In the function, the slope will be multiplied by 1/2, and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
Answers
Answer
Option Y is correct.
Explanation
We are told that the slope is multiplied by (1/2) and the y-intercept is increased by 3 units.
The original graph has a y-intercept (point where the graph crosses the y-axis) at point y = 1. Adding 3 units to that, changes the y-intercept to y = 4.
And that leaves options X and Y as viable answers.
But the original graph is positive sloping, and multiplying the slope by (1/2) only spreads the graph out more along the y-axis, it doesn't change the direction of the graph like option X has been changed to be negative sloping. This would only happen if the slope was multiplied by a negative number.
So, this leaves us with only Option Y as the viable answer.
And to be absolutely sure, we can go further and calculate the slope of the original graph and the graph in option Y.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For the original question,
(x₁, y₁) and (x₂, y₂) are (0, 1) and (-1, -1)
[tex]\text{Slope = }\frac{-1-1}{-1-0}=\frac{-2}{-1}=2[/tex]For the option Y,
(x₁, y₁) and (x₂, y₂) are (0, 4) and (-1, 3)
[tex]\text{Slope = }\frac{3-4}{-1-0}=\frac{-1}{-1}=1[/tex]1 is indeed half of 2. This confrims our answer.
Hope this Helps!!!
Related Questions
Graph the line that contains the point (3,-6) and has a slipe of 1/2
Answers
to graph the line we first need to get its equation. The equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
[tex]\begin{gathered} y-(-6)=\frac{1}{2}(x-3) \\ y+6=\frac{1}{2}x-\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2}-6 \\ y=\frac{1}{2}x-\frac{15}{2} \end{gathered}[/tex]Once we have the equation we can find another point on the line. If x=1 then y=-7, hence we have the point (1,-7).
Now we graph the points (1,-7) and (3,-6) and jo
Hello what is the question to both parts and what is the monthly payment
Answers
In general, the monthly payment formula is
[tex]M=\frac{P(\frac{r}{12})(1+\frac{r}{12})^n}{(1+\frac{r}{12})^n-1}[/tex]In our case,
[tex]P=19300,r=0.061,n=3\cdot12=36[/tex]Where r=6.1%=0.061 and the number of payments is 12months*3years=36 monthly payments. Thus, the answer is
[tex]\begin{gathered} \Rightarrow M=19300\cdot\frac{\frac{0.061}{12}(1+\frac{0.061}{12})^{36}}{(1+\frac{0.061}{12})^{36}-1} \\ \Rightarrow M=588.0182\ldots \\ \Rightarrow M\approx588.02 \end{gathered}[/tex]The monthly payment is $588.02
What is the x and y intercepts of the line 2x-5y=20
Answers
The x-intercept and the y-intercept of the original equation of line 2x-5y=20 is (10,0) and (0,-4).
What is defined as the x and y intercepts?An intercept is a y-axis point by which the slope of a line passes. It is the y-coordinate of a point on the y-axis in which a straight line or a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope as well as c is the y-intercept.The x-intercept occurs where y=0, and the y-intercept occurs where x=0.
2x-5y=20 is the original equation of the line.
1) Substitute 0 for y to obtain 2x - 5(0) = 20, that equals 2x = 20.
Now, find x by dividing all sides by 2, and x = 10, resulting in the x-intercept (10,0)
2) Substitute 0 for x to obtain 2(0) - 5y = 20, which equals -5y = 20.
Now, find y by dividing all sides by 5, and y = -4, implying that the y-intercept is (0,-4).
Thus, the x-intercept and the y-intercept of the original equation 2x-5y=20 is (10,0) and (0,-4).
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Find GH. BC 19 GH 9x - 3 FE 5х + 1 option A: 2 option B: 6 option C: 15. option D: 51
Answers
Since FE and BC are given to be parallel, the figure BCEF is a trapezium.
The line GF divides the sides BF and CE equally. Hence, we can say that GH is parallel to side FE and BC.
Hence, the trapeziums BCHG and FEHG are similar.
Hence, the ratio between sides can be expressed as,
[tex]\frac{\text{BC}}{GH}=\frac{GH}{FE}[/tex][tex]\begin{gathered} \frac{19}{9x-3}=\frac{9x-3}{5x+1} \\ 95x+19=(9x-3)^2 \\ 95x+19=81x^2-2\times3\times9x+9 \\ 95x+19=81x^2-54x+9 \end{gathered}[/tex][tex]0=81x^2-149x-10[/tex]Using discriminant method, the equation can be solved as,
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-149)\pm\sqrt[]{(-149)^2-4\times81\times(-10)}}{2\times81} \end{gathered}[/tex]The positive solution to the equation is x≈2.
So,
[tex]\begin{gathered} GH=9\times2-3 \\ =15 \end{gathered}[/tex]Hence, GH=15.
Complete the truth table.
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q
-
pЛ-4
P+
-(p+q)
F F
T
T
F
F
T
T T
F
T
T
חד
F
T
F
T
F
T
F
T
וד
F
וד
F
T
רד
F
F
Answers
given the function
[tex](-p\rightarrow q)\rightarrow(q\rightarrow-r)[/tex]option 1
P=T
Q=T
R=T
then
-P=F
-R=F
-P -> q=V
q ->-r= F
then
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 2
P=T
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 3
P=T
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 4
P=T
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 5
P=F
Q=T
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 6
P=F
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 7
P=F
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 8
P=F
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]And you're fine that on his way to work he waits time for the bus is roughly uniformly distributed between 8 minutes and 17 minutes 1 day he time his weight and writes down a number of minutes ignoring the 2nd run a solution to 3 decimal places
Answers
We have the waiting times uniformly distributed between 8 and 17 minutes. As he ignore the seconds, we have a discrete distribution with values 8 to 16.
We have to find what is the probaility that the waiting time is 10 minutes.
We can find this probability knowing that 10 is one class out of 17-8=9 classes with equal probability.
So the probability is:
[tex]P(X=10)=\frac{1}{9}\approx0.111[/tex]We now have to calculate the probability that the waiting time is between equal or higher 11 and less than 13. This include classes 11 and 12 (and not 13), so we include 2 classes out of 9. Then, the probability is:
[tex]P(11\le X\le13)=\frac{2}{9}\approx0.222[/tex]Answer:
P(X=10) = 0.111
P(11<=X<13) = 0.222
I need to now the answer for a and b
Answers
Knowing that there is a total of 250 6th grade students that participated in the challenge:
a. You can identify that:
-The percentage of students that participated in lifting leights is 8%.
A percent can be written as a decimal number by dividing it by 100:
[tex]\frac{8}{100}=0.08[/tex]Therefore, the number of students that participated in that exercise is:
[tex](250)(0.08)=20[/tex]- The percentage of students that participated in running is 30%.
Therefore, the number of them that participated in this exercise is:
[tex](250)(\frac{30}{100})=75[/tex]- Notice that the percentage of students that participated in swimming is 5%.
Hence, the number of them that participated in this exercise is:
[tex](250)(\frac{5}{100})\approx13[/tex]b. Notice that the number of students who chose walking is:
[tex](250)(\frac{17}{100})\approx43[/tex]Therefore, the total number of students that chose swimming, walking, and lifting weight is:
[tex]13+43+20=76[/tex]Notice that that number is greater than the number of students who chose running.
Hence, the answers are:
a. Lifting Weights:
[tex]20\text{ students}[/tex]Running:
[tex]75\text{ students}[/tex]Swimming:
[tex]13\text{ students}[/tex]b. Joseph is right, because there are 76 students who chose swimming, walking, and lifting weights, and there are 75 students who chose running.
The maximum load of a horizontal beam that is supported at both ends varies jointly as the width and the height and inversely as the length between the supports. A beam 6m long, 0.1m wide, and 0.06 m high supports a load of 360kg. What is the maximum load supported by a beam 16m long, 0.2m wide, and 0.08 m high?
Answers
Answer:
[tex]360kg[/tex]Explanation:
Here, we want to get the maximum load supported
From the first part of the question, we have it that:
The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports
Mathematically, we have that as:
[tex]g\text{ = k }\times\frac{wh}{l}[/tex]where k is the proportionality constant
Now, let us get the value of k
We substitute the first set of values as follows:
[tex]\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}[/tex]Now, using this value of k, we want to get the value of g
Mathematically, we have that as:
[tex]g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg[/tex]Diamonds are weighed in carats.
A carat is gram.
5
What is the weight in grams
of the largest diamond in the world,
the 3106-carat Cullinan diamond?
plss help
Answers
Answer:
621.2 grams
Step-by-step explanation:
One carat is 0.2 grams
Multiply that by 3106 to get 621.2 grams
Factor the following expression completely:
x² 18x + 80 =
Help please ad thanks!
Answers
Answer:
[tex]18 {x}^{3} + 80[/tex]
Step-by-step explanation:
[tex] {x}^{2} \times 18 {x}^{1} + 80 \\ {x}^{2 + 1} x18 + 80 \\ {x}^{3} x18 + 80 \\ 18 {x}^{3} + 80[/tex]
What's the answer please and thank you
Answers
step 1
Find the slope
we take the points
(5,-30) and (8, -48)
m=(-48+30)/(8-5)
m=-18/3
m=-6
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-6
point (5,-30)
substitute
-30=-6(5)+b
-30=-30+b
b=0
therefore
y=-6xFind the volume of this cylinder. Use 3 for . V = 7r2h 12 cm 5 cm V~ [?]cm Enter
Answers
Looking at the figure, the diameter of the cylinder is 12 cm and its height is 5 cm
The radius is half the diameter, so we have r = 6 cm.
Now, using the volume formula, we have:
[tex]\begin{gathered} V=\pi r^2h \\ V=3\cdot6^2\cdot5 \\ V=3\cdot36\cdot5 \\ V=540 \end{gathered}[/tex]So the volume of the cylinder is 540 cm³.
State the x and y intercepts of the given graphs.
Answers
Answer:
• x-intercept: (3, 0)
,• y-intercept: (0, -2)
Explanation:
x-intercept
The x-intercept is the point at which the graph crosses the x-axis.
From the graph, the x-intercept is at (3, 0).
y-intercept
The y-intercept is the point at which the graph crosses the y-axis.
From the graph, the y-intercept is at (0, -2).
A car is traveling at 25 mph during rush hour. How far does the car travel in 3 minutes and 45 seconds? Round your answer to the nearest foot
Answers
Given:
The speed of car is 25 mph.
Explanation:
Determine the speed of car in foot per second.
[tex]\begin{gathered} 25\text{ mph=25 mph}\cdot\frac{1.46667\text{ fps}}{1\text{ mph}} \\ =36.6675 \end{gathered}[/tex]So car travel 36.6675 feet in 1 second.
Determine the time in seconds.
[tex]\begin{gathered} 3\text{ min 45 sec=3}\cdot60sec+45\text{ sec} \\ =180+45\text{ sec} \\ =225\text{ sec} \end{gathered}[/tex]Determine the distance travelled by car in 3 minutes 45 seconds.
[tex]\begin{gathered} 36.6675\cdot225=8250.1875 \\ \approx8250 \end{gathered}[/tex]So car travell 8250 feet.
Answer: 8250
H= {(1, 0), (3, b), (5, b)}
Give the domain and range of H.
Write your answers using set notation.
Answers
Please answer :-Factorize x²+1.
Answers
The given expression is
[tex]x^2+1[/tex]We can not factorize this expression bt the normal factorizing ways
Because it is a binomial with + as a middle sign can not be distributed into 2 factors
Then there is no factorizing for the given binomial
If the sign between the two terms is (-), then we can factorize it into two same factors with different middle sign
We can use the complex numbers to factorize it
[tex]\begin{gathered} x^2=(x)(x) \\ 1=(i)(-i) \\ (x)(i)+(x)(-i)=(xi)-(xi)=0 \\ (x+i)(x-i) \end{gathered}[/tex]Then the factors are (x + i) and (x - i)
[tex]x^2+1=(x+i)(x-i)[/tex]Answer:
x^2+1
Step-by-step explanation:
The expression is not factorable with rational numbers.
Jackie claims that points with the same x- and y- coordinates must lie in Quadrant l or Quadrant lll. Do you agree or disagree? Explain your answer.
Answers
It is known that in the I and III quadrants, the signs of the x- and y- are the same.
Jackie claims that the points with the same x - and y - coordinates must lie in the I or III quadrant.
His claim is true.
The points with the same x - and y - coordinates are of the form (a,a) or (-a,-a). If the point is of the form (a,a), it lies in the quadrant I
If the point is of the form (-a,-a), it lies in quadrant III.
A board game uses a spinner to determine how many spaces a player will move forward on each turn. The probability is 1/2 that the player moves forward 1 space, and moving forward 2 or 3 spaces each have 1/4 probability. What is the expected value for the number of spaces a player moves forward on a turn?
Answers
ANSWER
1.75
EXPLANATION
The expected value of an event X is the sum of the products of each value of the event and the probability of the event resulting in that value.
In this case,
[tex]E\lbrack X\rbrack=1\cdot P(1\text{ }forward)+2\cdot P(2\text{ }forward)+3\cdot P(3\text{ }forward)=1\cdot\frac{1}{2}+2\cdot\frac{1}{4}+3\cdot\frac{1}{4}[/tex]Solve,
[tex]E\lbrack X\rbrack=\frac{1}{2}+\frac{1}{2}+\frac{3}{4}=\frac{7}{4}=1.75[/tex]Hence, the expected number of spaces the player moves in a turn is 1.75.
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 201 km south and 160 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
Answers
The time it would take to get closest to Mt Rainier, t ≈ 8.53 × [tex]10^{-3}[/tex] hours.
What is the separation of a line from a point?The perpendicular distance of a point to a line is the closest distance between them. The length of the perpendicular segment connecting a point to a line is the distance between them.
It would take roughly 5.12 minutes to go to the closest point to Mount Rainier.
The following justifies why the value is accurate:
The given parameters are;
The flight's direction is 201 kilometres south and 160 km east.
Mount Retainer is situated 56 kilometers east and 40 kilometers south of JBLM.
Flight velocity is 800 km/h.
The travel path's slope, in m, is given as follows:
m = -201/160
=1.2
The equation of the path is therefore;
y+201 = -1.2(x-160)
y = -1.2(x-160) - 201
The required slope for the perpendicular distance from the travel path to the Mt Rainier, m', is therefore;
m' = -1/m
Which gives;
m' = 1/1.2
The equation of the line is therefore;
y+ 40 = 1/1.2(x-56)
y = 1/1.2(x-56)-40
The coordinates of the point where the two lines meet is therefore;
-1.2(x-160)-201 = 1/1.2(x-56)-40
solving this we get
x = 22.46
y = -67.83
The magnitude of the distance in km is, d = 71.451
The time it will take to be closest to Mt. Rainier, t, is given as follows;
t = 71.451/800
t = 8.9×[tex]10^{-3}[/tex]
The time it would take to get closest to Mt Rainier, t ≈ 8.53 × [tex]10^{-3}[/tex] hours.
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please help me out quickly huge point for grab please let your answer be correct
Answers
Answer:
first is T second is F
Step-by-step explanation:
simplify this expression 2 (times) x (times) 3 (times) y
The first to answer I will give branliest
Answers
The simplified expression of the expression 2 x 3 x y is 6y
How to simplify the expression?From the question, we have the following statement that can be used in our computation: 2 (times) x (times) 3 (times) y
Express as numbers
So, we have
2 x 3 x y
Evaluate the products of the numbers
So, we have the following representation
2 x 3 x y = 6 x y
Evaluate the products of the number and the variable
So, we have the following representation
2 x 3 x y = 6y
The above expression cannot be further simplified
Hence, the expression is 6y
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The surface areas of two similar figures are 16 in2 and 25 in2. If the volume of the larger figure is 500 in3, what is the volume of the smaller figure?
Answers
The volume of the smaller figure is 256 in³.
Given, the surface area of two figures are 16 and 25.
volume of the larger figure is 500.
volume of smaller figure =?
Similar figures have a scale factor k, (let k be >1, so k is the ratio of a distance in the larger figure to the corresponding distance in the smaller one)
First, we calculate for the ratio of the surface areas of the given figures. From the given above, the ratio is equal to 25:16
Then, we calculate for the ratio of the perimeters or sides of the figures by getting the square root of the ratio in figure 1.
ratio of perimeter or side = 5:4
The ratio of the volumes of the figures is equal to the cube of the ratio in figure 2.
ratio of volumes = (5:4)³ = 125:64
Using this ratio and the volume of the larger figure,
500 in³/x in³ = 125/64
x in³ = 500×64/125
x in³ = 256 in³
The value of x from the equation is 256. Therefore, the volume of the smaller figure is 256 in³.
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(Please help. Will be marked brainliest) Clifford is making a really big white cake for his sister’s birthday. The recipe calls for 1.5 times as much flour as sugar. It also calls for
1
2 as much butter as sugar. All the butter, flour, and sugar together total 7.5 cups. How much butter, sugar and flour does Clifford need?
Answers
After solving the equation, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
What is an equation?Equation, also referred to as a declaration of equality between two expressions that contain variable- and/or number-based components. Since equations are essentially questions, the development of mathematics has been driven by efforts to systematically find answers to those questions.
There are many different types of equations that vary in complexity, ranging from simple algebraic equations that only call for addition or multiplication to differential equations, exponential equations that employ exponential expressions, and integral equations. They serve as an expression for many physics laws.
Let flour be f, sugar be s, and butter be b
We have given that
f = 1.5s ...1
b = 1/2(s)
= 0.5s ...2
And
F + B + S = 7.5 cups
Lets substitute the vales of f and b in F + B + S, and we get
1.5s + 0.5s + S = 7.5 cups
2S + S = 7.5
3S = 7.5
S = 7.5/3
S = 2.5 cups
Flour = (1.5)2.5
= 3.75 cups
Butter = (0.5)2.5
= 1.25 cups
Thus, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
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What is the third stage of a plant's life cycle called, when the plant is small, has only a few leaves, has a soft stem, and has small roots?
Answers
Answer:
Growing to maturity
Step-by-step explanation:
The seedling progresses to full maturity as it continues to grow. Many things are needed during the life cycle of a plant while it's growing.
I hope this helps you! Please tell me if I'm wrong.
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I need help what would be the 20th term in this sequence? 7, 14, 21, 28, 35... NUMBER 7
Answers
Cm, this is the solution:
This is the sequence given:
7, 14, 21, 28, 35
d = 7 (Common difference)
An = 7n (Arithmetic sequence)
The 20th term is:
A20 = 7 * 20
A20 = 140
need help with math paper only one page
Answers
Proportional relation
The slope
The blue slope is negative and the green one is positive, if you realize it your slope has to be positive.
To calculate the slope (m)
y = m x +b
m = (y2-y1)/ (x2-x1)
____________________
You can take two points from the graph for example
Points (x, y)
Point 1 (0, 0); x1= 0 ; y1= 0
point 2 (300, 450); x2= 300 ; y2= 450
m = (450 - 0)/ (300 - 0)
m = 45/ 30
m = 3/2
_____________________
The equation that represents the graph
y= 3/2 x
________________________________
Table
Grams of fish (x); the number of calories (y)
y= 3/2 x
x= 300 Grams of fish
y= 3/2 (300)
y= 450
450 calories
______________
x= 1
y= 3/2 (1)
y= 3/2 = 1.5
1.5 calories
_____________
x= 1000
y= 3/2 (1000)
y= 3000/2 = 1500
1500 calories
_______________________
y = 2001 calories
y= 3/2 x
2001 = 3/2 x
x= 2001 *2/3
x= 1334
1334 grams of fish
I really need help on the do you mind helping
Answers
the quation of the given graph is,
[tex]y=(x+3)^2-1[/tex]Find the domain and range. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.positive quadratic with closed end point at (-5,2) and open end point at (3,2) vertex=(-1,0)The domain is:AnswerAnswer,AnswerAnswerThe range is: AnswerAnswer,AnswerAnswer
Answers
• For domain { -5 ≤x < 3 } : [ -5 ;3),
( take notice of the square bracket that indicates a closed dot/ circle, and open bracket that indicates open circle/dot)
• For range : { 0≤ y≤ 2} : [0;2]
( take note that our graph extends up to y -value = 2 , our minimum being 0 , we put close brackets because it starts at 0 and end at 2 .)
What is the distance between the points (4,3) and (1,-1) on the coordinateplane?
Answers
ANSWER
A. 5 units
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]In this case, the points are (4, 3) and (1, -1). The distance between them is,
[tex]d=\sqrt[]{(4-1)^2+(3-(-1))^2}=\sqrt[]{3^2+(3+1)^2}=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5[/tex]Hence, the distance between the given points is 5 units.
In the 2.5 minutes between innings in a baseball game, a hotdog launcher launches 12 hotdogs into the crowd. Clara, a member of the mascot team, wants to know how long she has to launch each hotdog. What is the unit rate in seconds per hotdog?
Answers
The unit rate in seconds per hotdog is 12.5 seconds.
The time between the innings in a baseball game is 2.5 minutes.The hotdog launcher has to launch a total of 12 hotdogs into the crowd within the time between the innings.Clara is a member of the mascot team. She has a limited amount of time to launch each hotdog.Let us convert the time in minutes to seconds.2.5 minutes equals 2.5*60 seconds.The time is 150 seconds.The total number of hotdogs to be launched is 12.The amount of time available for each hotdog is the rate at which she can launch hotdogs into the crowd.The unit rate in seconds per hotdog is 150/12.The unit rate in seconds per hotdog is 12.5 seconds.To learn more about rate, visit :
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