Answers
The constant of variation for the given graph is 1/4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Given that the equation of the line in the graph is a direct variation equation.
Direct variation equations are of the form,
y = k x, where k is a constant number called constant of variation.
We have to find the value of k.
y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).
It is enough to find the slope of the given line.
Take two points from the graph, let it be (4, 1) and (-4, -1).
Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4
The value of k is 1/4.
Hence the value of constant of variation is 1/4.
Learn more about Slope here :
https://brainly.com/question/2491620
#SPJ1
Related Questions
Mariana and her best friend are attending a concert in a large auditorium. They just climbed up 125 steps. The number of steps they climbed can be represented by
zero
positive
negative
Answers
The number of steps they climbed can be represented by positive
How to represent the number of steps?From the question, we understand that they climbed up
Upward movements are usually represented by the positive sign
This means that:
Steps = 125 or +125
Hence, the number of steps they climbed can be represented by positive
Read more about positive numbers at
https://brainly.com/question/1782403
#SPJ1
The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
Answers
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
When first hired, Deondre was earning $5.85 per hour. He has worked his way up in the business and is currently making $12.30 an hour. What is the absolute and relative change in Deondre's hourly pay from when he was first hired to now?
Answers
Answer:
$6.45/hour
110.26%
Step-by-step explanation:
The absolute change is the difference between salaries now ands then.
12.30 - 5.85 = 6.45
The relative change in the percent increase.
percent increase = (new number - old number)/(old number) × 100%
percent increase = (12.3 - 5.85)/(5.85) × 100%
percent increase = 110.26%
Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)
Answers
The rule that describes the transformation is (x, y) - (-y, -x).
What is transformation?Transformation is the process of using rules to transform some graphics into something else.When a shape is either reflected, rotated, or translated, the coordinates of the vertices that make up the shape change.The four different forms of transformations—Translation, Reflection, Rotation, and Enlargement—are depicted in the following illustrations.The underlying coordinate system remains fixed while an object transformation modifies the coordinates of each point on the object in accordance with some rule. • A coordinate transformation expresses each point of the object in the new coordinate system by defining it in terms of the old one.The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.
The rule that describes the transformation is (x, y) - (-y, -x).
To learn more about transformation, refer to:
https://brainly.com/question/2689696
#SPJ9
Evaulate u^2-4u+2 when u=-2
Answers
You can just replace [tex]u[/tex] with 2:
[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]
Alternatively, you can complete the square.
[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]
When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)
Answers
Here, 12 is the mode.
Step-by-step explanation:
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.
So let's talk in brief:-
First, we arrange it in ascending order.
3,3,6,6,9,9,12,12,12,12
and now as we see that we get 12 as the most repeated ones.
reference link-
Find the mode of 5,6,9,6,12,3,6,11,6,7 - Brainly.inhttps://brainly.in
#m76
A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed: JOB TIMES (minutes) A B C D E Workstation A 27 18 70 26 15 Workstation B 45 33 30 24 10 Click here for the Excel Data File a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B.
Answers
1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.
2. The determination of the amount of idle time for Workstation B is 37 minutes.
Johnson's Sequencing Rule:According to Johnson's sequencing rule, start listing jobs with minimum completion time first.
If the job occurs at Workstation A, list it on the left side. If the job occurs at Workstation B, list it on the right side, as below:
Data and Calculations:JOB TIMES (minutes) A B C D E
Workstation A 27 18 70 26 15
Workstation B 45 33 30 24 10
The first job with a minimum completion time is Job E at Workstation B.
The second job with a minimum completion time after Job E is Job B at Workstation A.
The third job with a minimum completion time after Job B is Job D at Workstation B.
The fourth job with a minimum completion time after Job D is Job A at Workstation A.
The last job is Job C at Workstation B.
The sequence that minimizes total completion time is as follows:
B A C D E
A B
Calculation of Idle Time at Workstation B:Job Workstation A Workstation B Idle Time
In Out In Out Workstation B
B 0 0+18 = 18 18 18+33 = 51 18
A 18 18+27 = 45 51 51+45 = 96 19
C 45 45+70 = 115 115 115+30 = 145 0
D 115 115+26 = 141 145 145+24 = 169 0
E 141 141+15 = 156 169 169+10 = 179 0
Total Idle Time at Workstation B = 37 (18 + 19)
Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.
Learn more about Johnson's job sequencing rule at https://brainly.com/question/6484513 and https://brainly.com/question/15970710
#SPJ1
Question Completion with Answer Options:1. A-B-C-D-E
2. E-D-B-C-A
3. D-C-B-A-E
4. B-A-C-D-E
5. C-A-B-D-E
math stuff who ever answers right gets brainlest answer
Answers
Answer:
Median is 83
Range: 61
Step-by-step explanation:
The median is the number in the middle. The range is the max. number subtracted from the min number.
Evaluate 4s^2 for s = 1/4. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
Answers
Answer:
1/4
Step-by-step explanation:
Given [tex]\displaystyle{s=\dfrac{1}{4}}[/tex] and we have to evaluate [tex]\displaystyle{4s^2}[/tex]. We can do by substituting the given value s = 1/4 in 4s² term:
[tex]\displaystyle{4\cdot \left(\dfrac{1}{4}\right)^2}\\\\\displaystyle{4\cdot \dfrac{1}{16}}\\\\\displaystyle{\dfrac{1}{4}}[/tex]
Therefore the value is 1/4
Evaluate the given algebraic expressions replacing x with -2 and y with 1
3x^2
Answers
Answer:
12
Step-by-step explanation:
3x^2
because the information provided states that x = -2, that is what we are going to replace x with.
3(-2)^2
the next step is to evaluate the power because that is next in PEMDAS.
(-2)^2 = 4
that leaves us with:
3 * 4 = 12 ( the " * " represents the multiplication sign)
hope this helps!
Which of the following similarity statements about the triangles in the figure is true?
Right triangle P Q R has angle Q marked as a right angle. A segment is drawn from point Q to side P R. The point where the segment intersects side PR is point S. Angle P S Q is marked as a right angle.
A. Triangle P Q R is similar to triangle P S Q, which is similar to triangle Q S R.
B. Triangle R Q P is similar to triangle S Q P, which is similar to triangle R S Q.
C. Triangle Q R P is similar to triangle Q S P, which is similar to triangle Q S R.
D. Triangle P R Q is similar to triangle Q P S, which is similar to triangle R Q S.
Answers
Answer:
Answer B is correct
Maths-4
What is the smallest number that is divisible by each of the numbers given below
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
5040
3780
1260
2520
None of the above
Answers
Answer:
5040 is the right answer
Step-by-step explanation:
5040/1=5040
5040/2=2520
5040/3=1680
5040/4=1260
5040/5=1008
5040/6=840
5040/7=720
5040/8=630
5040/9=560
5040/10=504
To save $5,000 for a vacation in 3 years, how much money must be invested each
year if the investment earns 5% interest compounded annually? Round to the
nearest dollar.
$15,762
$1,586
$3,000
$1,667
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]
The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
How are annual payments or cash flows calculated?The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.
This can be achieved using the future value and present value formulas or factors.
We can also use an online finance calculator, as follows:
Data and Calculations:Future value = $5,000
Investment period = 3 years
Annual compound interest = 5%
N (# of periods) = 3 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $5,000 ($4,531.56 + $468.44)
Results:
PMT = $1,510.52
Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)
Total Interest = $468.44
Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
Learn more about periodic payments at https://brainly.com/question/24244579
which expression is equivalent to 7x^2 sqrt 2x^4 times 6 sqrt 2x^12 if x ≠ 0
Answers
The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
How to determine the equivalent expression?The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]
Evaluate the product
[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]
This gives
[tex]42x^2 \sqrt{4x^{16}[/tex]
Take the square root of 4
[tex]2*42x^2 \sqrt{x^{16}[/tex]
Take the square root of x^16
[tex]2*42x^2 *x^8[/tex]
So, we have:
[tex]84x^{10[/tex]
Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
Read more about equivalent expression at:
https://brainly.com/question/2972832
#SPJ1
Answer:
Step-by-step explanation:
The equivalent expression of is
How to determine the equivalent expression?
The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
Evaluate the product
This gives
Take the square root of 4
Take the square root of x^16
So, we have:
Hence, the equivalent expression of is
Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8
Answers
Using the elimination method, the value of x in the system of equations is calculated as: 8.
How to Solve a System of Equations by Elimination?To solve a system of equations given using the elimination method, do the following:
Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:
4x - 10y = 2 --> eqn. 1
-15x + 10y = -90 --> eqn. 2
Add
-11x = -88
Divide both sides by -11
x = 8
Learn more about system of equations on:
https://brainly.com/question/14323743
#SPJ1
What number represents the smallest value? .3 or .33
Answers
Answer:
.3
Step-by-step explanation:
.33 is .03 greater than .3
The number which represents the smallest value between 0.3 and 0.33 is the number 0.3.
Given are two decimal numbers.
0.3 and 0.33
It is required to find the number which is the smallest between these two.
The number 0.3 can be written as 0.30.
And the other number is 0.33.
In order to find the smallest number, check the digits from left to right.
The first digit after the decimal point of both numbers is 3.
The second digit after the decimal point is 0 for 0.30 and 3 for 0.33.
Here 0 is smaller than 3.
So, 0.30 is smaller than 0.33.
Hence, the smallest value is 0.3.
Learn more about Decimal Numbers here :
https://brainly.com/question/17326405
#SPJ3
This is multiple choice pls help
Answers
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
What is it? I am not sure
Answers
Answer: I think its A
Step-by-step explanation: maybe
slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.
Answers
The height of the ramp above the ground is 1.55 meters.
The difference between the height of the tree is 33.20 meters
How to find sides of a right triangle?The situation forms a right angle triangle.
Therefore, the height the ramp above the ground can be calculated as follows:
Using Pythagoras theorem,
sin 15 = opposite / hypotenuse
sin 15 = x / 6
cross multiply
x = 6 sin 15
x = 6 × 0.2588190451
x = 1.55291427062
x = 1.55
Therefore, the height of the ramp above the ground is 1.55 meters
tan 36 = opposite / adjacent
tan 36 = x / 60
x = 60 tan 36
x = 43.5925516803
x = 43.60 meters
tan 52 = y / 60
60 tan 52 = y
y = 76.7964979316
y = 76.79 meters
The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters
learn more on right triangle here: https://brainly.com/question/8036473
#SPJ1
What is the domain of y = 4 log5 (x - 3)?
A. all real numbers
B. all real numbers greater than 4
C. all real numbers greater than 5
D. all real numbers greater than 3.
Answers
The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
How to determine the domain?The function is given as:
[tex]y=4\log_5(x-3)[/tex]
Set the expression in bracket greater than 0
x -3 > 0
Add 3 to both sides
x > 3
Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
Read more about domain at:
https://brainly.com/question/1770447
#SPJ1
Factor:
y(a−b)-(a−b)
Answers
Answer: [tex](a-b)(y-1)[/tex]
Step-by-step explanation:
Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].
The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. (-3, 1)
Answers
The information given illustrates that the graph of the function decreasing.
How to illustrate the information?We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.
Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.
So according to the given graph on the interval (-3, 1) the graph is decreasing.
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
Hence, write down the smallest integer value of x that satisfies 7(6+x) -x>0
Answers
Answer:
-6
Step-by-step explanation:
[tex]7(6+x)-x > 0[/tex]
[tex]42 + 7x-x > 0[/tex]
[tex]42+6x > 0[/tex]
[tex]6x > -42[/tex]
[tex]x > -7[/tex]
The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.
Write the equation in slope-intercept form of the line that has slope
3 and y-intercept (0,1)
Answers
Answer:
y = 3x + 1
Step-by-step explanation:
The formula for equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
Now, since we have coordinates, we will get the equation as;
(y - y1)/(x - x1) = m
(y - 1)/(x - 0) = 3
y - 1 = 3x
y = 3x + 1
A cylindrical container has a radius of 17 inches and a height of 63 inches, how many gallons will it hold?
Answers
Answer:
=57198.98
Step-by-step explanation:
Volume of Cylinder = pi x radius^2 x height
= pi x 17^2 x 63
=57198.9774439
=57198.98
t
Use the table to the right, which shows the age distribution of those who earned less than
minimum wage in a recent year. If a worker is randomly selected from those surveyed, what
y is the probability that the person is younger than 65?
na
Ci
20
ar
The probability that the person is younger than 65 is
(Type a decimal rounded to three decimal places as needed.)
CID
Age
16-19
20-24
25-34
35-44
45-54
55-64
65 and older
Working Below Minimum
Wage (thousands)
350
412
318
200
107
51
49
Answers
The probability that a person chosen at random is younger than 65 is 0.967.
What is the probability?Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.
The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)
(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)
1438 / 1487 = 0.967
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table
6 steps
Answers
The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607
How to determine the regression equation?The table of values is given as:
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Next, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 305Sum of Y = 15.5Mean X = 61Mean Y = 3.1Sum of squares (SSX) = 34Sum of products (SP) = -14.5r = -0.9607Regression Equation = ŷ = bX + a
b = SP/SSX = -14.5/34 = -0.42647
a = MY - bMX = 3.1 - (-0.43*61) = 29.11471
So, the regression equation is
y = -0.42647x + 29.11471
And the correlation coefficient is -0.9607
Read more about regression at:
https://brainly.com/question/14313391
#SPJ1
If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?
Answers
Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
Step-by-step explanation:
± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]
= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]
Rearranging, we get:
= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r* ) is 2.75%. The average inflation premium is 2.05%, and the maturity risk premium is estimated to be 0.1 3 (t 2 1)%, where t 5 number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds
Answers
Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%
How is the default risk premium found?The default risk premium can be found as:
=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium
Solving gives:
= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)
= 0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)
= 1.2%
The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.
This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.
Find out more on default risk premium at https://brainly.com/question/8873408
#SPJ1
Please help to solve these 3 questions
Answers
Based on the number of goals scored in the football matches, the mode is 4 goals. The median is 3 goals and the mean goals scored is 2.6 goals.
What are the statistics from the football matches?The mode is the number of goals that was scored in the most matches. This number is 4 goals as this was scored in 6 matches.
To find the median, order the numbers:
0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6
The median is:
= (3 + 3) / 2
= 3
The mean is:
= (0 + 0 + 0 + 0 + 1 + 1 + 2 +2 +2 + 3 + 3 + 3 + 4 + 4+ 4 + 4 +4 + 4 + 5 + 6) / 20
= 2.6 goals
Find out more on mean at https://brainly.com/question/1136789
#SPJ1