The statement that correctly describes related variables is given as follows:
Two variables are related when a discernible pattern exists between them.
What are related variables?Two variables are said to be related if one variable can be written as a function of another, that is, the output variable can be written as a function of the input variable.
There are multiple relations between variables, such as linear, quadratic and exponential relations. What is common for all these relations is that a pattern exists between these variables, meaning that the third option gives the correct option.
The pattern is identified from a sample of observations of these two variables, in which it is verified how the dependent variable varies according to the independent variable.
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verify the linear approximation at (0, 0). f(x, y) = y + cos2(x) ≈ 1 + 1 2 y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
In the given question, we have to verify the linear approximation at (0, 0).
f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Let f(x, y) = √(y+cos^{2}x)
f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)
f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]
f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]
f(x, y) ≈ 1+0(x-0)(1/2)(y-0)
f(x, y) ≈ 1+1/2y
Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
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The complete question is:
Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........
How do you write an equation of the line containing the given point and perpendicular to the given line?
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
What is the end behavior as x → − [infinity] f/x →?
Using the concept of limit, As the x tends to -infinity value, In the expression f/x, The answer is f/x tends to large(infinity) value with negative magnitude.
What do you mean by limit in mathematics?A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals. A limit describes the value that a function approaches as its inputs approach a certain value. All calculus is based on the concept of a limit.
What is the limit rule?According to product law for limits, the limit of a product of functions is equal to the sum of the limits of each individual function. The limit of a quotient of functions is equal to the quotient of the limit of each function, according to the quotient law for limits.
as [tex]\lim_{x \to \infty} \frac{f}{x}[/tex]
=f/ -infinity
=- [infinitely large value]
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Solve the following equations:
Solving multi-step equations
1) 3x+7+ 6x = 34
2) b-9+6b=30
What does ∆ mean in calculus?
In lambda expressions and lambda (λ) phrases, the Greek letter lambda () is used to signify binding a variable in a function. You can have typed or untyped lambda calculus.
Functions can only be used in typed lambda calculus if they are able to accept the "type" of data that the input is. The Greek symbol lambda () is commonly used to represent wavelength, which is equal to the speed (v) of a wave train in a medium divided by its frequency (f): wavelength = v/f. The majority of the time, students struggle to understand calculus because they don't practice after class, can't concentrate in class, have gaps in their math knowledge, and believe it's a waste of time.
The actions you can do to make calculus simple are listed below. Calculus is the most difficult math topic, and very few students, whether in high school or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract and easier to understand because it is more concrete. The mean number of events within a particular period of time or space is denoted by the Greek letter lambda () in the Poisson distribution formula. For instance, = 0.748 floods annually.
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Correct Question:
What does λ mean in calculus?
What is the discriminant and nature of roots of 2x² 3x 5 0?
The quadratic equation [tex]2x^{2}+3x-5=0[/tex] has a discriminant of 49.
In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its classification or solution. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots include a conjugate pair of complex roots.
For an equation, [tex]ax^{2}+bx+c=0[/tex]
Discriminant, D = [tex]b^{2}-4ac[/tex]
Given in question,
[tex]2x^{2}+3x-5=0[/tex]
a = 2
b = 3
c = -5
D = [tex]3^{2}[/tex] - 4(2)(-5)
= 9 + 40
= 49
Hence, the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] is 49.
Correct Question :
What is the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] ?
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How many triangles can be drawn given 2 sides and a non-included angle?
Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.
What is meant by Angle ?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays known as the vertex is referred to as an angle's sides. Angles are often measured using one of two different units. The degree is the measurement unit that is most widely used. A straight angle is 90 degrees when a circle is divided into 360 equal degrees.To learn more about Angle refer to:
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Solve the following system of equations and show all work. y = −x2 +4y = 2x + 1
The solution to the system of equations is x = 3/2 and y = 7/4.
The given system of equations can be written as:
y = -x^2 + 4
y = 2x + 1
To solve this system of equations, we can use the substitution method. First, we'll substitute the expression for y in the second equation into the first equation. We can then solve the resulting equation for x.
In the first equation, [tex]y = -x^2 + 4[/tex] . Substituting this expression into the second equation, we get:
[tex]-x^2 + 4 = 2x + 1[/tex]
We can rearrange the terms on the left side of the equation to solve for x. To do this, we'll subtract 4 from both sides, then add x^2 to both sides:
-4 = 2x + 1 - 4
-4 + 4 = 2x + 1 - 4 + 4
0 = 2x - 3
Now, we'll divide both sides of the equation by 2 to solve for x:
0/2 = (2x - 3)/2
0 = x - 3/2
We can rearrange the terms on the right side of the equation to solve for x. To do this, we'll add 3/2 to both sides:
0 + 3/2 = x - 3/2 + 3/2
3/2 = x
Now that we have the value of x, we can substitute it into either equation to solve for y:
[tex]y = -x^2 + 4y = -(3/2)^2 + 4y = -(9/4) + 4[/tex]
y = 7/4
Therefore, the solution to the system of equations is x = 3/2 and y = 7/4.
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The table shows the total number of text messages that Ashley sent over 4 days. Write an equation to find the total number of messages sent in any number of days. Use the equation to find how many text messages Ashley would send in 30 days.
Answer:
1d=25m
30d=?
cross mutiply
30×25=750messages
Answer:
The equation is m = 25d
Ashley would send 750 text messages after 30 days.
Step-by-step explanation:
The equation is y = mx + b
We see that each day the number of text increase by 25, so our equation is
m = 25d
Now we ask how many text messages Ashley would send in 30 days. We need to put 30 in for d and solve it.
m = 25(30)
m = 750 text messages
So, Ashley would send 750 text messages in 30 days.
What is the formula of line segment?
Answer:
The length of the line segment is
d = √(x₂ - x₁)² + (y₂ - y₁)²
Solve for Z.
X= 2/3(Y+Z)
Answer: Z=[tex]\frac{3}{2}[/tex]x-y
Step-by-step explanation: first multiply both by the reciprocal of 2/3 to cancel it. the reciprocal of 2/3 is 3/2
x(3/2)=y+z
then to solve for x, move the to the left side by -y on both sides
you're then left with z=x(3/2)-y
What is an example of a complex equation?
An example of a complex equation is the Navier–Stokes equations, which are used to describe the motion of fluids and are one of the most important equations in fluid mechanics.
What is complex equation?A complex equation is a mathematical expression that contains multiple variables, operations, and powers. This can include exponents, logarithms, trigonometric functions, and other variables. Complex equations can be used to solve problems or to make predictions, and can be used in a wide range of fields, including economics, engineering, and physics.
These equations consist of a set of partial differential equations that describe the motion of a fluid, such as air or water, and the forces acting on it. The Navier–Stokes equations are used to predict the behavior of liquids and gases in a wide range of applications, from aeronautics, to weather prediction, to oceanography.
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How would you describe a rigid transformation?
A transformation that leaves a geometric figure's size or shape unaltered is known as a rigid transformation (also known as isometry). is a unique type of metamorphosis in which a figure's size or shape are left unaltered.
What is rigid transformations?During a rigorous alteration of the geometric object, the distance between each pair of its points is maintained. In other words, an object's size and shape are maintained through a hard transformation. For example, the rigid transformation of a triangle preserves the triangle's angles and lengths. Consider a rigid form distortion that resembles a cardboard shape.
There are translations, reflections, and isometric rotations. As a result, none of these changes have an impact on the figure's size. If neither the size nor the shape of the figures are changed, the figures are constant.
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solve the logarithmic equation. log 10 (x raise to power 2 - 4x )=2
Answer:
[tex]x=2+2\sqrt{ 26}[/tex]
[tex]x=2-2\sqrt{ 26}[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_{10}(x^{2}-4x)=2[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^2=x^2-4x[/tex]
[tex]\implies 100=x^2-4x[/tex]
[tex]\implies x^2-4x=100[/tex]
Add the square of half the coefficient of the term in x to both sides of the equation:
[tex]\implies x^2-4x+\left(\dfrac{-4}{2}\right)^2=100+\left(\dfrac{-4}{2}\right)^2[/tex]
[tex]\implies x^2-4x+\left(-2\right)^2=100+\left(-2}\right)^2[/tex]
[tex]\implies x^2-4x+4=100+4[/tex]
[tex]\implies x^2-4x+4=104[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex]\implies (x-2)^2=104[/tex]
Square root both sides:
[tex]\implies x-2=\pm \sqrt{104}[/tex]
[tex]\implies x-2=\pm \sqrt{4 \cdot 26}[/tex]
[tex]\implies x-2=\pm \sqrt{4} \sqrt{ 26}[/tex]
[tex]\implies x-2=\pm 2\sqrt{ 26}[/tex]
Add 2 to both sides:
[tex]\implies x=2\pm 2\sqrt{ 26}[/tex]
Therefore, the solutions are:
[tex]x=2+2\sqrt{ 26}[/tex][tex]x=2-2\sqrt{ 26}[/tex]What is the mean deviation of 8 9 12 15 16 20?
8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
What is the mean deviation?The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.
It is a statistical summary of statistical variability or dispersion.
So, the sum of all the values:
8 + 9 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 34 = 200
A number of observations:
= 10
Formula: Mean = (sum of all observations)/(Total number of observations)
Now, calculate using the formula as follows:
Mean = (sum of all observations)/(Total number of observations)
Mean = (200 / 10)
Mean = 20
Now, we must determine how far the provided values are from the mean.
20 - 8 = 12
20 - 9 = 11
20 - 12 = 8
20 - 15 = 5
20 - 16 = 4
20 - 20 = 0
24 - 20 = 4
30 - 20 = 10
32 - 20 = 12
34 - 20 = 14
Formula:
Mean deviation = (sum of the distance of each value from mean) / (Total number of observations.)
Sum of each value's deviation from the mean = 12 + 11 + 8 + 5 + 4 + 0 + 4 + 10 + 12 + 14 = 80
Mean deviation = 80 / 10 = 8
Therefore, 8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
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Complete question:
What is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34?
the rational roots theorem - state the possible rational zeros for each function (please show work)
f(x)=3x^2+2x-1
Answer: x=-1 x=1/3
Step-by-step explanation:
f(x)=3x²+2x-1
[tex]3x^2+2x-1=0\\\\3x^2+(3x-x)-1=0\\\\(3x^2+3x)-x-1=0\\\\3x(x+1)-(x+1)=0\\\\(x+1)(3x-1)=0\\\\x+1=0\\\\x=-1\\\\3x-1=0\\\\3x=1[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\x=\frac{1}{3}[/tex]
What are the possible rational zeros of f X X 4 6x 3 3x 2 17x 15?
The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
Have given ,
f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex]
This is a fourth degree polynomial.
Using the rational root theorem, the possible zeros of the polynomial are the factors of 15.
We know that
Factors of 15 = ± 1, ±3, ±5, ±15
Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
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Х
15
9
18
9
y
17
9
4
Is this relation a function?
yes
no
To be a relation of a function for every value of x there must be a single value of y thus the given relation is not a function.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given table,
At x = 9
y = 9 and y = 3
Since at a single value of x there exist two values of y thus it will not be a function.
Hence "The provided relation is not a function since there must only be one value of y for a relationship to be considered a function.".
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How do you expand a 3 term binomial?
The expanded form of a 3-term binomial is typically written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial is given by ax^2 + bx + c = a(x^2 + bx/a + c/a).
1. Take the coefficients of the binomial (which are the constants a, b and c)
2. Multiply the coefficient a with the remaining terms in the binomial (x^2 + bx + c).
3. Simplify the expression by multiplying the coefficient a with the terms (x^2 + bx/a + c/a).
4. The result is the expanded form of the 3-term binomial ax^2 + bx + c.
The expanded form of a 3-term binomial can be written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial can be obtained by multiplying the coefficient a with the remaining terms in the binomial (x^2 + bx + c) and simplifying the expression.
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Simplify the expression xy+x^2+2xy+y^2-3x^2
Write the equation of the line of fit.
y = 5x+20 Carlos plays the game for 25 minutes. Use the
equation of the line of fit to predict his score.
Answer:
145
Step-by-step explanation:
y = 5(25) + 20
y = 125 + 20
y = 145
Which of the following is a step in copying a line segment?
Copying of line segment involves 6 steps.
How to copy a line segment?Steps to copy line segment are:
1) Draw a point that will serve as the new line segment's endpoint.
2) Open the compass width from the original line segment's beginning with the compass pin in that position.
3)Place the compass pin at the new line segment's plotted point using the above-mentioned step's adjusted compass width, and then draw an arc in the area where the new line segment is to be situated.
4) Decide where the other end of the new line will be on the arc.
5) Draw a line from the location chosen in the previous step to the point designated as the start of the new line segment.
6) The original line segment's length and the length of the line depicted above are equal.
Copying of line segment involves 6 steps.
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Q Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
How do you find the missing length of a triangle on a calculator?
By using a² + b² = c² this formula we can find the missing length of a triangle.
A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.
If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:
a² + b² = c²
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:a = √(c² - b²)
If leg b is unknown, then:b = √(c² - a²)
For hypotenuse c missing, the formula is:c = √(a² + b²)
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what is the slope of the line that contains the points
Answer: 0
Step-by-step explanation:
The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.
Maria has ridden 44 miles of a bike course. The course is 80 miles long. What percentage of the course has Maria ridden so far?
Answer:
55percent
Step-by-step explanation:
[tex]\frac{44}{80} =0.55\\0.55x100\\55[/tex]
y = 4/5x + 8
2x+y = -6
Plot two lines by clicking the graph.
Answer:
Just use Desmos
Step-by-step explanation:
Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14
9
2
km14, start fraction, 2, divided by, 9, end fraction, start text, space, k, m, end text taxi ride. The cost per kilometer is constant. As a simplified proper fraction
The cost per kilometer for Emanuel's taxi ride is given as follows:
$9/4.
How to obtain the cost per kilometer?To obtain the cost per kilometer of the tax ride, we apply the proportion, dividing the total cost by the distance of the taxi ride.
From the text given in this problem, the parameters are given as follows:
Total cost: $32.Total distance: 14 and 2/9 kilometers = 14 + 2/9 kilometers = 14.22 kilometers. (conversion of mixed number to decimal).Then the cost per kilometer for Emanuel's taxi ride is found applying the proportion as follows:
Cost per kilometer = 32/14.22 = 2.25.
We have that the fraction equivalent of .25 is given as follows:
1/4.
Thus the proper fraction that represents the cost is given as follows:
2 + 1/4 = 8/4 + 1/4 = $9/4.
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which statement correctly compares the function shown on this graph with the function y=6x+1
The correct statement regarding the comparison of the linear functions is given as follows:
D. The function shown on the graph has a lower slope and a lower starting point.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the output variable y relative to the input variable x, that is, the change in y when x is increased by one.
Function y in this problem in this problem is given as follows:
y = 6x + 1.
Considering the slope-intercept definition, we have that:
The slope is of 6.The starting point is of 1.From the graphed function, we have that:
The slope is of 5, as when x increased by 2, from x = 0 to x = 2, y increased by 10, from -6 to 4.The starting point is of -6, which is the value of y when the function crosses the y-axis, that is, when x = 0.Thus option D is correct.
Missing InformationThe graph is given by the image shown at the end of the answer.
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If triangle LMB is dilated by a scale factor of 0.5, which of the following statements is not true?
A. Triangle LMN is similar to triangle L’M’N’.
B. Triangle L’M’N’is smaller than triangle LMN
C. The sides of triangle LMN are congruent to the sides of triangle L’M’N’.
D. The angles of triangle LMN are congruent to the angles of triangle L’M’N’.
According to the properties of geometry the correct option is C.
What is geometry?
The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.
Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.
If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.
Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.
It is given that LMN is dilated by a scale factor of 0.5.
Since scale factor is lies between 0 to 1, therefore it shows the compression.
Therefore sides of L'M'N' is smaller than LMN.
Since corresponding angles of similar figure are congruent.
So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.
Therefore option C is correct.
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2 1/2 divided by 4
please help asap
Answer:0.625
Step-by-step explanation: