given f (x) = 2x + 7 describe how the value of k affects the slope and y intercept of the graph of g compared to the graph of f 9 (x) = (2x +7) - 6
Answers
The slope of both functions remains the same, there is no effect of the value of k on a slope.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.
The given functions are :
f(x) = 2x + 5
g(x) = ( 2x + 5) -3
From the graph of both functions,
Let us consider two pairs of coordinates to find the slope,
For f(x)
(0,5) and ( -2, 1)
The slope of f(x)
m= ( 1- 5) / (-2 -0)
m= 2
For g(x) at (0,2) and (-1, 0) slope of g(x),
m = ( 0-2) / (-1-0)
m = 2
The slope remains unaffected.
y-intercept of f(x) , put x = 0
⇒ y = 5
y-intercept of g(x) , put x = 0
y =(0+ 5) -3
y = 2
Change in the value of y-intercept due to the value of k = -3.
Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:
The slope of both functions remains the same, there is no effect of the value of k on a slope.
Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.
The graph is attached.
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Related Questions
consider the correlation between heights of fathers and mothers and the heights of their sons. refer to the accompanying technology output. should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? why or why not?
Answers
Yes, the multiple regression equation should be used for predicting the height of a son based on the height of his father and mother because the P-value in the ANOVA table is very low.
What is multiple regression equation?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A single dependent variable and numerous independent variables can be analyzed using the statistical approach known as multiple regression. In order to forecast the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
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-(9m + 7) algebra question please help me!!
Answers
A right triangle has one angle that measures 54°. What is the measure of the other acute angle?
Answers
Answer: 36
Step-by-step explanation:
Since all triangle angles add up to 180 we just add up both the angle measure we know and then subtract by 180.
54+90=144
180-144=36
The acute angle measure is 36 degrees.
answer:
36 degrees
step-by-step explanation:
all the angles of a triangle add up to be 180 degrees. so subtract 90 and 54 degrees to get the answer. hope that helps!
a pair of fair dice is cast. what is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even? a) 0.4545 b) 0.3056 c) 0.3667 d) 0.2778 e) 0.1389 f) none of the above.
Answers
The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.
Given that,
A fair set of dice is thrown.
We have to find given that the total of the numbers falling above them is even, what is the probability that at least one of them is a 1.
We know that,
A fair set of dice is thrown.
The total of the numbers falling above them is even.
The probability that at least one of them is a 1 is
(5/36)/(8/36)
5/18
0.2778
Therefore, The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.
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As the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000, what happens to the probability of getting between 40% and 60% heads? What happens to the probability of getting exactly 50% heads?
answer choices
a. Both of those probabilities increase.
b. Both of those probabilities decrease.
c. The first probability increases, but the second one decreases.
d. The first probability decreases, but the second one increases.
Answers
Both of those probabilities decrease, hence Option (B) is the correct answer.
Given, the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000.
we have to find the effect on the probability of getting exactly 50% heads.
In 10 tosses,
we have to get heads 5 times,
P(X = 5) = (1/2)^5(1/2)^5
P(X = 5) = (1/2)^10
In 100 tosses,
we have to get heads 50 times,
P(X = 50) = (1/2)^50(1/2)^50
P(X = 50) = (1/2)^100
and so on.
It is clear that the probability of getting 50% heads decreases.
Also, Probability of getting heads between 40% and 60% decreases.
Hence, both of those probabilities decrease.
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you observe 40 crickets on an island after crickets were first introduced 2 years ago. at how many crickets must have been introduced?
Answers
Crickets must have been introduced at the lambda = 2 is 20.
Given:
you observe 40 crickets on an island after crickets were first introduced 2 years ago , at the lambda = 2 how many number of crickets must have been introduced .
Let x be the crickets must have to been introduced.
Number of crickets = observed crickets / lambda value
we know that,
Observed crickets = 40
lambda value = 2
substitute these values
Number of crickets = observed crickets / lambda value
= 40 / 2
= 20 crickets.
Therefore Crickets must have been introduced at the lambda = 2 is 20.
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Full question:
you observe 40 crickets on an island after crickets were first introduced 2 years ago. at lambda = 2 how many crickets must have been introduced?
convert these unlike fractions to equivalent like fractions and add them. you must use the lcd to get the answer correct. if possible, reduce the final sum.1523
Answers
The simplest form expression for the addition of the fractions given using the lowest common multiple of the denominator is 2/3.
A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.In Mathematics, a fraction is defined as a part of the whole thing. For example, ½ represents half of a whole number or a thing
Given the fractions :
1/4 + 5/12
The lowest common multiple of the denominator ;
A lowest common multiple of 4 and 12 = 12
1/4 + 5/12 = (3 + 5) / 12
1/4 + 5/12 = 8/12
Expressing in simplest form :
8/12 = 2/3
Therefore, the simplest form expression of the addition is 2/3
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Find an expression which represents the difference when (2x − 6) is subtracted
from (7-5) in simplest terms.
Answers
Answer:
-2x + 8
Step-by-step explanation:
(2x - 6) is subtracted from (7 - 5).
First term that into an equation.
Because our first term is being subtracted from our second one, our equation is written as:
(7 - 5) - (2x - 6).
Simplify the first term by subtracting:
7 - 5 = 2
Now simplify the second term by multiplying 2x - 6 by -1 to get them out of the parenthesis. We do this because there is a negative sign in front of it.
-1 (2x - 6)
-2x + 6
Now our equation is:
2 - 2x + 6
Combine like terms:
2 + 6 = 8
So -2x + 8
(2x - 6) subtracted from (7 - 5) is -2x+8
consider the following time series. t 1 2 3 4 5 6 7 yt 121 111 106 99 95 93 88 (a) construct a time series plot. what type of pattern exists in the data? the time series plot shows a seasonal pattern. the time series plot shows a linear trend. the time series plot shows a nonlinear trend. the time series plot shows a horizontal pattern. (b) use simple linear regression analysis to find the parameters for the line that minimizes mse for this time series. (round your answers to two decimal places.) b0
Answers
The time series plot is attached below
The parameters for the line that minimizes mse for this time series 119.714 - 4.9286t
What is time series ?
A time series is a group of data points that have been indexed chronologically in mathematics. A time series is most frequently a sequence captured at a series of equally spaced moments in time. As a result, it is a collection of discrete-time data.
These four elements are: -Secular trend, which describes movement over time; -Seasonal variations, which depict seasonal changes; -Cyclical fluctuations, which relate to periodic but not seasonal variations; -Irregular variations, which are additional nonrandom sources of variations in series.
t' = 28 / 7
= 4
Y' = 700 / 7
= 100
∑(t - t') (y - y') = -138
∑(t - t')² = 28
b1 = -138 / 28
= -4.9286
b0 = Y' - b1t'
= 100 - (-4.9286*4)
= 119.714
[tex]T_{t}[/tex] = 119.714 - 4.9286t
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How do you divide Powers with the same base?How dou you raise quotients(fractions) to a power(exponents)
Answers
The admission fee to play virtual reality is $12. It cost an additional x dollar to rent virtual reality equipment to play in the games. The total cost for 8 people to play virtual reality with equipment is $400. How much will it cost for one person to rent virtual reality equipment?
Answers
Answer:
$38
Step-by-step explanation:
400 ÷ 8 = 50 per person plus admission
minus admission
50 - 12 = 38
Oliver and his little brother made up a game using coins. They flip the coins toward a cup and receive points for everyone that makes it in. Oliver starts with 16 points, and his little brother starts with 27 points. Oliver gets 2 points for every successful shot, and his brother, since he is younger, gets 1 point for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have?
Answers
Oliver and his little brother will have an additional shot of 11shots and they both have 38points
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.
Represent the number of additional shot made by the brothers as x and the common point made by both of them be y
therefore,
16+2x=y equation 1
27+x= y equation 2
subtract equation 1 from 2
11-x= 0
therefore x= 11
substitute 11 for x in equation 2
y = 27+ 11
y= 38
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The time T it takes to travel some distance varies inversely with the rate r of travel. if it takes 2 hours to get somewhere traveling 40 mph how long would the same trip take you instead if you traveled 10 mph
Answers
The same trip will be 8 hours long if you traveled at 10 mph
How to determine how long the trip would take with 10 mph?
Variation is a concept that deals with variability or change in mathematics. Variation is defined as any change in some quantity due to a change in another
Given: The time T it takes to travel some distance varies inversely with the rate r of travel. This implies:
T α 1/r
T = k/r where k is the constant of proportionality
if it takes 2 hours to get somewhere traveling 40 mph. Then:
2 = k/40
k = 2 x 40 = 80
How long would the same trip take you instead if you traveled 10 mph will be:
T = k/r
T = 80/10
T = 8 hours
Therefore, the same trip take you 8 hours if you traveled 10 mph
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Brad is playing with blocks he has 18 blocks and wants to make an array of the same number of blocks in each row what are all the different ways he could arrange the blocks
Answers
There are several different ways that Brad could arrange the blocks to create an array with the same number of blocks in each row. For example, he could create a 3x6 array by arranging the blocks into three rows of six blocks each. Alternatively, he could create a 6x3 array by arranging the blocks into six rows of three blocks each. He could also create a 2x9 array by arranging the blocks into two rows of nine blocks each. Or he could create a 9x2 array by arranging the blocks into nine rows of two blocks each
TL;DR: 3x6, 6x3, 2x9 and 9x2.
The table shows the number of minutes per day students spend outside of school reading and doing their math homework. A table is shown. The number of minutes reading: fifteen, fifteen, fifteen, twenty, thirty, thirty, thirty, thirty, forty-five, and sixty. The number of minutes doing math homework: twenty-five, thirty, thirty, thirty, thirty, forty, forty-five, forty-five, fifty-five, and sixty. What is the difference of the means as a multiple of the approximate mean absolute deviations?
Answers
Answer:
i need points
Step-by-step explanation:
line has a slope of –
5 and includes the points (5,–
7) and (2,p). What is the value of p?
Answers
Answer:
p=8
Step-by-step explanation:
y= -5x + b
( -7) = -5(5) + b
-7= -25+b
add 25 both sides
-7+25=-25+25+b
18=b
y= -5x+18
p=-5(2)+18
p=8
For the function, locate any absolute extreme points over the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.) h(x) = x3 – 5x2 - 6x, -2 sxs 10 absolute maximum (x, y) = -.519,1.627 x absolute minimum (x, y) = ( 3.852, – 40.146)
Answers
For the function that is locate any absolute extreme points over the given interval h (x) - x 3 - 5x2 - 6x, 10 a we get absolute maximum for x and y (-0.380, 0.488) (10, 350) and absolute minimum for x and y (-2, -22) and (4.38, -52.924)
Both critical point lies in domain -2 [tex]\leq[/tex] n [tex]\leq[/tex] 10. We know that h (n) is not define at both side of interval end point so n = -2 and n = 10 are critical point,
The critical point are point where f(n) is defined and its derivative is zero or undefined.
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3. a pair of 6-sided dice is thrown. someone tells you that both the dice are showing an even number. with this information, what is the probability of the total (when you sum up the dice) being equal to 8?
Answers
The probability of the total being equal to 8 is 1/9 or 11.11%.
To calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8. Since both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6). Therefore, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.
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The length
17inches
more than half of its width. Which expression
represents the area of Nadine's new bed?
A) L+17
B) L + 34
C)2L² - 34L
D)2L² – 34
Answers
Answer:
C
Step-by-step explanation:
length = 17 + width/2
2×length = 34 + width
width = 2×length - 34
area of a rectangle
length × width = length × (2×length - 34) =
= 2×length² - 34×length
which is the answer option C.
Samantha i working in ale. Her weekly pay i $475 plu %5 of her total ale for the week. Samantha ell x dollar in a particular week. Write a function f(x) which can be ued to determine her pay for the week. Ue thi function to determine Samantha’ pay to the nearet cent for a week when her ale total i 8150
Answers
The function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.
Explain the meaning of the term percentage?%, which is a relative figure being used denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.As per the stated question-
Weekly pay of Samantha = $475.
Sales percentage = 5% of the sales.
Let 'x' be the sales done for the week.
Then, function models for the pay of the week.
f(x) = 475 + 5%x
f(x) = 475 + 5x/100
Thus, the function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.
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(b)(3) an annealing process is provided for the sample after cold work, what are the three stages during annealing (in sequence)?
Answers
The three stages of an annealing process in the sequence is recovery, recrystallisation, and gain growth.
Sequence:
In math, a series is defined as the sum of the elements of a sequence.
Given,
Here we need to find the are the three stages during annealing when an annealing process is provided for the sample after cold work.
In order to find the stages of the annealing process, first we have to know the definition of annealing process,
A process which is used to enhance ductility and counter the increase in hardness by cold working is known as annealing.
This one is to deal with residual stresses we first can reheat the glass to a high temperature known as annealing point and let it cool slowly so that the outside and inside cool at about the same rate.
And the resultant will have little to no residual stresses making annealed glass.
In the first stage recovery stage of annealing recovers the physical properties of the metals.
Second stage is recrystallisation, and gain growth.
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The sampling distribution for a goodness of fit test is the a. Poisson distribution b. t distribution c. normal distribution d. chi-square distribution
Answers
The chi-square distribution serves as the sampling distribution for the goodness of fit test since it quantifies how well the distribution derived from the data fits the empirical distribution.
What is sampling distribution?The sampling distribution is the probability distribution of a statistic that is obtained by repeated sampling of a certain population. The mean or mode of a population's mean or mode of a variable is one example of the many different choices for a statistic that are described in this passage. The sampling distribution of a proportion is obtained by repeating your survey or poll for each possible sample of the population. For instance, instead of asking 1,000 cat owners what cat food they prefer, you could conduct a number of polls.
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which of the following expressions are equivalent to…
Answers
Answer: none of the above
Explanation: as it's - -8/-4 it means the answer is negative which none of the answers provided are so it's none of the above
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.
Answers
The equation of circle for both the parts will be as,
(a) (x-3)² +(y-2)²= 4
(b) x²+y² = 1
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main Body:
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)² +(y -k)² = r²
The given circle is ...
(x -2)² +(y -2)² =2²
(x -2)² +(y -2)² = 4
__
(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:
x²+y² = 1
Hence the equation of circle is such.
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f(x) = −2|x + 4|; h(x) = f(-x) describe the transformation
Answers
The vertex of the function is transformed from (-4,0) to (4,0). The expression will be transformed from f(x) = −2|x + 4| to h(-x) = -2|-x + 4|.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the absolute function is f(x) = −2|x + 4|. The transformed function is calculated as,
f(x) = −2|x + 4|
h(-x) = −2|-x + 4|
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Seven cities are being considered as potential locations for the construction of at most four wastewater treatment plants. The table below provides the data for the situation. Missing entries indicate that a pipeline cannot be constructed
The capacity of a pipeline (in gallons per hour) is a direct function of the amount of wastewater generated, which is a function of the population. Approximately 500 gallons per 1000 residents are discharged in the sewer system per hour. The maximum plant capacity is 100,000 gal/hour. Further, we impose the requirement that all wastewater produced in any given city is treated in a single wastewater treatment plant 1. Write a mathematical program to determine the set of treatment plants that minimize total cost 2. Solve this problem with Excel
Answers
The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.
The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:
Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7
Subject to:
x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)
x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)
x1 + x4 <= 1 (3)
x2 + x4 <= 1 (4)
x3 + x4 <= 1 (5)
x4 + x5 <= 1 (6)
x4 + x6 <= 1 (7)
x4 + x7 <= 1 (8)
x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)
The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.
To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.
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The graph shows a proportional relationship between the variables y and x. Write an equation to model the relationship. Use pencil and paper. Explain how you know there is a proportional relationship if you are given either an equation or a graph.
Answers
Answer: y=20x
Step-by-step explanation: 40/2=20, 80/4=20, etc.
There are 20 per every-one
Find the reciprocal of 1 5/9 Find the reciprocal of 9/14 Ue pencil and paper. Explain how finding the firt reciprocal implifie finding the econd reciprocal
Answers
The reciprocal of 1 5/9 is 9/14 and the reciprocal of 9/14 is 14/9.
What is reciprocal?The multiplicative inverse of a number is referred to as the reciprocal.
In other words, 1 divided by a number is the definition of the reciprocal.
Any given number multiplied by its reciprocal will always yield the value 1.
If x is any real number, then 1/x will be the reciprocal of that number.
For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8.
So, the reciprocal of the fractions is:
(A) 1 5/9
9+5/9
14/9
Reciprocal: 9/14
(B) 9/14
Reciprocal: 14/9
Therefore, the reciprocal of 1 5/9 is 9/14 and the reciprocal of 9/14 is 14/9.
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tinga says 6:8 is equivalent to 36:72. what did tina do wrong?
Answers
George has been selling 5,000 t-shirts per month for $8. 50. When he increased the price to $9. 50, he sold only 4,000 t-shirts. What is the demand elasticity? if his marginal cost is $4 per shirt, what is his desired markup and what is his initial actual markup? was raising the price profitable?.
Answers
Demand elasticity came in at -4.6154. The actual markup was 0.2167 as opposed to the desired markup of 0.5789. The increase was therefore not profitable.
What is division?A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
The demand elasticity,
=[(Q1-Q2)/(Q1+Q2)] / [(P1-P2)/(P1+P2)]
[(8000-5000)/(8000+5000)] / [(9.5-10.5)/(9.5+10.5)]
[(3000/13000)] / [-1/20}
60000/-13000
=-4.6154
The desired markup,
(9.5-4) / 9.5
= 0.5789
The actual markup,
1/4.6154
= 0.2167
The demand elasticity was -4.6154. The desired markup was 0.5789 and actual markup was 0.2167. Hence, The increment was not profitable.
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