Suppose that 25 students in an AP Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.
Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
There are 25 students, hence n = 25.70% do not commit any error, hence 30% do and p = 0.3.The probability that at least one commits an error is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.3)^{0}.(0.7)^{30} = 0.000023[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.000023 = 0.999977[/tex]
There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.
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What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth. –12, 20 –2.73, 2, 2.73 –1.73, 1.73, 2 –20, 12
The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.
What is a factor of polynomial?The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\
To find the roots of a polynomial, equate these factors of a polynomial to zero.
The given polynomial equation is,
[tex]x^4+x^2=4x^3-12x+12[/tex]
Take all the terms left side of the equation,
[tex]x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0[/tex]
The factor form of the polynomial on solving the above equation, we get,
[tex](x-2)(x-2)(x-1.73)(x+1.73)=0[/tex]
Equate all the factors to zero, to find the roots. The roots we get are,
[tex]2,2,1.73,-1.73[/tex]
Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.
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Answer:
–1.73, 1.73, 2
Step-by-step explanation:
No links just the Answer please!!!
Answer:Its -3.5
Step-by-step explanation:
Graph the line that represents the equation .
y = -2/3 x + 1
i really need ive tried multiple times and got it wrong every time
Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?
The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
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can someone help me? it’s due in a few hours
Answer:
cars value decreases in value exponentially
Step-by-step explanation:
cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time
The points represent the vertices of a polygon. Use a matrix to find the coordinates of the image after the given transformation. Graph the preimage and the image.
A(2, 3), B(–1, –4), and C(2, –2); a translation 1 unit left and 4 units down. 30 points
The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.
Given the points A(2, 3), B(–1, –4), and C(2, –2), the translation 1 unit left and 4 units down gives:
A'(1, -1), B'(-2, -8) and C'(1, -6)
The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)
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A cylinder and a cone have the same volume. The cylinder has a diameter of 4 inches and a height of 3 inches. The cone has a diameter of 6 inches. What is the height of the cone?
We are given a cylinder and a cone of same volume i.e
[tex] \longrightarrow[/tex] Volume of cone = Volume of cylinder
And also the diameter of the cylinder is given 4 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf \dfrac{Diameter}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{4}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 2 inches
The height of cylinder is 3 inches. And the diameter of the cone is 6 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf\dfrac{Diameter}{2} [/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{6}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 3 inches
First, let us recall the Formulas of volume of cylinder and cone:
[tex] \quad\longrightarrow\quad \sf {Cone = \dfrac{1}{3}\pi r^2 h }[/tex]
[tex] \quad\longrightarrow\quad \sf {Cylinder = \pi r^2 h }[/tex]
Now, we know that the volume of cone is equal to the volume of cylinder
[tex] \implies\quad \sf{\dfrac{1}{3}\pi r^2 h = \pi r^2 h }[/tex]
On putting the values:
[tex] :\implies\quad \sf{\dfrac{1}{3}\pi \times 3^2 \times h = \pi \times 2^2 \times 3 }[/tex]
[tex] :\implies\quad \sf{\dfrac{1}{\cancel{3}}\times 3.14 \times\cancel{ 9 }\times h = 3.14 \times 4 \times 3 }[/tex]
[tex] :\implies\quad \sf{3.14 \times 3 \times h = 3.14 \times 12 }[/tex]
[tex]: \implies\quad \sf{ h = \dfrac{ \cancel{3.14} \times 12 }{ \cancel{3.14} \times 3} }[/tex]
[tex] :\implies\quad \sf{ h =\cancel{ \dfrac{12}{3}}}[/tex]
[tex] :\implies\quad \underline{\underline{\pmb{\sf{h = 4 inches }}} }[/tex]
ㅤㅤㅤㅤㅤ~Hence the height of the cone is 4 inches.
Help on this pleasee
Answer: 40 degrees
Step-by-step explanation:
15 POINTS
Write an equation in standard form for the given circle
A.) (x+3)^2 + (y+6)^2 = 16
B.) (x-3)^2 + (y+6)^2 = 16
C.) (x+3)^2 + (y-6)^2 = 16
D.) (x-3)^2 + (y-6)^2 = 16
Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2
---Center = (h, k)
---Radius = r (this value will need to be squared in the final answer)
Center = (-3, -6)
---h = -3
---k = -6
Radius = 4
Equation: (x + 3)^2 + (y + 6)^2 = 16
Correct Answer: A
Hope this helps!
Translate the following phrase to an expression: the difference between twenty and twice a number.
Answer:
20 - 2n
n = a number
troy organizes a samll party there are 30 glasses of drinks at the party 20 of which contain an orange flavored drink what is the probability that a randomly selected drink will be orange flavored
Answer:
66(2/3) %
Step-by-step explanation:
There are 30 possible outcomes because there are 30 cold drinks.
The Probability of orange flavored 20/30 = 2/3 = 0.6666....
66.6666....%= 66(2/3) %
Good afternoon, please help me with this question and if u get it correct ill give u the brainlest
Answer:
5/6
Step-by-step explanation:
it comes out originally like 10/12 but if your simplify it it's 5/6
Answer:5/6
Step-by-step explanation: 12-2 =10 so 10/12 which simplifies to 5/6
PLEASE HELP!! It's due tomorrow and I don't understand it..
The length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. Write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches. 4x2 32x − 80 = 0 4x2 32x 60 = 0 2x2 32x − 80 = 0 x2 16x 60 = 0.
The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
What is the area of the rectangle?The area of the rectangle is the product of its length and its breadth.
As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².
Now we know the area is the product of length and breadth, therefore,
[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]
[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]
Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
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Answer:
A.) 4x2 + 32x − 80 = 0
Step-by-step explanation:
Just took the test
How to find the measure of an interior angle inside a regular polygon
Answer:
Step-by-step explanation:
[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides
The measure of an interior angle inside a regular polygon is given by;
[tex]\rm S = (n -2) \times 180[/tex].
What is the interior angle?An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.
An Interior Angle is an angle inside a shape.
As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.
Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.
The measure of an interior angle inside a regular polygon is determined by the following formula;
[tex]\rm S = (n -2) \times 180[/tex]
S = sum of interior angles and n = number of sides of the polygon.
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What would you drink to survive a extra 30 years?
A. Lean
B. Orange Juice
C. Mug
y = x + 2
5x - 4y = -3
Solving systems by equations
Answer: x = 5, y = 7
Step-by-step explanation:
1. First, put the variables together/rearrange:
y - x = 2 & 5x - 4y = -3
2. Cancel out variable x by multiply the first equation by 5:
5y - 5x = 10 & 5x - 4y = -3
3. Add equations:
y = 7
4. Then determine x by plugging y back into the first equation y = x + 2:
x = 5
Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?.
As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
Given function is:
[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]
What is a function?A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.
Divide the numerator and denominator of the given function by x.
[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]
[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]
As we know that as x approaches the infinity 1/x approaches 0.
So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]
[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]
Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
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Simplify this please
(5ab²c)^2
Answer:
25a^2b^4c^2
Step-by-step explanation:
step 1:
Remove the bracket by multiplying all the power inside the bracket with the power outside the bracket.
5^2a^2b^2x2c^2=25a^2b^4c^2
Write the following expression using an exponent.
1x(4.5)x(4.5)x(4.5)x(4.5)x(4.5)=
Answer:
4.5^5
Step-by-step explanation:
Answer:
(4.5)^5
Step-by-step explanation:
I’m thinking trapezoid and rhombus but I don’t know
What is f(4) for the function f(x) = 2x + 5?
f(4) =
Answer:
f(4) = 13
Step-by-step explanation:
f(4) = 2(4)+5
f(4) = 13
Answer:
13
Step-by-step explanation:
f ( x ) = 2x + 5
To find : f ( 4 )
f ( 4 ) = f ( x )
Here,
x = 4
So,
f ( 4 ) = 2 ( 4 ) + 5
= 2*4 + 5
= 8 + 5
f ( 4 ) = 13
Which angles are complementary to each other?
Answer:
<1 and <2
Step-by-step explanation:
Complementary angles are two angles which their measure add up to 90 degrees.
There are only one angle pair that meet this requirement:
angle 2 and angle 1
There are 100 cm in a meter. write an expression to find the number of centimeters in 8 meters.
Help me with this question plss
Answer:
800m
Step-by-step explanation:
If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)
(x+2)(x+7) Write in simplified form
Answer:
x^2+9x+14
Step-by-step explanation:
x×(x+7)+2×(x+7)
x^2+7x+2x +14
x^2+9x+14
Determine the solution to the system of equations below.
x - 3y = 1
3x-5y = 11
Pls answer for 50 brainlist!!
Answer:
[tex]\boxed{\sf{x=7 \quad y=2}}[/tex]
Step-by-step explanation:
To solve this problem, isolate it on one side of the equation.
x-3y=1 and 3x-5y=11x-3y=1: x=1+3y
x=1+3y
Substitute.
x=1+3y= 3(1+3y)-5y=11
Solve.
3+4y=11
Subtract by 3 from both sides.
3+4y-3=11-3
Solve.
11-3=8
Rewrite the problem down.
4y=8
Divide by 4 from both sides.
4y/4=8/4
Solve.
8/4=2
y=2
x=1+3y
x=1+3*2
Solve.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract1+3*2
Multiply.
3*2=6
Add.
1+6=7
x=7
Therefore, the correct answer is x=7 and y=2.I hope this helps you! Let me know if my answer is wrong or not.
The school has $3,582 to spend on markers. Each package of markers costs $9. How many packages of markers can the school buy?
packages
Answer:
398
Step-by-step explanation:
3582 / 9 = 398
What is the word form for 407,219?
A
Four hundred seventy thousand and two hundred ninety
B
Four hundred seventeen thousand, two hundred nineteen
C
Four hundred seven thousand, two hundred nineteen
D
Four hundred seven thousand, two hundred and nineteen
Answer:
C or D Both basically
Step-by-step explanation:I read them
100 POINTS !! The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 70 meters per second can be modeled by the parabola f(x) = x − 0.002x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground. A.height: 125 m; distance: 500 m B.height: 250 m; distance: 22 m C. height: 500 m; distance: 125 m D. height: 22 m; distance: 250 m
Answer:
height: 125m; distance: 500m
Step-by-step explanation:
x = 250
f(x) = x − 0.002x2
f(x) = 250 − 0.002(250 )2
= 250 − 0.002(62,500)
= 250 − 125
= 125
250 times 2 = 500
[tex]\\ \rm\rightarrowtail y=x-0.002x^2[/tex]
So
Put 250[tex]\\ \rm\rightarrowtail y=250-0.002(250)^2[/tex]
[tex]\\ \rm\rightarrowtail y=250-0.002(62500)[/tex]
[tex]\\ \rm\rightarrowtail y=250-125[/tex]
[tex]\\ \rm\rightarrowtail y=125m[/tex]
This is max heightDistance:-
2×height2×125500m