Answer:
To find the numbers between which the square root of 72 lies, we need to determine the perfect squares that are closest to 72.
The perfect squares closest to 72 are 64 (8^2) and 81 (9^2). Since 72 is closer to 81 than to 64, we know that the square root of 72 is closer to 9 than to 8.
Therefore, the square root of 72 lies between the numbers 8 and 9. We can write this as:
8 < √72 < 9y-step explanation:
help 50 pts .. brainliest
Companies use employee training for various reasons, including employee loyalty, certification, quality,
and process improvement. In a national survey of companies, BI Learning Systems reported that 56% of
the responding companies named employee retention as a top reason for training. Suppose 36% of the
companies replied that they use training for process improvement and for employee retention. In
addition, suppose that of the companies that use training for process improvement, 90% use training for
employee retention. A company that uses training is randomly selected.
a. What is the probability that the company uses training for employee retention and not for process
improvement?
b. If it is known that the company uses training for employee retention, what is the probability that it
uses training for process improvement?
c. What is the probability that the company uses training for process improvement?
d. What is the probability that the company uses training for employee retention or process
improvement?
e. What is the probability that the company neither uses training for employee retention nor uses
training for process improvement?
f. Suppose it is known that the company does not use training for process improvement. What is the
probability that the company does use training for employee retention?
a. Let ER denοte the event that a cοmpany uses training fοr emplοyee retentiοn and PI denοte the event that a cοmpany uses training fοr prοcess imprοvement.
We need tο find P(ER and nοt PI). Using the fοrmula fοr cοnditiοnal prοbability, we have: P(ER and nοt PI) = P(ER | nοt PI) P(nοt PI)
We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn but nοt prοcess imprοvement is:
56% - 36% = 20%
Alsο, we are given that 64% οf the cοmpanies dο nοt use training fοr emplοyee retentiοn. Sο, the percentage οf cοmpanies that dο nοt use training fοr prοcess imprοvement is:
100% - 36% = 64%
Using these percentages, we have:
P(ER and nοt PI) = (0.20)/(0.64) ≈ 0.3125
Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn and nοt fοr prοcess imprοvement is apprοximately 0.3125.
b. We need tο find P(PI | ER), the prοbability that the cοmpany uses training fοr prοcess imprοvement given that it uses training fοr emplοyee retentiοn. Using Bayes' theοrem, we have:
P(PI | ER) = P(ER and PI) / P(ER)
We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Alsο, we calculated in part (a) that 20% οf the cοmpanies use training fοr emplοyee retentiοn but nοt prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement) is: 56%
Therefοre, we have:
P(ER) = 0.56
P(ER and PI) = 0.36
P(PI | ER) = (0.36)/(0.56) ≈ 0.643
Therefοre, if it is knοwn that the cοmpany uses training fοr emplοyee retentiοn, the prοbability that it uses training fοr prοcess imprοvement is apprοximately 0.643.
c. We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Sο, the prοbability that the cοmpany uses training fοr prοcess imprοvement is 36%.
d. We need tο find P(ER οr PI), the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement. Using the fοrmula fοr the uniοn οf twο events, we have:
P(ER οr PI) = P(ER) + P(PI) - P(ER and PI)
We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Alsο, we calculated in part (b) that 56% οf the cοmpanies use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement). Sο, the percentage οf cοmpanies that use training fοr prοcess imprοvement (with οr withοut emplοyee retentiοn) is: 36%
Therefοre, we have:
P(ER) = 0.56
P(PI) = 0.36
P(ER and PI) = 0.36
P(ER οr PI) = 0.56 + 0.36 - 0.36 = 0.56
Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement is 0.56.
e. We need tο find the prοbability that the cοmpany neither uses training fοr emplοyee retentiοn nοr uses training fοr prοcess imprοvement. This is the cοmplement οf the event that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement, sο we have:
P(neither ER nοr PI) = 1 - P(ER οr PI) = 1 - 0.56 = 0.44
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The sum of two numbers is 29. The difference between 4 times the first number and the second number is 6. Find the two numbers.
Answer:
Let's call the two numbers x and y.
From the problem statement, we know that:
x + y = 29 (Equation 1)
4x - y = 6 (Equation 2)
We can solve for one variable in terms of the other by rearranging Equation 1:
y = 29 - x
Substitute this expression for y in Equation 2 and solve for x:
4x - (29 - x) = 6
5x - 29 = 6
5x = 35
x = 7
Now that we know x = 7, we can use Equation 1 to solve for y:
x + y = 29
7 + y = 29
y = 22
Therefore, the two numbers are 7 and 22.
Answer:
the two numbers are x = 7.2 and y = 21.8.
Step-by-step explanation:
Let's call the first number x and the second number y. We can set up two equations based on the information given:
x + y = 29 (equation 1)
4x - y = 6 (equation 2)
We can use these two equations to solve for x and y.
To do so, we can use the method of substitution. Solving equation 1 for x, we get:
x = 29 - y
We can then substitute this expression for x into equation 2:
4(29 - y) - y = 6
Simplifying and solving for y:
116 - 4y - y = 6
115 - 5y = 6
-5y = -109
y = 21.8
So one of the numbers is y = 21.8. To find the other number, we can substitute this value back into equation 1:
x + 21.8 = 29
x = 7.2
Therefore, the two numbers are x = 7.2 and y = 21.8.
Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.
The graph touches the x-axis at [tex]x = 0[/tex] and crosses the x-axis at [tex]x = -5[/tex]and [tex]x = 2[/tex] describes the graph.
What is the x-axis?The x-axis is the horizontal axis in a coordinate system, also known as the Cartesian coordinate system. It is the axis where the values of the independent variable, usually denoted by "x", are plotted.
What is a graph?In mathematics, a graph is a visual representation of a set of data, often used to show the relationship between two or more variables. Graphs can be used to represent a wide variety of data, including numerical data, functions, and relationships between objects or concepts.
According to the given informationThe statement that describes the graph of [tex]f(x) = -x^{4} + 3x^{3} + 10x^{2}[/tex] is:
"The graph touches the x-axis at [tex]x = 0[/tex] and crosses the x-axis at [tex]x = -5[/tex] and [tex]x=2[/tex]."
To see this, we can factor in the equation:
[tex]f(x) = x^{2} (x^{2} - 3x + 10)[/tex]
Then we can use the quadratic formula to find the roots of the quadratic factor:
[tex]x = [3+ \sqrt{9-40} /2[/tex]
[tex]x = [3 ± \sqrt{-31} ]/2[/tex]
Since the discriminant is negative, the roots are imaginary and the quadratic factor does not have any real roots. Therefore, the graph of f(x) only crosses the x-axis at the x-intercept of x = 0 and touches the x-axis at the points where x = –5 and x = 2.
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How does coverage for a business relate to individual insurance? Compare and contrast the different types of individual insurance with business insurance. What are the similarities of individual insurance and business insurance? What are the differences between the two types of insurance? Give an example of each type of insurance.
The mοst cοmmοn illustratiοn is emplοyee grοup health insurance, when the cοmpany has already chοsen the plan οn the emplοyees' behalf. Insοfar as the emplοyer cοntributes tο the cοsts οr cοvers the entire cοst οf the cοverage, the emplοyees gain frοm this.
What dο yοu mean by individual insurance?Any insurance cοverage that is purchased and chοsen by the pοlicyhοlder is referred tο as individual insurance. Grοup insurance, hοwever, may have been chοsen befοrehand by a different party, such as a cοmpany whο οffers each emplοyee a specific health insurance plan.
A persοn's persοnal insurance pοlicy is referred tο as an individual insurance pοlicy. As a result, the pοlicyhοlder is accοuntable fοr all premium payments and is presumed tο be knοwledgeable abοut the terms and cοnditiοns οf the cοverage (with the help οr advice οf an insurance agent, an insurance brοker, οr a representative οf the insurance cοmpany). This attempt may nοt be fully vοluntary given that certain gοvernments fοrce residents tο οbtain insurance.
Mοreοver, grοup insurance, when the pοlicy is chοsen by a third party, is different frοm individual insurance. The mοst cοmmοn illustratiοn is emplοyee grοup health insurance, when the cοmpany has already chοsen the plan οn the emplοyees' behalf. Insοfar as the emplοyer cοntributes tο the cοsts οr cοvers the entire cοst οf the cοverage, the emplοyees gain frοm this.
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Which expression is equal to the product of 1/3 and 2 1/4?
1/3*4/9
3/1*4/9
1/3*9/4
1/3*1/4
3/1*9/4
Answer:
the answer is 1/3*9/4
Answer: 1/3*9/4
Step-by-step explanation: I did a test.
Write an equation to model the fish population y in a fishery that has a linear growth rate of 40 new fish each season *, and an initial population of 1250 fish.
After how many seasons will the population reach 1690 fish? Write an equation for a second fish population that grows by 60 new fish each season with an initial population of 1100 fish. After how many seasons will they have the same population?
Graph your equations in the coordinate plane.
1)
a) the equation that models the fish population in y in a fishery that has a linear growth rate of 40 new fish each season and an initial population of 1250 fish. is: y = 40x + 1250
b) it will take 11 seasons for the fish population to reach 1690 fish.
2) a) The equation for a second fish population that grows by 60 new fish each season with an initial population of 1100 fish is: y = 60x + 1100
b) after 7.5 seasons, both fish populations will have the same population.
What is the computation for the above?1) To model the fish population y in the fishery with a linear growth rate of 40 new fish each season and an initial population of 1250 fish, we can use the equation:
y = 40x + 1250
where x is the number of seasons.
To find after how many seasons the population will reach 1690 fish, we can substitute y with 1690 and solve for x:
1690 = 40x + 1250
Subtracting 1250 from both sides, we get:
440 = 40x
Dividing both sides by 40, we get:
x = 11
Therefore, it will take 11 seasons for the fish population to reach 1690 fish.
2) To write an equation for a second fish population that grows by 60 new fish each season with an initial population of 1100 fish, we can use the equation:
y = 60x + 1100
where x is the number of seasons.
To find after how many seasons the two populations will have the same population, we can set the two equations equal to each other and solve for x:
40x + 1250 = 60x + 1100
Subtracting 40x and 1100 from both sides, we get:
150 = 20x
Dividing both sides by 20, we get:
x = 7.5
Since x represents the number of seasons, we can conclude that after 7.5 seasons, both fish populations will have the same population.
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The area of a square is represented by 9x2 - 42x + 49. Find the length of each side.
O (9x-7)
O (3x-7)(3x+7)
O (3x-7)
O (3x+7)
O cannot be determined
Answer:
3x-7
Step-by-step explanation:
A square’s area represents (ax+b)^2. Let’s expand that. [tex]a^2x^2+2abx+b^2[/tex] now, we can notice this fits perfectly when a=3 and b=-7. Therefore one side length of the square is 3x-7.
CAN SOMEONE HELP WITH THIS QUESTION?✨
By answering the presented question, we may conclude that f'(x) = nx, function f(x) = xn (n-1) Where n is the function's power.
what is function?Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.
If you have a function y = f(x) and wish to discover the value of the derivative at a certain point x = a, use the notation:
lim(h -> 0) f'(a) h = [f(a + h) - f(a)]
This equation indicates the difference quotient's limit as h approaches 0. You may also use the derivative formula for power functions:
f'(x) = nx, f(x) = xn (n-1)
Where n is the function's power.
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Aubrey wants to know how students in her school feel about the new intramural sports program being developed. She randomly selects the names of 100 students and e-mails them a survey. She waits for responses and records data from the 32 surveys that are returned to her. Is her sample biased? Explain.
Her sample is in fact biased, as the sampling method used was voluntary sampling, which results in self-selection bias.
What is voluntary sampling and why it is biased?Voluntary sampling is a type of sampling method in which individuals are invited to participate in a study or survey based on their willingness or availability to do so. In other words, individuals choose to participate in the study, rather than being selected randomly by the researcher.
Voluntary sampling is chosen for this problem as the students had the option to answer the e-mail or not.
A limitation of voluntary sampling is that the individuals who choose to participate in the study may not be representative of the larger population from which they were drawn, leading to biased results.
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use each of the three corresponding base and height pairs to find the area of the triangle. Will the area be the same of each calculation? explain
The area of the triangle depends on the base and height pair used, and different pairs will result in different areas.
What is triangle?A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.
Here,
I'll provide a general explanation of how to calculate the area of a triangle using different base and height pairs.
The area of a triangle is calculated using the formula:
Area = (base * height) / 2
So, if you have three different base and height pairs for a triangle, you can calculate the area using each pair and see if the area is the same for each calculation.
For example, let's say we have the following base and height pairs for a triangle:
Pair 1: base = 4, height = 5
Pair 2: base = 6, height = 3
Pair 3: base = 8, height = 2
Using the formula, we can calculate the area of the triangle for each pair:
Area 1 = (4 * 5) / 2 = 10
Area 2 = (6 * 3) / 2 = 9
Area 3 = (8 * 2) / 2 = 8
As you can see, the area is not the same for each calculation. However, the sum of the areas of the triangles formed by each pair of base and height would always be equal to the area of the triangle formed by the overall base and height.
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determine the value of b²- 4ac
12x² + 5x -2=0
-8x+6>-30 what is the answer
Answer: x< 4.5
Step-by-step explanation:
-8x+6>-30
-8x>-36
x<4.5
I been struggling with this answer for 30 mins now can someone please help me
Bobbi owes a total of $10,455.75 in taxes.
What is taxes?Taxes are compulsory financial charges imposed by governments on individuals or entities based on income, property, or goods/services.
To compute the tax owed by Bobbi, we can use the following steps:
Calculate Bobbi's taxable income by subtracting the standard deduction and personal exemption from her total income:
Taxable income = $68,000 - $6,350 (standard deduction) - $4,050 (personal exemption) = $57,600
Determine the tax bracket in which Bobbi's taxable income falls:
Bobbi's taxable income of $57,600 falls in the 25% tax bracket.
Calculate the tax owed by Bobbi by applying the marginal tax rates to her taxable income. We can use the following formula:
Tax owed = (Taxable income - Previous tax bracket limit) x Marginal tax rate + Previous tax amount
In Bobbi's case, we need to calculate the tax owed in three steps, since her taxable income falls in the 10%, 15%, and 25% tax brackets:
For the first $9,325 of her taxable income, Bobbi owes 10% in taxes:
Tax owed = ($9,325 - $0) x 0.10 + $0 = $932.50
For the next $28,625 of her taxable income (up to $37,950), Bobbi owes 15% in taxes:
Tax owed = ($37,950 - $9,325) x 0.15 + $932.50 = $3,825.75
For the remaining $19,650 of her taxable income (up to $57,600), Bobbi owes 25% in taxes:
Tax owed = ($57,600 - $37,950) x 0.25 + $3,825.75 = $5,697.50
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can you help me with this task please? thank you!!
Answers:
7. 4/50 + 30/50 = 34/50 = 17/25
8. 8/12 - 7/12 = 1/12
9. 90/100 + 2/100 = 92/100 = 23/25
10. 16/36 + 9/36 = 25/36
11. 17/15 - 5/15 = 2/15
12. 7/16 + 6/16 = 13/16
13. 8/20 + 5/20 = 13/20
14. 2/14 + 7/14 = 9/14
The speed of light is 299,792,458 meters per second. How would you write the approximate speed in scientific notation
Answer:
3 * 10^8 m/s.
Step-by-step explanation:
The given number is close to 300 million so an approximate speed is
3 * 10^8.
A recipe calls for 14 teaspoons of sugar to make 168 milliliters of coffee what is the constant of proportionality that relates the number of milliliters of coffee made y to the Numbers of teaspoons of sugar used x
Answer:
Step-by-step explanation:kk
The constant of proportionality that relates the number of milliliters of coffee made y to the number of teaspoons of sugar used x is 12.
Why is that, therefore, if K is the proportionality constant?When two variables are directly or indirectly proportional to one another, their relationship can be represented as y = kx or y = k/x, where k denotes the direction of the relationship between the two variables. It is known as the proportionality constant, or k.
We must determine the ratio of the two amounts in order to determine the constant of proportionality that connects the number of teaspoons of sugar used x to the number of millilitres of coffee brewed y.
Considering the information provided, we understand that:
168 millilitres of coffee require 14 tablespoons of sugar.
As a result, the following is the relationship between the quantity of coffee prepared and the quantity of sugar used in teaspoons:
y/x = 168/14
Reducing the ratio:
y/x = 12
This indicates that 1 teaspoon of sugar is needed to make every 12 millilitres of coffee.
As a result, 12 is the constant of proportionality that links the quantity of coffee created (y) to the quantity of sugar utilised (x).
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I really need help, please. I have question one but I can't figure out the rest.
4.3.4 Practice: Solving Systems of Linear Equations by Substitution
Practice
M/J Grade 8 Pre-Algebra Sem 1
Points Possible:10
Name:
Caine Jones
Date:
Your Assignment
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
4. You will use substitution to solve this system. Which variable will you substitute for and why? Show the equation that results from the substitution. (2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
1. The equation to represent the number of pages Amir has read is y = 35x, where x is the number of days Amir has been reading and y is the number of pages he has read.
2. Let's say that Jesse started reading on Saturday, and Amir started reading on Sunday. If x is the number of days Amir has been reading, then Jesse has been reading for x + 1 days. The equation to represent the number of pages Jesse has read is y = 30(x + 1), where y is the number of pages Jesse has read.
3. The system of equations is:
y = 35x
y = 30(x + 1)
4. We will substitute y in the second equation with y from the first equation. We can do this because both equations represent the number of pages each person has read. So we have:
35x = 30(x + 1)
5. Solving for x:
35x = 30x + 30
5x = 30
x = 6
So it will take Amir 6 days to catch up to Jesse.
To find the number of pages they have read, we can use either of the original equations. If Amir has been reading for 6 days, he has read:
y = 35x = 35(6) = 210 pages
If Jesse has been reading for 7 days (one day more than Amir), he has read:
y = 30(x + 1) = 30(7) = 210 pages
So when Amir catches up to Jesse, they will both have read 210 pages.
6. Amir will catch up to Jesse in 6 days. At that time, they will each have read 210 pages.
Answer: i got number 1 :)
6 days
210 pages
Step-by-step explanation:
As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.
Now since he reads 35 pages per day.
Then mathematically;
y = 35x
For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)
To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that
Also; y = 30(x + 1)
Equating the two situations
35x = 30(x + 1)
35x = 30x + 30
35x -30x = 30
5x = 30
x = 30/5
x = 6 days
This means that it will take Amir 6 days to catch Jese.
The number of books they would have read by then is y = 35x = 30(x + 1)
= 35 * 6 or 30(6+1)
= 210
One of your co-workers is giving a presentation on the results of an analysis the two of you have been working on. Someone in the audience points out that the data system you used has frequent errors. How should you deal with this comment?
Answer:
As a co-worker, you should support your colleague by offering to address the question. Here are some steps to consider:
Acknowledge the concern: Begin by thanking the person for their comment and acknowledging their concern about the data system. This will help to show that you are open to feedback and willing to listen.
Provide context: If appropriate, offer some context about the data system that was used. For instance, if the system was chosen due to budget or resource constraints, you can explain why that decision was made.
Offer a solution: Explain what steps were taken to ensure the accuracy of the data, despite the known issues with the system. If there were steps taken, share those with the audience. Alternatively, offer to follow up with the audience member after the presentation with more information on how the team plans to address the issue.
Stay professional: Be calm, professional, and open-minded throughout the conversation. Avoid getting defensive or argumentative. Instead, focus on addressing the issue in a constructive manner.
By following these steps, you can help to address the concern in a professional and effective manner.
which expression does not belong? explain
The expression that does not belong with the other three is B. x ² - 8 ˣ because C. The different expression is the one that is not a polynomial.
How to find the expression ?Expression 2 is not a polynomial because it contains a term (8^x) with a variable in the exponent, which is not allowed in a polynomial. All the other expressions are polynomials. This expression therefore does not belong.
Polynomials are mathematical expressions that consist of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.
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please help me i’m struggling
The correct option is- "Similar figures are said to be congruent: a dilation could possess a scale factor of 1. Due to the differing lengths of comparable sides, similar figures are really not congruent."
Explain about the congruence and similarity?Congruence:
Even though two things are all the same size and shape, they may not be facing the same direction. Like sea stars oriented differently, they still make sense.Or imagine two knights from a chess set, one on a higher shelf and an additional one on a minor ledge. They can nonetheless be congruent even though they are in distinct three-dimensional planes. They remain consistent.Similarity:
Similarity refers to having the same proportions and shape, but not always the same size. Angles of comparable figures will just be equal, while side lengths are frequently not.Congruent shapes are automatically comparable to one another, while the opposite is not true. Similar figures are all congruent, however not all congruent figures include similar figures.Thus, the correct option is- "Similar figures are said to be congruent: a dilation could possess a scale factor of 1. Due to the differing lengths of comparable sides, similar figures are really not congruent."
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simplify these expressions 13xyz +9 +2xyz + 3 and 6ab + (-2ab) + 4 + 6
The expressions are simplified to give;
15xyz + 12
4ab + 10
What are algebraic expressions?
Algebraic expressions are simply defined as mathematical expressions that are known to contain variables, constants, coefficient, factors and terms.
These algebraic expressions are also known to be made up of mathematical operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFloor division, etcFrom the information given, we have that;
13xyz +9 +2xyz + 3
Now, collect the like terms, we have;
13xyz + 2xyz + 9 + 3
Add the values
15xyz + 12
6ab + (-2ab) + 4 + 6
expand the bracket and collect like terms
4ab + 10
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-Point O is the center of regular octagon ABCDEFGH. Find the image of the given point for the given rotation. 90° rotation of A about O. -The image of A is ___?
The image of A about O after 90 degrees rotation is C
What is rotation?Rotation refers to the movement of an object around an axis or center point.
In the problem, the rotation of A 90 degrees about O in the clockwise direction of rotation involves moving in the said direction to make the angle 90 degrees
In an octagon, each angle in the center is solved by
= 360 / 8
= 45
Hence each step in the clockwise rotation covers angle 45 degrees> In the figure from A to B is 45 degrees.
Moving from A to C in clockwise direction is equal to 90 degrees
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The sum of two numbers is 35. The first number minus twice the second number is 8. Find the two numbers
Answer:
the first number is 26
the second number is 9
Step-by-step explanation:
given the first number is x and the second number is y
then x + y = 35
x - 2y = 8 => x = 2y + 8
substitute 2 equations
(2y + 8) + y = 35
3y = 35 - 8
3y = 27
y = 27/3 = 9
x = 35 - y = 35 - 9 = 26
Answer:
The first number is 26
the second number is 9
Step-by-step explanation:
If x represent the first number.
Since the sum of the numbers is 35, the second number is 35-x.
Then the relation between the two numbers is by the equation :
x - 2(35-x) = 8 3x -70 = 8 . . . . simplify 3x = 78 . . . . . . . and by add 70 x = 26 . . . . . .and divide by 3 . . . this is the first number 35-x = 9 . . . . the second numberThe first number is 26 the second number is 9Help Please, I dont know what to do.
Answer: B: y=5x-5
Step-by-step explanation:
a. 15
b. 25
c. 88.5
d. not enough information
Answer:
B
Step-by-step explanation:
assuming DF is the diameter of the circle , then
the angle in a semicircle is 90° , that is
∠ DCF = 90° and Δ CDF is a right triangle
using Pythagoras' identity in the right triangle
CD² + CF² = DF²
CD² + 60² 65²
CD² + 3600 = 4225 ( subtract 3600 from both sides )
CD² = 625 ( take square root of both sides )
CD = [tex]\sqrt{625}[/tex] = 25
36. You drop a ham that weighs 9.25 lbs from a height of 1.45m. Right before it hits the ground, it has a velocity of 5.33m/s. Given that the impact of the ham and the tile floor has a coefficient of restitution or 0.35, how high will it bounce after impact? (1 point)
The ham will bounce to a height of 0.16 meters after the impact.
Define Potential Energy.It is the energy that an object possesses by virtue of its position or configuration, or as a result of its composition. The potential energy of an object can be converted into kinetic energy, which is the energy of motion.
initial potential energy of the ham:
PE = mgh
where m is the mass of the ham, g is the acceleration due to gravity, and h is the initial height from which the ham is dropped. Substituting the given values, we get:
PE = (9.25 lbs)× (1 kg/2.205 lbs) × (9.81 m/s²) × (1.45 m) ≈ 61.8 J
At the moment just before the ham hits the ground, all of this potential energy is converted into kinetic energy:
KE = (1/2)mv²
where v is the velocity of the ham just before impact. Substituting the given values, we get:
KE = (1/2) × (9.25 lbs) × (1 kg/2.205 lbs)×(5.33 m/s)²≈ 87.8 J
After the impact, some of this kinetic energy is lost due to the coefficient of restitution, which is the ratio of the velocity after impact to the velocity just before impact:
e = v'/v
where v' is the velocity after impact. Substituting the given values, we get:
0.35 = v'/5.33
Solving for v', we get:
v' ≈ 1.86 m/s
Now, we can use the conservation of energy to find the maximum height to which the ham bounces. At this point, all of the remaining kinetic energy has been converted back into potential energy:
KE = (1/2)mv'² = mgh'
where h' is the maximum height to which the ham bounces. Substituting the given values, we get:
(1/2) × (9.25 lbs) × (1 kg/2.205 lbs) ×(1.86 m/s)² = (9.81 m/s²) ×h'
Solving for h', we get:
h' ≈ 0.16 m
Therefore, the ham will bounce to a height of approximately 0.16 meters (or 16 centimeters) after the impact.
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The angle between 0 and in radians that is coterminal with the angle in radians is
The angle between 0 and 2π in radians is cοterminal with the angle 27π/4 in radians being 3π/4.
What is the cοterminal angle?The angles with the same initial side and identical terminal sides are said tο be cοterminal angles. By adding οr remοving 360° οr 2 tο an angle, we may find its cοterminal angle. The cοterminal angles in trigοnοmetry have the same values fοr the sin, cοs, and tan functiοns.
Here, we have
Cοterminal with the angle 27π/4 in radians
Tο find a cοterminal angle, add οr subtract any multiple οf 2π
27π/4 - 2π = 19π/4
19π/4 - 2π = 11π/4
11π/4 - 2π = 3π/4
Hence, The angle between 0 and 2π in radians that is cοterminal with the angle 27π/4 in radians is 3π/4.
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Look at the relative-frequency table below of the probability distribution of the discrete random variable X, with X = "the number of pets in a household."
x P(X = x)
0 .09
1 .29
2 .42
3 .15
4 .05
What is the expected value of pets in a randomly selected household?
Answer: The expected value of a discrete random variable is calculated by multiplying each possible value of the variable by its corresponding probability, and then adding up all of the products. Symbolically, the expected value of X is:
E(X) = Σ [x * P(X = x)]
where the summation is taken over all possible values of X.
Using the table given, we can calculate the expected value of pets in a randomly selected household as follows:
E(X) = 0*(.09) + 1*(.29) + 2*(.42) + 3*(.15) + 4*(.05)
E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.20
E(X) = 1.78
Therefore, the expected value of pets in a randomly selected household is 1.78.
Step-by-step explanation:
Help I cant figure this out....
hope this helps!
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