Answers
Fun, geometry disguised as probability.
That's a pentagon, which we can view as 10 right triangles with legs a and s/2 (half of s) and hypotenuse r. So area of the pentagon is
P = 10 × (1/2) a (s/2) = 10 (1/2) (3.2) (4.7/2) = 37.6
The area of the circle is πr² so the circle area is
C = π (4²) = 50.265482
The white area is the difference, C-P, and the probability we seek is the fraction of the circle that's white, so (C-P)/C.
p = (C-P)/C =1-P/C = 1-37.6/50.265482 = 0.251971
Answer: 0.25
Higher than I would have guessed from the figure.
Related Questions
A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With the level ground for a secure footing. Find, to the nearest inch, how far the base of the latter should be from the side of the building and how far up the side of the building the latter will reach.
Answers
Answer:
Distance of foot of ladder from building: 37.2 inches
Distance of top of ladder from building's base: 114 inches
Step-by-step explanation:
Please refer to the figure attached in the answer area.
A right angled triangle [tex]\triangle ABC[/tex] is formed by the ladder with the building where hypotenuse is the length of ladder.
Hypotenuse, AC = 10 foot
Also, we are given that angle made by the base of ladder with the ground is [tex]72^\circ[/tex].
We have to find AB and BC.
[tex]\angle BAC = 72^\circ[/tex]
Using trigonometric functions:
[tex]cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\$\approx$ 3.1 foot\\$\approx$ 37.2 inches[/tex]
[tex]sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\$\approx$ 9.5 foot\\$\approx$ 114 inches[/tex]
Distance of foot of ladder from building: 37.2 inches
Distance of top of ladder from building's base: 114 inches
I need help ples.
What is the volume of composite solid?
Answers
Answer:
58 13/32 ft. cubed
Step-by-step explanation:
Horizontal Shape: 6 x 5/2 x 7/4 = 26 1/4 ft.
Vertical Shape: 7/2 x 21/4 x 7/4 = 32 5/32 ft.
Total Volume: 26 1/4 + 32 5/32 = 58 13/32 ft. cubed
If this helped can I get brainliest :)
what is the quotient of the equation Below in simplest form? State any restrictions on the variable
Answers
Answer:
A
Step-by-step explanation:
Factor the numerators/ denominators where possible, that is
[tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] ÷ [tex]\frac{(x-5)(x+3)}{(x+4)(x+1)}[/tex]
Leave the first fraction, change division to multiplication and turn the second fraction upside down.
= [tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] × [tex]\frac{(x+4)(x+1)}{(x-5)(x+3)}[/tex]
Cancel the factors (x - 5) and (x + 4) from numerator/denominator
= [tex]\frac{-1}{(x-1)}[/tex] × [tex]\frac{(x+1)}{(x+3)}[/tex]
= [tex]\frac{-(x+1)}{(x-1)(x+3)}[/tex] , x ≠ 1, x ≠ - 3
Which description of the graph of the linear inequality y ≥ 7x – 4 is correct????The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
Answers
Answer:
It's the second description
Step-by-step explanation:
It's one of the inequality symbols for greater/less than or equal to, which means the line is solid. Then, y is greater than or equal to 7x-4 which means it will be shaded above the line.
Answer:
The correct answer is the 2nd option
Step-by-step explanation:
PLEASE!!!
A survey asks a random sample of 2500 adults in Ohio if they support an increase in the state sales tax from 5.25% to 5.50%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 30% of all adults in Ohio support the increase.
9. The standard deviation of X is
a. 22.91.
b. 27.39.
c. 5255.
d. 750.
10. The probability that X is at least 800 is
a. less than 0.0001.
b. about 0.015.
c. 0.025.
d. 0.05.
Answers
Answer:
Step-by-step explanation:
a) Total number of people surveyed, n = 2500
Let X denote the number in the sample that say they support the increase. If 30% of all adults in Ohio support the increase, it means that the percentage of all adults in Ohio that did not support the increase is
100 - 30 = 70%
This is a binomial probability because there are only two possible outcomes. Therefore,
Probability of success, p = 30/100 = 0.3
Probability of failure, q = 1 - p = 1 - 0.3
q = 0.7
Standard deviation = √npq
Standard deviation = √(2500 × 0.3 × 0.7) = 22.91
b) The probability that x is at least 800 is expressed as
P(x ≥ 800)
We would determine the probability by using the binomial probability calculator. Therefore,
P(x ≥ 800) = 0.01577
b. about 0.015.
Find the median of the data.
8,8,6,8,4,5,6
Answers
Answer: The median is 6
Step-by-step explanation:
4 5 6 6 8 8 8
4 5 6 6 8 8 8
what is the answer to -12= -2x-4x
Answers
Answer:
x = 2
Step-by-step explanation:
-12 = -2x - 4x
-12 = - 6x
x = -12/(-6) = 2
Answer:
Step-by-step explanation:
Please help me will give brainliest
Answers
Answer:
Mean = [26 + 31 + 39 + 32]/4 = 32
MAD = (1/4) x [|26 - 32| + |31 - 32| + |32 - 32| + |39 - 32|] = (1/4) x 14 = 3.5
Hope this helps!
:)
Answer:
3.5 putts
Step-by-step explanation:
Mean: 26 + 31 + 32 + 39 = 128/4 = 32
32 - 26 = 6
32 - 31 = 1
32 - 32 = 0
32 - 39 = 7
Mean Absolute Deviation (MAD): 6 + 1 + 0 + 7 = 14/4 = 3.5
~ hope this helps you, have a good day ~
You are assigned a computer generated 4-digit password to access your new voice mail account. If the
digits can not be repeated, how many passwords are possible?
b
34 different passwords are possible
5,040 different passwords are possible
40 different passwords are possible
10,000 different passwords are possible
d
Answers
Answer:
5,040 different passwords are possible
Step-by-step explanation:
Assuming that 4-digit means using only numeric values.
This is a permutations problem.
n = number of values used with number values only this is 10
r = the number used in each case without repeating in this case 4
nPr = n! / (n - r)!
nPr = 10! / (10-4)!
nPr = 10! / 6!
The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24
A quick hack for dividing factorials is to use cancelling.
10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)
= 5040
please help im having trouble with these problems
Answers
Answer:
B I think
Step-by-step explanation:
The graph of the function f(x) is shown
Which graph represents the function 4(2x)?
Answers
Answer:
[tex]8x[/tex]
Step-by-step explanation:
[tex]4 \: time \: 2x = 8x[/tex]
What is the domain of the following parabola? (5 points)
3
-2
-1/
x
1
xs1
All real numbers
ys2
Answers
Answer:
Step-by-step explanation:
The domain of this quadratic is "all real numbers." The function is defined for all x.
In ΔIJK, the measure of ∠K=90°, the measure of ∠J=76°, and JK = 3.6 feet. Find the length of IJ to the nearest tenth of a foot.
Answers
Hope it help!
40 - 80 -
60
40 - 80 + 80
60 + ?
4c =
40
20
?
Answers
Answer:
The answer is ZERO ( 0 )
Answer:
The accurate answer is 0 (zεʀο)
From the moment the first car started how many hours will it take the second car to catch up to the first
Answers
Answer:
HELP
Step-by-step explanation:
A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?
Answers
Answer:
[tex]\frac{7\pi}{4}[/tex].
Step-by-step explanation:
Given information:
Radius of circle = 8 cm
Area of sector = [tex]56\pi\text{ cm}^2[/tex]
Formula for area of sector is
[tex]A=\dfrac{1}{2}\theta r^2[/tex]
where, r is radius and [tex]\theta[/tex] is central angle in radian.
Substitute [tex]A=56\pi[/tex] and r=8 in the above formula.
[tex]56\pi=\dfrac{1}{2}\theta (8)^2[/tex]
[tex]56\pi=\dfrac{64}{2}\theta[/tex]
[tex]56\pi=32\theta[/tex]
[tex]\dfrac{56\pi}{32}=\theta[/tex]
[tex]\dfrac{7\pi}{4}=\theta[/tex]
Therefore, the measure of the sector in radians is [tex]\frac{7\pi}{4}[/tex].
Find the surface area of the figure. Round to the nearest hundredth.
Answers
SA of half of this cylinder:
1/2*2pi(3)^2+1/2*2pi*3*25
9pi+75pi
84pi cm^2 OR 263.89 cm^2
What is 3 1/2 times 2 4/5
Answers
Answer:
9 4/5
Step-by-step explanation:
You can rewrite them into decimal. It would be 3.5 times 2.8 and you get 9.8 or 9 4/5
Answer:
49 /5 = 9.8
Step-by-step explanation:
What is the area C in terms of
Answers
Hope this help
An aquarium in the shape of a rectangular prism has a bottom, no top, two square sides, and two sides
the same height as the square sides but twice their length. The total area of the five sides 15 2,592 in?.
Find the volume of the aquarium. Complete the explanation of your reasoning.
Let x represent the length and height of the square sides. Then the longer sides and the bottom measure
2x by x. The total area of the five sides, in terms of x, is A =____
So, the total area of the five sides,
A, is 2,592 in2. Solving for x we get x =____
The tank's volume is ____
in squared?
Answers
Answer:
volume = 11,664 units cubed
Step-by-step explanation:
2[tex]x^{2}[/tex] times 3 = bottom and sides
[tex]x^{2}[/tex] times 2 = ends
A = 6[tex]x^{2}[/tex] + 2[tex]x^{2}[/tex] = 8[tex]x^{2}[/tex]
2592 = A
2592/8 = 8[tex]x^{2}[/tex]/8
324 = [tex]x^{2}[/tex]
take square root of both sides
18 = x
so volume = length times width times height
2(18) times 18 times 18 = 11664
11664 units cubed
PLEASE HELP!!!! attached photo
Answers
Answer:
(-1, -2.5)
Step-by-step explanation:
The midpoint formula is just basicallyadding both of the x values and then dividing the sum of them by 2, after that you will be adding both y values and then dividing them by 2, then you will get the midpoint x and y coordinate values. You can look up midpoint formula on google to see how it's actually written. You have to make sure to add correctly when you are using the negative numbers, because they can actually turn the equations into subtraction. Keep in mind, it can beconfusing sometimes when you are working with positive and negative numbers together. So make sure to just double check your work and also to make sure you added correctly.
Brainliest please, I need a few more :D
How many 9’s are there between 1 and a 100?
Answers
Answer:
11
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
You've got 9
19
29
39
49
59
69
79
89
And then all of the numbers in the 90s
90, 91, 92, 93, 94, 95, 96, 97, 98, 99
99 counts as two
write an equation that represent the line. ASAP !!!!!! 40 POINTS + BRAINLIEST
Answers
Answer:
y = (3/2)x + 3
Step-by-step explanation:
slope is rise over run so 3 up and, 2 right
y-intercept is at (3,0)
hello!? what's 3 + 3
Answers
Answer:
6
Step-by-step explanation
Answer:
6
Step-by-step explanation:
if you have 3 apples and 3 banannas in all you have 6 fruits in total :)
3 bugs+ 3 ladybugs= 6 bugs
Hope this helps lol :)
Point L was plotted at (-4, 1), then L was transformed creating point L’ at (-1, -4).Which transformation rule could have been used to plot L’?
Reflection across the x-axis
a 180 degree rotation about the origin
A 270 degree rotation counterclockwise rotations about the origin
A translation using the rule (x,y) -->(x+3, y -5)
Answers
Answer:
you would go down 2 from the point
Step-by-step explanation:
WILL MARK BRAINLIEST! If you buy 3 pounds of hamburg for $8.97, how much will it cost for 5 pounds of hamburg?
Answers
Answer:
14.95
Step-by-step explanation:
every 1 pound is 2.99 so you would do 2.99 * 5
Answer:
$14.95
Step-by-step explanation:
To find the slope or the cost per pound of hamburger you divide 8.97 by 5 in order to find out it costs 2.99 per hamburger. You then, multiply 2.99 by 5 to gather that to buy 5 pounds of hamburger it would cost $14.95.
30 points
In two or more complete sentences, discuss the advantages and disadvantages of investing in a CD versus investing in a basic savings account.
Answers
PLEASE HELP ME, I WILL GIVE U BRAINLIEST,
Answers
Answer:
around 9.8
Step-by-step explanation:
This is a right triangle, so to find x, you can use pythagorem theorem:
So...
23^2+x^2=25^2
529+x^2=625
x^2=96
x is around 9.8
Answer:
9.79 or 9.9
Step-by-step explanation:
Its around 9, estimation...
5(7 + 3x) - 12 how to simplify
Answers
To solve this we need to use this formula:
a(b+c)=ab+ac
5(7+3x)-12=35+15x-12=15x+23
Answer:
Step-by-step explanation:
Multiply the 5 to the 7 and 3x--> 35 + 15x -12. Then add 12 to the -12, making it 0 (inverse operations), and add 12 to the 35 making it 47 + 15x. :) Then you would simply divide the 15 by 15x (making the variable by itself). your answer for x should be 47/15. :> If I helped, please mark brainliest!!
How is the distributive property used when multiplying two binomials
Answers
Answer:
Step-by-step explanation:
When multiplying a binomial times a binomial, each term of the first binomial must be multiplied by each term of the second binomial. Like terms are then combined.
When multiplying two binomials, four multiplications must take place. These multiplications can occur in any order, as long as each of the first two terms is multiplied by each of the second two terms.
There are numerous ways to set up the multiplication of two binomials. The two basic formats, horizontal line-up and vertical line-up, are similar to what we saw in adding and subtracting polynomials. Let's investigate the simple product (x + 2)(x + 4) with a variety of set-ups. Start with the first term of the first binomial (the blue x).
• Distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).
• Then take the second term in the first binomial (including its sign: +2) and distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).
• Add the results, combining like terms when needed.
• This method will work with all polynomials, not just binomials times binomials.
Answer:
Distributive.
Step-by-step explanation:
I did the quiz.
