The combinations of ordered triplets that are possible is equal to: A. 18.
How to find the possible number of ordered triplet?Since the common difference (d) between the consecutive terms in an arithmetic progression (AP) is constant, we have:
d = y - x = z - y
Rearranging the terms, we have:
x = y - d
z = y + d
From the given equation:
x + y + z = 30
y - d + y + y + d = 30
3y = 30
y = 30/3
y = 10.
So the arithmetic progression (AP) is given by:
(10 - d), 10, (10 + d)....
Since the common difference (d) is a natural number which would be from 1 to 9, the combinations of ordered triplets that are possible is as follows:
Number of possibilities = 9 × 2
Number of possibilities = 18.
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Complete Question:
If x, y, z are three natural numbers in A.P. such that x + y + z = 30 then the possible number of ordered triplet (x, y, z) is?
A. 18
B. 19
C. 20
D. 21
What are 2 institutions from the Industrial Revolution? NEED ANSWER NOW PLEASE!!!!!!!
A. Corporations
B. National Institute of Space and Technology
C. Labor Unions
D. National Institute of Disaster Management
The institution from the industrial revolution is the national institute of space and technology. Hence, option B is correct.
What is Industrial Revolution?Agrarian and handcraft economies were replaced by industrialized and machine production during the Industrial Revolution in modern history. New modes of living and working were made possible by these technical advancements, which profoundly altered society.
In the 18th century, this practice started in Britain and then extended to other regions of the world. The English economics professor Arnold Toynbee (1852–83), who originally used the word to characterize Britain's economic growth from 1760 to 1840, although it had been used by French writers earlier.
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Select the expression that represents this real-world situation.
There are p people on the bus. At the next stop, 8 people get off and 5 more get on. Write an expression to show how many people are on the bus.
p − 8 + 5
p + 8 − 5
p x (8 + 5)
p ÷ (8 − 5)
The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
What is an expression?An expression is a combination of numbers, symbols, and/or operators that represents a quantity, a value, or a computation. Expressions can include variables, which are letters that represent unknown values, and can be manipulated and evaluated using mathematical operations like addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they are used in various areas of mathematics, including algebra, calculus, and geometry, as well as in many other fields such as physics, engineering, and economics.
According to the given information:The expression that represents the real-world situation is:
p - 8 + 5
Explanation:
Initially, there are p people on the bus. Then, 8 people get off, which is represented by the subtraction of 8 from p (p - 8). After that, 5 more people get on the bus, which is represented by adding 5 to p - 8, giving us the final expression: p - 8 + 5. This expression simplifies to p - 3, which represents the final number of people on the bus.
Therefore, The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
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When we hear an echo we are experiencing which of the following characteristics of sounds waves
Answer:
diourfd
Step-by-step explanation:
Before each class, I either drink a cup of coffee, a cup of tea, or a cup of water. The probability of coffee is 0.7, the probability of tea is 0.2, and the probability of water is 0.1. If I drink coffee, the probability that the lecture ends early is 0.3. If I drink tea, the probability that the lecture ends early is 0.2. If I drink water, the lecture never ends early. 1) What’s the probability that I drink tea and finish the lecture early? 2) What’s the probability that I finish the lecture early? 3) Given the lecture finishes early, what’s the probability I drank coffee?
Answer:
1. Probability of drinking tea and finishing the lecture early = 0.2 * 0.2 = 0.04 or 4%
2. Probability of finishing the lecture early = 50% (0.3 + 0.2).
3. Probability of drinking coffee = 0.21 or 21% (0.7 * 0.3)
Step-by-step explanation:
a) Data and Calculations:
Probability Early Ending Expected Probability
Coffee 0.7 0.3 0.21
Tea 0.2 0.2 0.04
Water 0.1
b) The probability of drinking coffee, tea, or water is the chance that the lecturer drinks either coffee or tea or water. The combined probability of the three actions is always 1. The expected probability is the weighing of the probabilities with another event, ending the lecture early. This is obtained by multiplying their respective probabilities.
!!!!Plz Help!!!! How does the slop of AB compare with the slope of the parallel line as you move points A, B, and C? What conclusion can you draw about the relationship between the slopes of parallel lines?
Answer:
As points, A and B move, the slope of the two lines change but remain equal to each other. As point C moves, the slope does not change but remains equal to each other since the line through C is drawn parallel to AB.
I can canclude that slope of any two parallel lines are equal
Step-by-step explanation:
solve the following question
14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4
15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°
What is a trigonometric equation?A trigonometric equation is an equation that contains a trigonometric ration.
14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows
Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,
We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that
(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°
= 1² + 1² - 4cos²45°
We know that cos45° = 1/√2. So, we have
1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²
= 1 + 1 + 4/2
= 2 + 2
= 4
So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4
15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows
Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1
We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that
2(cos²θ - sin²θ) = 1
2(cos2θ) = 1
cos2θ = 1/2
Taking inverse cosine, we have that
2θ = cos⁻¹(1/2)
2θ = 30°
θ = 30°/2
θ = 15°
So, θ = 15°
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Ellie is building a dollhouse. She has boards that are two different lengths. One long board is 7 inches longer than the total length of three of the short boards. Draw a picture showing how the short and long boards are related.
Ellie is building a dollhouse and she has four boards according to the question.
One long board is 7 inches longer than THE TOTAL LENGTH of three of the short boards.
Therefore, if she has boards A, B, C and D then board A equals the addition of boards B, C and D plus an additional 7 inches. We can put this into pictures as shown below;
From the pictures shown, whatever are the lengths of b, c and d, e simply add them up and add 7 to the result to derive the length of a.
B = b
C = c
D = d
A = (b + c + d) + 7
Use the graph to determine the domain and range of the function.
Q
(-8,5)
20-
16-
-20-16-12-8-4
(-12,-11)
8-
st
-8-
-12-
-16-
-20
(1-1)
(-2,-4)
X
4 8 12 16 20
Q
5
hs
HEE
The domain is
(Type your answer in inte
The domain is {-8, -12, 1, -2} and the range is {5, -11, -1, -4}
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
(-8,5) (-12,-11) (1-1) (-2,-4)
The domian is the set of the input values
Using the ordered pairs as a guide, we have
Domain = {-8, -12, 1, -2}
For the range, we have
The range is the set of the output values
So, we have
Range = {5, -11, -1, -4}
Hence, the range is {5, -11, -1, -4}
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What is the base higher and area
Answer:
5
8
20
Step-by-step explanation:
Answer:
Base: 6 units. Height: 4 units. Area: 24 units.
Step-by-step explanation:
To find the base of the parallelogram, it is literally the bottom line of the parallelogram. In this case, it is the line below the x-axis that is also parallel to it. To find the length of the base line, just count the squares between both ends of the line. There are 6 squares, so the base is 6 units long. To find the height of the parallelogram, you count the squares (units) between the bottom and top lines of the parallelogram, both parallel to the x-axis. There are 4 squares between the lines, so the height of the parallelogram is 4 units. To find the area of a parallelogram, multiply the base by the height. 6 * 4 = 24, so the area of the parallelogram is 24 units.
In Exercises 9 to 14, find the limit of each function at the given point, or explain why it does not exist. 10. f(z) = Arg z at Zo--1 11. f(z) = (1-Im z)-1 at z,-8 and then at zo-8 +1 12.f(z) = (z _ 2) log(z-21 at zo = 2 13, f(z) =-, z#0 at zo = 0 14. f(z) = 2+21,
Previous question
The limit of each function at the given point i n the question 10 to 14, is explained below.
Limit Of A function:A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.
When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a
10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.
11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.
However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.
12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.
13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.
14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.
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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compression strength of more than 1300 KN/m^2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with \sigma =60. Let \mu denote the true average compressive strength.What are the appropriate null and alternative hypothesis?
Answer:
The null hypothesis is: u >= 1300 KN/m^2
And the alternative hypothesis is:
u < 1300 KN/m^2.
Step-by-step explanation:
The null hypothesis describes hat there is no difference or assiciation between variables of a specific population or that it is a particular average value while the alternative hypothesis states otherwise.
In this case study, the null hypothesis is: u >= 1300 KN/m^2
And the alternative hypothesis is:
u < 1300 KN/m^2.
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 4% of students brought their lunch. 50 students brought their lunch. How many students in total are in Ridgewood Junior High School?
There is a total of 720 students are in Ridgewood Junior High School.
5% of students brought their lunch.
36 students brought their lunch.
the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Let there be x students in the Ridgewood Junior High School.
5% of students brought their lunch and equal to 36
so 5% of x = 36
5/100 * x = 36
x = 36*100/5
x = 36*20
x = 720
There is a total of 720 students are in Ridgewood Junior High School.
b) Use the graph to estimate the
value of x when y = 1
Answer:
Hey bro you're welcome.
Step-by-step explanation:
Into a single power and explanation pls
9^10 divided by 9 can be simplified to 9^(10-1) = 9^9
This is because when dividing a power by the same base, we can subtract the exponent by one.
In other words, 9^10 / 9 = (9999999999) / (9) = 99999999*9 = 9^9.
So, 9^10 divided by 9 is equal to 9^9.
Another way to think about this is that dividing a number by itself is the same as multiplying that number by 1, and 9^10 / 9 = 9^10 * 1 / 9 = 9^10 / 9^1 = 9^(10-1) = 9^9
In terms of real numbers, 9^10 is equal to 387420490 and 9^9 is equal to 3486784401. So 9^10 divided by 9 is equal to 3486784401.
\(\it \dfrac{9^{10}}{9}=9^{10}:9^1=9^{10-1}=9^9\)
church,
"From Martina's World"
Martina, a 3-year-old with flaming red hair and bright blue eyes, is admitted to the pediatric unit w
bronchitis. In addition to her medical condition, Martina has autistic disorder. Martina does not seem
nurse's presence in the room but is intensely occupied with a blue stuffed dog. The nurse is prepar
ister scheduled oral medications to the child. Martina's mother is present in the room.
What approach would help the nurse to establish a trusting relationship with Martina
To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.
To establish a trusting relationship with Martina, the nurse can employ several approaches:
Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.
Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.
Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.
Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.
Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.
By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.
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Complete Question:
What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?
PLS HELP ME :(
A model railroad track is 96 inches long. Estimate how many millimeters this is if 1 inch = 25.4 millimeters.
Answer:
2438.4
Step-by-step explanation:
multiply 96 by 25.4
can someone help me with my work so i can pass
The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.
Here, we have,
we know that,
The sum of the angles in a triangle add to 180
x+2x+6x = 180
Combine like terms
9x= 180
Divide by 9
9x/9 = 180/9
x = 20.
Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.
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complete question:
The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.
PLS HELP FIRST TO ANSWER GETS BRIANLEST
Answer:
2/6 (1/3 simplified), 0.33333, 33.33%
Step-by-step explanation:
Answer: 2/3 or 4/6 0.6 66.666%
Step-by-step explanation:
What are the potential solutions of log4x+log4(x+6)=2?
Penny makes 5 liters of applesauce. She saves 0.38 liter for dinner and puts the rest in jars.
If each jar holds 0.66 liters, how many jars can she fill?
Step-by-step explanation:
¹1litre =100cl
5 litres =500cl
0.66cl=y
cross multiply
500÷0.66 =7
Which of these are exponential decay or growth and how 1) y=250(1-t)^4 2) y=14(0.75)^x 3) y=475(1.05)^x
The decay function is 2) y = 14(0.75)^x and the growth function is 3) y = 475(1.05)^x
How to determine the decay and growth functions?From the question, the equation of the functions are given as
1) y=250(1-t)^4 2) y=14(0.75)^x 3) y=475(1.05)^x
Rewrite the equations properly
So, we have the following representation
1) y = 250(1-t)^4
2) y = 14(0.75)^x
3) y = 475(1.05)^x
An exponential function is represented as y = ab^x
This means that the first equation may or may not be an exponential function
When the other equations are compared, we have:
b = 0.75 in 2) y = 14(0.75)^x
b = 1.05 in 3) y = 475(1.05)^x
The value of b in this case is the factor
Also,
If b is less than 1, then the function is a decay function
If b is greater than 1, then the function is a growth function
0.75 is less than 1
So, the function y = 14(0.75)^x represents a decay function
1.05 is greater than 1
So, the function y = 475(1.05)^x represents a growth function
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Define a direct variation equation
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
The coordinate of the point after transformation is: (3, -4)
What is the coordinate after moving of point?The coordinate initially is given as (0, -4).
Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:
(0 - 1, -4)
= (-1, -4)
Moving by 4 units to the right means an addition of 4 units to x coordinate to get:
(-1 + 4, -4)
= (3, -4)
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Given: D is the midpoint of AB: E is the midpoint of AC
Prove: DE 1 BC
Complete the missing parts of the paragraph proof
Proof
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE
V
A(25, 20)
loro, o
CC
GDD
Elab, o)
slope of BC
BIOO)
C(2,0)
Therefore, because
DE I BC.
Answer:
Step-by-step explanation:
Slope of DE = \(\frac{y_2-y_1}{x_2-x_1}\)
= \(\frac{c-c}{a+b-b}\)
= 0
Slope of BC = \(\frac{y_2-y_1}{x_2-x_1}\)
= \(\frac{0-0}{2a-0}\)
= 0
Therefore, DE║BC because slopes of BC and DE are equal.
Function and notaion.
Answer: 45
Step-by-step explanation:
Function notation: is another way of writing a function to make it easy to understandInstead of the independent and dependent variables being x and y they are now x and f(x)f(x) can be interpreted as the y value at a given x value in this case f(-5) must be solved for, essentially saying what is y when the x value is -5\(f(-5)=2(-5)^{2} -5\)
\(f(-5)= 2(25) -5\)
\(f(-5) = 50-5\)
\(f(-5) = 45\)
Please help me with this
A person places $48800 in an investment account earning an annual rate of 3.1%,
compounded continuously. Using the formula V = Pert, where Vis the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.
What is compounding?Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.
We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:
Using the formula V = \(Pe^rt\)
Principal (P) = $48,800.00
Annual Rate (R) = 3.1%
Compound (n) = Compounding Continuously
Time (t in years) = 13 years
Result:
V = $73,019.78
V = P + I where
P (principal) = $48,800.00
I (interest) = $24,219.78
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.1/100
r = 0.031 rate per year,
Solving the equation for V:
V = \(Pe^rt\)
V = \(48,800.00(2.71828)^(0.031)(13)\)
V = $73,019.78
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HELppppppppppppppppp
9514 1404 393
Answer:
40 -8p -3w$4Step-by-step explanation:
Ms. Liu will have to pay 8p for p bags of popcorn, and 3w for w bottles of water. The amount she will have left will be these amounts subtracted from $40.
40 -8p -3w . . . . represents the money remaining
For p=3 and w=4, this evaluates to ...
40 -8(3) -3(4) = 40 -24 -12 = 4
Ms. Liu will have $4 left after her purchase.
What is the height of a rectangular prism, if the volume is 750 cm, the length 25 cm, and the width is 5 cm?
Answer:
6 cm
Step-by-step explanation:
Volume of a prism= Length X Width x height
750 = 25 x 5 x h
750= 125h
750/125 = 125h/125
h= 6
Answered by Gauthmath