To find the expected area of a circle when randomly selecting an integer n between 1 to 5 as the radius, calculate the area of each possible circle and find the average. The expected area, rounded to the hundredths, is approximately 34.54 cm².
Explanation:When you randomly choose an integer n between 1 to 5, and then draw a circle with a radius of n centimetres, the expected area is calculated by taking the average of the areas for all possible radii.
The area of a circle is given by the formula A = πr². Since the integer n can be 1, 2, 3, 4, or 5, we calculate the area for each of these radii and then find the average.
For n=1: A = π(1)² = π cm²For n=2: A = π(2)² = 4π cm²For n=3: A = π(3)² = 9π cm²For n=4: A = π(4)² = 16π cm²For n=5: A = π(5)² = 25π cm²Add all the areas and divide by the number of possible radii:
Expected Area = (π + 4π + 9π + 16π + 25π) / 5
Expected Area = (55π) / 5
Expected Area = 11π cm²
Now, use the value of π up to two decimal places (3.14) to get the expected area in hundredths of a square centimetre:
Expected Area ≈ 11 × 3.14 cm²
Expected Area ≈ 34.54 cm²
The expected area of the circle, to the nearest hundredths of a square centimetre, is approximately 34.54 cm².
The square root of 12 is between A.) 3 and 4 B.) 4 and 5 C.) 5 and 6 D.) 6 and 7
A convex polyhedron has 30 edges and 8 fewer vertices than faces. How many faces does the polyhedron have? Euler’s formula: V + F = E + 2 12 18 20 24
Answer:
C or 20
Step-by-step explanation:
Just got the answer on Edge :)
Answer:
c
Step-by-step explanation:
12 POINTS PLZ HELP ONLY HAVE 3 MINUTES LEFT
Which statement about histograms is true?
Data is organized in categories.
Data appears as bars that are all about the same height.
Data is organized in equal intervals.
Data appears as bars that do not touch.
Answer:
c
Step-by-step explanation:
The correct statement about Histogram is Data is organized in equal intervals.
What is Histogram?A histogram is a graphical representation of discrete or continuous data. The area of a bar in a histogram is equal to the frequency. The y -axis is plotted by frequency density (which is proportional to the frequency) and the x -axis is plotted with the range of values divided into intervals.
Given:
Equal in breadth and corresponding to equal class intervals are the bars. However, they can occasionally be displayed as a wider variety within their groups, such as in size classes.
The width and data being achieved, for instance, forces a true event of varying class sizes in education upon the base of the graph.
and, for the purpose of displaying evenly spaced-out numerical data. The bars should be in close proximity to one another but not overlap. You can view the frequency distribution of the data or the number of pieces of data contained in each interval using these intervals.
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Which of the following equations represents an inverse variation?
A.
6y = x
B.
1/2y = 1/x
C.
–x = y + 8
D.
y = 1/4x
An equation typically used to represent inverse variation is y = k/x, where k is the "constant of proportionality for inverse variation."
6y = x does not represent inverse variation, since y increases when x increases or x increases when y increases. This is an example of direct proportion and is thus not an answer.
1/2y = 1/x should be written as (1/2)y = 1/x, to emphasize that (1/2) is a coefficient of y. Let's solve for y to see what form the resulting equation has:
(1/2)y = 1/x => y = 2/x. This has the form y = k/x, and thus represents inverse variation. y decreases when x increases.
–x = y + 8 is a linear equation and thus could not possibly represent inverse proportion. The "offset," +8, also makes it impossible for –x = y + 8 to represent direct variation. Reject this answer choice.
y = 1/4x has the form y = (1/4)x, which resembles a rule for direct variation.
Note, however, that if you really meant y = 1 / (4x), or y = (1/4)(1/x), then this would be a case of inverse variation.
The only answer choice in this problem that clearly represents indirect variation is (1/2)y = 1/x (as I have already said, above).
Answer:5
Step-by-step explanation:
1/2y=1/x
y=2/x
Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?
Put these substances in order of density with the most dense first and the least dense last.
air
pumpkin pie
whipped cream
steel
Answer: Hello there!
We know that:
[tex]density = \frac{mass}{volume}[/tex]
This means that two of two objects whit the same size ( volume) the heaviest one is the more dense object.
The 4 that we have here are:
Air, Pumpkin pie, Whipped cream, and Steel
It is easy to assume that the steel is the more dense object.
The pumpkin pie comes second
third is the whipped cream, which is cream with a lot of tiny air bubbles inside
the less dense object is the air.
then the order is:
Steel, pumpkin pie, whipped cream, air.
You invest $300 in an account that has an interest rate of 1.3%, compounded monthly. How much money is in the account after 20 years? Round your answer to the nearest whole number.
Answer:
$389
Step-by-step explanation:
The formula for final value of compound interest is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here, we have
P = $300
r = 0.013
t = 20 years
n = 12
Substituting these values and find A
[tex]A=300(1+\frac{0.013}{12})^{12\cdot20}\\\\A\approx389[/tex]
Therefore, in 20 years, the account will have $389.
Please help ill give brainiest to who helps
Joey intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is divisible by 3? A. Each roll has a 0.117 probability of being divisible by 3. B. Each roll has a 0.333 probability of being divisible by 3. C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.
there are 2 numbers that could be divisible by 3, either 3 or 6
so there is a 2/6 probability
2/6 = 0.333
so the answer is B
How many ways can a librarian arrange 15 books on a top shelf if she has 20 books from which to pick?
Answer: 20!/5!
Step-by-step explanation:
In a right triangle angle C measures 40 degrees. The hypotenuse of the triangle is 10in long. What is the approximate length of the side adjacent to angle C?
The size of a bicycle is determined by the diameter of the wheel. You want a 24-in bicycle for Christmas. What is the circumference of one of the wheels? A 75.4 in B 75.3 in C 37.7 in D 37.6 in
The circumference of one of the wheels is:
Option: A 75.4 in.
Step-by-step explanation:The 24-in bicycle means that the diameter of the wheel of the bicycle isL 24 in.
We know that the wheel of the bicycle is in the shape of a circle.
This means that the diameter of circle is: 24 in.
Hence, the radius(r) of circle is: 12 in.
( since we know that the radius(r) of the circle is half the diameter(d) of the circle)
Now, we are asked to find the circumference of the circle.
The circumference(C) of the circle is given by:
C=2πr
i.e.
C=2×3.14×12
i.e.
C=75.36 in.
which to the nearest tenth is: C=75.4 in.
Quadrilateral LMNO is transformed according to the rule T(–2, 4). What are the coordinates of L’? (3, –3) (3, 5) (9, –1) (9, 3)
A transformation specified with a rule T (x, y) means that the figure is undergoing a process of translation. Translation means that only the positions of the coordinates are changed with no other change on the angle, lengths or any other characteristic aside from the position alone.
So since the rule is T (-2, 4) then this means that the figure is moved 2 units left and 4 units up.
The initial coordinates of point L is:
point L = (5, 1)
The coordinates of L’ then is:
point L’ = L(5, 1) + T(-2, 4)
point L’ = (5 – 2, 1 + 4)
point L’ = (3, 5)
Answer:
(3, 5)
(3,5) is the answer.
In EFG, mE = 30, mF = 60, and mG = 90. Which of the following statements about EFG are true?
Statements B, C, and F are all true based on the given angle measures in triangle EFG.
Let's reevaluate the statements with the given angle measures in triangle EFG:
m∠E = 30°
m∠F = 60°
m∠G = 90°
A. FG = √3/2 EF
FG = (EF * √3) / 2
This statement is true. FG is indeed equal to √3/2 EF.
B. EG = √3/2 EF
EG = (EF * √3) / 2
This statement is true. EG is equal to √3/2 EF.
C. EG = -√3 FG
EG = -√3 * FG
This statement is true. EG is equal to -√3 FG.
D. EF = -√3 FG
EF = -√3 * FG
This statement is true. EF is equal to -√3 FG.
E. EG = 2 FG
EG = 2 * FG
This statement is true. EG is equal to 2 FG.
F. EF = 2 FG
EF = 2 * FG
This statement is true. EF is equal to 2 FG.
Statements B, C, and F are all true based on the given angle measures in triangle EFG.
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Segment DE is midsegment of triangle ABC. What is the length of segment DE?
A) 5
B) 10
C) 15
D) 20
Answer:
B) 10
Step-by-step explanation:
If DE is midsegment of the triangle, we know that AC measures twice as DE.
In the problem we have that AC = x + 15 and DE = x + 5
Writing this as an equation we have:
[tex]x + 15 = 2(x+5)\\x+15=2x +10\\15-10=2x-x\\5=x[/tex]
Therefore x = 5 and the length of segment DE is:
x + 5 = 5 + 5 = 10
Therefore the correct answer is B) 10
A business’s assets are valued at $600,000, and the value depreciates 20% per year. Using the formula V(t) = V0(b)t, what is V0, what is (b), and what is the value of the assets after 5 (t) years? Show your work.
t = 5
V0 =
(b) =
Value after 5 years:
Can anyone PLEASE help geometry is my worst subject!
The perimeter of a triangle is 86 inches. The largest side is four inches less than twice the smallest side. The third side is 10 inches longer than the smallest side. What is the length of each side?
Segment RT is a mid-segment of triangle CDE. What is the length of segment CE?
A) 38 in.
B) 32 in.
C) 24 in.
D) 9.5 in.
The cycling tour has 340 bottles of water for each week. There are ten people on the tour. How many bottles of water is that for each person per week?
Find Y of the polygon
Which of the expressions are equivalent to the one below? Check all that apply. (10 + 8) • 2
Doug entered a canoe race. he rowed 3 1/2 miles in 1/2 hours what is his average speed in miles per hour
PLEASE HELP!
Cynthia is constructing a circle inscribed in a triangle.She has partially completed the construction as shown below.What should her next step be in the construction (worth 50 points)
A. Connect vertex B to the arc markings to complete the angle bisector
B.use a straightedge to find the angle bisectors for angles A and B
C. Connect three arc markings together to form the triangle
D.use the arc markings to determine the radius to construct the circle
Please explain!
The correct next step that Cynthia should do is to:
D. use the arc markings to determine the radius to construct the circle
The arc markings are actually used as the baseline in determining the center and the radius of the circle. The arc markings are created with the use of a compass. All other choices are completely irrelevant because what we need is the arc and not the angles. The angles do not create the circle. Letter C is also wrong because what we are trying to form is the circle and not the triangle. The triangle is already created.
find a1 for the geometric series with r=3 and s6=364
Answer both please !
36) the equation would be: 44 x 0.63 =
37) 6.1% = 0.061
59150 x 0.061 = 3608.15 increase
Someone please answer this for me
A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.
I believe this question asks for the total amount of area of wood that is needed to make 80 puzzles.
The formula for area of triangle is given as:
A = (1 / 2) b h
where,
b = is the base of the triangle = 3 in
h = height of the triangle = 4 in
So calculating for area of 1 on triangle (A1):
A1 = (1 / 2) (3 in) (4 in)
A1 = (1 / 2) 12 in^2
A1 = 6 in^2
We are given that we are to make 80 puzzles and each puzzle has 20 triangles, therefore the total amount of triangles we need to make is:
n = 80 * 20
n = 1600
Therefore the total area needed (A) is:
A = A1 * n
A = 6 in^2 * 1600
A = 9,600 in^2
is this correct? if not please let me know how to solve it
Annie found that 57 students in her school knew French and 23 of those students knew Spanish, as well. There were 11 students who did not know French but knew Spanish. There were 4 students who knew neither French nor Spanish. Which table best summarizes the data collected by Annie?
Knew Spanish Did not know Spanish Total
Knew French 57 34 91
Did not know French 11 4 15
Total 68 38 106
Knew Spanish Did not know Spanish Total
Knew French 12 34 46
Did not know French 11 4 15
Total 23 38 61
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 4 11 15
Total 27 45 72
Answer:
Table C is the correct option.
Step-by-step explanation:
We are given,
Number of students which knew French = 57
Number of students which knew both French and Spanish = 23
Number of students which knew Spanish but not French = 11
Number of students which knew neither French nor Spanish = 4
So, we get that,
Number of students not knowing French = 57 - 23 = 34
Hence, the table for the given situation is,
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Thus, option C is correct.
option C is correct-
Point C is the center of the circle. The measure of angle ACB is 12x – 7. Arc AB measures 10x + 7. Find the value of x.
Answer:
x=7
Step-by-step explanation:
Subtract 10x
from both sides of the equation.
12x−7−10x=7
Subtract 10x
from 12x
2x−7=7
Add 7
to both sides of the equation.
2x=7+7
Add 7 and 7
2x=14
Divide each term by 2 and simplify.
x=7