The worker B has a higher variance of σ² = 9 and standard deviation of 3
What is Standard Deviation?The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
Given data ,
Let the data of worker A = { 5, 4, 4, 6, 7, 5, 6, 3 }
Let the data of worker B = { 4, 8, 1, 9, 2, 9, 4, 3 }
Now , the mean of worker A = 5
The mean of worker B = 5
So , the standard deviation of worker A is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 5 )² + ( 5 - 4 )² + ( 5 - 4 )² + ( 5 - 6 )² + ( 5 - 7 )² + ( 5 - 5 )² + ( 5 - 6)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 12/8 )
SD = √1.5
Standard deviation σ = 1.2247449
And , the variance of worker A is σ² = 1.5
Now ,
The standard deviation of worker B is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 4 )² + ( 5 - 8 )² + ( 5 - 1 )² + ( 5 - 9 )² + ( 5 - 2 )² + ( 5 - 9 )² + ( 5 - 4)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 72/8 )
SD = √9
Standard deviation σ = 3
And , the variance of worker A is σ² = 9
Hence , the worker B has higher standard deviation
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A dress is on sale for - dollars. The regular price is 3 times as much. Jannie has enough Mooney to buy 2 dresses at the regular price. How many dresses can jannie buy at sale price?
1 dress
3 dresses
6 dresses
9 dresses
Which property is being illustrated x=y+4 and y+4=-22, then x=-22
The property illustrated for the given expression is substitution method.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Given that the two expressions are:
x=y+4 and y+4=-22
Here, the value of y + 4 is substituted in the value of x for the first expression.
Hence, the property illustrated for the given expression is substitution method.
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4.
X =
x
16
60°
_____y=_
-
y
Answer: what the hell the happened
Step-by-step explanation:
Which sentence best explains how the author creates
excitement in the passage?
1. He includes foreshadowing to indicate events
to come.
O2. He employs flashback to reveal shocking
background information.
3. He emphasizes the anticipation of waiting in
order to build suspense.
4. He changes the setting in order to
help support the use of parallel plots.
Answer:
He includes foreshadowing to indicate events
to come
There are 27 boys and 35 girls in the assembly hall and there are 15 boys and 17 girls in the laboratory room. Which room has the higher proportion of girls?
Write the slope-intercept form of the line with the given slope and point.
m=4; (2,3)
Enter the correct equation in the box.
Answer:
y = 4x-5.
Step-by-step explanation:
So with the form y = mx+b, you already have y = 4x+b.
Plugging in (2,3) (x=2, y=3), we have 3 = 4*2+b, giving b = -5.
This is a graph of y=x³.
How do we shift the graph of y=x^3 to get the graph of y=(x-2)³-4?
Answer:
2 right, 4 down
Step-by-step explanation:
By subtracting 2 inside the function, the graph is shifted 2 to the right and by subtracting 4, it is shifted 4 down.
To think of this more intuitively, in the original function, inputting 0 would yield the same output as plugging in a function with (x - 2) inside:
[tex]x^3=0^3=0\\(x-2)^3=(2-2)^3=0^3=0[/tex]
In addition, by subtracting -4, the value would always go down 4 from the original value of x^3:
[tex]x^3 = 0^3 = 0[/tex]
[tex]x^3-4 = 0^3-4=0-4=-4[/tex]
By putting these together we get the answer above.
What is the value of x? Enter your answer in the box. ___ units
Answer:
x = 28
Step-by-step explanation:
Consider the two triangles ΔAPR and ΔCDR
We see that AP ║ CD
Therefore m∠PAR = m∠CR, m∠APR= m∠CDR
Angle ∠R is common to both triangles
So the triangles are similar
Therefore the ratios of the sides must be the same ratio
[tex]\dfrac{AR}{CR} = \dfrac{PR}{DR}\\\\[/tex]
AR = x + 10
CR = x
PR = 42 + 15 = 57
DR = 42
PR = 42 + 15 = 57
Plugging in the values for these sides:
[tex]\dfrac{x + 10}{x} = \dfrac{57}{42}\\[/tex]
Cross-multiplying we get
[tex]42(x + 10) = 57x\\\\42x + 420 = 57x\\\\420 = 57x - 42x = 15x\\\\15x = 420\\\\x = 420/15\\\\= 28[/tex]
Please help can’t find the answer anywhere
Answer:
3 rd choice
Step-by-step explanation:
If you flip ΔABC over and lay it over ΔXYZ, you'll see how the sides correspond:
AB≅XZ
BC≅ZY
CA≅YX
just a quick addition to "MelRUZ" great reply above. Check the picture below.
You want to buy a $204,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest.
The monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.
Solution
To calculate the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan.
We'll need to first calculate the amount of the loan and then use the following formula to calculate the monthly payment:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
where M is the monthly payment P is the principal (loan amount) r is the monthly interest rate n is the number of paymentsFirst, we'll calculate the down payment:
Down payment = 204,000 * 0.10 = $20,400
Next, we'll calculate the loan amount:
Loan amount = 204,000 - 20,400 = $183,600
Now, we'll need to convert the 30 year loan term into the number of payments (n) and the interest rate into the monthly interest rate (r):
n = 30 years * 12 months/year = 360 payments
r = (Annual interest rate) / 12 months/year
Assuming an annual interest rate of 3.5%, the monthly interest rate would be:
r = 0.035 / 12 = 0.002917
Finally, we can plug the values into the formula to calculate the monthly mortgage payment:
M = 183,600 * 0.002917 * (1 + 0.002917)^360 / ((1 + 0.002917)^360 - 1) = $808.44
Therefore, the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.
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1. Which is a step in proof by mathematical induction?
Substitute n = k + 2 into the formula.
Assume the formula is true for some other value.
Prove the formula is true for n = k.
Assume that the formula is true for the (k + 1) term.
Therefore , the solution of the given problem of linear equation comes out to be it is true for some n=k, where k represents one of the values for which we want to prove the proposition.
What exactly is a linear equation?The equation y=mx+b serves as the basis for a regression model curve. The slope is B, and the y-intercept is m. Even if y or y were separate components, the foregoing sentence is occasionally referred to as a "mathematical formula combining two variables." Bivariate linear equations only have two variables. Application problems involving linear equations have no known solutions. The formula for a simple set of equations is Y=mx+b.
Here,
given :
=> n = k+2
In such situation, you can still use induction to demonstrate this claim for any numbers n2. (If you want to give it a try, it's a nice workout.) In the base situation, n=2 rather than n=1 would exist.
In order to be clear, I'd want to point out that the logical step does not consist of 'proving the assertion for n=k+1 given it is true for n=k.
The inductive step is to demonstrate that the assertion is true for n=k+1 after assuming that it is true for some n=k, where k represents one of the values for which we want to prove the proposition.
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Answer:
Assume the formula is true for some other value.
Step-by-step explanation:
It's the second step
n=k+2 isn't a thing
n=k "This is not part of a proof by mathematical induction."
Assume that the formula is true for the (k + 1) term. "This is not part of a proof by mathematical induction.
the perimeter of a playing field for a certain sport is 308 ft the field is a rectangle and the length is 44ft longer than the width. find the dimensions
The dimensions of the playing field are a length is 99 ft, and a width is 55 ft.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
Given that the length is 44ft longer than the width.
This means L = W + 44 ....(i)
Since the perimeter of a playing field is 308 ft
So 2(L+W) = 308
Substitute the value of the equation (i), and we get
2(W + 44 + W) = 308
2(2W + 44) = 308
4W + 88 = 308
4W = 220
W = 55
Substitute the value of W = 55 in equation (i), and we get
L = 55 + 44 = 99
Thus, the length is 99 ft, and the width is 55 ft.
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The passcode for a smartphone consists of 3 letters followed by 3 digits. How many of these passcodes contain vowels only?
The combination of the letters will be 60.
When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.
Given that the passcode for a smartphone consists of 3 letters followed by 3 digits.
The number of the vowels is:-
Vowels = { A, E, I, O, U} = 5
Number of letters = 3
The arrangements of the vowels will be:-
Number = ⁵C₃
Number = ( 5 x 4 x 3 )
Number = 60
Hence, the vowels can be arranged in 60 ways.
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A 5 foot wide painting should be centered on a 15 foot wide wall. Type the left side of an equation that can be used to determine how many feet (x) should be on each side of the painting.
The total length on each side of the 5 foot painting is given by the equation A = 5 feet each
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total length on each side of the 5 foot painting be A
Now , the equation will be
The length of the painting = 5 feet
The length of the wall = 15 feet
So , when 5 foot wide painting is centered on a 15 foot wide wall , the remaining space will be
2A = length of the wall - length of the painting
Substituting the values in the equation , we get
2A = 15 - 5
2A = 10 feet
Now , total length on each side of the 5 foot painting A = 10 / 2
On simplifying the equation , we get
The total length on each side of the 5 foot painting A = 5 feet
Hence , the equation is A = 5 feet
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Find the inverse of h(x)=2x^3+3
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{h(x)}{y}~~ = ~~2x^3+3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^3 + 3} \\\\\\ x-3=2y^3\implies \cfrac{x-3}{2}=y^3\implies \sqrt[3]{\cfrac{x-3}{2}}=y=f^{-1}(x)[/tex]
Solve the following system of equations:
−7x+3y=−48
3x+5y=−36
The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
−7x + 3y = −48 ...1
3x + 5y = −36 ...2
Multiply equation 1 by 5 and equation 2 by - 3, then we have
−35x + 15y = −240
−9x − 15y = 108
Add both equations, then we have
−44x = −132
x = 132 / 44
x = 3
Then the value of 'y' is given as,
3(3) + 5y = −36
9 + 5y = −36
5y = −45
y = −9
The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)
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Jada has some cube-shaped boxes. She stacks them inside an empty cube-shaped storage container. The container has side lengths of 60 inches (in.). Each box has side lengths of 20 in. After Jada stacks the boxes inside the container, there are still 32,000 in.3 of empty space remaining in the container. How many boxes does Jada stack inside the container? 22 23 27 31
Jada stacked 23 boxes inside the container.
What are cubes?Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, Jada put some cube-shaped boxes having lengths 20 in, in a cubed container has side lengths of 60 inches in.
After, Jada stacks the boxes inside the container, there are still 32,000 in³ of empty space remaining in the container.
We need to find the number of the boxes in the container.
Volume of cube = (side)³
Volume of container = 60³ = 216000 in³
Volume of the container covered by stacking the boxes =
216000 - 32000
= 184000 in³
Volume of each box = 20³
= 8000 in³
Number of boxes in the container = volume of the container covered by stacking / volume of each box
Number of boxes = 184000 / 8000
= 23
Hence, Jada stacked 23 boxes inside the container.
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Write this number in words 627,391
Answer:
six hindered twenty seven thousand three hundred ninety one
Step-by-step explanation:
please follow me
Determine the solution to the inequality.
1/4 | x + 1 | > 4
x≥-1 or x ≥ 17
x≥-17 or x ≥ 15
x≤-9 or x 27
x≤-2 or x ≥ 0
The solution to the inequality is x≥-1 or x ≥ 17. Option A
What are inequalities?Inequalities are simply described as non-equal comparison between numbers, variables, expressions, etc.
They are used to organize numbers based on their sizes in the number line.
From the information given, we have that;
1/4|x + 1| ≥ 4
It is important to note that the symbol. "| |" modulus states that a number cannot be negative irrespective of its direction in the number line
Now, let's solve the inequality
cross multiply
|x + 1| ≥ 4 ×4
Multiply the values
|x + 1| ≥ 16
collect like terms
x ≥ 16 + 1
x ≥ 17
x ≥ - 1
Hence, the values are 17 and -1
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Coen's test scores were 80, 90, 70, and 90. What was his weighted average if the tests were weighted 1, 2, 5, and
respectively?
The weighted average of the Coen's test scores is calculated to be 73.75
How to calculate the weighted averageEach data point is multiplied by its weight before being added together to determine the weighted average. After that, add the weights for each data point. Last but not least, divide the weight*value products by the total weights.
The weighted average is calculated as below
Weighted average = (80 * 1 + 90 * 2 + 70 * 5 + 90 * 8) / (1 + 2 + 5 + 8)
Weighted average = 73.75
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What is the missing step of her solution?
A. Simplify by combining like terms.
B. Simplify by using addition property of equality.
C. Simplify by using the multiplication property of equality.
D. Simplify by using the division property of equality
The missing step of the solution is : Simplify by combining like terms: Option A
What are like terms?You should understand that these are the terms that contain the same variable which has the same power.
The given question,
In step 2, the left side of the equation is 3/2 - 2x
We get 3/2 by adding 1/2 and 1 on the left side of the equation 1/2-2x+1=-13/2
As 1/2 and 1 are constants and all constant terms are like terms.
The second step would be simplify by combining like terms.
Therefore, the missing step of the solution is : Simplify by combining like terms.
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Sarah made 6 dozen cupcakes for a party at work. Some of her co-workers, c, each ate 3 cupcakes. Now, there are 45 cupcakes
left. Which equation represents this situation?
OA. (12 x 6)-(c x 3) = 45
OB. (cx 3)-12 = 45
OC. cx 3=45
OD. (12 x 6)- c = 45
Answer: A.
Step-by-step explanation:
Sarah made 6 dozen cupcakes which is (12 x 6)
Then if her co-workers or c ate 3 cupcakes EACH, it will be (c x 3)
and since they ate them it's subtraction with a left over of 45 cupcakes
Why should you do research beyond an article you read?
A. It may be native advertising
B. The source of the article may not be impartial
C. To learn about the alternative solutions
D. All of the above
Answer:
D. All of the above
Step-by-step explanation:
Answer:
D. All of the above
Step-by-step explanation:
If you were to base your reading on one article and nothing else, your chances of possibly misinterpreting information and sending false narratives are more possible. That is why you should always do as much research as you can.
A gardener wants to determine which of two brands of fertilizer is best for the plants in a garden. Before using one of the fertilizers on the entire garden, the gardener decides to conduct an experiment using 28 individual plants. Which of the two plans for randomly assigning the treatments should the gardener use? Explain.
Plan A: Choose the 14 unhealthiest-looking plants. Apply Brand X fertilizer to all 14 of those plants. Apply Brand Y fertilizer to the remaining 14 plants.
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
Plan A, because the unhealthy plants need the fertilizer the most and should be treated first
Plan B, because the sample of plants is randomly chosen
Plans A and B are equivalent because they both follow experimental design
Plans A and B are both poorly designed because there are not enough plants to test
The plans cannot be evaluated from the information given
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
What is a sample and its types?A sample is only a small portion of the population.
Let's imagine you were interested in determining the average income for all Americans in your population.
Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.
Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.
And the gardener decides to conduct an experiment using 28 individual plants.
Plan A will be a biased sampling and the experiment would not yield
desired results.
Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
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NSWERS
SALGTRIG4 1.3.005.
The equation of the horizontal line passing through (9, 2) is
Check the picture below.
1/4+ 2/5 ⭕️ 1/4+1/5
Compare using< >. =
We have compared the given expression using inequalities
[tex]1/4+2/5 > 1/4+1/5[/tex]
[tex]\frac{16}{20} > \frac{9}{20}[/tex].
What is the comparison of factor?
When evaluating a job, factor comparison is a systematic, scientific process that evaluates candidates according to a number of characteristics rather than grading the job as a whole.
Given:
[tex]1/4+2/5 \\ 1/4+1/5[/tex]
Cross multplying the fractions:
[tex]\frac{1}{4}+\frac{2}{5}[/tex] = [tex]\frac{4}{20}+ \frac{8}{20}[/tex]
= [tex]\frac{12}{20}[/tex]
=[tex]\frac{4}{5}[/tex]
Similarly ,
[tex]\frac{1}{4}+ \frac{1}{5}[/tex]=[tex]\frac{5}{20} +\frac{4}{20}[/tex]
=[tex]\frac{9}{20}[/tex]
Compare 4/5 and 9/20.
Find the LCD:
The multiples of 5 are 5, 10, 15, 20, 25, etc. The multiples of20 are 20, 40, 60, 80, etc. The lowest common multiple is 20 so we use that as the lowest common denominator.
Convert each fraction to its equivalent fraction using the LCD.
For 4/5, multiply numerator and denominator by 4 to have LCD = 20 in the denominator.
=[tex]\frac{4}{5} *\frac{4}{4}[/tex]=[tex]\frac{16}{20}[/tex]
For 9/20, 20 is the denominator.
Compare the fractions. Because there are like denominators you can compare the numerators.16 is larger and 9 is smaller so,
[tex]\frac{16}{20} > \frac{9}{20}[/tex]
so,
[tex]1/4+2/5 > 1/4+1/5[/tex]
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Identify the parent function that can be used to graph the function(x) = -2x + 2
a. f(x)=x²
f(x)=x
b. f(x)=[x]
1
(x) ==
Please select the best answer from the choices provided
OA
B
C.
d.
OD
א
f(x)=x is the parent function of the given function f(x) = -2x + 2
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=-2x+2
We have to find the parent function of the given function.
A parent function is the simplest function of a family of functions that preserves the definition of the entire family.
f(x)=x is the parent function because from this function we can make transformations that allow us to obtain the function f(x) = -2x + 2
Hence, f(x)=x is the parent function of the given function f(x) = -2x + 2
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Question 4 of 10
Which of the following graphs could represent a cubic function?
++++
B.
A.
OA. Graph A
OB. Graph B
OC. Graph C
OD. Graph D
D.
The graph of the cubic function [tex]f(x)=x^3[/tex] is plotted.
The correct answer is Option C.
Given data:
The graph of a cubic function is a type of polynomial graph that has the form [tex]f(x) = ax^3 + bx^2 + cx + d[/tex] , where 'a', 'b', 'c', and 'd' are constants.
The graph of the cubic function [tex]f(x) = x^3[/tex] is a smooth curve that passes through the origin (0,0) and extends into the four quadrants of the Cartesian coordinate system.
Y-Intercept:
The cubic function passes through the origin (0,0), so it has a y-intercept of (0,0).
X-Intercept:
The x-intercept occurs when f(x) = 0.
On solving for x:
[tex]x^3 = 0[/tex]
x = 0
So, the cubic function has an x-intercept of (0,0).
Hence, the cubic function is [tex]f(x)=x^3[/tex] and is plotted below.
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need help getting my answer
There are a total of 2285 people in the given town.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, fourteen percent of the town's population is above the age of 65.
Since there are 320 residents who are above the age of 65,
Thus,
14% of the population = 320
So,
1 % of the population = 320 /14
Thus,
Total population = 320/14 * 100
Total population of the town = 2285.71
Therefore, there are a total of 2285 people in the given town.
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The net for a cylindrical candy container is shown.
net of a cylinder with diameter of both circles labeled 1.6 inches and a rectangle with a height labeled 0.7 inches
The container was covered in plastic wrap during manufacturing. How many square inches of plastic wrap were used to wrap the container? Write the answer in terms of π.
1.84π square inches
2.4π square inches
5.68π square inches
6.24π square inches
The wrap has an area of 1.12π square inches.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The net of a cylinder with a diameter of both circles labeled 1.6 inches.
So, The complete circle or the circumference of the circle will be the length of the wrap which is,
= 2π×0.8.
= 1.6π and the height of the wrap is 0.7 inches.
Therefore, the area of the wrap is 1.6π×0.7 square inches.
= 1.12π square inches.
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Answer: The real answer is 2.4π square inches (B)
Step-by-step explanation:
(Get ready for a long explanation)
So, we are trying to find the Surface Area of the cylinder.
We need to use the formula (SA = 2πr^2 + 2πrh)
Looks like a very long formula, but let do it in parts.
So the first part is just finding the area of the circle and multiplying by 2 because there are two bases. The area formula for circles is (πr^2)
But this time put a 2 in there. (2πr^2)
Okay lets get started. The diameter is 1.6. The radius is half the diameter, so divide 1.6 by 2 and you will get 0.8 which is the radius.
Now times the radius by itself (0.8 * 0.8 = 0.64) Now times that by 2 (0.64 * 2 = 1.28) The answer should be in terms of pi so just put the pi symbol next to 1.28 (1.28π)
On to the next part, (2πrh) you are basically taking the circumference of either circle base, and multiplying that by the height, which is (0.7)
The formula for Circumference is (2πr)
We already have the diameter so we don't need times the radius by 2.
So take the diameter of the circle base (1.6) and multiply that by the height, which is (0.7)
(1.6 * 0.7 = 1.12π)
Now for the last part, we need to add the two values together to find the surface area.
The first value we found is (1.28π ) and the second is (1.12π)
Now add (1.28π + 1.12π = 2.4π)
Answer: 2.4π square inches
Sorry for the really long explanation. I took the same test and I got it right so here is proof that it is correct. Have a great day y'all.