Answer:
6%
Step-by-step explanation:
3/20=4/x
It is a indirect proportion so we reciprocal,
Then,
3/20=x/40
3×40=20×x
120=20x
x=120/20
x=6
The required probability for the given case is 0.4779.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The total number of students are 20.
And, the probability that a student cheats is 3/20 = 0.15.
The number of students chosen by the teacher is 4.
Thus, the probability that at least one student cheats can be found by binomial distribution as,
P(at least one student cheats) = ⁴C₁(0.15)¹(0.85)³ + ⁴C₂(0.15)²(0.85)² + ⁴C₃(0.15)³(0.85)¹ + ⁴C₄(0.15)⁴(0.85)⁰
= 4 × 0.15 × 0.6141 + 6 × 0.0225 × 0.7225 + 4 × 0.003375 × 0.85 + 1 × 0.00050625
= 0.4779
Hence, the probability that at least one student selected by the teacher does cheating is 0.4779.
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What is the empirical rule????
Answer:
The empirical rule, also known as the 68 - 95 - 99.7 rule, is a statistical rule that states that in regular distribution, virutally every piece of data will fall within three standard deviations. More specifically, 68% of the data will be within one standard deviation of the mean, 95% will lie in two standard deviations, and 99.7% will be within three standard deviations.
Step-by-step explanation:
Explanation above.
hope this helps :)
Answer:
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
Step-by-step explanation:
a triangular prism is covered with a foil label the label does not cover the two ends how much foil is necessary to cover the prism?
Step-by-step explanation:
13(16.5)+12(16.5)+5(16.5)
16.5(13+12+5) = 30(16.5) = 495 ft²
Eric wants to create a scale drawing of a house. The scale drawing needs to fit on a piece of paper that is 6 inches wide. The drawing itself must be ate least 3 inches wide. A. Drag numbers into the box to show an appropriate scale for the drawing. B. Use the Connect Line tool to create a drawing based on the scale you chose in Part A
To build a scale model we must take into account the original measurements of the original house.
What is a scale model?A scale model is a tool that allows us to build a structure with a smaller or larger size than the original that we take as a reference.
How to build a scale model?To build a scale model we must take into account all the measurements of the original object, in this case a house to be able to reduce it adequately to a smaller scale.
For example, if its sides are 30 meters long by 2 meters high and we want to make a scale of half the size, we must make its sides 15 meters long by 1 meter high.
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i need answers asap pleaseeee
Answer: A
Step-by-step explanation:
Our badminton team has finished $75\%$ of its season, during which we won $40\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses
Answer:
80%
Step-by-step explanation:
We can generalize from a specific example.
Let's assume that the season is 100 games long.
We have played 75% of the season, which is 75 games
We have won 40% of the games that we have played, so we have won 40% of 75 games, which is 30 games.
So, we must have lost 45 games.
To finish the season with as many wins as losses, of the 25 games we have left to play, we will have to win 20 games and lose 5.
To win 20 out of the last 25 games will be 20/25 = 0.80 = 80%
A wheel makes 13 revolutions to cover a distance of 65 m. Find the radius of the wheel.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Circumference of the wheel is :
[tex]\qquad \tt \dashrightarrow \:c = 2 \pi r[/tex]
c = circumference r = radiusNumber of revolutions = 13, and distance travelled is 65 m.
So, we can infer that :
[tex]\qquad \tt \dashrightarrow \:c = \frac{distance \: covered}{number \: of \: revolutions} [/tex]
Now, equate both the equations ~
[tex]\qquad \tt \dashrightarrow \:2 \pi r = \frac{distance \: covered}{number \: of \: revolutions} [/tex]
[tex]\qquad \tt \dashrightarrow \:2 \pi r = \frac{65}{13} [/tex]
[tex]\qquad \tt \dashrightarrow \:2 \pi r = 5[/tex]
[tex]\qquad \tt \dashrightarrow \:r = \frac{5}{2 \pi} [/tex]
[tex]\qquad \tt \dashrightarrow \:r = \frac{5}{3.14 \times 2} [/tex]
[tex]\qquad \tt \dashrightarrow \:r = \frac{5}{6.28} [/tex]
[tex]\qquad \tt \dashrightarrow \:r \approx0.8 \: m[/tex]
[tex]\qquad \tt \dashrightarrow \:r \approx80 \: cm[/tex]
radius of wheel is 80 cm[ To the hundredth place : 0.796 m ]
what is 128 : 144 in the form of n:1
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 128 and 144 is 16Divide both the numerator and denominator by the GCD
128 ÷ 16144 ÷ 16Reduced fraction: 89
Therefore, 128/144 simplified to lowest terms is 8/9.
please help this is due in 10 minutes!!!
Answer:
256/3π
Step-by-step explanation:
Volume of Sphere: [tex]\frac{4}{3}\pi r^3[/tex]
So by subbing into the equation:
[tex]\frac{4}{3} \pi 4^3[/tex] = 4/3π x 64 = 256/3 π
Solve 4+3(x-2)=2x-4.
Answer:
x=-2
Step-by-step explanation:
isolate the variable and the numbers
Answer:
-2
Step-by-step explanation:
4+3(x-2)=2x-4
distibute 3 to (x-2)
4+3x-6=2x-4
simplify
3x-2=2x-4
add -4 (becomes +4) to -2
3x+2=2x
subtract 3x
2=-x
divide the negative
-2=x
Help?? I could really use it
Answer:
16.5 m
Step-by-step explanation:
The triangle shown in the figure is a right triangle, so we can use the Pythagoreas Theorem.
a² + b² = c²
a² + 32² = 36²
a² + 1024 = 1296
a² = 272
a = √272
a = 16.5
Answer: 16.5 m
You borrow $300 at a simple interest rate of 4% per year. You make no payments for two years. How much do you owe after two years
Answer:
17
Step-by-step explanation:
I took the test
A standard number cube is rolled 30 times. Based on theoretical probability, how many of the 30 rolls are likely to be even numbers.
A. 13 B. 15 C. 17 D. 19 E. 21
The center of another circle is (-5,1) Its radius is √14 What is the equation of this circle?
Circular equations are typically organized like this:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is the center of the circle[tex]r[/tex] is the radius of the circleSolving the QuestionWe're given:
The center is (-5,1)The radius is [tex]\sqrt{14}[/tex]Plug the given information into the formula:
[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-1)^2=(\sqrt{14})^2\\(x+5)^2+(y-1)^2=14[/tex]
Answer[tex](x+5)^2+(y-1)^2=14[/tex]
Electric utility poles in the form of right cylinders are made out of wood that costs $27.96 per cubic foot. Calculate the cost of a utility pole with a diameter of 1 ft and a height of 20 ft. Round your answer to the nearest cent.
Answer:
$ 439.19
Step-by-step explanation:
Volume of a cylinder = pi r^2 h r = .5 ft h = 20 ft
V = pi (.5^2)(20)
multiply V * 27.96 to get $ 439.19
The end points of the diameter of a circle are (6, 0) and (-6, 0). What is the equation of this circle?
Circular equations are organized like this:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is the center of the circle[tex]r[/tex] is the radiusSolving the QuestionWe're given:
(6, 0) and (-6, 0) are the endpoints of the diameter of a circleTo find the equation of this circle, we must determine two things:
The center of the circleThe radiusTo determine the radius of the circle, find the distance between the given endpoints and divide by 2:
(6, 0) and (-6, 0)
⇒ There are 6 units between (0,0) and (6,0).
⇒ There are 6 units between (0,0) and (-6,0).
⇒ 6 + 6 = 12; the diameter of the circle is 12 units
⇒ 12 / 2 = 6
Therefore, the radius of the circle is 6 units.
To determine the center of the circle, find the midpoint of the given endpoints:
(6, 0) and (-6, 0)
⇒ The midpoint occurs at the very middle of these two points. The distance between the midpoint and (6,0) is equal to the distance between the midpoint and (-6,0).
⇒ We identified earlier that there are 6 units between (0,0) and (6,0), and that there are 6 units between (0,0) and (-6,0).
Therefore, the center of the circle is (0,0).
Plug the center and the radius into the equation:
[tex](x-h)^2+(y-k)^2=r^2\\x^2+y^2=6^2\\x^2+y^2=36[/tex]
Answer[tex]x^2+y^2=36[/tex]
Find the height of a triangle if the area is 42 square units and the base is 7 units.
Answer:
your answer is 12
Step-by-step explanation:
Base 7 Area 42
Using the formula
A= hb over 2
Solving for hb
hb=2A
b=2·42
7=12
hope this is not to confusing but the answer is 12.
The exchange rate is 1. 65 Bosnian markas per U. S. Dollar. The price of a refrigerator in Bosnia is 1964 markas while in the U. S. It is $1357. The real exchange rate is approximately
We will see that the real exchange rate is approximately 1.447 markas per U.S. dollar.
What is the real exchange rate?Here we need to perform a change of units procedure.
We know that the price of a refrigerator in Bosnia is 1964 markas, while in the US is $1357.
Then we can write the relation:
1964 markas = $1357
Now, we want to find the value in markas for a single dollar, then we divide both sides by 1357 to get:
(1964 markas)/1357 = $1357/1357
1.447 markas = $1
This means that the exchange rate is 1.447 markas per U.S. dollar.
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...............................
Answer:
804.2
Step-by-step explanation:
Formula
[tex]\pi r^{2}[/tex]
plug in
[tex]\pi *16^{2}[/tex]
≈ 804.24772
round to nearest tenth
≈ 804.2
need help will give brainlist
Answer:
(C) [tex]\frac{4x^{4} }{y{6}}[/tex]
Step-by-step explanation:
I’ve tried imputing the numbers but apparently I’m doing wrong so help please
Answer:
CB = sqrt (4a^2 + 6b^2)
Step-by-step explanation:
Using distance formula
d^2 = ( x1-x2)^2 + (y1-y2)^2
d^2 = (3a - -a)^2 + (b - -5b )^2
d^2 = (4a)^2 + (6b)^2
Answer: [tex]CB = \sqrt{16a^2 + 36b^2}\\\\[/tex]
Work Shown:
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\\\\CB = \sqrt{(3a-(-a))^2 + (b-(-5b))^2}\\\\CB = \sqrt{(3a+a)^2 + (b+5b)^2}\\\\CB = \sqrt{(4a)^2 + (6b)^2}\\\\CB = \sqrt{16a^2 + 36b^2}\\\\[/tex]
If that doesn't work, then your teacher may only want the stuff in the green box. So that would be either b-(-5b), or b+5b, or 6b
HELPP worth 95 points Use the Internet to identify a major league ballpark in which the distance from home plate to the center field fence and the height of the center field fence require that a ball hit 2 ft above the ground will necessitate an angle of elevation less than to just clear the center field
so Ive come to decide to pick the Yankees ballpark however the feet from the center field to home plate is 408 ft
through i don't understand what way do they want me to solve this, it was said to use the tangent ratio and inverse.
please help I'm struggling ):
Answer: try the US cellar field
Home plate is 400ft
Field fence height is 8ft
Angel of elevation is 0.85
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
x² + 8x + 7
Step-by-step explanation:
A = bh
B = x + 7
H = x + 1
A = (x+7)(x+1)
= x² + x + 7x + 7
= x² + 8x + 7
Look at the image below.
Find the area of the parallelogram.
Answer:
35
Step-by-step explanation:
i got it on khan
Answer: 18
Step-by-step explanation: I got it on the Khan test don't trust the first one. ,,ԾㅂԾ,,
Find the volume of the pyramid. Assume the base is a rectangle.
Work Shown:
A = area of the base
A = length*width
A = 9*10.1
A = 90.9
V = volume of the pyramid
V = (1/3)*(Area of the base)*(height)
V = (1/3)*(90.9)*(6)
V = 181.8
The units for the volume are in cubic inches. The result is exact.
whats the mode of 1,1,2,2,4,4,4
Answer: 4
Step-by-step explanation: Mode is highest occurring number
How do you write 0.66 as a percentage
To find the percentage, we must move the decimal place to the right two times. After doing this, 0.66 written as a percentage is 66%.
Answer:
66%
Step-by-step explanation:
All you do is put the decimal places two please to the right or do the number times 100. .66 times 100= 66%
Nine more than three times a number.
suppose h(t)=-0.2t^2+2t models the height, in feet of a ball that is kicked into the air where as t is given time in seconds. after how many seconds does the ball reach maximum height. what is the maximum height of the ball after how many seconds does the ball reach the ground
Answer:
Step-by-step explanation:
h=vt-16t²+s
t= -b/2a
t= -2/.4
t=5 seconds
h= -0.2(5)²+2(5)
h= -0.2(25)+10
h= -5+10
h= 5ft
It takes 5 sec. to reach its max height so it will take 5 sec. to hit the ground so 5+5=10 10 sec. total.
Angle RAT measures how many degrees ? 10 20 30.0
The angle RAT which is made with AR and AT line and shown in the figure of protector, measures 30 degrees.
How to measure the angle in protector?Protector is the most useful device to measure the angle between two lines. To measure the angle between two lines using the protector following steps is followed:
Place the protector center point at the vertex of unknown angle.One side of angle should be place at 0 mark line of this device.Other side of angle will be equal to the angle shown in protector on that line.In the given figure, The angle Between AR and AT line is 30 degrees shown in protector.
Thus, the angle RAT which is made with AR and AT line and shown in the figure of protector, measures 30 degrees.
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Determine the central and radius of the circle of equation given below
x2+y2-4x+6y-12=0
Answer:
centre = (2, - 3 ) and radius = 5
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 4x + 6y - 12 = 0 ( add 12 to both sides )
x² + y² - 4x + 6y = 12 ( collect x/ y terms )
x² + 4x + y² + 6y = 12
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(-2)x + 4 + y² + 2(3)y + 9 = 12 + 4 + 9
(x - 2)² + (y + 3)² = 25 ← in standard form
with (h, k ) = ( 2, - 3 ) and r = [tex]\sqrt{25}[/tex] = 5
Answer:
center of the circle = (2, -3)
radius of the circle = 5
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Given equation:
[tex]x^2+y^2-4x+6y-12=0[/tex]
Collect like terms:
[tex]\implies x^2-4x+y^2+6y-12=0[/tex]
Add 12 to both sides:
[tex]\implies x^2-4x+y^2+6y=12[/tex]
Complete the square for both variables.
Add 4 to both sides for x. Add 9 to both sides for y.
[tex]\implies x^2-4x+4+y^2+6y+9=12+4+9[/tex]
[tex]\implies (x^2-4x+4)+(y^2+6y+9)=12+4+9[/tex]
Factor the two variables:
[tex]\implies (x-2)^2+(y+3)^2=25[/tex]
Therefore:
center of the circle = (2, -3)radius of the circle = √25 = 5