The equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
What is slope-intercept form?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point
Given that, a line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7, we need to find the equation of the line,
The line is
3x-2y = 7
Converting into slope-intercept form,
3x-2y = 7
2y = 3x - 7
y = 3x/2 - 7/2
We know that, the slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line = -2/3
Therefore, the equation of the asked line is, y = -2x/3 + c....(I)
Put x = 6 and y = 2 in equation to find c,
2 = -4 + c
c = 8
Therefore, put c = 8 in equation (i)
y = -2x/3 + 8
Hence, the equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
Learn more about slope intercept form, click;
https://brainly.com/question/29146348
#SPJ1
In a right triangle, sin (4x-5)^\circ(4x−5) ∘ = cos (3x+4)^\circ(3x+4) ∘ . Find the smaller of the triangle’s two acute angles.
The smaller of the triangle’s two acute angles is 65 degrees
What is acute Angle?Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.
Given:
Angles in a triangle
[tex]sin (4x-5)^\circ= cos (3x+4)^\cir[/tex]
Since, sin [tex]\theta[/tex]= cos(90 - [tex]\theta[/tex]),
cos(90 - (4x - 5 )) = cos(3x +4)
cos(85 - 4x) = cos (3x+4)
Cancel out the cosine functions to have:
85- 4x = 3x+ 4
81 = 7x
x= 11.57
Hence, the smaller of two acute angles is 11.57 degrees
Learn more on acute angles here;
brainly.com/question/6979153
#SPJ1
Answer:
27
Step-by-step explanation:
A map used a scale of 1/2 cm = 75 kilometers. The actual distances between various cities are given below. Find the distance Between the cities on the map.
The distance between the cities on the map is given by the equations
a) The distance of 50km = ( 1/3 ) cm
b) The distance of 280km = ( 1 13/15 ) cm
c) The distance of 142 1/2 km = ( 19/20 ) cm
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 distance on the map be represented as A
Now , the equation will be
The scale on the map is given by 1/2 cm = 75 km
So , 1 km = ( 1/2 ) / 75 cm
1 km = ( 1/150 ) cm
a)
when the distance = 50 km
The distance on the map = 50 x ( 1/150 ) cm
The distance on the map = ( 1/3 ) cm
b)
when the distance = 280 km
The distance on the map = 280 x ( 1/150 ) cm
The distance on the map = ( 1 13/15 ) cm
c)
when the distance = 142 1/2 km
The distance on the map = 142 1/2 x ( 1/150 ) cm
The distance on the map = ( 19/20 ) cm
Hence , the equation is solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
completing the square is a strategy that is sometimes required to complete a quadratic equation. show your knowledge of this strategy by researching the topic completing the square. include the steps and provide an example as to how it can be used.
Completing the square is a strategy that is sometimes required to complete a quadratic equation, the steps and provide an example as to how it can be used are:
creating vertex form from a quadratic expression.determining the quadratic expression's minimum and maximum values.a quadratic function graph.quadratic equation solution.the quadratic formula's development.Writing a quadratic expression so that it contains the perfect square is known as "completing the square" in algebra. In plain English, the act of "completing the square" can be described as taking the quadratic equation "ax2 + bx + c = 0" and changing it to "a(x + p)2 + q = 0."
Example: expression is x2 - 7x.
A = 1; B = -7 when the above expression is compared to ax2 + bx + c.
The term that needs to be added, according to the formula, to convert the given expression into a perfect square trinomial is (b/2a)2 = (-7/2(1))2 = 49/4.
The term that needs to be added to make the given expression a perfect square trinomial, then, from both approaches, is 49/4.
Learn more about Completing Square:
https://brainly.com/question/24860429
#SPJ4
Isabella bought a T-shirt for $85, after sales tax is added is added the final cost was $97.75. what was the percent of sales tax?
97.75 - 85 = 12.75
This means the amount of tax was $12.75.
If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:
12.75 ÷ 85 = 0.15 = 15%
Sales tax is 15%.
The key in the calculation is to divide by the original price of the shirt.
HELPP!!!!
A 3-foot girl casts a shadow 7 feet long. She is standing next to a tree that casts a
28-foot shadow. How tall is the tree?
Answer:
12 feet
Step-by-step explanation:
This example can be solved using a proportion. The ratio between the height of the girl and her shadow is equal to the ratio of the height of the tree and its shadow.
Ratio of girl height to shadow length: [tex]\frac{3}{7}[/tex]
Ratio of the tree height and its shadow: [tex]\frac{x}{28}[/tex]
The proportion can be written: [tex]\frac{3}{7}=\frac{x}{28}[/tex]
The relationship between the denominators happens to be obvious, so this can be solved easily. 7 times 4 is 28, and since the ratios are equal, 3 times 4 must be X.
[tex]3\times4=12\\x=12[/tex]
The tree is 12 feet tall!
helppppppppppppppppp
Answer:
3 * 8 = 42, divide that by 38, then put it inside the cool looking v sign, and that will give you 89 weed leaves left as trim. Take the 21 add that with the divisor of the previous problem, then you get 25 PLUS the breadsticks, and you get 96. Last step is 96 - 29 = how much bud is left to smoke!
Hope this helped!
Find the product and conjugate of (-12+4i).
Answer:
The product of (-12 + 4i) and its conjugate is (-12 - 4i).
The conjugate of (-12 + 4i) is (-12 - 4i).
∣
5
�
∣
=
∣5x∣=
15
15
Answer:
x = -3 & 3
Step-by-step explanation:
∣5xI = 15
divide both sides by 5:
(∣5xI)/5 = 15/5
∣xI = 3
I-3I = 3 AND I3I = 3
so:
x = -3 & 3
What is the standard deviation of 10,18,21,22,24,25,26,28,29,30
Kayla held a pole in the swimming pool.the bottom of the pole was at a depth of 3feet. How should Kayla mark the level of the bottom of the pole on a number line? Explain how you determine this
Answer:
Step-by-step explanation
How to evaluate 1000(1.02)^30 + 1000(1.05)(1.02)^29 + 1000(1.05)^2(1.02)^28 + ... ... + 1000(1.05)^28(1.02)^2 + 1000(1.05)^29(1.02) using a geometric progression series?
The sum of the given geometric series is given by 79545.8567
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³,.....
Given here: The expression 1000(1.02)³⁰+ 1000(1.05)(1.02)²⁹+ 1000(1.05)²(1.02)²⁸ + ......
Clearly we can observe that the given sum is a geometric progression with common ratio =1.05/1.02
The given sum is a sum of first 29 terms of the G.P
Thus Sₙ = a(rⁿ - 1) / (r - 1)
S₂₉=1000×1.02³⁰(1.029²⁹-1) /1.0294-1
=1811.36(2.291106-1)/0.0294
=1811.36(1.2911)/0.0294
=79545.8567
Hence, The sum of the given geometric series is given by 79545.8567
Learn more about a geometric progression here:
https://brainly.com/question/4853032
#SPJ1
I need a math answer
The quotient after the long division of the expression is 2x² +8x -3.
What is a long division method?Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too.
The long division method will be done as below,
x - 3 ) 2x³ + 2x² -27x + 2( 2x² +8x -3
-2x³ +6x²
________________
8x² - 27x + 2
-8x² +24x
_________________
-3x + 2
3x - 9
______________________
-7
Hence, the quotient after the long division of the expression is 2x² +8x -3 and the remainder is -7.
To know more about the long division method follow
https://brainly.com/question/25289437
#SPJ1
please help asap
• it would mean sm and make my day
Answer:
x < -2 or x > 5
Step-by-step explanation:
We want to write the compound inequality.
There is an open circle at -2 and a line going to the left.
x < -2
There is an open circle at 5 and a line going to the right.
x > 5
We use an or since they are not connected.
x < -2 or x > 5
Random variables x; and Xz have the following distribution: . x2 f(x1,x2) 0.00 10.00 20.00
x1 5.00 0.20 0.14 0.06
10.00 0.11 0.07 0.12
20.00 0.08 0.02 0.20
Find P(X; < 20,X2 > 10) (write up to second decimal place)
After using the distribution, the value of P(X(1) < 20, X(2) > 10) is 0.18.
The distribution of random variables x(1) and X(2) have given below:
We have to determine P(X(1) < 20, X(2) > 10).
We have to determine the joint probability.
From the table we can see that the value of x(1) is less than 20 is (5, 10) and x(2) greater than the (10, 20).
P(X(1) < 20, X(2) > 10) = P(5, 10) + P(10, 20)
From the table
P(X(1) < 20, X(2) > 10) = 0.06 + 0.12
P(X(1) < 20, X(2) > 10) = 0.18
To learn more about random variables link is here
brainly.com/question/17238189
#SPJ4
The complete question is:
Random variables x(1) and X(2) have the following distribution:
Find P(X(1) < 20, X(2) > 10) (write up to second decimal place)
The manager of Jerry’s Barbershop recently asked 15 customers to punch in a time card when first arrive at the shop and to punch out right after they paid for their haircut, and used the data on the cards to measure how long (in minutes ) it took Jerry and his barbers to cut hair. He also recorded the amount of money spent by each of the 15 customers as well as the customers stage of life (Child, Teen, or Adult).
Identify the population in the above scenario. (2 pts.)
Identify the variables and their units (if any). (6 pts.)
Variable 1: Unit:
Variable 2: Unit:
Variable 3: Unit:
Population: The customers of Jerry's Barbershop. Time is taken to cut hair: Minutes. Amount of money spent: Currency (e.g. dollars).
Stage of life: Categorical (Child, Teen, or Adult)
What is a population?A population is a discrete group of people, animals, or things that can be recognized by at least one common trait for the purposes of data collection and analysis in statistics and other fields of mathematics.
As per the given information, the required solution would be as:
Population: The customers of Jerry's Barbershop.
Variables and their units are, as follows:
Time taken to cut hair: Minutes
Amount of money spent: Currency (e.g. dollars)
Stage of life: Categorical (Child, Teen, or Adult)
Learn about the population here:
https://brainly.com/question/27991860
#SPJ1
1. [1/4 Points] DETAILS PREVIOUS ANSWERS For each absolute value inequality, write an equivalent compound inequality. (a) (x +31 < 1 is equivalent to ____ < x+3< ______
b) |x-6|≥ 2 is equivalent to x-6≤ ______
or x-6≥
The inequalities are :
x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27
|x - 6| ≥ 2 ⇒x- 6 ≥ 2 and 6 - x ≤ 2
What are inequalities ?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.
The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.
Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The inequalities are :
x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27
|x - 6| ≥ 2 ⇒x- 6 ≥ 2 and 6 - x ≤ 2
To learn more about Inequality refer to :
https://brainly.com/question/13589585
#SPJ1
the procedure below searches for the value in . it returns if is found and returns otherwise. which of the following are true statements about the procedure? i. it implements a binary search. ii. it implements a linear search. iii. it only works as intended when is sorted.
True statements about the procedure implement a linear search, So the correct option is, ii only.
Linear search, also known as sequential search, is a simple search algorithm that iterates through an array or a list of elements one by one, starting from the first element, until the desired element is found.
The basic steps of linear search are:
Start at the first element of the array/listCompare the element with the search keyIf the element is not equal to the search key, move to the next elementRepeat steps 2 and 3 until the desired element is found or the end of the array/list is reached.The time complexity of the linear search is O(n), where n is the number of elements in the array/list.
This means that the algorithm takes n steps in the worst-case scenario to find the desired element in an array/list of n elements. Linear search is generally less efficient than other search algorithms like binary search for large data sets.
Linear search can be used on unsorted arrays/lists as well as on sorted arrays/lists. It is a simple and easy-to-implement algorithm and is suitable for small data sets or when the data is not sorted and the data changes frequently.
In addition, a linear search algorithm can also be used to find the index of the element in the array/list if the element is found.
To know more about time complexity:
https://brainly.com/question/30352246
#SPJ4
A right circular cone has a base radius of $6,$ and a lateral surface area of $12 \sqrt{34} \cdot \pi.$ find the volume of the cone.
The volume of the cone is 36π * 2√(34).
The formula for the lateral surface area of a right circular cone is:
A = π * r * l
where A is the lateral surface area, π is the constant pi, r is the radius of the base, and l is the slant height of the cone.
Given that the lateral surface area of the cone is 12√(34) * π, we can write:
[tex]12\sqrt{(34)} * \Pi = \Pi * r * l[/tex]
Dividing both sides by π and r, we can find the slant height:
l = 12√(34) / r
= 12√(34) / 6
= 2√(34) units
The volume of a right circular cone can be found using the formula:
V = (1/3) * π * r^2 * h
where V is the volume,
π is the constant pi,
r is the radius of the base, and
h is the height of the cone.
Since the cone is a right circular cone, the slant height is also the height of the cone,
So we can substitute l for h:
V = (1/3) * π * r^2 * l
= (1/3) * π * 6^2 * 2√(34)
= 36π * 2√(34)
For more questions on Volume of cone
https://brainly.com/question/12004994
#SPJ4
Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows. 42 89 38 27 60 67 73 9 27 38 59 50 87 54 48 20 33 85 52 90 50 50 52 35 46 35 35 46 37 46 Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Percent of Wetlands Lost COVOU AWN NONE 377 3555788 22666 000 26 99 07 >XXXXX 5 77 How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) These data are strongly skewed left. The percentages are concentrated from 20% to 60%. These data are fairly symmetric, perhaps slightly skewed right. There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. There are no gaps in the data. There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. The percentages are concentrated from 60% to 90%.Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows. 42 89 38 27 60 67 73 9 27 38 59 50 87 54 48 20 33 85 52 90 50 50 52 35 46 35 35 46 37 46 Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Percent of Wetlands Lost COVOU AWN NONE 377 3555788 22666 000 26 99 07 >XXXXX 5 77 How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) These data are strongly skewed left. The percentages are concentrated from 20% to 60%. These data are fairly symmetric, perhaps slightly skewed right. There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. There are no gaps in the data. There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. The percentages are concentrated from 60% to 90%.
The stem-and-leaf plot of the given data is attached.
A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:
The percentages are concentrated from 20% to 60% as these concentrations have more than one values. These data are fairly symmetric, perhaps slightly skewed right, considering the midpoint, 4.5, there are fairly equal number of values on each side, perhaps a little more on the right side.There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands, as there are no values corresponding to 1, or no values between 10 and 19 percent.Learn more about Stem-and-leaf plot:
https://brainly.com/question/26678606
#SPJ4
(x^2 + 7x) / (9 - x^2)
The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).
What is the simplified form of the expression?Given the expression in the question;
(x² + 7x) / (9 - x²)
To simplify, first factor out x form x² + 7x
(x × x + 7 × x) / (9 - x²)
Factor out x
x (x + 7) / (9 - x²)
Next, simplify the denominator
x (x + 7) / (9 - x²)
Rewrite 9 as 3²
x (x + 7) / (3² - x²)
Now, since both terms are perfect squares
a² - b² = (a + b)(a - b)
Hence,
x(x + 7) / ( 3 + x )( 3 - x )
Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).
Learn more about perfect squares here: https://brainly.com/question/29056294
#SPJ1
solve 9.12divided by 3.8
Not sure about this answer
Answer:
B
Step-by-step explanation:
All that they were asking for is what is given to you, so B would be right
HELP ASAP
The dimensions of a triangle are shown below.
What is the area of the triangle in square meters?
Answer:
Step-by-step explanation:
A = B⋅H/2
Base = 10 m
Height = 12m
10⋅12= 120
120/2=60²
1. Explain IKEA's brand image. The video mentions how the brand at one point had French influence but then decision. 2. Describe IKEA's sustainability initiatives. What impact has Gen Z had on holding retailers accountable to act 3. Some businesses use sustainability as a marketing tactic as opposed to a mission true to its core. Do you be
1. KEA's brand image is centered around affordability, simplicity, and modern design.
2. IKEA has a strong commitment to sustainability, with initiatives that include reducing waste, using sustainable materials in its products, and investing in renewable energy.
3. Sustainability is an increasingly important issue for consumers, and many businesses use it as a marketing tactic to appeal to environmentally-conscious consumers. l IKEA is one such company, and its commitment to sustainability is reflected in its long-term goals and initiatives, as well as its focus on sustainable product design and operations.
How to explain the brand imageThe company's "Democratic Design" philosophy reflects this, emphasizing the importance of quality, sustainability, and affordability in its products.
The company has set ambitious goals to become more environmentally friendly, such as producing as much renewable energy as it consumes by 2020 and becoming climate positive (i.e., reducing its net greenhouse gas emissions) by 2030.
In recent years, Gen Z has been a major driving force behind holding retailers accountable for their environmental impact, and IKEA has responded to this by continuing to focus on sustainability and transparency in its operations.
Learn more about brand on:
https://brainly.com/question/24456504
#SPJ1
what is the answer to 9x3x5x32x9x3x5
Answer:
583,200
Step-by-step explanation:
Hope it helps! =D
Answer:
583200
Step-by-step explanation:
Let V denote the set of all differentiable real-valued functions defined on the real line. Prove that V is a vector space with the operations of addition and scalar multiplication.
V is a vector space with the operations of addition and scalar multiplication.
Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.
Let V denote the set of all differentiable real-valued functions defined on the real line.
You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.
On a different note, you cannot say that
f+g=f(t)+g(t)
but you can say that (f+g)(t)=f(t)+g(t)
So V is a vector space with the operations of addition and scalar multiplication.
Know more about scalar multiplication
https://brainly.com/question/26649852
#SPJ4
Solve the equation filling in the steps (do not use any spaces): 2(x-3) + 21 = -3
Step 1: Distribute to get
Step 2: Combine like terms to get
Step 3:
Step 4:
Word Bank:
2x=-18
-1x=-24 2x=-21 x=-21/2 2x+15=-3
2x-3+21=-3 x-24 x=-9
-1x+21=-3 2x-6+21=-3 2x+18=-3
Blank 1:
Blank 2:
Blank 3:
Blank 4:
The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.
What is value?Value is the worth of something in terms of the benefits, importance, or usefulness it provides. It is the relative importance or worth of something, as compared to other things. It is what people deem to be important, and it can vary depending on the individual or context. Value is not equivalent to price, which is the monetary cost of something. Value is an intangible concept and can represent the overall benefit or worth of an item, service, or experience. It can also refer to an individual’s moral or ethical standards. Value is subjective, meaning that it is based on a person’s individual beliefs and values. It is also malleable and can change over time. People can assign value to different objects, experiences, or relationships, based on what they find meaningful and important.
Distribute to get: 2x-6+21=-3
Combine like terms to get: 2x+15=-3
Solve for x: x=-21/2
Explain the problem: The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.
To learn more about value
https://brainly.com/question/843074
#SPJ1
Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
The distance Derick walked from 12 pm to 4.45 pm is 16.625 miles
How to find the distance'The distance is solved form the concept of speed which is defined as the ratio of distance with time
The formula for speed is
= distance covered / time taken
The time taken in the journey is
= from 12 pm to 4:45 pm = 4 hours 45 minutes = 4.75 hours
distance covered
= speed * time consumed
= 3.5 mph * 4.75 hours
= 16.625 miles
Learn more on distance at:
https://brainly.com/question/2854969
#SPJ1
Two investments totaling $56,500 produce an annual income of $2480. One investment yields 8 % per year, while the other yields 2 % per year. How much is
invested at each rate?
The first investment is $22500 and second investment is $34000.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Two investments totaling $56,500 produce an annual income of $2480.
let the two investments be x and y.
So, x + y = 56500.........(1)
and, One investment yields 8 % per year, while the other yields 2 % per year then
0.08x+0.02y=2480.......(2)
Solving equation (1) and (2) we get
0.08(56500-y)+0.02y=2480
4520-0.08y+0.02*y=2480
-0.06y=-2040
y= 34000
and, x=56500-y =22500
Hence, the investments were $22500and $34000.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ1
U.S. companies lose $63.2 billion per year from workers with insomnia. Workers lose an average of 7.8 days of productivity per year due to lack of sleep (Wall Street Journal, January 23, 2013). The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers.
6 5 10 5 6 9 9 5 9 5 8 7 8 6 9 8 9 6 10 8
a. What is the mean number of hours of sleep for this sample?
b. What is the variance? Standard deviation?
The mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.
Standard deviation, denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called the root-mean-square deviation. 0 is the smallest value of standard deviation since it cannot be negative. When the elements in a series are more isolated from the mean, then the standard deviation is also large
Mean [tex]& =\frac{\text { Sum of all data }}{\text { Total number data }} \\[/tex]
[tex]& =\frac{6+5+10+5+6+9+9+5+9+5+8+7+8+6+9+8+9+6+10+8}{20} \\& =\frac{148}{20} \\\end{aligned}$$[/tex]
= 7.4
Thus, the mean of the number of hours of sleep for the above sample is 7.4.
To find: the variance and standard deviation for the above sample.
Standard Deviation=[tex]\sqrt{\frac{\sum f_i\left(x_i-\mu\right)^2}{n-1}} \\[/tex]
[tex]& \sigma \quad=\sqrt{\left\{\begin{array}{l}(6-7.4)^2+(5-7.4)^2+(10-7.4)^2+(5-7.4)^2+(6-7.4)^2 \\+(9-7.4)^2+(9-7.4)^2+(5-7.4)^2+(9-7.4)^2+(5-7.4)^2 \\+(8-7.4)^2+(7-7.4)^2+(8-7.4)^2+(6-7.4)^2+(9-7.4)^2 \\+(8-7.4)^2+(9-7.4)^2+(6-7.4)^2+(10-7.4)^2+(8-7.4)^2\end{array}\right\}} \[/tex]
[tex]& \sigma=\sqrt{\frac{\left\{4(6-7.4)^2+4(5-7.4)^2+2(10-7.4)^2+5(9-7.4)^2+4(8-7.4)^2+(7-7.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{\left\{4(-1.4)^2+4(-2.4)^2+2(2.6)^2+5(1.6)^2+4(0.6)^2+(-0.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{58.8}{19}} \\& \sigma=\sqrt{3.0947} \\[/tex]
[tex]& \sigma \quad=1.759186 \\[/tex]
Variance = 3.0947
Therefore, the mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.
For more such questions on variance and Standard deviation
https://brainly.com/question/13074796
#SPJ4
