypassing any other vertices, a triangle is produced. To visualize this, suppose a corner of the cube were removed with a knife; picture that cut surface as a triangle.
On the other hand, if a plane coincides with four points on the cube and outlines a square shape, it creates what's called a "square cross-section." This transpires when said plane parallels one side of the cube while intersecting only the midpoints of its opposite face's edges.
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Full question is:
Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base
A triangle
B square
C. rectangle
D pentagon
E circle
A company sells cereal in two different-sized boxes. The smaller box has the dimensions shown below. The height of the smaller box is 80% of the height of the larger box, while the other two dimensions are the same for both boxes. What is the volume of the two boxes?
Answers
Since the other two dimensions are the same for both boxes, we only need to compare the volumes based on their height.
Let's assume the height of the larger box is h, then the height of the smaller box is 0.8h.
The volume of the larger box is:
V1 = lwh = (8)(11)(h) = 88h
The volume of the smaller box is:
V2 = lwh = (8)(11)(0.8h) = 70.4h
Therefore, the volume of the larger box is 88h and the volume of the smaller box is 70.4h.
Let H be the height of the larger box. Then the height of the smaller box is 0.8H.
The volume of the larger box is given by:
V_large = L × W × H
The volume of the smaller box is given by:
V_small = L × W × 0.8H
Since the length and width are the same for both boxes, we can factor them out:
V_large = L × W × H
= (L × W × 1) × H
= A × H
V_small = L × W × 0.8H
= (L × W × 0.8) × H
= 0.8A × H
where A = L × W is the area of the base of each box.
Therefore, the volume of the smaller box is 0.8 times the volume of the larger box.
We can also write this as:
V_small/V_large = 0.8
So, if we know the volume of one of the boxes, we can find the volume of the other box by multiplying by 0.8.
Without specific information about the dimensions of the boxes, we cannot calculate their volumes.
A student wants to know which type of pizza the students at his high school prefer. Which
option would give a unbiased, representative sample:
Average
Answers
Answer:
Step-by-step explanation:
In November 1998, former professional wrestler Jesse “The Body” Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:
Ventura was running on a third-party ticket and most polling methods are better suited to a two-candidate race.
Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.
The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.
But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.
SAMPLING BIAS
A sampling method is biased if every member of the population doesn’t have equal likelihood of being in the sample.
So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.
Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.
One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.
Use the given vectors to find v• w and v•v. v= - 8i – 3j, w= - 9i – 7j
Answers
Using the given vectors v and w, we found v•w = 66 and v•v = 73.
To find v • w, which is the dot product of vectors v and w, we need to multiply the corresponding components of the two vectors and then add the products. In other words,
v • w = (-8i)(-9i) + (-3j)(-7j)
= 72 + 21
= 93
So, v • w = 93.
To find v • v, we again need to multiply the corresponding components of vector v and then add the products. In other words,
v • v = (-8i)(-8i) + (-3j)(-3j)
= 64 + 9
= 73
So, v • v = 73.
Note that the dot product of a vector with itself (like v • v) is also known as the magnitude squared of the vector. In this case, ||v||² = v • v = 73.
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please help! it is matrices, so it should be rlly easy.
Answers
B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.
How to find the determinant of the matrix BWe can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:
|B| = (-2 × -2) - (1 × 5)
|B| = 4 - 5
|B| = -1.
Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.
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Find the value of x.
Answers
The value of x in the chord is 3 units.
How to find line segment when chord intersect?The chord intersection theorem states that the products of the lengths of the line segments on each chord are equal.
Therefore,
6(x + 5) = 4(2x + 6)
Open the brackets
6x + 30 = 8x + 24
subtract 8x from both sides of the equation
6x - 8x + 30 = 24
-2x + 30 = 24
subtract 30 from both sides of the equation'
-2x + 30 - 30 = 24 - 30
-2x = -6
divide both sides by -2
x = -6 / 2
x = 3
Therefore,
x = 3
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help me please Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Answers
Answer:
A) m∠3 + m∠6 = 90
Step-by-step explanation:
Angles 3 and 6 are complementary angles. This means they add up to 90 degrees. Since you know the angle that is a right angle due to the box, you know these angles add up to 90 degrees
to manufacturing floor
T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.
Answers
Answer:
To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.
First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:
m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4
where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).
Using point-slope form, we get the equation of the line CD as:
y - 48 = (-1/4)(x - 0)
y = (-1/4)x + 48
Now, we can find the perpendicular distance from point T to the line CD as follows:
d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)
d = 42 / sqrt(17) ≈ 10.21
Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).
The base of a chest shaped as a rectangular prism is 12 feet² and the height is 4 feet.
What is the volume?
Answers
Answer:
The answer is 576
Step-by-step explanation:
the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.
Can someone help me find if the function is increasing or decreasing and why the c intercept is (look at the photo)
Answers
Express 1:0.2:0.75 in their simple form
Answers
The given ratio 1:0.2:0.75 can be expressed in its simplest form as 5:1:3/4.
To express 1:0.2:0.75 in its simplest form, we need to find the common factor that can divide all the numbers in the ratio without leaving a remainder.
First, we can convert 0.2 to a fraction by dividing 2 by 10, which gives us 1/5. Thus, the ratio can be rewritten as
1:0.2:0.75
= 1:2/10:0.75
= 1:1/5:0.75.
To find the common factor, we can convert all the numbers to fractions with a denominator of 5. We do this by multiplying the first number by 5/5, the second number by 1/1, and the third number by 5/4.
This gives us,
5/5:1/5:15/20.
Next, we can simplify the ratio by dividing all the numbers by their greatest common factor (GCF). In this case, the GCF is 1/5.
Dividing all the numbers in the ratio by 1/5 gives us,
5:1:15/4.
Finally, we can simplify 15/4 by dividing both the numerator and denominator by 5. This gives us 3/4. Thus, the final simplified ratio is 5:1:3/4.
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answer pls my state test is cominggggg
Answers
Answer:
- 9/16
Step-by-step explanation:
When multiplying fractions, you can multiply them straight across.
We can focus simply on the fractions first and then add the negative back in later since you always get a negative number when you multiply a negative and positive number:
- (3 /4) * (3 / 4)
- (3 * 3) / (4 * 4)
- (9/16)
-9/16
Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.
Answers
The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons
What are arithmetic operations?Arithmetic operations are operations involving addition, subtraction, multiplication, and division.
The distance Brynen travels each way to his new job = 27 miles
The distance his car gets per gallon of gas = 35 miles
The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;
The distance Brynen travels = 27 × 2 × 5 = 270 miles
The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35
7 25/35 = 7 5/7
The volume of gas he will use to and from work this week is; 7 5/7 gallons
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A local city government wants to display the ages of the city citizen. Would it be better to organize the data using a dot plot or a histogram, and why?
Answers
If local city government wants to display the ages of the city citizen, It would be better to organize the data using a histogram.
A histogram is a graph that shows the distribution of a set of continuous data. The ages of city citizens can be considered as continuous data, as there are many possible values for age within a certain range.
A dot plot, on the other hand, is a graph that shows the distribution of a set of discrete data. Discrete data are values that can only take on specific, isolated values, like shoe sizes or the number of siblings a person has.
A histogram would be more effective for displaying the distribution of the ages of city citizens because it can show the range of ages in a more continuous manner, and provide a more precise representation of the frequency of the different age groups.
A dot plot, on the other hand, would be less effective, as it could be difficult to represent every age value as a single dot, and the resulting graph may not provide a clear indication of the distribution of ages.
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The company performed another experiment in which they tested three website designs to see which one would lead to the highest probability of a purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. what is the probability that a customer who visited made a purchase?
Answers
The probability that a customer who visited any of the three website designs made a purchase is 4.5%.
To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.
We can do this by taking the mean of the three probabilities:
Mean probability = (4.5% + 5.2% + 3.8%) / 3
= 13.5% / 3
= 4.5%
This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.
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Find the sum:
125 (base 7) + 256 (base 7)
Answers
The sum of 125 (base 7) and 256 (base 7) is 404 (base 7). To compute it, we convert each number to base 10, add them, and then convert the result back to base 7.
Write each number in expanded form using powers of 7.
125 (base 7) = 1 x 7² + 2 x 7¹ + 5 x 7⁰ = 49 + 14 + 5 = 68
256 (base 7) = 2 x 7² + 5 x 7¹ + 6 x 7⁰ = 98 + 35 + 6 = 139
Add the two numbers together to get the sum in decimal form.
68 + 139 = 207
Convert the decimal sum to base 7 using repeated division by 7.
Divide 207 by 7 to get a quotient of 29 and a remainder of 4. Write down the remainder as the rightmost digit in the base 7 representation. Divide 29 by 7 to get a quotient of 4 and a remainder of 1. Write down the remainder as the next digit to the left in the base 7 representation.
Divide 4 by 7 to get a quotient of 0 and a remainder of 4. Write down the remainder as the leftmost digit in the base 7 representation.
So the sum of 125 (base 7) and 256 (base 7) is 404 (base 7).
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solve the following system of equations algebraically for all values of x and y
Answers
The values of x, y, and z based on the system of equations will be (-2,4,7).
How to solve the equationx + 3y + 5z = 45
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35
6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62
7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7
4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2
x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4
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Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
what is the nearest tenth to 3.5
Answers
The number is already rounded to the nearest tenth
Answer: 3.5
Step-by-step explanation: i got it right on the quiz
Drag each tile to the correct location on the table. Each tile can be used more than once.
Match each equation to the value(s) of x that make the equation true.
Answers
Sure, here are the solutions for each equation:
3(x-5) = 2(11) has a solution of x = 7.
4(3x+7) = 512x + 8 has no real solution.
3(x+1)- 2x = x + 3 has a solution of x = 9.
3 = 3 is true for all values of x, so it doesn't have a specific solution.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.
Here,
1. 3(x-5) = 2(11)
To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.
2. 4(3x+7) = 512x + 8
To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.
3. 3(x+1)- 2x = x + 3
To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.
4. 3 = 3
This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.
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Complete the following using compound future value. (Use the Table provided.)
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Time
6 years
Principal
$ 15,300
Rate
8 %
Compounded
Quarterly
What is amount &
Interest?
Answers
Answer:
We can use the formula for compound interest to calculate the amount and interest:
A = P * (1 + r/n)^(n*t)
I = A - P
Where:
P = Principal = $15,300
r = Rate = 8% = 0.08
n = Compounding frequency per year = 4 (since it is compounded quarterly)
t = Time period = 6 years
Plugging in the values, we get:
A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28
I = 23,659.28 - 15,300 = $8,359.28
Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.
I hope this helps.
Please help me this is so hard. Please if you help i give you 60 points. This is really hard for me and i dont get this.
Answers
Answer:
The discriminant is:
(-3)^2 - 4(1)(18) = 9 - 72 = -63
Since this discriminant is negative, f(x) does not have any real number solutions.
On a computer screen, lengths and widths are measured not in inches or millimeters but
in pixels. A pixel is the smallest visual element that a computer is capable of processing. A
common size for a large computer screen is 1024 × 768 pixels. (Widths rather than heights are
conventionally listed first.) For the following, assume you’re working on a 1024 × 768 screen.
1. You have a photo measuring 640 × 300 pixels and you
want to enlarge it proportionally so that it is as wide as the
computer screen. Find the measurements of the photo after it
has been scaled up. Explain how you found the answer.
2. a. Explain why you can’t enlarge the photo proportionally so
that it is as tall as the computer screen.
b. Why can’t you correct the difficulty in (a) by scaling the
width of the photo by a factor of 1024 ÷ 640 and the
height by a factor of 768 ÷ 300
Answers
To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:
Scaling factor = 1024 ÷ 640 = 1.6
We can then use this scaling factor to find the new dimensions of the photo:
New width = 640 × 1.6 = 1024 pixels
New height = 300 × 1.6 = 480 pixels
Therefore, the new dimensions of the photo are 1024 × 480 pixels.
2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.
b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.
To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:
scaling factor = screen width / photo width = 1024 / 640 = 1.6
Now we can use this scaling factor to find the new height of the photo:
new height = photo height x scaling factor = 300 x 1.6 = 480 pixels
Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.
2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.
2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.
Find the volume of the composite solid. Round your answer to the nearest hundredth.
Answers
Therefore, the volume of the composite solid is approximately 1357.28 cubic feet, rounded to the nearest hundredth.
What is volume?Volume is a measure of the amount of space occupied by an object or a substance. In other words, it is the three-dimensional space that an object or substance occupies. The SI unit for volume is cubic meters (m³), although other units such as cubic centimeters (cm³) and liters (L) are also commonly used.
Here,
The composite solid is made up of a hemisphere and a cone with the same base radius and height. The volume of the hemisphere is given by (2/3)πr³, and the volume of the cone is given by (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 6 feet and the height is 12 feet, we can find the volumes of the hemisphere and the cone as follows:
Volume of hemisphere = (2/3)π(6³)
= 288π cubic feet
Volume of cone = (1/3)π(6²)(12)
= 144π cubic feet
The total volume of the composite solid is the sum of the volumes of the hemisphere and the cone, which is:
Total volume = Volume of hemisphere + Volume of cone
= 288π + 144π
= 432π
To find the numerical value of this volume, we can use the approximation π ≈ 3.14 and round the result to the nearest hundredth:
Total volume ≈ 432(3.14)
= 1357.28 cubic feet
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a camper lights an oil lantern at 12 noon and let’s it burn continuously
Answers
The amount of oil in the lantern at 12 noon is 64.33 ounces
Calculating the amount in the lantern at 12 noon?The time can be represented with x and the amount with y
Note that
x = number of hours from 12 noon
So, we have the following ordered pairs
(x, y) = (0, y) (2, 63), (5, 61)
Using the slope formula, we have
(y - 63)/(0 - 2) = (61 - 63)/(5 - 2)
So, we have
(y - 63)/-2 = -2/3
This gives
y - 63 = 4/3
Add 63 to both sides
y = 63 + 4/3
Evaluate
y = 64.33
Hence, the amount in the lantern at 12 noon is 64.33 ounces
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Complete question
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at 12 noon?
Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5
Answers
The area of the similar triangle B is derived to be equal to 1.8 which makes option B correct.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
We shall represent the hight of triangle B with the letter h so that;
h/2 = 3/5
h = (2 × 3)/5 {cross multiplication}
h = 1.2
area of triangle B = 1/2 × 3 × 1.2
area of triangle B = 1.8
Therefore, the area of the similar triangle B is derived to be equal to 1.8
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The stemplot below represents the number of bite-size snacks grabbed by 32 students in an activity for a statistics class.
A stemplot titled Number of Snacks has values 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 27, 29, 29, 29, 32, 32, 34, 38, 42.
Which of the following best describes the shape of this distribution?
skewed to the left
bimodal symmetric
skewed to the right
unimodal symmetric
Answers
Answer: The stemplot shows that the distribution is unimodal and skewed to the right.
The stem values (tens digits) are:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4
The leaf values (ones digits) are:
5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 7, 9, 9, 9, 2, 2, 4, 8, 2
The data is unimodal because there is one clear peak in the distribution. The data is skewed to the right because the long tail of the distribution extends to the right, with a few large values pulling the mean to the right.
Therefore, the best description of the shape of this distribution is skewed to the right.
There are 200 end-of-the-year school dance tickets available. Students who have perfect attendance are able to purchase them in advance. If 18 tickets were purchased in advance, what percent of the tickets were purchased in advance?
Answers
Thus, 9 percent of the total dance tickets available is found to be purchased in advance.
Explain about the percentage:Although the usage of percent and percentage differs slightly, they both signify the same thing. It is customary to use percent or the symbol (%) along with a numerical value. One tenth of something is one percent.
Hence, it can be expressed as a fraction as well as a decimal. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.Given data:
Total dance tickets = 200
Advanced purchased tickets = 18
Let x be the percentage of advance booked tickets.
Then,
x% of 200 = 18
x*200 / 100 = 18
2x = 18
x = 18/2
x = 9%
Thus, 9 percent of the total dance tickets available is found to be purchased in advance.
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 66 m wide.
Find the area of the training field. Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
0
$6 m
808
m
X
m²
5
m²
Answers
The area of the training field that has the shape of a rectangle and two semicircle would be = 9,755.46m²
How to calculate the area of the training field?To calculate the area of the training field, the area of the rectangle and the two semicircles should be determined and added together.
The area of rectangle = length×width
where:
length = 96m
width = 66m
area of rectangle = 66×96 = 6,336m²
Area of the two semicircle = Area of a circle = πr²
radius = diameter/2 = 66/2 = 33m
area of a circle= 3.14×33×33 = 3419.46m²
Therefore the area of the training field = 6,336m²+3419.46m² = 9,755.46m²
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26) What is the area of Rectangle A?
is 1 unit square.
Rectangle A
Answers
The required area of the rectangle is 8 sq. units
What is rectangle?Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.
According to question:From the diagram
Length = 4 units, width = 2 units
Area of rectangle = length×width
Area of rectangle = 4×2
Area of rectangle = 8 sq. units
Thus, required area of the rectangle is 8 sq. units
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