Answer:
0.430 (nearest thousandth)
Step-by-step explanation:
Using binomial probability relation :
p = 0.81
n = 4
x = 4
1 - p = 1 - 0.81 = 0.19
Recall ;
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 4) = 4C4 * 0.81^4 * 0.19^(4-4)
P(x = 4) = 1 * 0.43046721 * 1
P(x = 4) = 0.43046721
P(x = 4) = 0.430 (nearest thousandth)
what values for m and n that make this number sentence true: 1/2+9/10+m+n=2.
1/2+9/10+m+n=2 is true when m and n have values { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }.
What is number?
An arithmetic value known as a number is used to calculate and represent a quantity.
Given, 1/2+9/10+m+n=2
m+ n = 2 - 1/2 - 9/10
m+ n = 3/5
m = 3/5 - n
So, If n= 0, m = 3/5
Hence, we can define as { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }
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Help with special right triangles rounding
Answer:
9.8 units-----------------------------------
Hypotenuse of an isosceles triangle is √2 times the leg:
x = √12 × √2 = √24 = 4√6 ≈ 9.8 units (rounded to the nearest tenths)10. A new bank customer with $3,000
a money market account. The
wants to open
simple interest rate of 1.1%.
bank is offering a
a. How much interest will the customer earn in
20 years?
b. What will be the account balance after
20 years?
Answer:
a. $660
b. $3660
Step-by-step explanation:
a. 1.1% = 1 years
22% = 20 years
22% = 0.22
Take 3000 times 0.22 = $660
So, they will earn $660 interest in 20 years
b. $3000 + $660 = $3660
$3660 is their account balance after 20 years
What is special about rigid transformations?
transformations and rigid body symmetric transformations. Geometric figures' sizes and shapes are unaltered throughout a stiff transformation (also known as an isometric transformation).
What type of transformation is rigid Why?A stiff transformation in mathematics, commonly referred to as a Euclidean transformation or a Euclidean isometric transformation, is a geometric transformation of Euclidean space that keeps the Euclidean distance between each pair of points. Transformations of rigid bodies can take the shape of rotations, translations, reflections, or any combination of these.
transformations and rigid body symmetric transformations. Geometric figures' sizes and shapes are unaltered throughout a stiff transformation (also known as an isometric transformation). a unique kind of metamorphosis when the characters' sizes or shapes are left unaltered.
Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]
and, here s = half the perimeter,
[tex](a + b + c)/2.[/tex]
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What are the 3 parameters used in a for loop in Python?
Range with three parameters: start, end, step.
Now, According to the question:
What are the 3 loops in Python?
The three types of loop control statements are:
break statement.continue statement.pass statement.What are the three parameters in range in Python?
The range() function in Python works by taking three inputs as parameters which are start_value, stop_value, and step value. The range() function returns an immutable sequence of numbers starting from the start_value, and increments the values by the value given in the step_value, and stops at the stop_value.
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What is the inverse of 8?
The additive inverse of the number 8 is " -8 " .
The Inverse (Additive) of the number is defined as the number that is added to a given number to make the sum zero ;
that means : If a number is added to its additive inverse, then the sum of both numbers becomes 0 .
So , that means to find the additive inverse of "8" , we have to find the number such that on adding it to 8 , we get the sum as 0 .
let the additive inverse of 8 be = x ;
So , x + 8 = 0 ;
x = -8 .
So , putting the value in above equation, 8 - 8 = 0 .
Therefore , the additive inverse is "-8" .
The given question is incomplete , the complete question is
What is the additive Inverse of 8 ?
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1: The drama department sold a total of 360 tickets to there Friday and Saturday night shows. They Sold three times as many tickets for Saturday's show than for Fridays show.
A: Write a system of equations to represent this scenario
B: How many tickets were sold for Friday, and Saturday? Is there more than one solution?
C: Graph the system of equations on a coordinate plane. Label the axes.
D: Justify algebraically that your solution is correct.
(A) Given question can be represented in the system of linear equations as x + y = 360,
y =3x
(B) 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
(C) We have drawn the graph for the solution.
(D) We have justified our answers by using the substitution method.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Let x number of tickets sold on Friday and y number of tickets sold on Saturday.
By using the given condition,
x + y = 360 ----------(I)
y =3x -------(II)
Put y = 3x in equation (I), we get
x + 3x = 360
4x = 360
x = 90
Now put x = 90 in equation (I), and we get
90 + y = 360
y = 270
Hence, 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
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For what values of x and y are the triangles to the right congruent by HL?
For x = 5 and y = 3 the given triangles are congruent.
What is congruent triangles?
In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.
Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.
Let the given triangles are congruent.
So, their sides are equal.
⇒ x = y + 2 ..(1)
3y = x + 4 ..(2)
Plug value of x in equation (2)
3y = (y + 2) + 4
3y = y + 6
2y = 6
y = 3
Plug y = 3 in equation (1)
x = 3 + 2
x = 5
Hence, for x = 5 and y = 3 the given triangles are congruent.
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What are the dimensions (in cm) of the enlarged picture?
A teacher is showing a picture on a screen.
The picture is 12cm by 8cm.The screen is 2.4m by 2m
The teacher enlarges the image on the screen so it is as big as possible without distorting its proportions.
Answer:
Below
Step-by-step explanation:
Picture is .12 x .08 m
2 m / .08 m = 25
2.4 m / .12 m = 20 <===== limiting factor ( 20 is less than 25)
so it would be 20 * (.12) X 20(.08) = 3.84 m^2
Calculate the perimeter of the irregular shape please show ur work Bc I have too
Answer:
34 cm
Step-by-step explanation:
the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2
4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34
How do you find the height and area of an isosceles triangle?
To find the height of an isosceles triangle, we square the length of one of the equal sides and subtract the square of half the base, and the area can be easily calculated if the height and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle.
isosceles triangle
an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.
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Which of these is, or describes, a geometric sequence with a common ratio of 2? select two answers that are correct.
A geometric sequence with a common ratio of 2 is E . F( n ) = 5 * 2^n where n = 1 , 2 , 3 .
Given :
A. -5 , -3 , -1 , 1 , 3
common ratio r = -3/-5
it is not the option
B . 0.0625 , 0.125 , 0.25 , 0.5 , 1
Common ratio :
r = 0.125 / 0.0625
= 0.5
it is not the option .
C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2
a2 = 1/2 * a1
= 2/2
= 1
common ratio = 1/2
it is not the option
D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3
a2 = a1 + 2
= 3 + 2
= 5
common ratio = 5/3
it is not the answer
E. F( n ) = 5 * 2^n where n = 1 , 2 , 3
a1 = 5 * 2^1
= 10
a2 = 5 * 2^2
= 20
common ratio = 20 / 10
r = 2
It is the correct option.
F. f ( n ) = n^2 where n = 1 , 2 , 3
a1 = 1^2
a2 = 2^2
= 4
common ratio = 4/1 = 4
it is not the correct option.
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Full question :
Which of these is, or describes, a geometric sequence with a common ratio of 2? select two answers that are correct.
A. -5 , -3 , -1 , 1 , 3
B . 0.0625 , 0.125 , 0.25 , 0.5 , 1
C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2
D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3
E. F( n ) = 5 * 2^n where n = 1 , 2 , 3
F. f ( n ) = n^2 where n = 1 , 2 , 3
According to the rational root theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. negative five-halves, –2, 1, ten-thirds which is an actual root of f(x)?
As per the rational root theorem, the actual root of the polynomial is - 5/2
The term polynomial refers the algebraic expression in which the exponents of all variables should be a whole number
Here we have given that f(x) = 6x⁴ + 5x³ – 33x² – 12x + 20. and we need to find which is an actual root of f(x).
In order to find the root for the polynomial we have to apply each value as the replacement of x in the polynomial.
And then we have to find in which one makes the polynomial result as zero.
First we have to take the value of x as -5/2, then the polynomial equation be like,
Here we have to substitute x=-5/2, then we get
=> f(-5/2) = 6(-5/2)⁴ + 5(-5/2)³ - 33(-5/2)² - 12(-5/2) + 20
=> f(-5/2) = 6(625/16)-5(125/8)-33(25/4)+30+20
when we simplify this one then we get,
=> f(-5/2)=(1,875-625-1,650+400)/8
=> f(-5/2)=0/8
Here we know that if we zero by any number we get the result as zero.
Therefore, f(-5/2)=0 then x=-5/2 is a root of f(x)
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Answer:
its A
Step-by-step explanation:
Just took the test
For a certain oscillator the net force on the body with mass m is given by fx = -cx^3. One-quarter of a period is the time for the body to move from x=0 to x=A. Calculate this time and hence the period. Express your answer in terms of the variables A, m, and c.
The time period is T = √[(4π^2mA^2)/mw^2A^2].
In the given question, we have to calculate this time and hence the period.
By conservation of energy :
1/2*mw^2A^2 = 1/2*mv^2+1/2*mw^2x^2
V^2 = w^2(A^2−x^2)
V = w√(A^2-x^2)
dx/dt = w√(A^2-x^2)
[tex]\frac{dx}{\sqrt{A^2-x^2}}[/tex] = w*dt
[tex]\frac{dx}{A\sqrt{(1-(x/A)^2}}[/tex] =w*dt
put (x/A)^2 = v
dx/A=dv
[tex]\int_{0}^{1} \frac{dv}{\sqrt{1-v^2}} = \int_{t=Io}^{t=t}w\times dt[/tex]
[tex][sin^{-1}(1)-sin^{-1}0]=wt[/tex]
π/2=wt
t= π/2w
[∴w=2π/T]
t= πT/2*2* π
t=T/4
Where T is time period
F = -kx
a = -k/m*x
ma = -kx
a = -w^2x
(standard equation of S.H.H)
w = √(k/m)
T = 2π/w
T = 2π√(m/k)
[k = mw^2]
T = √[(4π^2mA^2)/mw^2A^2]
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What is the sample space of rolling a 6 sided number cube?
The sample space of rolling a 6 sided number cube is the set of all possible outcomes of rolling the number cube. The sample space for a 6 sided number cube is the set of numbers 1,2,3,4,5, and 6.
When rolling a 6 sided number cube, the sample space is the set of all possible outcomes, which are the numbers from 1 to 6. This means that the sample space includes each of the six numbers, with no bias towards any particular number. Each of the six numbers has an equal chance of being obtained when rolling the number cube.
The sample space of a 6 sided number cube is also known as a discrete sample space, since all of the possible outcomes are predetermined and known. The sample space of a 6 sided number cube is finite and can be easily calculated by listing all the possible outcomes. Since there are 6 possible outcomes, the sample space consists of 6 elements.
The sample space of a 6 sided number cube can be easily visualized by imagining a six-sided die being rolled and each side being labeled with a number from 1 to 6. This demonstrates that the sample space of a 6 sided number cube is a discrete sample space, and each of the six numbers has an equal chance of being obtained.
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Rays are shown from point P, the center of dilation, through the vertices of angles QRS. Dilate angles QRS by a scale factor of 2
The dilation of the angle with vertices QRS has been dilated by scale factor 2.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given angle QRS.
The length of QS = 2 grids and RS = 3 grids.
By dilated by 2 scale factor.
The length QS must become 2 x 2 = 4 grids and RS by 3 x 2 = 6 grids.
The R and Q must be in dotted lines as shown below.
Q'R'S' is the dilated figure.
Hence "The angle with vertex QRS has been enlarged by a scale factor of 2".
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I almost thought that this had no solutions, but I'm not sure, could anyone help me on this? I would deeply appreciate it!
Consider the equation 2x = 3x. Does this equation have one solution, no solution, or infinite solutions? Explain your reasoning
Answer:
one solution because when you isolate the x terms:
2x-3x=0 and you combine like terms
-x=0
and divide by negitive one because -x is (-1)(x)
you get x=0
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
It appears this problem has no solution, buttt let's look closer.
2x and 3x are like terms, meaning they can be added and subtracted because they both have x!
So let's combine these like terms and see what we get...
2x = 3x
0 = 3x -2x
0 = 1x
x = 0 / 1
x = 0
The only solution is 0! No other number is possible.
What is the example of linear inequality in two variables?
4x + 8y ≤ -24 is the example of linear inequality in two variables.
What is a linear inequality equation?Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
For example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
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3) Find the percentage change. State whether the change is an increase or decrease.
a)
A
Before: 34 shirts
Now: 62 shirts
b)
Original: 36.79
New: 22.88
Answer:
(a) The percentage change is 82.35 . The change is decreasing.
(b) The percentage change is -37.80. The change is decreasing.
Step-by-step explanation:
(a) percentage change- the change between two values in percent is called a percentage change .
formula - final value-initial value /initial value *100
here , 62-34/34*100
since , the value is positive , the value is increasing .
(b) percentage change- the change between two values in percent is called a percentage change .
formula - final value-initial value /initial value *100
here , 22.88-36.79/36.79*100
since , the value is negative , the value is decreasing.
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Answer:
a) 82% Increase
b) -37% decrease
Step-by-step explanation:
a)
Percentage :-
= ((62-34) / 34) * 100
= 82.3529 ≈ 82% ------> increase
b)
Percentage:
= ((22.88-36.79) / 36.79) * 100
= -37.8 ≈ -37% ------> decreased
I hope my answer helps you
Please help with this geometry problem and explain it step by step
Answer:
x = 8
Step-by-step explanation:
In a triangle, if two angles are congruent, then the opposite sides are congruent.
Since you are told that angles A and C are congruent, then their opposite sides, BC and AB are congruent.
That makes BC = AB.
3x - 3 = 2x + 5
x = 8
A company has 95,000 online followers and gains 100 new followers every day. Another
company starts with 0 online followers and gains 350 new followers every day.
After how many days will the two companies have the same number of followers?
The number of days when the two companies will have the same number of followers is 380 days.
How to calculate the number of days?The first step is to form linear functions that represent the information of the two companies. The form of the functions is:
Total followers = initial number of followers + (number of new followers x number of days)
The linear function that represents the online followers for the first company is:
Total followers = 95,000 + 100d
The linear function that represents the online followers for the second company is: Total followers = 350d
When the companies have the same number of followers the two above equations would be equal 95,000 + 100d = 350d
95,000 = 350d - 100d
95,000 = 250d
d = 95,000 / 250
d = 380
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The longest ladder on the fire truck reaches 95 feet. A building has 20 stories, and each story is 18 feet high. what is the highest story that the ladder can reach?
(A) 5th story
(B) 6th story
(C) 10th story
(D) 18th story
(Somebody please help me answer this question I rlly need help with this!)
Answer:
Rounding down to the nearest whole number, we get 5 stories. The correct answer is, therefore (A) the 5th story.
Step-by-step explanation:
To solve this problem, we need to find the number of stories the ladder can reach by dividing the length of the ladder by the height of each story.
The longest ladder on the fire truck reaches 95 feet, and each story is 18 feet high, so the highest story that the ladder can reach is:
95 feet / 18 feet/story = <<95/18=5.28>>5.28 stories
Daphne participated in a challenge for National November Writing Month. All of the stories she
wrote for the challenge were more than 4 pages long.
Let z be the number of pages in a story. Which inequalities represent lengths of stories
more than 4 pages long? Select ALL that apply.
1: X <4
2: x >4
3: 4> x
4: 4< x
None of the given option is correct as for relating z i.e number of pages and pages wrote by Daphne we need a variable z in options.
What are inequalities?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. When two quantities are equal, we use the sign "=," and when they are not equal, we use the symbol "," which stands for "not equal." The first value may be greater than (>), less than (<), greater than equal to (>=), or less than equal to (<=) the second value if the two values are not equal.
The words "inequality" and "inequalitas," which mean "unequal, unlike, distinct," and "changeable," respectively, derive from the Old French and Latin, respectively. The magnitude, number, and intensity of two quantities or expressions are compared using this phrase.
For given situation correct relation will be z>4 which is not given in any of the option.
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a political scientist investigated the effect of political advertisements on the way that people voted in the presidential election. they want to do a hypothesis test to determine if political advertisements influenced the vote of less than 31% of all voters. the political scientist randomly surveyed 2509 voters and asked if political advertisements influenced the way the person voted. 709 said the advertisements did influence their vote. calculate the test statistic. round your final answer to two decimal places.
The probability of the influenced voters, if The political scientist randomly surveyed 2509 voters, 709 said the advertisements did influence their vote, is 0.283.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.
Given:
The political scientist randomly surveyed 2509 voters, n = 2509,
709 said the advertisements did influence their vote, S = 709,
Calculate the probability of influenced voter as shown below,
[tex]Probability = S / n[/tex]
Probability = 709 / 2509
Probability = 0.283
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What is the solution Ofsimultaneous equations 5x 3y 8 and 3x Y 2?
The solution of the simu1taneous equation 5x−3y=8; 3x+y=2 is x=1andy=−1.
What is simultaneous equations?Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an endless number of solutions.A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. In order to create a single equation that contains the other unknown, one of the unknowns must be removed or eliminated. It is best to use examples to explain the process. Example Address the parallel equations. 3x + 2y = 36 (1) 5x + 4y = 64 (2) . y = 6 So, x = 8 and y = 6 is the complete solution.Consider the equation 3x+y=2
Multiply the equation by 3 so that we can eliminate y
3(3x+y=2)=3×2
9x+3y=6
Adding it with 5x−3y=8
9x+3y+5x−3y=6+8
14x=14
x=1
Putting the value of x in equation 3x+y=2
3×1+y=2
3+y=2
y=2−3
y=−1
So, we have x=1andy=−1
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How many numbers less than 1000 are divisible by 3?
There are 333 numbers less than 1000 that are divisible by 3.
To find this, you can divide 1000 by 3 to get 333 with a remainder of 1. Since the numbers less than 1000 that are divisible by 3 do not include 1000, you subtract 1 from 333 to get 332. However, 0 is also divisible by 3, so you should add 1 to 332 to get 333 as the final answer.
In mathematics, what is a divisible?When a number divides evenly (i.e., leaves no residue), it is said to be divisible. For instance, since 2 can be divided by 34 equally, 34 may be divided by 2. 34 is not divisible by 3 since doing so would leave us with a remainder.
How are three divided?A whole number is said to be divisible by three according to the three-digit rule of division if the sum of all of its digits is precisely divided by three. Without actually doing division, it is possible to establish whether a number may be divided by three.
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How do you find the multiplicity of roots?
The multiplicity of a root of a polynomial can be determined by the factorization of the polynomial.
If a root is repeated multiple times, then this root is said to have a higher multiplicity. For example, if a polynomial has the form a(x-r)^2, then the multiplicity of root r is 2. This is because the polynomial can be written as a(x-r)(x-r), and the root r is repeated twice.
To calculate the multiplicity of a root, the polynomial must be factored into its linear factors. The multiplicity of each root is then equal to the power of the corresponding linear factor. For example, if a polynomial is factored into (x-r)^3(x-s), the multiplicity of root r is 3 and the multiplicity of root s is 1.
In general, if a polynomial is written in the form [tex]a*(x-r1)^k1*(x-r2)^k2*...*(x-rn)^kn[/tex], then the multiplicity of root ri is ki. Therefore, the multiplicity of the roots can be calculated by factoring the polynomial and finding the power of the linear factors.
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6 less than a number in algebraic expression
Answer:
Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:
x-6
what is the answer in decimal form?
The standard deviation of the given population is 7.72.
What is population?
All of the components of the data set are included in the population, as are parameters like mean and standard deviation that can be used to measure the population. The term "population" denotes the complete group of individuals, things, events, etc.
Given data,
53, 36, 36, 44, 31
We know that,
Standard deviation of a population is given by :
= √ [ ∑ ( X - ц )²/N
Where, X = each data point
ц = mean of data of population
N = No. of data points in population = 5
We need mean,
So, mean of data of population = (53 + 36 +36 +44 + 31)/5
= 40.
So, By applying formula :
SD = √ [ ∑ ( X - ц )²/N ]
= √1 / 5 [ (40-53)² + (40-36)² + (40-36)² + (40-44)² + (40-31)²
= √ ( 169 + 16 + 16 + 16 + 81 )/5
= √298/5
=7.72.
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Math work-related tasks
Francine can make a dress in 18 hours.Her mother can make a dress in 6 hours. They decide to work together . How long will it take them to make a dress ? Choose from the answers below .
A.4 hours
B. 4 hours and 30 minutes
C. 5 hours
D. 12 hours
Answer:
D. 12 hours
Step-by-step explanation:
I am guessing that they want you to find the average time together, or the mean.
Add 18 hours and 6 hours together to get 24 hours.
To get the average, you have to divide the total hours by the amount people involved.
Since there are 2 groups (2 people) that have an outcome of 18 hours and 6 hours, 24 hours/2 people is a 12 hour average.