The probability of each outcome can be calculated using basic probability formulas, such as the multiplication rule and the addition rule is 1/2
Probability is the branch of mathematics that deals with the likelihood of events occurring. In this scenario, we are looking at the probability of a concrete beam failing by shear or flexure.
When three failed beams are randomly selected, the type of failure is determined for each one. We want to find the probability of each possible outcome, where X represents the number of beams among the three selected that failed by shear.
To list the outcomes in the sample space, we can use the following notation: S for shear failure and F for flexure failure. The possible outcomes are:
SSS, where all three beams failed by shear. In this case, X = 3.
SSF, where two beams failed by shear and one by flexure. In this case, X = 2.
SFS, where two beams failed by shear and one by flexure. In this case, X = 2.
FSS, where two beams failed by shear and one by flexure. In this case, X = 2.
SFF, where one beam failed by shear and two by flexure. In this case, X = 1.
FSF, where one beam failed by shear and two by flexure. In this case, X = 1.
FFS, where one beam failed by shear and two by flexure. In this case, X = 1.
FFF, where all three beams failed by flexure. In this case, X = 0.
Each outcome has a different value of X, which represents the number of beams that failed by shear.
Then the probability is calculated as,
=> 1/2
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Exhibit 2-1 Production possibilities curve data Consumption Goods Capital Goods
10 0
9 1
7 2
4 3 0 4
In Exhibit 2-1, according to the information, the opportunity cost of producing 3 units of capital is: A) 3 units of consumption goods B) 4 units of consumption goods C) 6 units of consumption goods D) 7 units of consumption goods.
The answer is C) 6 units of consumption goods.
What is Cost of producing?
The overall cost incurred by a business to manufacture a product or provide services is referred to as the cost of production. Supplies and raw materials consumed during production, as well as labor costs, are often included in production costs.
The opportunity cost of producing 3 units of capital is 6 units of consumption goods, as we can see from the data in the production possibilities curve.
Moving from producing 4 units of capital to producing 3 units of capital involves giving up 3 units of consumption goods (from 7 to 4), and moving from producing 3 units of capital to producing 2 units of capital involves giving up another 3 units of consumption goods (from 4 to 1).
Therefore, the opportunity cost of producing 3 units of capital is 6 units of consumption goods.
So, the answer is C) 6 units of consumption goods.
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Identify the function of the figure below this is trigonometry by the way
The graph shown is the graph of the cotangent function.
What is the graph of Cotangent?
The graph of the cotangent function, cot(x), is a periodic function that has a period of 2π. The cotangent function is the reciprocal of the tangent function, so its graph is related to the graph of the tangent function.
Like the tangent function, the cotangent function has singularities at x = (n + 1/2)π where n is an integer. At these points, the function has a vertical asymptote, meaning it approaches positive and negative infinity as x approaches (n + 1/2)π from either side.
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create a file lab2.py and define three classes, polygon, rectangle, triangle (see next page for a visual representation)
Lab2.py is a Python script that creates and manipulates three custom classes. The classes are as follows:
1. Person: This class stores information about a person, such as their name and age.
2. Student: This class inherits from the Person class and adds additional information, such as the student's major and GPA.
3. Instructor: This class also inherits from the Person class and adds additional information, such as the instructor's department and course load.
A file lab2.py and define three classes, polygon, rectangle, triangle is:
class Polygon:
def __init__(self, number_of_sides):
self.number_of_sides = number_of_sides
class Rectangle(Polygon):
def __init__(self, length, width):
Polygon.__init__(self, 4)
self.length = length
self.width = width
def area(self):
return self.length * self.width
class Triangle(Polygon):
def __init__(self, base, height):
Polygon.__init__(self, 3)
self.base = base
self.height = height
def area(self):
return 0.5 * self.base * self.height
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Part B
Question
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the
average number of customers per hour. Create : inequality in standard form that represents the restaurant owner's
desired revenue.
Type the correct answer in each box. Use numerals instead of words.
The inequality in standard form that represents the restaurant owner's
desired revenue is x² + 2x - 80 ≤ -65.
What are Inequalities?Inequalities are defined as the expressions consisting of both variables and constants connected by inequality signs like ≠, >, <, ≤ and ≥.
Part A :
Cost : 10 + x
Customers : 16 - 2x
Part B :
Given that,
Hourly revenue = Price paid by each customer × average number of customers per hour.
Price paid by each customer = 10 + x
Average customers per hour = 16 - 2x
Given that the restaurant owner wants a minimum revenue of $130 per hour.
(10 + x) (16 - 2x) ≥ 130
(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130
160 + 16x - 20x - 2x² ≥ 130
-2x² - 4x + 160 ≥ 130
Dividing the equation throughout by -2,
x² + 2x - 80 ≤ -65
The inequality sign changes as we multiply or divide with a negative number.
Hence the required inequality is x² + 2x - 80 ≤ -65.
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The complete question is given below.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Part A
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.
Part B
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.
commutative property of (32)-5+7?
Answer:
= 34
Step-by-step explanation:
(32)-5+7
32 - 5 + 7
= 32 + 2
= 34.
Graph the equation y=-x+4 intercepts
The area of this triangle is 64.8 km². Find the height h.
18 km is the base.
The height of the triangle is?
Answer: 16.2 km
Step-by-step explanation:
The height of the triangle can be found using the area formula for triangles:
Area = (1/2) × base × height
Rearranging the formula to solve for the height gives:
height = (2 × Area) / base
In this case, the area of the triangle is 64.8 km² and the base is given as 8 km. So, the height of the triangle can be calculated as:
height = (2 × 64.8 km²) / 8 km
height = 16.2 km
Answer:
7.2 km
Step-by-step explanation:
the formula for the area of a triangle is 1/2*b*h where b is its base and h is its height. now let's solve for the height
64.8=1/2*18h
64.8=9h
64.8/9=h
7.2 km=h
What is the volume of this right cone?
O 40 cm³
O 300 cm³
O 400 cm³
O 480 cm³
15.6 cm
12 cm
10 cm
The volume of the right cone is (c) 400π cm cube
How to determine the volume of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius = 10 cm
Height = 12 cm
The volume of the cone is calculated as
Volume = 1/3πr²h
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3π * 10² * 12
Evaluate
Volume = 400π
Hence, the volume is 400π cm cube
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A real estate investor buys a house and lot for $50,000. He pays $1,400 to have it painted, $2,500 to fix the plumbing, and $1,600 for grading a driveway. At what price must he sell the property in order to make a 20% profit?
A) $66,600
B) $49,760
C) $52,000
D) $52,800
E) $44,480
Help
Answer:
$66,600
Step-by-step explanation:
First you add everything up.
50,000 + 1,400 = 51,400
51,400 + 2,500 = 53,900
53,900 + 1,600 = 55,500
Now you need to get 20% of 55,500
20% of 55,500 is 11,100
Now you add them
55,500 + 11,100 = 66,600
A car tire company is testing a new tire that has proposed improved performance in wet conditions. An experiment was performed on a closed, half-mile track in wet conditions with the same car and driver. Two trials were performed with standard and new Wet Condition tires. What would the tire company MOST LIKELY infer based on this data?
Responses
A There is no hypothesis provided.There is no hypothesis provided.
B The hypothesis was neither verified or refuted.The hypothesis was neither verified or refuted.
C The hypothesis of the company is refuted.The hypothesis of the company is refuted.
D The hypothesis of the company is verified.
Answer:
B
Step-by-step explanation:
Based on the information provided, it is not possible to determine the hypothesis of the tire company. Therefore, options C and D can be eliminated.
Option A suggests that no hypothesis was provided, which may be possible. However, it is implied that the hypothesis was related to the proposed improved performance in wet conditions of the new tire. Therefore, option A may not be the best answer.
Option B suggests that the hypothesis was neither verified nor refuted. This is a common outcome in many experiments, and it is possible that the tire company may draw this conclusion based on the data. Therefore, option B is the most likely answer.
So, the tire company MOST LIKELY would infer that the hypothesis was neither verified nor refuted based on this data.
i need some help on this problem please
Answer:
C
Step-by-step explanation:
180-2x-2=180*7/9
x=19
A barge traveled 24 miles upstream on a river in 8 hours.The return trip took the barge 3 hours.What is the rate of the current,in miles per hour?
The rate of the current is 5/11 of the speed of the barge in still water.
Rate of the Miles per HourLet's call the speed of the barge in still water "s" (in miles per hour) and the speed of the current "c" (also in miles per hour).
When the barge travels upstream (against the current), its effective speed is reduced by the speed of the current, so the speed of the barge relative to the riverbank is (s - c). On the return trip, the current is going in the same direction as the barge, so the effective speed of the barge relative to the riverbank is (s + c).
We can use the formula distance = rate x time to set up two equations based on the information given:distance upstream = (s - c) x 8 miles
distance downstream = (s + c) x 3 miles
We also know that the two distances are equal, since the barge ends up back where it started. So we can set these two expressions equal to each other and solve for the unknown variable, c:(s - c) x 8 = (s + c) x 3
Expanding and simplifying, we get:8s - 8c = 3s + 3c
5s = 11c
c = 5s/11
Therefore, the rate of the current is 5/11 of the speed of the barge in still water.
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If △ EFG ∼ △ ABC
, What value of x will make the two triangles similar?
Answer:
the value of x will be 9 they all are similar so we will just take ratios and do cross multiplication
a hotel is looking over its occupancy, the number of rooms sold, over the course of the last 20 days. the data are provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the interquartile range? round your answer to two decimal places. hotel occupancy 131 135 139 124 124 121 124 135 124 helpcopy to clipboarddownload csv provide your answer below:
The interquartile range is 16.00
To construct a box and whisker plot in Excel using the Quartile.INC function for the given data, follow these steps:
1) Enter the data into a column in Excel.
2) Select the data column and click on the "Insert" tab in the top menu.
3) Click on "Insert Statistic Chart" and select "Box and Whisker" from the dropdown menu.
4) In the "Chart Elements" menu on the right, click on the arrow next to "Axis Titles" and select "Primary Vertical Axis Title" to add a title for the y-axis.
5) Label the y-axis "Number of Rooms Sold".
6) Right-click on the y-axis and select "Format Axis" from the dropdown menu.
7) In the "Number" menu, select "Number" as the category and set the number of decimal places to 0.
8) In the "Chart Elements" menu, click on the arrow next to "Chart Title" and select "None" to remove the chart title.
9) The resulting box and whisker plot should show the quartiles, the median, and any outliers.
To find the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3). The Quartile.INC function in Excel returns the exclusive quartiles (i.e., does not include the median in either quartile), so the interquartile range is calculated as:
IQR = Q3 - Q1
Using the Quartile.INC function with the given data, we get:
Q1 = 78.5
Q3 = 94.5
Therefore, the interquartile range is
IQR = Q3 - Q1 = 94.5 - 78.5 = 16
Rounding to two decimal places, the interquartile range is 16.00.
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Find a quadratic equation with integer coefficients that has the given solution set.
{-10, 9}
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
If the given solution set is {-10, 9}.
Then the quadratic equation can be written in factored form as:
(x + 10) (x - 9) = 0
Expanding the product,
x² + x - 90 = 0
Therefore,
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
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Find the cosine of the angle between the plane 4x-5y+z=4 and the plane 5x-4y+3z=-2
Given the planes [tex]4x-5y+z=4[/tex] and [tex]5x-4y+3z=-2[/tex], find the angle between them.
Using the formula,
[tex]\theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]
Where vector, [tex]A= < 4,-5,1 >[/tex] and vector [tex]B= < 5,-4,3 >[/tex].
Plug these values into the formula above...
[tex]\Longrightarrow \theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{(4)(5)+(-5)(-4)+(1)(3) }{\sqrt{(4)^2+(-5)^2+(1)^2}\sqrt{(5)^2+(-4)^2+(3)^2} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{\sqrt{42}\sqrt{50} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{10\sqrt{21} } )[/tex]
[tex]\Longrightarrow \theta \approx 20.2\textdegree[/tex]
If one dose of elixir is 6 mL, how many doses are there in 500 mL?
Answer:
83 There is an elixir
total quantity of elixir = 500 mL
quantity of elixir use in one dose = 6 mL
number of dose in 500 mL = 500/6
83.333
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The value of the equation is 4.19p = -6.1
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
2.3p - 10.1 = 6.5p - 4 - 0.01p
On simplifying , we get
Adding 4 on both sides , we get
2.3p - 6.1p = 6.49p
Subtracting 2.3p on both sides , we get
4.19p = -6.1
Now , the value of the equation similar to 4.19p = -6.1 is 2.3p - 6.1p = 6.49p
Hence , the equation is 4.19p = -6.1
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Ruby was out at a restaurant for dinner when the bill came. Her dinner came to $27. After adding in a tip, before tax, she paid $34.29. Find the percent tip. Note, please just input the number. NO PERCENTAGE SIGN...remember percent increase/decrease
The percent tip Ruby left was 27%.
What is percent?
A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
Calculate the tip amount:
The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:
Tip = Total cost - Cost of meal
Tip = $34.29 - $27
Tip = $7.29
Calculate the percent tip:
The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:
Percent tip = (Tip / Cost of meal) x 100%
Percent tip = ($7.29 / $27) x 100%
Percent tip = 27%
Therefore, the percent tip Ruby left was 27%.
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Cual es la mitad de 183
Let A be a random variable the represents the money you earn from Job A and let B be a random variable that represents the money you earn from Job B. The mean amount earned from Job A is $220 with a standard deviation of $30. The mean amount you earn from Job B is $180 with a standard deviation of $35.
a) On average how much more do you make from Job A?
b) What is the standard deviation of the difference in the amount you make (A – B)
c) Your mom really doesn’t want you working two jobs. She offers you the following deal. If you quit Job B, in addition to what you make in Job A, she will give you half of your average Job A salary plus $100. Would you take the deal if making the most money was most important to you? Explain.
The given statement indicates that (a) Your average pay is $40 (b) The standard deviation is 45.12 (c) If you retain both positions, your anticipated income is $400.
The significance of standard deviation?Because it aids in comprehending observations when the data is dispersed, standard deviation is significant. The standard error of the data will be higher the more evenly spread the data is.
a) On average, you make $220 - $180 = $40 more from Job A.
b) The standard deviation of the difference in the amount you make from Job A and Job B is given by:
σ(A - B) = √[σ(A)² + σ(B)²]
= √[(30)² + (35)²]
≈ 45.12
c) To determine whether to take the deal, we need to compare the expected earnings from the two scenarios. If you quit Job B and accept your mom's offer, your total earnings would be:
Earnings = (1/2) × $220 + $100 = $210
On the other hand, if you keep both jobs, your expected earnings would be:
Earnings = $220 + $180 = $400
Since $400 is greater than $210, you would not take the deal if making the most money is the most important thing to you.
It is important to remember that this choice may also be influenced by aspects like the amount of time and effort needed for each work, the chance for professional advancement, job security, and other non-financial considerations.
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A line passes through point (-6, 1)and has a slope of 3. Write an equation in Ax+By=Cform for this line. CO Use integers for A, B, and C.
An equation in Ax + By=C form for this line include the following: -3x + y = 19.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (-6, 1), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (1) = 3(x - (-6))
y - 1 = 3x + 18
y = 3x + 18 + 1
y = 3x + 19
In standard form, we have:
-3x + y = 19.
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he auditors for a health insurance company are reviewing the bills from client's stays at hospitals from last year. the length of stay in days for hospital visits from 20 randomly sampled bills is provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the value of the third quartile? round your answer to two decimal places. hospital length of stay (days) 7 6 7 6 7 8 3 2 6 provide your answer below:
The value of the third quartile is approximately 7.00, rounding it up to two decimal places.
In order to construct a box and whisker plot using Excel and the QUARTILE.INC function we will follow the steps -
Enter the data into a column in Excel.Select the column of data.Click on the "Insert" tab and select "Insert Statistic Chart."Choose "Box and Whisker" from the chart types.The box and whisker plot will be displayed.Using the given data, the third quartile (Q3) can be found using the QUARTILE.INC function in Excel as follows -
Enter the data into a column in Excel.Use the formula =QUARTILE.INC(data, 3) to find the third quartile (Q3).Using this method, rounding the result to two decimal places we get,
Q3 = QUARTILE.INC({7, 6, 7, 6, 7, 8, 3, 2, 6}, 3)
Q3 ≈ 7.00 (rounded to two decimal places)
Therefore, the value of the third quartile is approximately 7.00.
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Let t
be the time in weeks. At time t=0
, organic waste is dumped into a pond. The oxygen level in the pond at time t
is given by
f(t)=t2−t+1t2+1
.
Assume f(0)=1
is the normal level of oxygen.
(a) On a separate piece of paper, graph this function.
(b) What will happen to the oxygen level in the lake as time goes on?
The oxygen level will eventually return to its normal level in the long-run.
(c) Approximately how many weeks must pass before the oxygen level returns to 75
% of its normal level?
weeks (Round to at least two decimal places.)
The graph is plotted and attached
The oxygen level will be increasing as time goes on
In 0.5 weeks the oxygen level will return to 75% of its normal level
What will happen to the oxygen level in the lake as time goes on?This is the end behavior of the graph, of the function f(t) = t^2 − t + 1, the graph shows that as t tends to infinity. the oxygen level will continue to increase.
The graph is plotted and attached
From the problem. the normal level of oxygen is at f(0) = 1
75% of 1 = 0.75
From the graph, the oxygen level will return to normal level in 1 week(1, 1) and at 0.5 the oxygen level is 0.75, (0.5,0.75). This is the vertex of the graph.
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if (xy)/2=7 and x^2+y^2 = 28 find (x+y)^2
Answer:
Step-by-step explanation:
Expanding (x + y)^2, we get:
(x + y)^2 = x^2 + 2xy + y^2
We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:
(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42
Therefore, (x + y)^2 = 42.
What can be combined with 2x2? Select
all that apply.
Answer:
its only -11x^2
Step-by-step explanation:
2x^2 and -11x^2 have the same variable.
Find the exact value of the following expression for the given value of 0. Do not use a calculator tan (0/2) if 0x/2 If 0 x/2, then tan (0/2) (Simplify your answer. Type an exact answer, using radicals as needed.)
The exact value of the expression tan(0/2) for the given value of 0 is 0.
In mathematics, it is important to understand how to simplify expressions and solve for their exact values. One such expression is tan(0/2), where 0 is a given value. In this explanation, we will break down the steps to simplify this expression and find its exact value without using a calculator.
The expression we are given is tan(0/2), which can be simplified using the formula for the tangent of half an angle. This formula states that tan(x/2) = sin(x) / (1 + cos(x)).
In our given expression, we have x = 0, so we can substitute it into the formula and get:
tan(0/2) = sin(0) / (1 + cos(0))
Now, we know that sin(0) = 0 and cos(0) = 1, so we can simplify further:
tan(0/2) = 0 / (1 + 1) = 0/2 = 0
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Identifying a Graph from an Equation
Which graph represents a function with amplitude 4 and period pi?
The graph of the function f(x) = 4sin(2x) is illustrated in the image.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know sin(x) is a periodic function with amplitude 1 and a period of 2π.
Therefore, A periodic function with amplitude 4 and period π would be,
f(x) = 4sin(2x).
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The table shows the population of a city decreases over time. Calculate the average rate of
change of the population per year from year 20 to year 50.
Year
Population
1972
1,090,000
1982
1,060,000
1992
2002
940,000 860,000
2012
800,000
2022
770,000
The average rate of change of the population per year is -5666.66
How to determine the average rate of change of the population per yearFrom the question, we have the following parameters that can be used in our computation:
Year Population
1972 1,090,000
1982 1,060,000
1992 940,000
2002 860,000
2012 800,000
2022 770,000
Given that the year is from 1972, we have
year 20 = 1992 940,000
year 50 = 2022 770,000
So, we have
Average rate = Difference in values/Difference in years
This gives
Average rate = (770,000 - 940,000)/30
Evaluate
Average rate = -5666.66
Hence, the rate is -5666.66
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Which of the following are like terms?
Select 3 correct answer(s)
Question 1 options:
3x2 & 3x4
3x4 & 2x4
3y2 & 3x2
2x2 & 3x2
x2 & y2
2x & 3x
4x2 & 4x
The like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
What is like terms?Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same are called like terms,
Examples: 7x and 2x are like terms because they are both "x".
Given are some pairs of expressions, we are asked to identify which are like terms,
We know that, according to the definition of the like terms,
Like terms are those terms which contain the same variable which is raised to the same power,
Therefore, the expressions showing the like terms are,
3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
Because, they have same variable with same powers.
Hence, the like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
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