The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
According to the statement
we have given that the statement and we have to find the derivative of that term.
So, We know that the
The given equation is
[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]
Now find the derivative of that term
We find the derivative of the given term is with the help of the FTC.
And then
[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]
Then the equation become is
[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]
So, this is the derivative of the given equation.
So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
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David reflects the word 'MOM' over the y-axis and notices
that is still reads the same. Is the same true for the word
'DAD'? Use letter symmetry to explain why or why not.
The reflection of the word DAD across the y-axis is not the same
How to determine the true statement?The statement is given as:
MOM, when reflected over the y-axis = MOM
The above is true because the letters M and O have reflectional symmetry across the y-axis
However, the letter D do not have a reflectional symmetry across the y-axis
So, the letters would not remain the same when reflected
Hence, the reflection of the word DAD across the y-axis is not the same
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Find an equation for the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)
The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2
Given,
Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)
We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.
Thus,
The equation for the plane through the points
Here,
The formula of equation of the plane passing through three non collinear points
[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]
by substituting the values in the formula of equation of the plane
x-0 y-1 z-1
1-0 0-1 1-1 = 0
1-0 1-1 0-1
x y z
1 -1 0 = 0
1 0 -1
x(1) - (y-1)(-1) - (z-1)(-1) = 0
x + y - 1 + z - 1 = 0
x + y + z + 2 = 0
x + y + z = 2
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
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The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
For given question,
We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)
We need to find an equation for the plane through the given three points.
We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,
[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]
Assume that for given points,
[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]
So, the equation of the plane passing though given points would be,
[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]
Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
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Find the dimensions of a rectangle with an area of 2x^2-7x-10
Answer:
Step-by-step explanation:
I gotcha my dude.......
x-5 and 2x+3
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Answer:
1: Linear
2: Linear
Step-by-step explanation:
Scenario 1:
Equation: y=8x (where x represents # of hours worked)
The graph would be linear.
Scenario2:
Equation: y=5x (where x is the # of boxes of donuts purchased)
The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )
A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.
- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x
I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.
find the gradient of 15y-6x=8
Answer:
2/5 or 0.4
Step-by-step explanation:
First we have to make equation into the gradient slope form :
y=mx+c m is gradient and c is y-intercept
15y-6x=8
First we add 6x to both sides :
15y = 6x+8
Now we divide both sides by 15 :
y = 6x+8 / 15
Split the fraction on the right :
y = 6x/15 + 8/15
6x/15 = 6/15x
Our gradient will be 6/15 = 2/5 or 0.4
Hope this helped and have a good day
When constructing a perpendicular line through a point on a line, how can you verify that the lines constructed are perpendicular? (1 point)
Check the angles used in the construction with a straightedge to ensure consistency.
Check the distance along the lines at several places with a compass to ensure they are the same length.
Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles.
Check the distance between the lines at several places with a compass to ensure they are equidistant
If you know the slope of the lines, you can also use these methods:
- see if the slopes multiplied by each other are -1 (should be if they're perpendicular)
- test if the slopes are opposite reciprocals (if they are, they are perpendicular)
Ashley has two equations that she found to be valuable models for her research. She thinks that if she can find the intersection of the two graphs, she will be able to identify a key point to her studies. At what point do these equations intersect?
4y –x = 9
y = 2x − 3
(3,3)
(3,-3)
(-3,-3)
(-3,3)
The equations intersect at the point (3 ,3 ).
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
4y –x = 9 (1)
y = 2x − 3 (2)
You should replace the variable y of equation 1 to equation 2. Then, you will have:
4*(2x-3)-x=9
8x-12-x=9
8x-x=9+12
7x=21
x=3
If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3
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Coordinates of G=(,),() and H=(,)(,)
Help Me please! Thankss
The coordinates of the missing points G. and H are G(a, y) and H(a,0) respectively
What is a right angles triangle?A right angled triangle is a triangle that has 3 sides and angle with one of its angles to be 90 degrees.
From the given triangle, the measure of the x-coordinate point of G and H will be equal.
Since the line GH intersects the x-axis and the point where the line intersects the x-axis is where y = 0, hence the coordinate H is (a, 0) and the measure of G is (a, +y)
The y-value of G can be any positive value on the y-axis
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Complete the inequality statement.
13.01 ___ 13.1
1. =
2. >
3.
13.1 = 13.10
---> 13.1 > 13.01
---> 13.01 < 13.1
The correct answer is <
A hamster is 2 1/2 inches long a rabbit is 3 1/2 times as long as a hamster how long is the rabbit
Slope=
Help me please thanks
Answer:
0
Step-by-step explanation:
In cartesian graphs, the slope or a gradient of a fully horizontal line will always be 0.
Study island
Need help on this question fast pls help
Answer:
D is correct
Step-by-step explanation:
Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels. Corresponding angles are congruent. You are able to prove that 2 pairs of angles are congruent so the triangles are similar. All of the answers show that the 2 triangles share angle B as the first part of the answer.
find the perimeter and area of the polygons
Answer:
Below in bold.
Step-by-step explanation:
This figure is a trapezoid.
We can find the missing side length by applying the Pythagoras Theorem to the right triangle on the left of the figure.
The dotted line has length 12 cm and the base of the triangle = 25 - 18 = 7 cm
So x^2 = 12^2 + 7^2 (where x = missing length)
= 144 + 49
= 189
x = √189
= 13.75 to nearest hundredth
So the perimeter
= 18 + 12 + 25 + 13.75
= 68.75 cm.
Area of a trapezoid = 1/2 (a + b) * h.
Area = 1/2 *(18 + 25) * 12
= 258 cm^2.
Thirteen-year-old noel was taking her algebra test but was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" this is an example of?
The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.
What is the concept exhibited by the thirteen year old as given in the task content?It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".
Such concept may be attributed to Intuitive thought.
This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.
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Julia is casting a play with 4 main roles. Six students
have tried out. How many different combinations of 4
students can Julia cast from the 6 students?
Using the combination formula, it is found that Julia can take 15 combinations.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:
[tex]C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
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Graph f(x) = 2 sin x.
Use 3.14 for π.
Please see the picture below
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is: $20,000 loan from a partner. $30,000 of profits from the last year of operations. $3,000 payable to a supplier. $100,000 in capital balances of the partners.
The correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations. What is the uniform partnership act?The Uniform Partnership Act (UPA) governs corporate partnerships in various states in the United States. When a partner dissociates, the UPA provides regulations for the dissolution of the partnership. Several revisions to the Uniform Partnership Act have been made over the years (UPA). The Revised Uniform Partnership Act refers to the revised act and changes (RUPA).The Uniform Partnership Act also governs partnership formation, liabilities, assets, and fiduciary obligations.Marshaling of assets:
The process of organizing the balance sheet elements (assets and liabilities) in a specified sequence is referred to as the marshaling of assets and liabilities. In other words, it is the process of organizing the various assets and liabilities on a balance sheet in a particular order.The order is the amount owed to a supplier, the amount of a loan from a partner, the amount of the partners' capital balances, and the number of profits from the previous year of operations.Therefore, the correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations.Know more about the uniform partnership act here:
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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:
(1) $20,000 loan from a partner.
(2) $30,000 of profits from the last year of operations.
(3) $3,000 payable to a supplier.
(4) $100,000 in capital balances of the partners.
Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator?
The number of ways people can get off the elevator is 604800 ways.
In this question,
Number of people, n = 7
Number of floors, r = 10
The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.
Number of ways people can get off the elevator can be calculated as
⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]
⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]
⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]
⇒ 604800 ways.
Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.
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No links, provide full answer
The value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
What are the family of solutions behind an equation of the form p · q = k?
In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:
p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k
Then, we proceed to find the solutions for x and y in terms of k:
2 · x + √(4 · x² + 5) = k
2 · x = k - √(4 · x² + 5)
4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5
2 · k · √(4 · x² + 5) = k² + 5
4 · k² · (4 · x² + 5) = (k² + 5)²
4 · x² + 5 = (k² + 5)² /(4 · k²)
4 · x² = (k² + 5)² /(4 · k²) - 5
x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.
2 · y = 5 / k - √(4 · y² + 5)
4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5
(10 / k) · √(4 · y² + 5) = 25 / k² + 5
(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²
4 · y² + 5 = (k² / 100) · (25 / k² + 5)²
4 · y² = (k² / 100) · (25 / k² + 5)² - 5
y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.
Therefore, the value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
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Find the area of the figure with the coordinates, S(-3, 5), A (1, 5), L(2, 1) and T(-6, 1).
Answer: a = 24 units²
Step-by-step explanation:
Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.
In the formula, h is the height, a is a base, and b is the other base.
[tex]\displaystyle a=\frac{a+b}{2} h[/tex]
[tex]\displaystyle a=\frac{4+8}{2} 4[/tex]
[tex]\displaystyle a=\frac{12}{2} 4[/tex]
[tex]\displaystyle a=(6)4[/tex]
[tex]\displaystyle a=24\; \text{units}^{2}[/tex]
URGENT!! ABCD is a quadrilateral. The point G is on the side which forms that AG=AB and CB=CG
The tangent to the circle at point A Is the along the side CD at point L
The extension of the leg CB is located at point K.
Prove AD=AG
ADG is an equilateral triangle, then, line AD is equivalent to line AG.
How to prove the statementFrom the information given, we have to prove that;
AD=AG
It is important to note that the triangle ADG is an equilateral triangle.
The properties of an equilateral triangle are;
All the sides are equalAll the angles are congruent and equal to 60°It is a polygon with three sidesSince ADG is an equilateral triangle, then, line AD is equivalent to line AG
Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.
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Find the length of the radius of a circle with a center at –7 2i and a point on the circle at 33 11i.
The length of the radius of a circle exists 41 units.
How to estimate the length of the radius of a circle?
Given: The center exists at -7+2i and a point in the circle at 33+11i.
The radius of the circle exists given by the following formula;
The radius of the circle [tex]$=\sqrt{x^{2}+y^{2}}$[/tex]
The center exists at -7 + 2i and a point in the circle at 33 + 11i.
[tex]$&x(33-(-7)), y(2 \mathrm{i}-11 \mathrm{i}) \\[/tex]
simplifying the equation, we get
[tex]$&\mathrm{x}(33+7), \mathrm{y}(-9 \mathrm{i}) \\[/tex]
[tex]$&\mathrm{x}(40), \mathrm{y}(-9(-1)) \\[/tex]
[tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex]
The center of the circle exists at [tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex].
The length of the radius of a circle exists,
Radius [tex]$}=\sqrt{x^{2}+y^{2}} \\[/tex]
substituting the values of x and y, we get
Radius[tex]$}=\sqrt{40^{2}+9^{2}} \\[/tex]
Radius [tex]$}=\sqrt{1600+81} \\[/tex]
Radius [tex]$=\sqrt{1681} \\[/tex]
Radius = 41 unit
Therefore, the length of the radius of a circle exists 41 unit.
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Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 5 13 , x in quadrant i
The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.
According to the statement
We have given that the sin(x) = 5/13 , x in quadrant iii
And we have to Find the value of cos x using the following:
So, For this purpose, we know that the trigonometry terms are:
sin2(x) + cos2(x) = 1;
or cos2(x) = 1-sin2(x)
And
cos2(x) = 1-(-5/13)2 =
cos2(x) = 144/169;
We know that the
In quadrant III both the sin and cos are negative so
cos(x) = -12/13 (after taking square roots).
And
Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.
Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).
Now
sin(x + x) = sinx * cosx + cosx * sinx
= (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169
And
cos(x + x) = cosX * cos(x) - sinx*sinx
= (-12/13)(-12/13) - (-5/13)(-5/13)
= 119/169
So,
You could use the tan double angle formula, but it is easiest to use
tan(2x) = sin(2x)/cos(2x) = (120/169) / (119/169)
= 120/119.
So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.
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pls help me urgetnly pls help me
The size of the largest angle of the pentagon will be 150°.
How to illustrate the information?A pentagon is the polygon that has five sides. It should be noted that the interior angle of a regular pentagon is 540°.
The given ratio is 2:3:4:4:5. Therefore, the size of the largest angle of the pentagon will be:
= 5/(2+3+4+4+5) × 540
= 5/18 × 540
= 150°
In this case, the size of the largest angle of the pentagon will be 150°.
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Evaluate the following integral or state that it does not exist (Calculus 2) Please show step by step explanation!
Answer:
[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x=2(e-1)[/tex]
Step-by-step explanation:
Given definite integral:
[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x[/tex]
Integration by substitution:
Substitute u for one of the functions to give a function that's easier to integrate.
[tex]\textsf{Let }u=\sqrt{x}[/tex]
Find the derivative of u and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{2\sqrt{x}}[/tex]
[tex]\implies \text{d}x=2 \sqrt{x}\:\text{d}u}[/tex]
[tex]\implies \text{d}x=2u\:\text{d}u[/tex]
Use the substitution to change the limits of the definite integral from x-values to u-values:
[tex]\textsf{When }x=0 \implies u=\sqrt{0}=0[/tex]
[tex]\textsf{When }x=1 \implies u=\sqrt{1}=1[/tex]
Therefore, the limits are unchanged.
[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x+\text{C}$\end{minipage}}[/tex]
Substitute everything into the original integral and solve:
[tex]\begin{aligned}\implies \displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x & =\displaystyle \int^1_0 \dfrac{e^u}{u} \cdot 2u\:\:\text{d}u \\\\ & = \displaystyle \int^1_0 2e^u\:\:\text{d}u \\\\ & = 2 \int^1_0 e^u\:\:\text{d}u\\\\ & = 2 \left[ e^u\right]^1_0\\\\ & = 2 \left[e^1-e^0\right]\\\\& = 2(e-1)\end{aligned}[/tex]
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To select the correct student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.
Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.
Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.
Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.
Disclaimer: The question is incomplete. Please read below to find the missing content.
Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
A) n
B) n-1
C) n+1
D) [X - μ / (s / n)]
The degrees of freedom depends on the number of parameters you are estimating.
8=
i-1
In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation
So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so
Degrees of freedom for students t distribution is B) n-1
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
A) f(x) = x^2 +8(x+2)
Step-by-step explanation:
We will start by putting y=0
0 = x^2+8(x+2) -Apply distributive property
0 = x^2+8x+16
0=(x+4)(x+4)
0=x+4, 0=x+4
x=-4
There is only one zero, and that is x=-4
Brainiest would be appreciated.
First one
Because
If we solve for x
x²+8(x+2)=0x²+8x+16=0x²+4x+4x+16=0(x+4)(x+4)=0x=-4Option A
determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
A. none of these
B. quadratic
C. linear
D. exponential
The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.
According to the statement
we have given that:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
And we have to find that The type of model that best fits the given situation.
So, according to the linear representation model
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
y = mx + c
And Slope of a function is
m = y₂ - y₁ / x₂ - x₁
Then
m = 5500 - 5000 / 19 - 20
m = -500
So, the equation become
y = -500x +c
And find the value of by putting the values.
So, c = 15000
And the equation become
y = -500x + 15000.
According to this linear model is perfect for this situation.
So, The linear representation model is best for this situation.
Learn more about linear representation here
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Help and get what you want.
Answer:
70°
Step-by-step explanation:
This is a question on angle properties.
Angle K + 35 + 75 = 180 (Sum of angles in a triangle)
Angle K + 110 = 180
Angle K = 180 - 110 = 70°
Answer:
angle k = [tex]\boxed {70}^\circ[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠k + 75° + 35° = 180°
⇒ ∠k + 110° = 180°
⇒ ∠k = 180° - 110°
⇒ ∠k = 70°
can someone help me with the graph I don't get it thanks
Answer: Refer to the histogram diagram below
The frequency table is in another attachment, and may be optional.
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Explanation:
The first task is to sort the values from smallest to largest. Luckily the data set is already sorted for us.
The smallest number is 22. This is the min. Since we're doing intervals of 10 percent, this means the first bin spans from 20% to 29%, assuming we're only involving whole number percentages. Then the next bin is from 30% to 39%, and so on, until reaching the last bin of 90% to 99%
The bin labels are shown along the bottom of the histogram.
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The height of each bar represents how many students are in that specific bin. The first bar is 1 unit tall because there's only one student in the 20% to 29% range (that 22% mentioned earlier).
The next bar is 2 units tall because of the scores of 30% and 37%. They are in the range from 30% to 39%
The next bar is 4 units tall because of the scores 45,46,46,49.
This process is done with the other values to get the histogram you see below.
The frequency table is shown in a separate attachment, but your teacher may only want the histogram part. I would ask him/her for clarification.
The third column of the frequency table is optional to show where all the scores fit (and to help confirm the frequencies). This will help confirm the answer. Most histograms commonly only show the first two columns.
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While it's a good thing to know how to do this by hand, it's recommend to use software to generate the histograms when it comes to real world applications. Eg: making a presentation to the boss.
The program I used was LibreOffice which is free and effectively identical to excel. There are other options you could pick from.
Side note: There are no gaps between the bars when it comes to histograms. In contrast, a bar chart will have gaps.
