The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275
Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.
x P(x) [tex]x^2[/tex] x P(x) [tex]x^2[/tex] P(x)
7 0.10 49 0.7 4.9
14 0.20 196 2.8 39.2
21 0.25 441 5.25 110.25
28 0.45 784 12.6 352.8
-----------------------------------------------------
∑x P(x) = 21.35
∑[tex]x^2[/tex] P(x) = 507.15
Mean = ∑x P(x) = 21.35
and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275
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which expression is missing from step 7?
Answer:
C
Step-by-step explanation:
Because they are two in a addiction like A+B, but they are elevated to the second.
If the solution was D we would have one square in all the espression.
The expression for missing term is (d - e)². The correct option is (A).
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The 8th step of the problem is given below,
(1 + d²) + (e² + 1) = d² - 2de + e²
Comparing it with the 7th step (√(1 + d²))² + (√(e² + 1))² = ?
It can be found that the missing term is,
d² - 2de + e²
= (d - e)²
Hence, the missing term in the 7th step is given as (d - e)².
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What is the degree of the polynomial 7x^3+2x^2y^4z
The polynomial 7x3+2x2y4z has a degree of 7.
Degree polynomial: What is it?The highest exponential power in a polynomial equation is called the polynomial's degree. Any polynomial's degree is determined solely by its variables; coefficients are to be disregarded. The degree of a polynomial is p for an nth degree polynomial function with real coefficients and x as the variable with the highest power n, where n accepts whole integer values (x).
based on the provided statement
Let's add exponents to determine each term's degree.
Degree of 7x³ (= x³) is =3
Degree of 2x²y⁴z (= 2+4+1) is = 7
Among all these degrees, 7 is the highest number and hence the degree of the given polynomial is 7.
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Let f(x) = x²+1 and g(x)=3 x . Evaluate each expression. (g ₀ f) (1/2)
The value of the expression (g ₀ f) (1/2) is 15/4
In this question, we have been given two functions f(x) = x² + 1 and g(x) = 3x.
We need to evaluate an expression. (g ₀ f) (1/2)
We know that the composite function is a function where the output of one function becomes the input of another function.
First we find the composite function (g ₀ f) (x)
(g ₀ f) (x)
= g(f(x))
= 3(f(x))
= 3 (x² + 1 )
= 3x² + 3
So, (g ₀ f) (x) = 3x² + 3
Now, we find the value (g ₀ f) (1/2)
(g ₀ f) (1/2)
= 3(1/2)² + 3
= 3(1/4) + 3
= 3/4 + 3
= 15/4
Therefore, the value of the expression (g ₀ f) (1/2) is 15/4
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Two cars start at the same time from two towns 792 kilometers apart and meet in 9
hours. One car can travel 8 km faster than the other car. How far did each car Travel
before they meet?
The distance the slower and faster car travelled are 360 km and 432 km respectively.
How to find the distance travelled by each car?Two cars start at the same time from two towns 792 kilometres apart and meet in 9 hours.
One car can travel 8 km faster than the other car.
let
x = speed of the slower car
x + 8 = speed of the faster car
The cars meet in 9 hours and both cover a distance of 792 km.
Therefore,
speed = distance / time
distance = time × speed
Hence,
9x + 9(x + 8) = 792
9x + 9x + 72 = 792
18x = 792 - 72
18x = 720
divide both sides by 18
x = 720 / 18
x = 40
Therefore,
speed of the slower car = 40 km per hour
speed of the faster car = 48 km per hour
Hence,
how far the slower car go(distance) = 40 × 9 = 360 km
how far the faster car go(distance) = 48 × 9 = 432 km
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The expressions that can be used to determine the area of the rectangle are:
12 x 7
7 . 10 + 7 . 2
The expressions that can be used to determine the perimeter of the rectangle are:
2 x (12 + 7)
7 + 12 + 7 + 12
2 . 7 + 2 . 12
The expression that cannot be used to find either the area or the perimeter of a rectangle is: 7 + 12
What is the area and the perimeter of a rectangle?A rectangle is a 2-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals which bisect each other at right angles.
The area of a rectangle is the product of the width and the length.
Area of a rectangle = length x width
12 x 7 = 84 units²
7 . 10 + 7 . 2
70 + 14 = 84
The perimeter of a rectangle is the distance round the rectangle.
Perimeter of a rectangle = 2 x (length + width)
2 x (12 + 7)
2 x 19 = 38 units
7 + 12 + 7 + 12 = 38
2 . 7 + 2 . 12
14 + 24 = 38
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What is the quotient of 57.15 and 4.5
Answer: 12
Step-by-step explanation: You're welcomed
The quotient of the decimal numbers 57.15 and 4.5 is 12.7.
The given decimal numbers are 57.15 and 4.5.
What is a quotient?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, 57.15/4.5
4.5|57.15|12.7
57.15
_______
0
Therefore, the quotient of the decimal numbers 57.15 and 4.5 is 12.7.
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CCSS ARGUMENTS Determine whether each statement is true or false. If false, give a counterexample. If true, explain your reasoning.
Two triangles with three pairs of corresponding congruent angles are congruent.
Two triangles with three pairs of corresponding congruent angles are congruent: Always TRUE
What exactly does "triangle congruency" mean?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So, the statement says that:
Two triangles with three pairs of corresponding congruent angles are congruent.The statement will always be true as it satisfies the congruency condition of AAA.Therefore, "two triangles with three pairs of corresponding congruent angles are congruent" is Always TRUE.
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1. A crystal is cut into a shape formed by two square pyramids joined at the base. Each pyramid has a base
edge length of 5.7 mm and a height of 3 mm. What is the volume of the crystal to the nearest cubic
millimeter?
The volume of the square pyramid is 32.49 cubic mm.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubes.
Given that crystal is cut into a shape formed by two square pyramids joined at the base. Each pyramid has a base edge length of 5.7 mm and a height of 3 mm.
The volume of the pyramid will be calculated as below:-
V = ( L W H ) / 3
V = ( 5.7 x 5.7 x 3 ) / 3
V = 32.49 cubic mm
Therefore, the volume of the square pyramid is 32.49 cubic mm.
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How am I supposed to do this? I know that the x = 11, but I have no clue on what to do from there
Find m∠CED.
Answer: 140°
Step-by-step explanation:
x = 11
5 x 11 = 55
55 - 15 = 40
The 5x-15 = 40°
tHe 3x+7 is opposite, so it also equals 40°
40 + 40 = 80°
360° - 80° = 280
280 divided by 2 = 140°
URGENT: DUE TODAY
In the picture, k || p, m 21 = 2x + 24, and mz3 = 10x. Find m<2.
Answer:
C
Step-by-step explanation:
Can yall help me on this please please Ill give brainlist and 100 points
Answer:
d) (-2)⁶/(-2)⁴
Step-by-step explanation:
Given that,
→ (-2)⁴/(-2)²
→ 16/4 = 4
Then the equivalent expression is,
→ (-2)⁶/(-2)⁴
→ 64/16 = 4
Hence, option (d) is correct.
given the function C(r) = (r-6)(r+6)(r-5)
it’s C-intercept is
it’s r- intercepts are
The C-intercept at (0, 180) and r- intercepts at (6, 0), (-6, 0), and (5, 0).
What is the intercept of a function?The points on each axis where the function crosses will be the intercepts. Therefore, the p-intercept will be at the point where r = 0, and the r-intercepts will be at the point where C = 0.
We have been given the function as
C(r) = (r-6)(r+6)(r-5)
We have to determine the C-intercept and r- intercepts.
We should plug in 0 for r and solve.
Solving for the C-intercept
Plug in 0 for r.
C(0) = (0-6)(0+6)(0-5)
C(0) = 180
The C-intercept is (0, 180)
Solving for the r-intercepts, we get
Set the function equal to 0.
0 = (r-6)(r+6)(r-5)
Solve for the zeros.
(r-6) = 0 ⇒ r = 6
(r+6) = 0 ⇒ r = -6
(r-5) = 0 ⇒ r = 5
The r-intercepts are (6, 0), (-6, 0), and (5, 0)
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What is the classification for this polynomial?
-6a²b5 + a²
Click on the correct answer.
monomial
binomial
trinomial
An observation deck extends 310 feet out above a valley. The deck sits 260 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given
by h=-16² +260. How long will it take for the object to be 4 feet above the valley floor?
The time that it will take for the object to be 4 feet above the valley floor will be 4 seconds.
How to illustrate the information?It should be noted that the object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-16² +260.
Therefore, the time that it will take for the object to be 4 feet above the valley floor will be:
h=-16² +260.
4 = -16t² + 260
4 + 16t² - 260 = 0
16t² - 256 = 0
Collect like terms
16t² = 256
t² = 256/16
t² = 16
t = ✓16
= 4
The time is 4 seconds.
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Need help with these two problems
Step-by-step explanation:
you don't know the Pythagoras formula yet ?
this is something you need to remember for life. this you will encounter everywhere (not just in school) :
c² = a² + b²
in a right-angled triangle c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs of the triangle.
4.
the legs of this right-angled triangle are the pole and the ground distance to the cable fixture on the ground.
the cable itself is the Hypotenuse (as the right angle is the angle between the pole and the ground distance).
so,
cable² = 8² + 6² = 64 + 36 = 100
cable = sqrt(100) = 10 m
5.
here we have a right-angled triangle with the direct distance between the points being the Hypotenuse, and the x and y coordinate differences are the legs.
so, we have
distance² = (3 - -3)² + (0 - -1)² = 6² + 1² = 36 + 1 = 37
distance = sqrt(37)
please note that since we are squaring, the direction of the differences and their signs do not matter. the square will turn positive and negative distances into positive numbers.
Ayúdame, es para mañana
Answer: 1) x=20° 2) x=50°
Step-by-step explanation:
1)
[tex]x+20+x+30=90\\2x+50=90\\2x+50-50=90-0\\2x=40\\Divide\ both\ parts\ of \ the\ equation\ by\ 2:\\x=20^0[/tex]
2)
The sum of adjacent angles is always 180 degrees.
[tex]x+80+x=180\\2x+80=180\\2x+80-80=180-80\\2x=100\\Divide\ both \ parts\ of\ the\ equation\ by\ 2:\\x=50^0[/tex]
A bag contains 180 cars. Some are red and the rest are blue. There are 14
red cars for every blue car.
How many red cars are in the bag?
012
O 114
06
O 168
Answer:
114
Step-by-step explanation:
If you use the probability of statistics equation ax+bx+cx=x^3 and plugin the numbers you will get 114 as your answer.
Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5?
The difference is a binomial with a degree of 5.
The difference is a binomial with a degree of 6.
The difference is a trinomial with a degree of 5.
The difference is a trinomial with a degree of 6.
The difference is a binomial with a degree of 6.
What is Degree of polynomial?
The highest power of the variable in a polynomial is called the degree of the polynomial.
The polynomials are given as;
(a³b + 9a²b² - 4ab⁵) and (a³b - 3a²b² + ab⁵)
Now, The difference of the polynomial calculated as;
(a³b + 9a²b² - 4ab⁵) - (a³b - 3a²b² + ab⁵)
a³b + 9a²b² - 4ab⁵ - a³b + 3a²b² - ab⁵
12a²b² - 5ab⁵
Hence, Degree of polynomial = 1 + 5 = 6
So, The difference is a binomial with a degree of 6.
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please help it’s urgent thank you!
The difference in height between 30 meters up the cliff and 87 meters up the cliff will be 57 meters.
The distance between the albatross flying at 100 meters above the surface of the ocean and the shark swimming 30m below the surface is 130 meters.
How to calculate the value?It should be noted that the distance in height between 30 meters up the cliff and 87 meters up the cliff will be:
= 87 - 30
= 57 meters.
The distance between the albatross flying at 100 meters above the surface of the ocean and the shark swimming 30m below the surface will be:
= 100 - (-30)
= 100 + 30
= 130 meters
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for each pair of real numbers a does not equal b, define the operation * as (a*b)=(a+b)/(a-b). What is the value of ((1*2)*3)?
The value of ((1*2)*3) is 0
How to determine the value
From the information given, we have the real number operation as;
(a*b) = (a+b)/ (a-b)
Given the expression;
((1*2)*3)
Now, let's solve the bracket first, we have;
( 1 * 2 )
Where;
a = 1
b = 2
( 1 * 2 ) = ( 1 + 2 ) / 1 - 2
Simplify further
= 3/ -1
= -3
Substitute into the operation;
( -3 * 3)
Where;
a = -3
b = 3
( -3 * 3) = ( -3 + 3) / -3 - 3
Simplify further
= 0/ -6
= 0
Thus, the value of ((1*2)*3) is 0
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Anyone know how to do this?
Answer:
The square root of 48 to the nearest tenth is 6.9
Simplify the expression.
3(x + 3y) - 5(x - y)
The simplification of the expression 3(x + 3y) - 5(x -y) is -2x + 14y.
According to the given question.
We have an expression
3(x + 3y) -5(x -y)
As we know that, the simplification of an expression means to write an equivalent expression which contains no similar terms.
Therefore, the simplificantion of the expression 3(x + 3y) - 5(x -y) is given by
3(x + 3y) - 5(x -y)
= 3x + 9y - 5x + 5y (by distributive rule)
= 3x - 5x + 9y + 5y
= -2x + 14y (adding and subtracting the like terms)
Hence, the simplification of the expression 3(x + 3y) - 5(x -y) is -2x + 14y.
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Identify the pattern and find the next three terms.
0.2,1,5,25,125, .......
Answer:
625,3125,15625
Step-by-step explanation:
Because it is ×5, so 125×5=625, 625×5=3125...
HELP ASAP PLEASE
13. <1 and < 2 are supplementary. If <1 = 2y = 9 and m<2 = 3y-4, what is the measure of <1?
*
m<1 = 35
m<1 = 101
m<1 = 13
m<1 = 79
Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.
Hence, option D)79° is the correct answer.
What is the measure of ∠1?Supplementary angles refer to the pair of angles that sum up to 180 degree.
Given the data in the question;
∠1 and ∠2 are supplementary∠1 = 2y + 9∠2 = 3y - 4Measure of ∠1 = ?Since ∠1 and ∠2 supplementary angles, they will sum up to 180 degree.
∠1 + ∠2 = 180°
(2y + 9) + (3y - 4) = 180
Solve for y
2y + 9 + 3y - 4 = 180
5y + 5 = 180
5y = 180 - 5
5y = 175
y = 175/5
y = 35
Hence, the measure of ∠1 will be;
∠1 = 2y + 9
∠1 = 2(35) + 9
∠1 = 70 + 9
∠1 = 79°
Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.
Hence, option D)79° is the correct answer.
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Solve each equation. Check each solution. 3/x =5
The solution of the given equation 3/x = 5 is at x = 3/5.
According to the given question.
We have an equation 3/x = 5.
As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Here, we have to find the solution of the equation 3/x = 5 is given by
3/x = 5
⇒ 3 = 5x (multiplying x both the sides)
⇒ 3/5 = x (dividing both the sides by 5)
⇒ x = 3/5
Hence, the solution of the given equation 3/x = 5 is at x = 3/5.
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Jacob runs 3.75 miles a day. His current total is 165 miles. What should Jacob do to see how many days it took him to run that far?
Answer:
Step-by-step explanation:
calculate the miles with the distance
6+ [(x + 5) / x^2 +3x-10/x-1]
On simplifying the given equation, the answer is
[tex]\frac{{9x^{2} - 15x^{2} + 4x}}{{x^{2} (x-1)} }[/tex]
What does algebraic simplify mean?
Solving a math issue is the same thing as simplifying an equation. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to perform.
Finding the value or values that make the equation—or math sentence—true is the process of solving.
[tex]6 + [\frac{x+5}{x^{2}} + \frac{3x - 10}{x-1} ]\\[/tex]
On simplifying it,
[tex]6 + \frac{(x+5)(x-1) + (3x-10x^{2} )}{x^{2} (x-1)} \\\\6 + \frac{x^{2} -x + 5x +3 x^{3} - 10x^{2} }{x^{2} (x-1)} \\\\6 + \frac{3x^{3} -9x^{2} + 4x }{x^{2} (x-1)} \\\\\frac{6x^{3} - 6x^{2} + 3x^{3} - 9x^{2} +4x }{x^{2} (x-1)} \\\\\frac{9x^{2} - 15x^{2} + 4x}{x^{2} (x-1)}[/tex]
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Solve the linear system
4x +9y = -72
4x + 9y = 54
Step-by-step explanation:
9y=-72-4×
put x =1
9y=-72-4×1
9y=-72-4
9y=-76
What are the coordinates of the point on the directed line segment from (-9, -10) to (-5, -2) that partitions the segment into a ratio of 5 to 3?
help plis
====================================================
Explanation:
Refer to the diagram below.
Let's define these two point labels
A = (-9, -10)
B = (-5, -2)
which are the two given endpoints of the segment. Let's add in point C such that
C = (-5, -10)
Notice triangle ABC is a right triangle. The 90 degree angle is at point C.
--------------------
The x coordinates of points A and C are -9 and -5 respectively. This is a gap of 4 units. Split this into 8 pieces to find each is 4/8 = 0.5 units wide. Why 8? Because the "ratio 5 to 3" has a total of 5+3 = 8 parts.
Since the first number of that ratio is 5, we'll move 5 parts to the right of point A. So we'll move 5*0.5 = 2.5 units to the right of A.
We go from A(-9,-10) to D(-6.5, -10)
Take note how the segments AD and DC are in ratio 5:3
--------------------
The y coordinates of B and C are -2 and -10 in that order. This is a gap of 8 units. Split this into 8 equal parts, and each part is 1 unit tall.
Start at point C and move upward 5 of those parts, ie 5*1 = 5 units up. You should arrive at point E(-5, -5) shown in the diagram below.
Then draw a vertical line upward from point D until arriving at segment AB. At the same time, draw a horizontal line from point E until arriving at segment AB. Both approaches should get to point (-6.5, -5) which is the final answer. This is denoted as point F in the diagram below (marked in red).
Can someone just help? no one seems to be getting my question for some reason, and i sent like 7 of the same question.
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
What is the triangle?A triangular is a geometry with 3 sides and three angles. The triangle has angles that sum up to 180 °.
In a triangle, the opposing side will be short if the angle is small, while the other side will be longer if the angle is larger.
The sides of the triangle are in ascending order, then we have
WY < YZ < WX < XY < XZ
Then the sequence of the angles is given as,
∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
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