1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:
-3x + 12y = 15
-3x/ -3 + 12y/ -3 = 15/ -3
x + 4y = -5
So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.
2. Are Systems AAA and BBB equivalent?
Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.
In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST.
Answer:
ST = 12 units
Step-by-step explanation:
Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6 ST = 8(21 - ST)
6 ST = 168 - 8 ST ( add 8 ST to both sides )
14 ST = 168 ( divide both sides by 14 )
ST = 12 units
suppose x is the number of times a woman is selected when 3 people are randomly chosen (without replacement) from a group of 2 women and 2 men. what are the possible values of x?
Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.
When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:
WWx (two women and one of either gender)
WMx (one woman, one man, and one of either gender)
MWx (one man, one woman, and one of either gender)
MMx (two men and one of either gender)
In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.
In outcome 1 (WWx), a woman is selected twice, so x = 2.
In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.
In outcome 4 (MMx), no women are selected, so x = 0.
Therefore, the possible values of x are 0, 1, 2, and 3.
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Select the correct answer from each drop-down menu.
Observe the given functions.
Complete the sentences to compare the two functions.
Over the interval ____, the average rate of change of g is greater than the average rate of change of f. As the value of x increases, the average rates of change of f and g _________, respectively. When the value of x is equal to 7, the value of _________
It can be further generalized that a quantity increasing exponentially will ___ exceed a quantity increasing linearly.
The correct answer for each of the math expressions is given below:
1. (4,5)2. remain constant and increase3. g(x) exceeds the value of f(x)4. eventuallyWhat is a Graph?The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.
These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Hence, given that in the graph,
f(x) = 4x + 3
g(x) = [tex]\frac{5}{3} ^x[/tex]
Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.
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the prices of houses in the us is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. a real estate agent takes a random sample of 30 houses and records the mean price. what is the best description for the sampling distribution? skewed to the right with a mean of 383,500 and a standard deviation of 52,823 skewed to the right with a mean of 383,500 and a standard deviation of 289,321 approximately normal with a mean of 383,500 and a standard deviation of 52,823 approximately normal with a mean of 383,500 and a standard deviation of 289,321
The sampling distribution of the mean price of 30 houses is a normal distribution with a mean of $383,500 and a standard deviation of $52,823 is the correct description among the following given for sampling distribution.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
This can be calculated as:
Standard Deviation of Sampling Distribution =
(Standard Deviation of Population) / (√Number of Samples)
= $289,321 / √30
= $289,321 / 5.4772
= $52.823
Therefore, the sampling distribution of the mean price of 30 houses is a normal distribution with a mean of $383,500 and a standard deviation of $52,823.
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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
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What number is 30% less than 40?
Answer: 30% less than 40 is 28
Step-by-step explanation:
Answer:
The answer is 28.
Step-by-step explanation:
I'm bad at proving stuff but that's the answer I promise. (quick tip, you are more likely to get answers if you give more points. :D)
Jody is picking a movie to watch this evening.
Of the movies in her cabinet, 9 are romantic
comedies. She will pick one movie at random.
If the probability of the selected movie being
a romantic comedy is 25%, how many movies
are on the shelf?
The number of movies on the shelf is given as follows:
36 movies.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For this problem, the parameters are given as follows:
Probability of 25% = 1/4.Number of desired outcomes is of 9.Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:
1/4 = 9/x
x = 9 x 4
x = 36 movies.
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in nine bernoulli trials, what is the probability that there will be more than the expected number of failures?
The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.
In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.
Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:
E(X) = np
where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:
E(X) = 9p
If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.
To calculate this probability, we need to use the binomial distribution formula, which is given by:
[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]
where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.
Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:
P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰
= 0.2461
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a lamppost, cab, bent at point a after a storm. the tip of the lamppost touched the ground at point c, as shown below: triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet. what is the height, in feet, of the portion ab of the lamppost?
The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.
Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.
Let's call the height of AB "x". We can use the tangent function to solve for x:
tan(55) = x/20
Multiplying both sides by 20:
x = 20 tan(55)
Using a calculator, we get:
x ≈ 27.8 feet
Therefore,
The height of the portion AB of the lamppost is approximately 27.8 feet.
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Answer: 20 tan 55
Step-by-step explanation:
took test and got it right
what happens to the equation of f(x) = 1/x, if it's translated 4 units up and to the right 3 units
The cost for renting a car is $75 plus $0.30 for every mile driven. Which equation,
written in function notation, represents this situation where R represents the total
cost for the rental and d represents miles driven?
R(d) = 0.30d + 75
R = 75d + 0.30
R(d) = 75d + 0.30
R = 75.30
Answer:R(d)=0.30d+75
Step-by-step explanation:
Note: This equation, as requested, only shows the cost of
rental on a daily basis. In order to solve for more than 1
day the equation should be: Cost = .3r+ 100d or something
similar... with r representing miles driven, d representing
total number of days for the rental.
what is 10000 = 8000(1 + .04t) interest is simple 4%. how long would it take for 8000 to grow to 10000
The number of years to grow the amount from $8,000 to $10,000 will be 6.25 years.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
The equation is given below.
10000 = 8000(1 + .04t)
Where 't' represents the number of years. Then solve the equation for 't', then we have
10000 = 8000(1 + 0.04t)
1.25 = 1 + 0.04t
0.04t = 0.25
t = 0.25 / 0.04
t = 6.25 years
The number of years to grow the amount from $8,000 to $10,000 will be 6.25 years.
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NEED AN ANSWER QUICKLY PLEASE I WILL GIVE BRAININEST
Hi. I need 8 expressions that are equivalent to 31(2760q - d)
Answer: is 1 of them 31(2760)q -d)
Find the value of x.
34°
4x²
Answer:
give the diagram please
Can you please find the area and perimeter
The area and perimeter of the figures are( 15a³b⁴ and 10a²b⁴ + 6ab²), (6m³n² and 4m² + 10mn²) and (8m³n and 4√[m(m+2y²)] + 8mn)
What is the area and perimeter of the figures1.
The area of the rectangle can be calculated using the formula;
A = l * w
A = 5a²b⁴ * 3ab²
A = 15a³b⁴
The perimeter of the rectangle is
P = 2(l + w)
P = 2[(5a²b⁴) + (3ab²)
P = 10a²b⁴ + 6ab²
2.
The area of a triangle is given by
A = 1/2 b * h
A = 0.5 * 4m² * 3mn²
A = 6m³n²
The perimeter of the triangle is calculated as
P = 4m² + 7mn² + 3mn²
P = 4m² + 10mn²
3.
The area of the triangle is given as;
A = 1/2 * b * h
A = 0.5 * 4mn * 4m²
A = 8m³n
The perimeter of the triangle is
Using Pythagoras theorem to find the hypothenuse side
The third side is 2√[m(m + 2n²)]
The perimeter of the triangle is = 4√[m(m+2y²)] + 8mn
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Which of the following statements about the product of 3–√2 and 75−−√ is true?
its b is true I just took it
HELP DUE IN 20 MINS!!!!!
Boris's company makes solid balls out of scrap metal for various industrial uses. His current task is to make a batch of lead balls with radius 3 in. If he has a 3 total of 28,260 in³ of lead, how many balls can he make? Use 3.14 for , and do not round your answer.
The number of balls that he can make is given as follows:
249 balls.
How to obtain the volume of a sphere?The volume of a sphere of radius r is given by the equation presented as follows:
V = 4πr³/3.
Considering the radius of 3 inches, the volume of each ball is given as follows:
V = 4π x 3³/3
V = 113.1 in³.
He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:
28260/113.1 = 249 balls.
(rounding down, as there will not be enough material for the 250th ball).
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I'm stuck on this question and I need help
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
Answer:
56 crickets
Step-by-step explanation:
A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each
day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 25 21 19 13
Which of the following graphs shows the relationship given in the table?
The corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)
What is a linear function?
A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.
A Girl scout is selling cookies to raise money for her troop.
She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day.
This result is shown in the table:
Time(in days) Number of boxes
1 25
3 21
4 19
7 13
The graph for the given data is attached below.
This forms a straight line.
By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.
That is y=-2x+27.
Hence, the corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)
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Answer: Its D.
Step-by-step explanation:
A welder has two pieces of half-inch pipe, one of length 23 ft and another of length 3 ft. What is the total length of the two welded together?
The total length of the two welded together is 26ft.
What is addition and subtraction?The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).
Given that the length of the two pieces of the pipe is 23ft and 3ft.
The total length of the two welded together is:
23 + 3 = 26ft
Hence, the total length of the two welded together is 26ft.
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assume that earth is a sphere with radius 3960 miles a town is at latidtude 32 n find the distance in miles from the town to the north pole
The distance from the town to the North Pole is approximately 2290 miles.
To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.
The length of the meridian arc can be calculated using the formula:
Length = (π/180) x radius of the Earth x angle in degrees
where π is approximately 3.14159, and the radius of the Earth is 3960 miles.
Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.
Plugging in these values into the formula, we get:
Length = (π/180) x 3960 miles x 58°
Length = (3.14159/180) x 3960 miles x 58
Length ≈ 2290 miles
Therefore, the distance from the town to the North Pole is approximately 2290 miles.
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Oliver tries to cut a piece of metal 30 centimeters long the price of metal ends up being 29. 4 centimeters long what is the percent error
The percent error in the specified situation is 2%.
The actual length of the metal is 30 centimeters, and the measured length is 29.4 centimeters. The difference between the actual and measured lengths is:
30 - 29.4 = 0.6 centimeters
The absolute error is the magnitude of this difference:
|0.6| = 0.6 centimeters
To find the percent error, we divide the absolute error by the actual value and multiply by 100:
percent error = (absolute error / actual value) x 100%
= (0.6 / 30) x 100%
= 2%
Therefore, the percent error is 2%.
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
x+y=-4
-x-y=4
The following system of equations has no solutions, the correct option is A.
How to find the solution to the given system of equation?For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.
We have given that;
system of equations are
x+y=-4.....1
-x-y=4......2
Now,
Rearranging the equation 2
-4=x+y
Its equal to equation 1
Therefore, the system of equations will have no solution.
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Expand and simplify (2x^2+3)(4x+5)-8x(x^2-2)
Answer:
[tex]10x^2+28x+15[/tex]
Step-by-step explanation:
[tex](2x^2+3)(4x+5)-8x(x^2-2)\\\\=(2x^2)(4x)+(2x^2)(5)+(3)(4x)+(3)(5)-8x^3+16x\\\\=8x^3+10x^2+12x+15-8x^3+16x\\\\=10x^2+28x+15[/tex]
which of the following statements about approaches to political risk management is not true? question 26 options: passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards. passive political risk management assumes that it is difficult, if not impossible, to systematically model political risk. active political risk management assumes that positive and negative political events in any country are neither independent nor random events. active political risk management assumes that political events unfold in observable patterns that statistical methods can detect.
The statement which is not true is a. Passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards
Passive political risk management does not deter managers from fully or partially hedging their bets against political risk exposure. This management describes a strategy for controlling political risk that involves altering how a firm carries out a business to reduce political risk. This is generally performed without necessarily using financial instruments to safeguard against any degree of political risk.
It may entail taking necessary steps to spread the firm's operations across other geographies and regions, choosing joint venture partners with strong political influence, determining local contacts, and preserving strong ties with local individuals associated with politics. Even if a firm doesn't use active hedging tactics, these activities can efficiently assist it to lessen its exposure to political risk.
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Doranda was given two paid vacation days by her employer when she started her new job. She will receive an additional three days per year of paid vacation for each year she remains with the company up to a maximum of four work weeks of paid vacation time. Part A
The expression for the number of paid vacation days for x years is
2 + 3x.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of paid vacation days = 2
Now,
She will receive an additional three days per year of paid vacation for each year she remains with the company.
This means,
For x years,
Number of paid vacation days = 2 + 3x
Now,
The expression for x years.
= 2 + 3x
Thus,
2 + 3x is the expression for the number of paid vacation days for x years.
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The complete question.
A)
Write an expression for the number of paid vacation days for x years.
The number of students enrolled at a college 18,000 and grows 5% each year. What is the initial amount
Answer:
900
Step-by-step explanation:
5% of 18,000
a student has an average of 85% on the unit tests, 83% on the final test, 89% on the class project, and 91% on homework submissions. if the unit tests count for 30% of the final grade, the final test counts for 40%, the class project counts for 20%, and homework submissions count for 10%, what is the weighted average grade of the student?
The weighted average grade of the student is 85.6% calculated by multiplying the weight of each category with the average score of that category, and summing up the results.
To find the weighted average grade of the student, we can use the following formula:
Weighted average = (weight of category 1 x average of category 1) + (weight of category 2 x average of category 2) + ... + (weight of category n x average of category n)
where n is the number of categories being considered.
Using this formula and the information given in the question, we can calculate the weighted average as follows:
Weighted average = (0.30 x 85%) + (0.40 x 83%) + (0.20 x 89%) + (0.10 x 91%)
= 25.5% + 33.2% + 17.8% + 9.1%
= 85.6%
Therefore,
The weighted average grade of the student is 85.6%.
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Will has 7/8 gallon of cold water in the refrigerator. During the day, he drinks 3/4 gallon of the water.
How much cold water does he have left at the end of the day?
A. 1/8 gallon
B. 1/4 gallon
C. 1/2 gallon
D. 1 gallon
Answer: 1/8
Step-by-step explanation: 3/4 is the same as 6/8
7/8- 6/8 = 1/8
