The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.
Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.
The z-score formula is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.
Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.
If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:
z = (115 - 100) / 15 = 1
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determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
1.
What is the average rate of change between
the points (3,9) and (5, 15)?
Therefore, the average rate of change between the points (3,9) and (5,15) is 3.
What is coordinates?Coordinates are a set of values that locate the position of a point in space. In mathematics, coordinates are used to represent the position of points on a plane or in space, using a set of numerical values that correspond to the distance along each axis from an origin point. In two-dimensional Cartesian coordinate systems, for example, a point is represented by two numbers (x, y) that indicate its position relative to the x and y axes. In three-dimensional Cartesian coordinate systems, a point is represented by three numbers (x, y, z) that indicate its position relative to the x, y, and z axes.
Here,
The average rate of change between the points (3,9) and (5,15) is the slope of the line passing through those two points. We can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3,9) and (x2, y2) = (5,15).
slope = (15 - 9) / (5 - 3)
= 6 / 2
= 3
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I will mark you brainiest!
SSS is used to prove two triangles are congruent.
A) False
B) True
Answer:
A
Step-by-step explanation:
because___________________________________
Answer:
B) True
Step-by-step explanation:
SSS or Side-Side-Side is used to prove two triangles are congruent.
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
Answer:
x = 52.2
Step-by-step explanation:
Add 4x - 4y^2 = 36 and x + 2y^2 = 225
x + 2y^2 + 4x - 4y^2 = 225 + 36
5x = 261
x = 261/5=52.2
In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
Find X using the picture below.
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answer:
the answer would be 100 I guess
Question 17 (2 points)
Suppose that 10% of Peloton bikes are defective and should be replaced. Peloton
offers one-year warranties on their new bikes, and should a customer use the bike in
the first year and discover the defect, the bike will be replaced. Peloton also knows
that 75% of customers use the bike in the first year. What is the probability a
customer will actually make a valid warranty claim?
0.075
0.10
0.175
0.75
The probability that a customer will actually make a valid warranty claim is 0.075.
What is Probability?A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
According to question:The probability that a customer will make a valid warranty claim is the probability that the customer both uses the bike in the first year (which has a probability of 0.75) and discovers a defect (which has a probability of 0.10).
Using the multiplication rule of probability, the probability that both of these events occur is:
0.75 x 0.10 = 0.075
Therefore, the probability that a customer will actually make a valid warranty claim is 0.075.
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Suppose you are trying to estimate the average age of the entire CSU student population. You collect a sample of size n-163, and from your data you calculate x =20.1 s 1.8 round your answers to 3 decimal places) 1. The standard error of the mean for this data set is: 2. The approximate 95% margin of error is (Use the approximation method from the notes, in which the critical value is approximately 2.) 3. The approximate 95% CI for lage is
a) The standard error of mean for this data set is approximately 0.141.
b) The approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.
a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:
SEM = 1.8 / sqrt(163) ≈ 0.141
So the standard error of the mean is approximately 0.141.
b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:
MOE ≈ 2 * 0.141 ≈ 0.282
So the approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get
CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376
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Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then
If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.
What are angles of triangle?A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
First, we know that cot(0) = adjacent / opposite = 3/4.
In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.
The hypotenuse can be found using the Pythagorean theorem.
h² = adjacent²+ opposite²
h² = (-3)^2 + 4^2
h²= 9 + 16
h² = 25
h = 5
So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.
Using the definitions of the trigonometric functions, we can find the values of the other functions:
sin(0) = opposite / hypotenuse = 4/5
cos(0) = adjacent / hypotenuse = -3/5
tan(0) = opposite / adjacent = -4/3
csc(0) = hypotenuse / opposite = 5/4
sec(0) = hypotenuse / adjacent = -5/3
cot(0) = adjacent / opposite = 3/4 (given)
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1 On a map of scale 1:100 000, the distance between Tower Bridge
and Hammersmith Bridge is 12.3 cm.
What is the actual distance in km?
To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.
Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.
Now, 1 km is equivalent to 100 000 cm.
Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.
Hence, the actual distance in km is 1.23 km.
can anyone help me with this question triangles?
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
What is the slope of the line passing through the points (-1, -7) and (-9, -2)?
Answer:
m = -5/8
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -7) (-9, -2)
We see the y increase by 5 and the x decrease by 8, so the slope is
m = -5/8
AA contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
Model D) a spinner with 6 equal sections can be used to simulate the contestant's chances of winning.
Step-by-step explanation:
A spinner with 6 equal sections represents the possible outcomes of the game show, where each section represents a possible win or loss. Since the contestant has a 1 in 6 chance of winning, the spinner would have one section representing a win and five sections representing a loss. Each spin of the spinner would represent one try at the game show, and the probability of winning can be determined by calculating the theoretical probability of landing on the win section.
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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HELP ME ASAP PLEASE!!!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
What is the missing value in the equation shown below?
4/10+ ?/100= 7/10
A 1
B 3
C 10
D 30
Answer: D 30
Step-by-step explanation:
4/10 + 30/100
2/5 + 3/10
7/10
NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE
Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.67, and the standard deviation for y is 3.76. The regression equation is reported as
y = 3.3 + 1.13x
What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 0 and 1.)
A fraction of the variation in y that can be explained by the variation in the values of x is equal to 0.25189186354.
What is a regression equation?In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;
y = bx + c
Where:
b represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept, vertical intercept, or initial value.How to determine the fraction of the variation?In Mathematics and Statistics, the value of slope can be calculated by using the following mathematical expression;
[tex]b=r(\frac{S_y}{S_x})[/tex]
where:
r is correlation coefficient.Sy represent the sample standard deviation of the y-values.Sx represent the sample standard deviation of the x-values.By rearranging, we have:
[tex]r=b(\frac{S_x}{S_y})[/tex]
r = 1.13(1.67/3.76)
r = 0.50188829787
By taking the square of both sides, we have:
r² = 0.25189186354.
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Solve each proportion round to the nearest tenth
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
I will mark you brainiest!
Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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