The demand function of the question is expressed as;
D(q) = -²/₅₀₀₀q + 14.6
How to find the Demand Function?The formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
The coordinates we are given are;
(28000, 9) and (33000, 7)
Thus;
Slope; m = (7 - 9)/(33000 - 28000)
m = -2/5000
Now, the equation of a line in point slope form is;
y - y1 = m(x - x1)
Where (x1, y1) is (28000, 9)
y - 9 = (-2/5000)(x - 28000)
y - 9 = -²/₅₀₀₀x + 5.6
y = -²/₅₀₀₀x + 14.6
This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6
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What are the domain and range of the real-valued function f(x) = -3-√√4x - 12?
The domain of the real valued function as required is; [3, infinity).
The range of the function as required is; (-infinity, -3].
What is the domain of the function?By observation of the given function; the domain is the set of all real numbers except those for which;
4x - 12 < 0
4x < 12
x < 3.
Hence, the domain of the function is; [3, infinity).
The range as observed in the task content has a maximum value of; -3. Hence, the range of the function as required is; (-infinity, -3].
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Write a equation with the slope of 3 and goes through the point (2,5)
The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
What is the slope-point form of the line?
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:
y - 5 = 3(x - 2)
Expanding the right-hand side:
y - 5 = 3x - 6
Adding 5 to both sides:
y = 3x - 1
Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
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Help with this question?
Answer:
a.18%
b.68%
Step-by-step explanation:
for a you need to multiply 2 to get 18 out of 100 to get 18% and for b you need to multiply 4 to get 68 out of 100 to get 68%
The height of a cylinder is 20 cm. The
circumference of the base of the cylinder is 10 cm.
Which measurement is closest to the volume of the
cylinder in cubic cm?
A measurement which is closest to the volume of the cylinder in cubic cm is 158.87 cubic cm.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Next, we would determine the radius of the base of the cylinder:
Circumference of a circle = 2πr
10 = 2πr
Radius, r = 1.59 cm.
Substituting the given parameters into the volume of a cylinder formula, we have the following;
Volume of a cylinder, V = 3.142 × (1.59)² × 20
Volume of a cylinder, V = 158.87 cubic cm.
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Please help me I’m confused
Answer:
Below
Step-by-step explanation:
Here is what the graph should look like ...you can see that he will have 0 fence left to paint ( 0 = y ) when time = 3 hrs
Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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Consider the line 8x-5y=1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line ?
One loaf of bread weighs 0.68 kilogram. Six muffins weigh 1.12 kilograms. How much more do two loaves of bread weigh than the muffins? 0.08 0.12 0.24 1.30
Answer:
C) 0.24 kg
----------------------------
Find the weight of two loaves of bread:
0.68*2 = 1.36 kgFind the difference of weights of 2 loaves of bread and 6 muffins:
1.36 - 1.12 = 0.24 kgThe matching choice is C.
The difference of weights of 2 loaves of bread and 6 muffins:
= 0.24 kg
We have to given that,
One loaf of bread weighs 0.68 kilogram.
And, Six muffins weigh 1.12 kilograms.
Now, We can Find the weight of two loaves of bread:
Here, One loaf of bread weighs 0.68 kilogram.
Hence, the weight of two loaves of bread:
0.68 x 2 = 1.36 kg
Hence, the difference of weights of 2 loaves of bread and 6 muffins:
= 1.36 kg - 1.12 kg
= 0.24 kg
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Can the following fraction be simplified or expressed in a different form -
(5x-1)/x+4
Answer:
= 9x - 1
Step-by-step explanation:
[tex] \frac{(5x - 1)}{x} + 4 \\ = x \times \frac{5x - 1}{x} + 4(x) \\ = 5x - 1 + 4x \\ = 5x + 4x - 1 \\ = 9x - 1[/tex]
13. Landon is 6 ft. tall and measures his shadow to
be 8.3 ft. long. At the same time of day, he
measures a tree's shadow to be 17.6 ft. long. How
tall is the tree?
Answer: 12.72 ft.
Step-by-step explanation:
[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]
What are the exact value of a and b?
Answer:
a = 5, b = 5√3
Step-by-step explanation:
Use sin law
sin A/a = sin C/c
sin 30/a = sin 90/10
sin 30/(sin90/10) = a
a = 5
sin B/b = sin C/c
sin 60/b = sin 90/10
sin 60/(sin90/10) = b
b = 5√3
A football has a radius of 8 cm. What is the surface area of the football?
Step-by-step explanation:
A=4πr²
A = 4× 22/7 ×8²
A = 4 ×22\7×64
A=804.6m²
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own? How will the ratio change if Jim and Terrence each sell ten of their model cars?
As said, 48 model automobiles are driven by Jim at the moment, and the ratio might alter to 19:13.
What does a mathematical ratio mean?An organisation of the integers a and b stated as a/b is still a ratio if b is truly not comparable to 0. Two ratio with the same value are established by the percent formula. As an illustration, you might write your ration as follows: 1:3 when there is 1 man and 3 females.
You know there's an 8:6 ratio between the grand total of model cars Jim and Terrence possess.
As a result, you can respond to the assignment as follows: Assume Jim owns x different car models.
8/6 = x/36
x = 36*8/6
x = 288/6
x = 48
The new percentage of Jim's against Terrence's model vehicles will be as follows because both Jim & Terrence sell ten of their model cars:
(48-10)/(36-10) = 38/26 = 19/13
Jim's to Terrence's miniature automobiles will now be in a 19:13 ratio.
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please help me solve this quick!
On solving the provided question we can say that the quadratic equation is 3x²+15x+9=0
What is quadratic equation ?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is 3x²+15x+9=0
by Shridhara Charya formula method, we have
x=−0.697224
x=−4.30278
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What is 4x5+6n-3? It’s for my math homework due tomorrow
Answer:
=17 + 6n.
Step-by-step explanation:
[tex]4 \times 5 + 6n - 3 \\ = 20 + 6n - 3 \\ = 20 - 3 + 6n \\ = 17 + 6n[/tex]
Simplify the following expression using rational exponents. Assume all variables are positive.
a3/5⋅a3/4
Answer:
The simplified expression is a^(21/20).
Step-by-step explanation:
To simplify the expression, we can use the rule for multiplying two powers with the same base, which is to add the exponents.
a^(3/5) * a^(3/4) = a^(3/5 + 3/4) = a^(6/5 + 3/4)
We can then simplify the fractional exponent by finding a common denominator for the numerators, which is 20 in this case:
a^(6/5 + 3/4) = a^(6/20 + 15/20) = a^(21/20)
The simplified expression is a^(21/20).
Please help me answer this
The given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.
What are radical expressions?
An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.
We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].
On simplifying the expression, we get
⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]
⇒q . √q . q² . [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . √q [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]
Hence, the given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].
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7. The functions f(x)=2* and g(x)=8(2)* are both shown graphed.
The graph of g is certainly a vertical stretch of the function f by a
factor of 8. But, it is also a shift off by three units left. Can you
explain why this is using an exponent law?
The function g(x) = 8(2)^x is also a shift left by 3 units of f(x) = 2^x, as 8 = 2³, hence 8(2)^x = 2^(x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The functions for this problem are given as follows:
f(x) = 2^x.g(x) = 8(2)^x.8 is the third power of 2, hence:
8 = 2³.
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
8(2)^x = 2³ x 2^x = 2^(3 + x) = 2^(x + 3).
As x -> x + 3, a translation left 3 units happened.
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HELPPP PLEASE I NEED HELP
The rule A(x,y) ⇒ (-y,x) describes a transformation. The correct option is D.
What is a transformation of rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.
The transformation is described by the rule A(x,y) (-y,x). The right answer is D.
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Which expression does (sin 3x)(cos x) − (cos 3x)(sin x) simplify to?
cos 4x
sin -x
cos 2x
sin 2x
The given expression simplifies to sin 2x.
Option (D) is correct.
What are trigonometric ratios?
Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.
The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:
sin(A - B) = sin A cos B - cos A sin B
By comparing this formula to the given expression, we can see that:
A = 3x
B = x
Substituting these values into the formula, we get:
sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)
Hence, the given expression simplifies to sin 2x.
Option (D) is correct.
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In the diagram, ACDF∼VWYZ
. Find the value of y.
The value of the variable y is 3
How to determine the valueFrom the information given, we have that;
ACDF∼VWYZ
Given that the lengths are;
A= 12CD = 9YW = 6VZ = 3y -1Since the diagrams are equivalent, then,
A/VZ = CD/YW
substitute the values, we have;
12/3y - 1 = 9/6
cross multiply
3y - 1 = 12(6)/9
divide the values
3y - 1 = 8
collect like terms
3y = 9
Make 'y' the subject
y =3
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Kevin entered a pie eating contest. He ate 4 pies in 132 seconds. How many pies can he eat in 198 seconds?
Answer:
He can eat 6 pies in 198 seconds.
Step-by-step explanation:
Divide
132÷4=33
Divide
198÷33=6 pies in 198 seconds
Is 2/3 equal or bigger than 1/2
Answer: 1/2 is
Step-by-step explanation:
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 4x+10 and MP = 9x-5
X =
Answer:
x=5 and LN= 30, MP= 40
Step-by-step explanation:
Add like terms to both sides of the equation and you will get your answer
What else would need to be congruent to show that AABC= APQR by SSS?
B
A
A. AC = PQ
B. AB BA
C. BC= QR
D. ZAZP
C
Q
P
R
Given:
AC PR
AB=PQ
The condition which satisfy the congruency of the given triangle is
BC≈QR.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
To show that triangle ABC≈triangle PQR by SSS,
In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.
Given, AC≅PR, AB≅PQ.
The another one condition is BC≅QR.
Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.
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Thomas peters purchased a new suv for $32,984. He received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. What is the final price?.
The final price of Thomas Peters' new SUV is $30,309 , can be calculated by subtracting the rebates from the initial cost.
The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:
Final Price = $32,984 - $2,175 - $500
Final Price = $30,309
Therefore, the final price of Thomas Peters' new SUV is $30,309.
It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.
By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.
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please, help with this one
r log a + y log c
The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:
[tex]log a^b = blog a[/tex]
Using this rule, we can write the expression as:
[tex]r log a + y log c = log a^r + log c^y[/tex]
Now we can use the rule that says:
log a + log b = log ab
to combine the two logarithms:
[tex]log a^r + log c^y = log (a^r c^y)[/tex]
Therefore, the expression r log a + y log c simplifies to:
[tex]r log a + y log c = log (a^r c^y)[/tex]
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Which shows the expression x^2-1/x^2-x
in simplest form?
Answer:
x+1/x
Step-by-step explanation:
If F(x) = f(g(x)), where f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, find F'(4).
F'(4) =
Answer:
36.
Step-by-step explanation:
o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).
Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:
F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36
Therefore, F'(4) = 36.
The area of a rectangular red sticker is 33 millimeters.The perimeter is 28 millimeters. what are the dimensions of the sticker?
The dimensions of the sticker are 11 millimeters and 3 millimeters.
What is Area and Perimeter?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given is a sticker which is rectangular in shape.
Area of the sticker = 33 millimeters²
Perimeter of the sticker = 28 millimeters
Area of a rectangle = Length × Width
Perimeter of a rectangle = 2(Length + Width)
Let x be the length and y be the width of the rectangle.
x y = 33
2(x + y) = 28 ⇒ 2x + 2y = 28 ⇒ 2y = 28 - 2x ⇒ y = 14 - x
Substituting y = 14 - x in x y = 33,
x(14 - x) = 33
14x - x² = 33
-x² + 14x - 33 = 0
x² - 14x + 33 = 0
Factorizing the quadratic equation,
(x - 11) (x - 3) = 0
x - 11 = 0 or x - 3 = 0
x = 11 or x = 3
If x = 11, then y = 33/11 = 3
If x = 3, y = 33/3 = 11
Hence the dimensions are 11 millimeters and 3 millimeters.
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