Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:
A = {1, 2, 3, 4, 5 }
Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:
N: Set of all natural numbers
Z: Set of all integers
Q: Set of all rational numbers
R: Set of all real numbers
Z+: Set of all positive integers
A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.
Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members
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Would you rather…
Five Seconds of Summer’s tutoring service charges a base charge of $5 and $5 per hour.
Fall Out Boy’s tutoring service charges a base fee of $9 and $3 per hour. Whose service
would you rather use?
Can you graph it and explain it on a table and the substitution method
Answer: Fall Out Boy's service is cheaper than Five Seconds of Summer's service.
Step-by-step explanation: The cost of Five Seconds of Summer's tutoring service can be represented by the equation:
C = 5 + 5h
where C is the total cost and h is the number of hours.
The cost of Fall Out Boy's tutoring service can be represented by the equation:
C = 9 + 3h
To compare the cost of the two services, we can use the substitution method. We can set the number of hours (h) equal to a variable and substitute that variable into the equation for both services.
For example, if we set h = 4 (4 hours of tutoring), we get:
C(Five Seconds of Summer) = 5 + 5(4) = 25
C(Fall Out Boy) = 9 + 3(4) = 21
The cost of Fall Out Boy's service is $21 and the cost of Five Seconds of Summer's service is $25. Therefore, Fall Out Boy's service is cheaper for 4 hours of tutoring.
We can also graph the cost of the two services on a coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x
Service | Equation
Five Seconds of Summer y = 5 + 5x
Fall Out Boy | y = 9 + 3x
Henry pays $540.00 for one dozen collector’s edition baseball cards?
The cost of the one baseball card will be $45
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cost of one dozen baseball cards is $540. The cost of one baseball card will be calculated by dividing the total cost by 12.
Cost = 540 / 12
Cost = $45
Hence, the cost of one card will be $45.
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when publishing their results, the researcher feels that it would be unethical not to include the raw data which they have used to support their findings. so the researcher publishes the findings of the study, including all the supporting data on all the study participants, in a well known journal.
The most clearly violated principle of ethical research in this scenario is individual information should be kept private, only summary results should be made public.
Ethical research requires that the privacy and confidentiality of study participants be protected. This is because the information collected from participants is often sensitive and personal, and the participants may have trusted the researcher to keep their information private.
In this scenario, the researcher has published the raw data, including personal information such as each participant's name, residence, and medical history, which could potentially compromise the privacy of the participants.
This is a clear violation of the principle of confidentiality, as the participants may not have agreed to have their personal information made publicly available.
It is important for researchers to be transparent and honest in their reporting of results, but they also have a responsibility to protect the privacy of their participants.
The publication of raw data, including personal information, should only be done with the explicit consent of the participants or under special circumstances where it is necessary for scientific advancement or the public good.
In conclusion, while the researcher's intention of being transparent in their reporting of results is commendable, the publication of the raw data, including personal information, is a clear violation of the principle of ethical research and could have serious consequences for the privacy and confidentiality of the study participants.
Hence, the correct answer is D.
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--The given question is incomplete; the complete question is
"A researcher collects various pieces of information from volunteers for a study into the health effects of drinking and smoking. The information collected includes each volunteer's name, residence, age, height, weight, medical history and their history of smoking cigarettes and drinking alcohol. All participants agreed to provide their information after the researcher explained how it would be used.
When publishing their results, the researcher feels that it would be unethical not to include the raw data which they have used to support their findings. So the researcher publishes the findings of the study, including all the supporting data on all the study participants, in a well-known journal.
The principle of ethical research most clearly violated (if any) is:
A. the researcher has falsified results
B. the researcher has failed to report negative results
C. no ethical principles have been violated; there was no informed consent
D. individual information should be kept private, only summary results should be made public"--
Drag the files to the correct boxes to complete the pairs make each system of linear equations with the correct number of solutions 
A linear function is a function that represents a straight line on the coordinate plane. So the pairs 3x-y=4 and 6x-2y=8 make each system of linear equations with the correct number of solutions.
What is meant by linear?
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function.Students study the direct variation, slope-intercept form, standard form, and point-slope forms of four types of equations.A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.The phrase "affine function" is frequently used to distinguish such a linear function from another idea.A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions.3x - y = 4 6x-2y = 8
3x=4+y 6x = 8 + 2y
3x/3 = 4/3 + y/3 6x/6 = 8/6 + 2y/6
x = 4 + y/3 x = 4 + y/3
-3+y=7 -2x-4y = -8
y = 7 + 3 -2x = -8 +4y
y = 10 -2x/-2 = -8/-2 + 4/-2
x = -2(y-2)
y=-4x-5 y=-4x+1
Axis interception points of -4x-5: Axis interception pointsof -4x+1:
X Intercepts (-5/4,0), X Intercepts (1/4,0),
Y Intercepts (0,-5). Y Intercepts (0,1).
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TEXT ANSWER
A dog weighs 45 pounds 12 ounces. How much does the dog weigh in kilograms?
If needed, round your answer to the nearest hundredth.
Conversion ratios:
1 lb = 16 oz
.
•
.
• 1 kg = 2.2 lb
Use the equation editor to show your work.
Answer:
20.80 kg
Step-by-step explanation:
45 lb + 12 oz = 45 lb + 12/16 lb = 45.75 lb
45.75 lb × (1 kg)/(2.2 lb) = 20.80 kg
the rectangle below consists of 8 unit squares. what fraction of the rectangle is shaded?
A fraction of the rectangle is shaded = 1/4
Consider following diagram.
The rectangle below consists of 8 unit squares.
To find: fraction of the rectangle is shaded
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
Here, a rectangle consists of 8 unit squares. Out of 8 unit squares, 2 squares are shaded.
So, the fraction would be 2/8
We simplify above fraction 2/8 = 1/4
So, 1/4 of the rectangle is shaded.
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Exercise 1: ABC is a triangle such that AB=5cm. A=50°and AC=5cm 1) Construct the triangle ABC. 2) What is the nature of the triangle ABC? Justity. 3) Calculate ABC and ACB. 4) Draw the height [AH) issued from A to [BC]. 5) a. Calculate BAH and CAH. b. What does [AH] represents for BAC? Justify.
Answer:
2) Acute triangle, isosceles
3) Both are 65 degrees
4) (diagram)
5) a) both 25 degrees
b) midpoint
Step-by-step explanation:
2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.
3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)
So:
180-50/2 = 65
ABC and ACB = 65 degrees each
4) Construct the line AH down the middle like in the diagram I drew.
5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.
BAH = 180-90-65
BAH = 25 degrees
CAH = 50 - 25
CAH = 25 degrees
b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.
please help asap its due today
Answer:
c < 10 = The bag contains fewer than 10 carrots.
c > 10 = Catherine biked farther than 10 miles.
c < 20 = The chair is shorter than 20 inches
c > 20 = Carlos scored over 20 points
During the month of September the animal shelter saved 80 animals. In the month of October, the animal shelter saw an increase of 15% of animals being saved from the previous month. How many animals were saved in the month of October?
Answer: In the month of October, the animal shelter saved 92 animals.
Step-by-step explanation: In the month of October, the animal shelter saw an increase of 15% of animals being saved from the previous month. To calculate this increase, we can use the formula:
increase = (original number) x (percent increase)
In this case, the original number is 80 (the number of animals saved in September) and the percent increase is 15%. So:
increase = 80 x 0.15 = 12
This means that in October, the animal shelter saved an additional 12 animals beyond the 80 animals that were saved in September. To find the total number of animals saved in October, we add this increase to the original number:
animals saved in October = 80 + 12 = 92
So, in the month of October, the animal shelter saved 92 animals.
A plane figure has 2 sides that
each 5 inches and 2 sides that are each
3 inches. What is the perimeter of the
plane figure?
The perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.
What is the perimeter of a plane figureTo know the perimeter of a plane figure, we add up all the length of its sides or boundaries together. That is the sum total of the length of a plane figure is called its perimeter.
The plene figure has for sides who two of it is 5 inches each and the other two is 3 inches each.
thus we calculate for the perimeter as follows:
perimeter of the plane figure = 5 in + 5 in + 3 in + 3 in
perimeter of the plane figure = 16 inches
Therefore, the perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.
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use ratio test to determine if the series converges
The series for this problem is absolutely convergent, as the limit assumes a value lower than 1.
What is the ratio test?The infinite series for this problem is defined as follows:
[tex]\sum_{i = 1}^{\infty} \frac{1}{n!}[/tex]
Hence the general term is given as follows:
[tex]a_n = \frac{1}{n!}[/tex]
The limit is given as follows:
[tex]L = \lim_{n \rightarrow \infty} \left|\frac{a_{n + 1}}{a_n}\right|[/tex]
The (n + 1)th term is given as follows:
[tex]a_{n + 1} = \frac{1}{(n + 1)!}[/tex]
The factorial can be simplified as follows:
(n + 1)! = (n + 1) x n!.
Hence the limit will be calculated of:
1/[(n + 1) x n!] x n! = 1/(n + 1).
The result of the limit is given as follows:
[tex]L = \lim_{n \rightarrow \infty} \frac{1}{n + 1} = 0[/tex]
As the limit assumes a value of zero, the series is absolutely convergent.
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graphically solve x+y=3 and 3x-y=1
tanya incorrectly says that the solution of the systems of equations is (-3, -2). what is the correct solution? 6g-3h=-3 7=h-5g
The correct solution to the system of equation is (-2, -3)
How to determine the correct solutionFrom the question, we have the following parameters that can be used in our computation:
6g-3h=-3
7=h-5g
Divide through 6g-3h=-3 by 3
so, we have
2g-h=-1
Make h the subject
h = 2g + 1
So, we have
7 = 2g + 1 - 5g
Evaluate the equation
-3g = 6
So, we have
g = -2
This becomes
h = 2 * -2 + 1
Evaluate
h = -3
Hence, the solution is (-2, -3)
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Use synthetic division to show that x=-3 is a root of the polynomial function f(x)=x^3-4x+15
Answer:
Step-by-step explanation:
ans = x^2 - 3x + 5
Calculate the following, then convert your result to degrees, then give the quadrant of the terminal side.
The angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.
How to convert the angles from radian to degreeWe simplify each angles of the angle in the radian to a single fraction and then convert them to degree by multiplying by 180°/π as follows:
11π/4 + 2π/3 = (33π + 8π)/12 {12 is the LCM of the denominators}
11π/4 + 2π/3 = 41π/12
11π/4 + 2π/3 = 41π/12 × 180°/π
11π/4 + 2π/3 = 615°
The terminal side of 615° is in the 3rd quadrant
π/6 - 5π/4 = (2π - 15π)/12 {12 is the LCM of the denominators}
π/6 - 5π/4 = -13π/12
π/6 - 5π/4 = -13π/12 × 180°/π
π/6 - 5π/4 = -195°
π/6 - 5π/4 = 165° {changing -195° to positive angle by adding 360°}
The terminal side of 165° is in the 2nd quadrant.
9π/8 - π/2 = (9π - 4π)/8 {8 is the LCM of the denominators}
9π/8 - π/2 = 5π/8
9π/8 - π/2 = 5π/8 × 180°/π
9π/8 - π/2 = 225°/2
9π/8 - π/2 = 112.5°
The terminal side of 112.5° is in the 2nd quadrant.
Therefore, the angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.
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Using the same situation you described in #3, now interpret what the part-to-part ratio 2:1 means in the situation. Use complete sentences in your answer.
#3 situation
A classroom has 50 people.
The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So, how many boys and girls are there?
The answer would be :
2x+3x=50
5x=50
x=
x=10
2x= 2×10=20
3x =3*10=30
20 girls and 30 boys.
There are 30 boys and 20 girls in the classroom.
How to determine the number of boys and girls?Let the variable p represent the number of people. Next, we would translate the given word problem into an algebraic equation by using a ratio as follows;
Number of girls + Number of boys = Total number of people
2p + 3p = 50
5p = 50
Dividing both sides of the equation by 5, we have the following:
p = 50/5
p = 10 people.
For the number of girls, we have:
2g = 2(10)
2g = 20 girls.
For the number of boys, we have:
3g = 3(10)
3g = 30 boys.
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6. A parabola has focus (-1, 6) and directrix y = 4. Determine whether each point on
the list is on this parabola. Explain your reasoning.
a. (-1,5)
b. (1,7)
c. (3,9)
Answer:a
Step-by-step explanation:
Explain why [tex]\sqrt{7^3}[/tex] must be equal to [tex]7^\frac{3}{2}[/tex] if the Power of a Power Property is true for all rational exponents.
(√7)^3 is equal to 7^(3/2)
The Power of a Power Property
The Power of a Power Property states that when you have a base raised to an exponent, and that base is also raised to an exponent, you can simplify the expression by multiplying the exponents.
For example, (a^x)^y = a^(xy)
In the case of square root of 7^3, the expression (√7)^3 can be written in the form of base and exponent, where the base is √7 and the exponent is 3.
Now, we can use the Power of a Power Property to simplify the expression, by multiplying the exponents.
So, (√7)^3 = (7^(1/2))^3 = 7^(1/2 * 3) = 7^(3/2)
This means that the square root of 7^3 is equal to 7^(3/2) because the Power of a Power Property allows us to simplify the expression by multiplying the exponents.
It's worth noting that the square root of 7^3 is the same as taking the cube root of 7^3, which is 7^(3/3) = 7^1 = 7.
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What is the end behavior for f(x)=x^5
The end behavior for f(x)=x^5 is as x approaches infinity, f(x) approaches infinity and as x approaches negative infinity, f(x) approaches negative infinity
How to determine the end behaviorFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^5
Calculate f(oo) and f(-oo) i.e the function at infinity and negative infiniyt
So , we have
f(x) = (oo)^5 = +oo
f(x) = (-oo)^5 = -oo
This means that x increases with f(x)
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Which of the following are parallelograms? Choose ALL that apply.
Trapezoid
Square
Rectangle
Rhombus
Answer: all of the above
Step-by-step explanation:
Answer: square,Rectangle,Rhombus and trapezoid
Step-by-step explanation:
they all have pairs of parallel sides
Please mark me brainllest
Aaliyah and Yohance are having a competition to see who can read
more pages over the coming weekend. Aaliyah has bet Ms. Solomon that
she'll read 50 more pages than Yohance. Both scholars read at an
average rate of 40 pages per hour. Yohance says that he's going to read
for 7.5 hours this weekend. How many hours will Aaliyah need to read in
order to fulfill her promise of reading 50 more pages than Yohance?
50= 40
Mathematically, Aaliyah needs to read 8.75 hours (or 8 hours, 45 minutes) to fulfill her promise of reading 50 more pages than Yohance.
What are the mathematical operations?The mathematical operations used to determine the hours that Aaliyah needs to read this weekend to meet her target include multiplication, addition, and division.
In the first instance, we must determine the total pages read by Yohance this weekend using multiplication as follows: 300 (7.5 x 40).
Secondly, the additional pages Aaliyah will read are added to Yohance's to show the total pages read by Aaliyah.
Lastly, the total pages are divided by Aaliyah's reading speed or rate to determine the hours she requires.
Aaliyah Yohance
Average pages per hour 40 40
Additional page 50
Yohance weekend reading time = 7.5 hours
Total pages read by Yohance this weekend = 300 (7.5 x 40)
The total pages to be read by Aaliyah this weekend = 350 (300 + 50)
Aaliyah's total weekend reading time 8.75 hours (350/40)
Thus, for Aaliyah to read 50 more pages than Yohance, she needs 8.75 hours to fulfill her promise.
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Cual pesa menos marca con una x la casilla correspondiente ?
Las pesas de menor masa son listadas como sigue:
32 hectogramos 80 decigramos 9500 decigramos 90 gramos 5 kilogramos 8500 hectogramos¿Cuál es la pesa de menor masa?
En esta pregunta tenemos seis casos de tres pesas, entre las cuales debemos determinar cuál tiene la menor masa. Esto implica el uso de la conversión entre unidades de masa a una única unica, tal que la pesa de menor capacidad será la de menor cantidad. El procedimiento se resume a continuación:
Convertir las masas a una única unidad.Elegir la masa de menor numeración.Caso 1
32 hectogramos - 3200 gramos
4 kilogramos - 4000 gramos
500 decagramos - 5000 gramos
La pesa de 32 hectogramos reporta la menor masa.
Caso 2
35 gramos
4500 miligramos - 4.5 gramos
80 decigramos - 8 gramos
La pesa de 80 decigramos reporta la menor masa.
Caso 3
9500 decigramos - 950 gramos
6 kilogramos - 6000 gramos
70 hectogramos - 7000 gramos
La pesa de 9500 decigramos reporta la menor masa.
Caso 4
365 decigramos - 3650 gramos
90 gramos
30 decagramos - 300 gramos
La pesa de 90 gramos reporta la menor masa.
Case 5
75 hectogramos - 7500 gramos
5 kilogramos - 5000 gramos
6200 gramos
La pesa de 5 kilogramos reporta la menor masa.
Case 6
8500 hectogramos - 850000 gramos
30 kilogramos - 30000 gramos
900 decagramos - 9000 gramos
La pesa de 8500 hectogramos reporta la menor masa.
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the total amount of water a tank can hold is gallons. raul wants to find out how many -gallon buckets of water can be used to fill the tank. which expressions could be used to represent this scenario? select two options..
The volume of a tank can be calculated by multiplying its length, width, and height.
Therefore, the expression to calculate the total amount of water a tank can hold in gallons can be represented by V = lwh, where V is the volume, l is the length, w is the width, and h is the height of the tank.
To find out how many -gallon buckets of water it takes to fill the tank, we can divide the total amount of water the tank can hold by the size of each bucket. This can be represented by the expression: n = V/g, where n is the number of buckets, V is the total amount of water the tank can hold, and g is the size of each bucket.
For example, if the tank is 8 feet long, 4 feet wide, and 2 feet tall and each bucket holds 1 gallon of water, the total amount of water the tank can hold is V = (8)(4)(2) = 64 gallons. Thus, the volume of a tank buckets of water needed to fill the tank would be n = 64/1 = 64 buckets.
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Complete question : Raul has a tank with a capacity of 200 gallons and wants to use buckets that hold 5 gallons each. How many buckets does he need to fill the tank?
Jada invested $200 in an account that earns compound interest annually.
Which equations could be used to model the amount of money that Jada would have in the account after x years?
Part A
Select the two that apply.
a: y=200-(1-0.03)
b: y=200-(1+0. 03)²
c: y = 0.03-200³
d: y=200-1.03²
e: y = (1 + 0.03) - 200³
D
Part B
(1 point)
Use your equation from Part A to determine how much money Jada would have in her account after 36 months?
Enter your answer and your work or explanation in the space provided.
The equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex].
Jada would have in her account $218 after 36 months. The solution has been obtained by using the concept of compound interest.
What is compound interest?
When interest is calculated, it is done so using both the principal and the interest that has accumulated over the preceding period. Unlike simple interest, which does not take the principal into account when computing the interest for the following month, compound interest takes the principal into account. Compound interest is commonly represented by the letter C.I. in mathematics.
We know that formula for compound interest is
[tex]A= P(1 + \frac{r}{n} )^{nt}[/tex]
So, here A= y, P = $200 , n=1 and t=x and r = 0.03
Thus, we get
[tex]y= 200(1 + \frac{0.03}{1} )^{x}[/tex]
[tex]y= 200(1 + {0.03})^{x}[/tex]
So, the second equation is the correct one.
The amount of money Jada would have after 36 months means the amount after 3 years.
So, x=3
Putting this in the equation, we get
[tex]y= 200(1 + {0.03})^{3}[/tex]
y = 200 (1.09)
y = $218
Hence, the equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex] and Jada would have in her account $218 after 36 months.
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On the plot shown, assume the horizontal axis represents x and the vertical axis represents y. At what value of x does the function y(x) have a value of zero and a positive derivative?
At x =6 the function has a positive slope.
A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable. At x = 2 and x = 6, the function y(x) is zero, and it has a value of 1 for all other values of x. the dependent variable. Functions are essential for building physical relationships in both math and science.
A function, which generates one output from a single input, is an illustration of a rule. origin of the image. An illustration of this is Y=X2.
But
At x = 2, the function starts to decline and has a negative slope. negative derivative
while
At x = 6, the function increases with a positive slope, producing a positive derivative.
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Evaluate the expression by finding the absolute value.
|10| – |‐5| + |‐3|
The absolute value of the given expression is 8.
What is absolute value?Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
Given that an expression |10| - |‐5| + |‐3| we need to find its absolute value,
|10| - |‐5| + |‐3|
= 10 - 5 + 3
= 5 + 3
= 8
Hence, the absolute value of the given expression is 8.
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specify the number of significant figures in each of the following numbers and determine the result of the following calculation to the correct number of significant figures. 3.115 0.2281 712.5 45
The result of the calculation is 680.
The number 3.115 has four significant figures, the number 0.2281 has four significant figures, the number 712.5 has three significant figures and the number 45 has two significant figures. This means that when performing calculations with these numbers, the answer must be rounded to the least number of significant figures, which is two.
The calculation is 3.115 + 0.2281 + 712.5 - 45. Using the rules of significant figures, we can calculate this as 3.1 + 0.2 + 713 - 45.
The result of the calculation is 675.3 and this must be rounded to the least number of significant figures, which is two. Therefore, the result of the calculation is 680.
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A spherical balloon is expanding at the rate of 60 pie in^3/sec. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 inches?
30 is the fast surface area of the balloon expanding when the radius of the balloon is 4 inches
Now, According to the question:
A spherical balloon is expanding at the rate of 60 pie cubic inches /sec.
The radius of the balloon is 4 inches.
Now, Solving the problem:
By using formula:
The formula for the volume of a sphere is V = 4/3 π r³,
where V = volume and r = radius.
Volume = [tex]\frac{4}{3}\pi r^3[/tex]
We have that:
Differentiate the formula:
[tex]\frac{dV}{dt}=4\pi r^2.\frac{dr}{dt}= 60[/tex]
=> [tex]\frac{dr}{dt}=\frac{60}{4\pi r^2}[/tex]
We know that [tex]A=4\pi r^2,[/tex] and so we also have
[tex]\frac{dA}{dt}=8\pi r.\frac{dr}{dt}[/tex]
Plug in what we found for dr/dt and plug in r=4 to get:
[tex]\frac{dA}{dt}=8\pi r.\frac{60}{4\pi r^2}[/tex]
[tex]\frac{dA}{dt}=\frac{120}{r}=\frac{120}{4}[/tex]
[tex]\frac{dA}{dt}=30[/tex]
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Please help with writing linear functions
The function would be [tex]f(x)=\frac{1}{2}x + 1 \ and\ f(x)=\frac{1}{2}x - \frac{1}{2}[/tex]
What is linear function?
A linear function is one with one or two variables that does not have exponents. It is a function that has a straight line graph.
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. To find the equation of the linear function given the values of x and f(x), we can use two points and use the slope-intercept form of the equation.
A way to find the equation of the linear function is to use the point-slope form: f(x) = m(x-x1) + f(x1), where (x1,f(x1)) is a point on the line.
If we use the points (-4,-2) and (0,0) we can find the slope:
m = (0 - (-2)) / (0 - (-4)) = 2/4 = 1/2
then using point-slope form:
f(x) = 1/2(x - (-4)) + (-2)
f(x) = 1/2x + 1
so the equation of the linear function is f(x) = 1/2x + 1
Alternatively, we can use the two points (-2,-1) and (0,0) we can find the slope:
m = (0 - (-1)) / (0 - (-2)) = 1/2
then using point-slope form:
f(x) = 1/2(x - (-2)) + (-1)
f(x) = 1/2x - 1/2
so the equation of the linear function is f(x) = 1/2x - 1/2.
Therefore, equation f(x) = 1/2x+1 and f(x) = 1/2x - 1/2 represents the given values of x and f(x)
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PLS HELP answer these 5 questions! I need explanations and work! If you help me, you will get 50 points!! PLS HELP ASAP due TMR!!!
18) The expression with greater value are a and b. = 256 (19) the density of the object is X⁶ (20) The mass of the object is Y¹⁴ (21) The simplified expression is (3x)² (22) Tobe uses the multiplication law for the exponent
How to solve the problems?
The given parameters are
18) (a) 2³ · 2⁵ Using the multiplication law of indices, the two numbers are in the same base therefore add their powers
This implies 2³⁺⁵ = 2⁸ = 256
(b) (4)⁷/(4)³
Using the multiplication law of indices, the two numbers are in the same base therefore add their powers
4⁷⁻³ = 4⁴ = 256
(19) Mass = X¹⁵ grams
Volume = X³ cm₁
Density = Mass/Volume
= X¹⁵/X³³
X¹⁵⁻³ = X⁶
Density = X⁶
(20) Density = Y¹⁰ grams/cm³
Volume = Y⁴ cm³
Mass = Density*volume
Mass = Y¹⁰ · Y⁴
= Using the multiplication law of indices, the two numbers are in the same base therefore add their powers
Y¹⁰⁺⁴
= Y¹⁴
(21) [ (3x)¹/³ · (3x)²/³)] / (3x)²/³
Using both multiplication and division laws of indices
(3x)²⁻¹
This is equal to (3x)¹
(22) 8⁷· 8³ · 8²
Using the multiplication law of indices, the two numbers are in the same base therefore add their powers
8⁷⁺³⁺² = 8¹²
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