There are zero number of solutions the system of equations have.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=5/2x+2 ------(I) and 2y=5x+8 ------(II)
Substitute equation (I) in (II), we get
2(5/2x+2)=5x+8
5x+4=5x+8
5x-5x=8-4
Therefore, there are zero number of solutions the system of equations have.
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"Your question is incomplete, probably the complete question/missing part is:"
How many solutions does the following system of equations have? y=5/2x+2 and 2y=5x+8
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.
∣
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
(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 ).
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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.
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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)
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someone help me asap
The function that has the average rate of change of -4 over the interval [-2, 2] is (D) p(x).
What is the Average Rate of Change?
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.The formula for calculating the average rate of change can be given as [tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]Here, average rate of change of the function must be calculated over the interval [-2, 2].
(A) The average rate of change of the function m(x):
Here, a = -2, m(a) = -12, and b = 2, m(b) = 4
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{4-(-12)}{2-(-2)} \\\implies A(x)=4[/tex]
(B) The average rate of change of the function q(x):
Here, a = -2, q(a) = -4, and b = 2, q(b) = -12
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{q(b)-q(a)}{b-a}\\\implies A(x)=\frac{-12-(-4)}{2-(-2)} \\\implies A(x)=-2[/tex]
(C) The average rate of change of the function n(x):
Here, a = -2, n(a) = -6, and b = 2, n(b) = 6
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{n(b)-n(a)}{b-a}\\\implies A(x)=\frac{6-(-6)}{2-(-2)} \\\implies A(x)=3[/tex]
(D) The average rate of change of the function p(x):
Here, a = -2, p(a) = 12, and b = 2, p(b) = -4
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{-4-12}{2-(-2)} \\\implies A(x)=-4[/tex]
Therefore, the function that has the average rate of change of -4 over the interval [-2, 2] is (D) p(x).
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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
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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.
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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
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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)
4. Mark wants to find the area of a circle with a diameter of 8 cm. Which expressions can he use to find the area of
the circle in square centimeters? Choose all the correct answers.
A 2•4• (pi)
B 8• (pi)
C 4•4•(pi)
D 8²• (pi)
E 4² •(pi)
Answer:
B. the area is d x pi its the solution
what is the answer to 9x3x5x32x9x3x5
Answer:
583,200
Step-by-step explanation:
Hope it helps! =D
Answer:
583200
Step-by-step explanation:
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
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Answer:
27
Step-by-step explanation:
What is the domain of the table below?
Input|Output
-3
6
12
585
The domain of the table below is {-3, 6, 12}
How to determine the domain of the tableFrom the question, we have the following parameters that can be used in our computation:
The table of values
The domain of a function is the set of the input values
This means that the domain is
Domain = {-3, 6, 12}
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What is the standard deviation of 10,18,21,22,24,25,26,28,29,30
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:
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A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $38. The total cost to rent 2 chairs and 12 tables is $107. What is the cost to rent each chair and each table?
Answer:
Chair: $2.50
Table: $8.50
Step-by-step explanation:
First, let's create equations with the information given to us:
x= cost of a chair
y= cost of a table
5x + 3y = $38
2x + 12y = $107
The next step is to solve for x in terms of y. To do this, I will be using the equation 5x + 3y = $38.
5x + 3y = $38 [Subtract 3y from both sides]
5x = -3y + 38 [Divide by 5]
x =(-3/5)y + 38/5
Now that we have found the value of x in terms of y, we will plug it into the equation 2x + 12y = $107.
2x + 12y = $107
2 ((-3/5)y + 38/5) + 12y = 107 [Distribute]
(-6/5)y + 76/5 + 12y = 107 [Combine like terms]
(54/5)y + 76/5 = 107 [Subtract 76/5 from both sides]
(54/5)y = 459/5 [Multiply both sides by 5/54]
y = 17/2 or 8.5
So, the cost of a table is $8.50.
Now that we have found the price of the table, let's plug it into the equation 5x + 3y = $38 to find the price of the chair.
5x + 3y = $38
5x + 3 ( 17/2 ) = 38 [Distribute]
5x + 51/2 = 38 [Subtract 51/2 from both sides]
5x = 25/2 [Divide both sides by 5]
x = 5/2 or 2.5
So, the cost of a chair is $2.50.
So, the chair costs $2.50 while the table costs $8.50.
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Jon walked 98 feet in 11.5 seconds. What is his speed in miles per hour? (1 mi = 5280 ft)
Answer:To convert this to miles per hour, we need to first convert the distance to miles. We know that 1 mi = 5280 ft, so 98 ft = 98 / 5280 mi = 0.0184 mi.
Now we can use the formula speed = distance / time again, but this time using miles and hours as the units. So, speed = 0.0184 mi / (11.5 s / 3600 s/hr) = 0.0184 mi / 0.003194 hr = 5.8 mi/hr.
Step-by-step explanation:
Answer:
5.81 mph
Step-by-step explanation:
We want to first convert the number of feet to miles and then divide by the number of hours. Since we know that 5280 feet is one mile, we essentially want to find how many "groups" of 5280 are in some distance and that's the number of miles. We can do this by dividing.
[tex]\frac{98}{5280}\approx0.018561[/tex]
Now we want to find how many hours 11.5 seconds is. It's basically the same process as we divide this by the number of seconds in an hour 3600.
11.5/3600 = 0.00319
Now divide the distance over the time and this gives us approximately: 5.81 mph
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
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.
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solve 9.12divided by 3.8
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
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Given the table of values below, find the average rate of change of the function f(x) on the interval [4,9].
x 3 4 5 6 7 8 9 10
f(x) 77 97 131 155 160 177 212 245
Enter your answer as a reduced improper fraction, if necessary.
The average rate of change of the function f(x) on the interval [4,9] is equal to 23.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [4, 9]:
a = 4; f(a) = 97
b = 9; f(b) = 212
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (212 - 97)/(9 - 4)
Average rate of change = 115/5
Average rate of change = 23.
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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!
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.
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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
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
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Which point represents the origin? (2 points)
Part B: Starting from the origin, explain how to plot the following three points accurately:
(2, −2)
(−2, 1.5)
(−1, fraction 2 over 4 )
Answer:
The origin is the point (0,0)
(2,-2) Start at the origin and move 2 unit right along the x axis, from there move down 2 units. Place a point at that location.
(-2, 1.5) Start at the origin and move 2 units left along the x axis, from there move up 1.5 space and place a point.
(-1, 2/4) Start at the origin and move left 1 unit along the x axis, from there move up 1/2 a unit and place a point. 2/4 is the same as 1/2
Step-by-step explanation:
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.
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Yolanda invests $6,000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% a year. If she receives $580 each year., how much is invested in stocks?
The amount of money that Yolanda invested in the stock is x = $1600
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we will only formulate two equations:
(a) The sum of the amount to invest in stocks and bonds will be $6000:
x + y = 6000
(b) The percentage of stocks 6% and bonds 11% for a profit of $580.
0.06x + 0.11y = 580
x + y = 6000 ----⇒ x = 6000 - y
0.06(6000 - y) + 0.11y = 580
360 - 0.06y + 0.11y = 580
0.05y = 220
y = $4400
x = 6000 - 4400
x = $1600
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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).
