From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.
What is graphs?Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.
Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.
Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.
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Miss brown butt the following items to make a cake for her daughter's 13th birthday party quantity for flower is 5LB the unit costs $2.74 per LB the total cost is $6.54The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP that you need to cost is $7.49 per lb the total cost is $4.49Miss brown also needed to buy some eggs exhaust sole 6 for $4.85 and she needs to buy 1⁄2 dozen eggs calculate the cost of eggs calculated her total bill for the 4 items there is a 5% discount if you spend $50 on how much more money will she need to spend to get the discounts which is the best deal spent $50 And get the 5% Discounts Or purchase the four tems ?explain your reasoning.
The total cost of the ingredient to make the cake and the comparison to the percentage discount to get the best deal indicates that we get;
The total cost of the ingredient for the cake is $37.78The best deal is to purchase the 4 items and minimize spendingWhat is a percentage?A percentage is the representation of a proportion of an item per 100 of a set of items.
Quantity of flour = 5 lb
Unit cost for the flour = $2.74 per lb
Quantity of sugar = 2 1/2 lb
Unit cost of the sugar = $1.70 per lb
Quantity of butter = 2 lb
Unit cost of the butter = $7.49 per lb
Quantity of eggs required = 1/2 dozen
Cost of six eggs = $4.85
Miss Brown's total bill for the four items, C, is therefore;
C = 5 × 2.74 + (2 1/2) × 1.7 + 2 × 7.49 + 4.85 = 37.78
Her total cost for the four items, C = $37.78The discount available for purchases of $50 or more = 5% discount on the purchase
The amount of more money she will have to spend to get the 5% discount is therefore;
$50 - $37.78 = $12.22
Miss Brown will have to spend $12.22 extra to get the 5% discount
The 5% discount indicates that spending $50, Miss Brown only has to pay $50 - $50 × 5% = $47.5
Therefore, in order to get the discount, the total amount spent on the purchase is increase by $47.5 - $37.78 = $9.72, and the amount saved from the discount is $2.5, therefore;
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How likely is it for Bryson to choose a number greater than 4?
The probability of Bryson choosing a number greater than 4 is given as follows:
Amount of numbers that are greater than 4 / Total amount of numbers.
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 outcomes are given as follows:
Desired: numbers greater than 4.Total: all the numbers.Missing InformationThe problem is incomplete, hence the procedure to obtain the probability was described.
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Answer:
The answer is likely
Step-by-step explanation:
Box plot pls answer what is the outlier and a box plot represents the data excluding the outlier
Answer: The outlier is $95 and the plot is D.
Step-by-step explanation:
An outlier is the data value that's much larger or much smaller than the other data values. Here, that is $95.
Excluding this value, our smallest is $15 and the largest is $60. We plot a dot at both of these points.
The middle dot is the median. To find this, we will arrange the values in order and find the middle value. (We are excluding $95.) After doing this process, we see the middle dot is at 39.
$15, $20, $38, $60, $45, $40, $35, $50
$15, $20, $35, $38, $40, $45, $50, $60
----, ----, ----, $38, $40, ----, ----, ----
[tex]38 + 40 = 78, \;\;78 / 2\;\;\boxed{= 39}[/tex]
This means we have dots at 15, 39 and 60, leading us to answer D.
9. Find the sum of the first multiples of 5.
Answer:
75
Step-by-step explanation:
Use the arithmetic progression formula: S =n/2(2a + (n-1)d)
a = 5, d = 5, n = 5
S = 5/2((2(5) + (5-1)(5)) = 75
Please Explain and solve this problem. What trigonometric function would you use based upon the given information in the triangle shown below? ASAP
To solve the problem we would use tangent as a trigonometric function and find the unknown value.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
From the given triangle we observe that the given values are:
Angle B, side a and side b.
To find any of the unknows in the three we use the trigonometric function tangent.
Tan α = opposite side / adjacent side
For the given figure:
Tan B = b / a
Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.
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Help with my algebra homework
The evaluation of the function expressions gives:
(q + f)(5) = 1
(f - q)(2) = -2
(q f)(4) = 9
(f /q)(0) = 1
How to use the graph to evaluate the function expressions?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
From the graph, when c = 5, q(5) = 0, f(5) = 1. Thus:
(q + f)(5) = 0 + 1 = 1
From the graph, when c = 2, f(2) = 0, q(2) = 2. Thus:
(f - q)(2) = 0 - 2 = -2
From the graph, when c = 4, q(4) = 3, f(4) = 3. Thus:
(q f)(4) = 3 * 3 = 9
From the graph, when c = 0, f(0) = 4, q(0) = 4. Thus:
(f /q)(0) = 4/4 = 1
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Find the surface area (in square feet) of a right circular cylinder of height 4 feet whose base has radius 3 feet. Round the answer to the nearest tenth of a square foot.
Answer:
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
Step-by-step explanation:
To find surface area of a right circular cylinder we can use the formula,
A = 2πrh + 2πr^2
Here A is surface area,
π is mathematical constant ,
r is radius, and h is the height of the cylinder.
We have
r = 3 ft
h = 4 ft,
Now we put the values to find the surface area,
A = 2π × 3 × 4 + 2π ×3^2
A = 24π + 18π
A = 42π
A= 42×3.14 (we know π = 3.14 )
A = 131.88
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
help with this i hate multiple choce
For the function y = f(x). The statements are -
A. False
B. True
C. False
D. False
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The data points for the function y = f(x) is given.
The domain of a function is the set of "valid inputs" to the function, while the range of a function is the set of "all outputs" of the function.
The function y = f(x) represents the relation between the set of elements in the domain of f and the set of elements in the range of f, where the variable x represents an element from the domain of the function and f(x) represents an element of the range of the function.
The first row in the table lists all the inputs to the function f. The second row lists the outputs of f corresponding to the inputs in the first row.
(a) The given statement is false because the range of f is the set of all f(x) where x is in the domain of f: {-5,-3,0,2,6,7,9,10,13}
(b) The given statement is true because, according to the table, the given input x = -3 has an output of f(x)=2; that is, f(-3) = 2.
(c) The given statement is false because the domain of f is the set of all values of x for which f(x) is defined:
{1,2,30,1,2,3,0,1}
(d) The given statement is false because, according to the table, the given input x = 0 has an output of f(x)=3; that is, f(0) = 3.
Therefore, the three statements are false and one is true.
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A quadratic function has a vertex at the point (-1, 3) and passes through the point (-4, -6).
The quadratic function is of the given question is f(x) = [tex]-2x^{2}[/tex] + 10x + 1.
What is quadratic equation?When a, b, and c are constants and x is an unknown variable, the equation has the form [tex]ax^{2}[/tex] + bx + c = 0, which is known as a quadratic equation. The unknown variable x is solved for using the quadratic equation.
The largest power of the variable in a quadratic equation is two. The variable is now squared, but it may also have a coefficient, often known as a multiplier, in front of it. Two more components in the equation are made up of a constant and a variable with an exponent of 1.
In the given question,
The equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) can be written as:
y = [tex]a(x + 1)^{2}[/tex] + 3
Where a is a constant that determines the shape of the function. To find the value of a we can substitute the coordinates of the vertex and the point into the equation and solve for a.
Substituting (x, y) = (-1, 3) into the equation:
3 = [tex]a(-1 + 1)^{2}[/tex] + 3
Simplifying:
3 = [tex]a(0)^{2}[/tex] + 3
3 = 3
Since both sides are equal, a = 1.
Substituting (x, y) = (-4, -6) into the equation:
-6 = [tex]a(-4 + 1)^{2}[/tex] + 3
Simplifying:
-6 = [tex]a(-3)^{2}[/tex] + 3
-6 = 9a + 3
-9 = 9a
Divide each side by 9:
-1 = a
Since both values of a are equal, a = -1.
Therefore, the equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) is:
y = [tex]-(x + 1)^{2}[/tex] + 3
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Which quadratic inequality in vertex form represents
the relationship in the graph?
y²²(x-4)² +28
y>(x-4)²+28
y2-2(x+4)² +28
y>(x+4)² +28
Answer:
Y> (x - 4)² + 28
Step-by-step explanation:
Calculate the marked price on a bag of Cement selling 570 ksh after a discount of 5% is offered.
Answer:
541.5 ksh
Step-by-step explanation:
Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?O The theoretical probability for selecting a red card in each pick is 0.5. O For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far. O This is an example of the law of large numbers. O The relative frequency of selecting a red card changes with the increase in number of selections.
He then constructs a graph to visualize his results, For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.
Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,
The false statement is:
For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.
Option B is correct.
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Chose the fraction that correctly represents the ratio 5 to 15 in simplest form
The fraction that correctly represents the ratio of 5 to 15 in it's simplest form is option C. 1/3.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
The given ratio is 5 to 15.
Fraction in simplest form means that, the numerator and denominator cannot be factored by a common factor again.
In order to find the given ratio in simplest form, find the greatest common factor of both 5 and 15.
5 = 5
15 = 3 × 5
5 is the only common factor and so the greatest common factor of both 5 and 15.
5 / 15 = (5 × 1) / (5 × 3)
= 1/3
Hence 1/3 is the simplest form of the ratio 5 to 15.
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Your question is incomplete. The correct question is as follows.
Chose the fraction that correctly represents the ratio 5 to 15 in simplest form.
A. 2/3
B. 10/30
C. 1/3
D. 1/5
The answer to this problem
Answer:
A. (f+g)(x)=-2x^2-2x+8
Step-by-step explanation:
You combine like terms by adding
find an expression for sin (5 theta) as a fifth degree polynomial in the variable sin(theta) ?
On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ
What is trigonometry?The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.
The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.
the trigonometry
sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ
Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ
sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}
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Assuming that the relationship is exponential, which equation best represents the curve of best fit for this set of data?
The equation that best represents the curve of best fit for this set of data is y = ae^{bx}, where a and b are constants to be determined by the data points.
What is Equation?An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.
This equation is an example of an exponential function, which is used to model data that increase or decrease at an increasing rate. The constants a and b can be determined using a least-squares regression to find the line of best fit. The equation can then be used to extrapolate future values from the data points.
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Select the graph of y = 2 sinz+2
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The graph of y = 2 sin(x) + 2 is given by the following option:
Graph A.
How to graph the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, meaning that before the vertical shift, it oscillates between -2 and 2.
Due to the vertical shift, the function is going to oscillate between 0 and 4, with a period of 2π and no phase shift, crossing the midline of y = 2 at the origin, hence Graph A is the correct graph.
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Graph the following system of inequalities below and shade the feasible region.
y > -1
y≥ x²+ 1
(x-1)²+(y-1)² ≤ 16
(4marks)
The graph of the system of the equation y > -1, y≥ x²+ 1, and (x-1)²+(y-1)² ≤ 16 is attached with the feasible region of each part shaded
How to identify the graphs
The equation y > -1 is a horizontal line drawn at point y = -1 and shaded above the line because the sign is greater than. the line is dashed line line since the equation is not "greater than or equal to".
The equation y ≥ x²+ 1 is a parabolic equation
The equality sign attached to the greater than makes the line a solid line and because it is greater than the shading is inside the curve.
The equation (x - 1)² + (y - 1)² ≤ 16 is a equation of a circle
The equality sign attached to the greater than ("greater than or equal to") makes the line a solid line and because it is greater than the shading is inside the circle
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solve. a certain phone call costs 75 cents for the first 3 minutes plus 15 cents for each additional minute. if the call lated x minutes and x is an integer greater than 3, what is cost in dollars
(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35
While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes
According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15
cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315
, so we need to find whether the cost is greater than 315 cents.
(1) The cost of the phone call was less than $4.16. Not sufficient.
(2) The cost of the phone call was greater than $3.35. Sufficient.
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The compression ratio in a certain engine is 7.5 to 1. If the expanded volume of a cylinder is 15 cu in., what is the compressed volume?
On solving the provided question, we can say that inches if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
In a certain engine, the compression ratio is 7.5: 1.
A cylinder's enlarged volume is 45 in3 in.
We must determine the cylinder's compressed volume.
Let v represent the cylinder's compressed volume.
The aforementioned circumstance can be described as
7.5 : 1 = expanded volume : compressed volume
7.5/1 = 45/v
7.5 = 45/v
v = 45/7.5
v = 6 cubic inches .
Therefore, if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .
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PLEASE HELP ASAP WILL GIVE BRAINLIEST
The value of the length /MK/ is 10 units
How to find the length?Recall that in an isosceles reangle, two sides are equal and the base angles are equal
We can use the cosine rule to find the length MK
N² = K²+M² - 2KMCosN
This implies that /MK/² = 5²+5²-2*5*5*cos110
⇒25+25-50*-0.9990
= 50+49.95
=99.95 this can be approximated to 100
the /MK/ = √100= 10 units
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Find all real numbers z for which the equation (z-5)x^2-zx+5=0 has exactly one real solution.
By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.
For which values of z the quadratic equation has only one real solution?For a general quadratic equation:
a*x^2 + b*x + c = 0
We define the discriminant as:
D = b^2 - 4ac
The quadratic equation will have only one real solution only if the discriminant is equal to zero.
Here the quadratic is:
(z - 5)*x^2 - z*x + 5 = 0
Then the discriminant is:
(-z)^2 - 4*5*(z - 5)
And that must be equal to zero, then we need to solve:
z^2 - 20*(z - 5) = 0
z^2 - 20z + 100 = 0
Using the quadratic formula we will get:
[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]
So the quadratic equation has one real solution only for z = 10.
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Last week's and this week's low temperatures are shown in the table below Low Temperatures for 5 Days This Week and Last Week Low Temperatures This Week (F) Low Temperatures Last Week (F) Which measures of center the mean of this wer O the mean of the range of this O the mean absolute deviat the mean absolute devi 10 ariability are greater than 5 degrees? Select three choices temperatures temperature
The measures of the center or variability that are greater than 5 degrees are :
a) the mean of this week’s temperaturesb) the mean of last week’s temperaturesc) the range of this week’s temperaturesHow to find the center of variability ?The mean of the data on temperature this week and the last is :
= ( 4 + 10 + 6 + 9 + 6 ) / 5
= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6
The mean of the data on temperature last week and the last is :
= ( 13 + 9 + 5 + 8 + 5 ) / 5
= 8 degrees Fahrenheit
The range of this week's temperature is :
= 10 - 4
= 6 degrees Fahrenheit
All these measures of center are above 6 degrees.
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The full question is:
Temperatures for 5 Days This Week and Last Week
Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.
a) the mean of this week’s temperatures
b) the mean of last week’s temperatures
c) the range of this week’s temperatures
d)the mean absolute deviation of this week’s temperatures
e) the mean absolute deviation of last week’s temperatures
The Lopez family is looking to rent a large truck for their upcoming move. With Felipe's
Moving, they would pay $90 for the first day plus $1 per additional day. With Springdale
Rent-a-Truck, in comparison, the family would pay $40 for the first day plus $6 per additional
day. Before deciding on which company to use, Mrs. Lopez wants to find out what number of
additional days would make the two choices equivalent with regards to cost. How many
additional days would that be?
Write a system of equations, graph them, and type the solution.
The system of equation is written as follows
y = 90 + x
y = 40 + 6x
With regards to cost the choices will be equivalent in 10 day
How to write the system of system of equationsAssuming additional day is x
Felipe's Moving, they would pay $90 for the first day plus $1 per additional day:
= 90 + x
Rent-a-Truck, the family would pay $40 for the first day plus $6 per additional day.
= 40 + 6x
Equating both costs gives
90 + x = 40 + 6x
90 - 40 = 6x - x
50 = 5x
x = 10
in 10 days the cost will be same
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PLEASE ANSWER!!!
Russell surveys 200 randomly selected seventh-graders in his school and finds that 30 attend summer camp. If there are 780 seventh-graders in his school,
about how many are expected to attend summer camp?
Answer:
To estimate the number of seventh-graders who attend summer camp, we can use the sample proportion of 30 out of 200 students.
Let's call the population proportion of seventh-graders who attend summer camp "p".
The sample proportion can be estimated as:
p = 30/200 = 0.15
To estimate the number of seventh-graders in the entire school who attend summer camp, we can multiply the population size by the sample proportion:
Estimated number of seventh-graders attending summer camp = p * population size = 0.15 * 780 = 117
So, about 117 seventh-graders in the school are expected to attend summer camp.
Answer:
117 seventh-graders in the school are expected to attend summer camp.
Step-by-step explanation:
Given the following square, solve for x.
(7x+13) °
Answer:
x = 11
Step-by-step explanation:
square = a plane figure with four equal straight sides and four right angles.
so
7x + 13 = 90
7x = 90 - 13
7x = 77
x = 77 : 7
x = 11
------------------------
check
7 x 11 + 13 = 90
90 = 90
the answer is good
Solve for the equation of the tangent line. Question is attached below. Please show full working.
Answer:
y = 1/8x +1/64
Step-by-step explanation:
You want the equation of the line that is tangent to the curve y = x³ -x⁴ in exactly two places.
Points of intersectionSince the tangent line is not crossed, the difference between the line and the given curve is a 4th-degree polynomial with two roots, each of multiplicity 2. If those are 'a' and 'b', we can write for line y = mx +p, ...
mx +p -(x³ -x⁴) = (x -a)²(x -b)² = 0
x⁴ -x³ +0x² +mx +p = x⁴ -2(a+b)x³ +(a²+4ab+b²)x² -2ab(a+b)x +a²b²
Equating coefficients, we have ...
x⁴: 1 = 1x³: -1 = -2(a+b)x²: 0 = (a+b)² +2abx: m = -2ab(a+b)constant: p = a²b²SolutionThe coefficient of x³ tells us ...
a +b = 1/2
The coefficient of x² tells us ...
0 = (a +b)² +2ab
0 = (1/2)² +2ab
ab = -1/8
LineUsing these value, we can find the equation of the line to be ...
m = -2ab(a+b) = -2(-1/8)(1/2) = 1/8
p = (ab)² = (-1/8)² = 1/64
The equation of the line is ...
y = 1/8x +1/64
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Additional comment
To find the line, we did not need the coordinates of the points of tangency. They are ((1-√3)/4, (3-2√3)/64) and ((1+√3)/4, (3+2√3)/64).
The slope of the line is equal to the slope of the quartic at the point of inflection of its derivative, at x=1/4.
A city bowling league is holding a tournament in which the top 8 bowlers with the highest three-game totals are awarded cash prizes. First place will win $1250, second place $1132, third place $1014, and so on.
(a) Write a sequence a, that represents the cash prize awarded in terms of the place n in which the bowler finished
(b) Find the total amount of prize money awarded at the tournament.
The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.
What exactly is a sequence?
A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.
Now,
given award money for 1, 2, 3 places is given as $1250, $1132 and $1014
that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)
So, the sequence will be aₙ=$1250-118ⁿ⁻¹
where
n=place at which a bowler is placed.
Hence,
The sequence will be aₙ=$1250-118ⁿ⁻¹.
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Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y=x-2
y=x-1
The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
No matter how far we extend a parallel line, it will never meet another parallel line.
Given that,
y=x-2
y=x-1
For x = 1:
y = x - 2 = 1 -2 = -1
y = x - 1 = 1 - 1 = 0
For x = 2:
y = 2- 2 = 0
y = 2 -1 = 1
Plot the graph using the points.
The two lines have the same slope hence they are parallel lines.
Since, the two lines are parallel the system has no solutions.
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can someone explain why 4(8x + 2) = 4(7x + 2 + x)
On solving the provided question, we cans ay that the equation is 4(8x + 2) = 4(7x + 2 + x); when we put x = , LHS = RHS
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation is
4(8x + 2) = 4(7x + 2 + x)
32x + 8 = 28x + 8 + 8x
36x - 32x = 0
4x = 0
x = 0
when we put x = , LHS = RHS
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