For part (a), we need to find the derivative of the supply equation with respect to the number of units, x.
The supply equation is given by:
S(x) = 30 + 90p * In(4x + 5)
To find the derivative of S(x) with respect to x, we can use the chain rule:
[tex]\frac{dS(x)}{dx} =\frac{dS(x)}{dp}*\frac{dp}{dx}[/tex]
Since the derivative of S(x) with respect to p is 90 * In(4x + 5), we can substitute this into the equation above:
[tex]\frac{dS}{dx}=(90*ln(4x+5))*(\frac{dp}{dx} )[/tex]
This gives us the expression for the rate of change of supply price with respect to the number of units supplied.
For part (b), we need to find the rate of change of supply price when the number of units is 30. Substituting x = 30 into the equation above gives us:
[tex]\frac{Ds(30)}{dx} = (90*ln(4*30+5))*\frac{dp}{dx}[/tex]
For part (c), we need to approximate the price increase associated with the number of units supplied changing from 30 to 31. To do this, we can use the equation from part (a) to find the rate of change of supply price with respect to the number of units supplied and then multiply this rate by the change in the number of units (from 30 to 31).
The approximate price increase is given by:
[tex]\frac{dS(x)}{dx} *(x2-x1)=\frac{dS(x)}{dx}*(31-30)[/tex]
Substituting the appropriate values into this equation will give us the approximate price increase associated with the number of units changing from 30 to 31.
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Can I get some help with this?
The equations that represent given problem is
P + S = 384 and 2.50P + 1.25S = 696.25.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that the cost of 1 slice pizza is $2.50.
The cost of 1 bottle can of soda is $1.25.
In total sell for a day is 384.
Assume that you sell P slice of pizza and S number of soda bottle.
Thus your total sell is P + S.
Therefore, P + S = 384.
The cost 1 slice pizza is $2.50
Then the cost P slice of pizza is $2.50P.
The unit rate of soda bottle is $1.25.
Then the cost S bottles of soda is $1.25S.
Therefore the total sell for that day is 2.50P + 1.25S
2.50P + 1.25S = 696.25
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A researcher needs to assign 10 subjects, numbered 0 to
9, to one of two treatment groups: A and B. Use the table
of random digits, starting with the first row and first
column, to carry out the random assignment.
Table of Random Digits
1 07581 34728 65182 58648 53252 83952
2 23290 98227 30144 83191 12167 90414
3 79486 99776 71793 95330 58256 71156
4 46354 09077 98202 03946 07455 39303
5 00472 20787 54571 73719 04368 41032
Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1
A: 0, 2, 4, 6, 8
B: 3, 4, 7, 2, 8
B: 1, 3, 5, 7, 9
B: 2, 9, 1, 7, 4
OA: 0, 3, 6, 5, 8
A: 0, 7, 5, 8, 1
B: 3, 4, 2, 6, 9
In response to the question, we may say that As a result, the right answer expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To carry out the random assignment, we may utilise the following table of random digits:
Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.
Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.
We can get the following random assignment using this method:
A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9
As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
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Answer:
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
Step-by-step explanation:
THE ANSWER IS D
Solve. Write answers as an imaginary number. 3x^2=-12
80 POINTS
Answer:
Step-by-step explanation:
3x^2 = -12
divide both side by 3x^2 = -4
Solve the square root.x = ±√-4
this equation has no real solutions
Answer:
x = {- 2i; 2i}-------------------------------
GivenEquation 3x² = 12Solve as below3x² = - 12x² = - 4x = √-4x = ± 2√-1x = ± 2iWhich step shows the result of applying the subtraction property of equality?
Step
1
2
3
4
Step 1
Step 2
Step 3
O Step 4
(12x+8) +4=3
Solution
3x+2+4=3
3x+6=3
3x=-3
X=-1
Step 3 shows the result of applying the subtraction property of equality
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 1/4(12x+8)+4=3.
We need to find which step has the property of substitution.
The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount.
Given step 1 is 3x+2+4=3
Opened the brackets on left side and multiplied with 1/4.
Step 2: 3x + 6 = 3.
Added the numbers on the left.
Step 3: 3x = -3
Equal value subtracted or removed from two equal items will result in a new equal amount. So Subtracted both sides by 6.Step 3 shows the result of applying the subtraction property of equality
Step 4: x = -1
Divided both sides by 3.
Hence, in step 3 we have used the property of subtraction.
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Solve each equation. Round to the nearest ten-thousandth.
17(0.3x+5)
Answer:
first option
Step-by-step explanation:
using the property of logarithms
ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )
given
[tex]17^{(0.3x+5)}[/tex] = 12
take the ln of both sides
ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then
(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )
0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )
0.3x ≈ - 4.12293 ( divide both sides by 0.3 )
x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )
Use Figure 1 to evaluate the trigonometric function.
A right triangle with side a of length 13 opposite of angle A, and side b of length 6 opposite of angle B.136
Figure 1
Enter the exact answer.
tanB=
Change entry mode
Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit.
third side, AB= 14.318 Units and tanB = 0.461
How to find the value of tanB and third side?given:
BC=13 units
AC=6 units
solution:
using pythagoras theorem, we get
AB² = BC² + AC²
AB² = 13² + 6²
AB² = 169 + 36
AB² = 205
AB = 14.318 units
tanB = side opposite/side adjacent
tanB = AC/BC
tanB = 6/13
tanB = 0.461
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Using Pythagoras theorem, Third side, AB= 14.318 Units and tanB = 0.461
What is the Pythagoras theorem theory?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
How to find the value of tanB and third side?given:
BC=13 units
AC=6 units
solution:
using pythagoras theorem, we get
AB² = BC² + AC²
AB² = 13² + 6²
AB² = 169 + 36
AB² = 205
AB = 14.318 units
tanB = side opposite/side adjacent
tanB = AC/BC
tanB = 6/13
tanB = 0.461
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Status
Review
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
0 - 10,000
10,001 - 50,000
50,001 - 100,000
Progressive
Tax Rate
3%
5%
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
h
Answer:
final answer would be $6,550
Step-by-step explanation:
To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:
Income Range: $0 - $10,000
Progressive Tax Rate: 3%
Tax Owed: $0 - $10,000 * 3% = $0 - $300
Income Range: $10,001 - $50,000
Progressive Tax Rate: 5%
Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500
Income Range: $50,001 - $100,000
Progressive Tax Rate: 5.5%
Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500
Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.
choose the answer that best describes the statement. probality can be used to determine the likelihood of specific .
The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.
Probability
A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.
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A recipe for a sports drink calls for 5/8 cup of powder for every 2 quarts of water. If Dionne uses 3 quarts of water, how many cups of powder are needed?
Answer: i think 15/8 but, im not sure
Step-by-step explanation:
whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
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MULTIPLE CHOICE Question 2 Look at the drawing below. Which of the following statements, if true, would alone prove pllq? Select all that apply. There are at least two correct answers.
Answer:
no c is right answer
Step-by-step explanation:
angle b and e should be supplementary
Answer:
A, B and C
Step-by-step explanation:
Statement A
According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.
Statement B
According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.
Statement C
According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.
Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.
Statement D
∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary. However, this does not given enough information to prove p ║ q.
to specify that x1 must be at most 75% of the blend of x1 , x2 , and x3 , we must have a constraint of the form
The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)
The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,
Abd here we must have to find the linear constraint of the form of the variables.
While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.
And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.
Here the term of blend refers the sum of the terms,
Then the linear constraint form of the variables is written as,
=> X1 =< 0.75 (X1 + X2 + X3)
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A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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Two different meal combinations at a chicken restaurant have the same number of total calories.
- The first meal has 8 chicken nuggets and a large order of fries.
- The second meal has 12 chicken nuggets and a small order of fries.
- The larger order of fries contains 288.5 calories.
- The small order of fries contains 193.5 calories.
Which equation and solution can be used to determine n, the number of calories in each chicken nugget?
A 12 n-288.5=8 n-193.5 ; n=24.1
B 8 n+193.5=12 n+288.5 ; n=23.75
C 193.5+12 n=288.5+8 n ; n=24.1
D 8 n+288.5=12 n+193.5 ; n=23.75
The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n
And n = 24.1
Option (C) is correct.
What is a linear equation?
A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.
To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:
8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories
We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:
193.5 + 12 n = 288.5 + 8 n
Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:
n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75
Therefore, the number of calories in each chicken nugget is 24.1 calories.
Hence, option (C) is correct.
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I need a little bit of help with this one
Step-by-step explanation:
boy come ladies yer wait for you
hvb-amor-jon
Which quantity is multiplied by pi in the formula for the area of a circle?
The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius
How to determine the multiplied quantity?From the question, we have the following parameters that can be used in our computation:
Area of a circle
The formula for the area of a circle is represented as
A = πr²
Express the formula as a product
So, we have the following representation
A = π * r²
In the above formula, we can see that the square of r is multiplied by pi
Hence, the required quantity is the square of the radius of the circle
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The linear regression equation for the data set is...
Answer: C
Step-by-step explanation: Because
in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
Denominator is 3 more than numerator. If both are increased by 2, the result is 2/3.
Eqn 1:
Eqn 2:
Answer:
Step-by-step explanation:
let numerator=x
denominator=x+3
again
[tex]\frac{x+2}{x+3+2} =\frac{2}{3} \\3(x+2)=2(x+5)\\3x+6=2x+10\\3x-2x=10-6\\x=?[/tex]
x=4
number is
[tex]\frac{4}{4+3} \\=\frac{4}{7}[/tex]
Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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Point B is located at
(-3,0)
(3,0)
(0,3)
(0,-3)
Answer:
(3,0)
have a nice day.(I needed 20 charecters so yeah i needed to say this)
Answer:
(3,0)
Step-by-step explanation:
The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph). We are 3 units to the right. The second number in the ordered pair tells us how far up or down from (0,0) we are. You do not go up for down so that number should be zero.
Can someone solve this please
Answer: B
Step-by-step explanation:
The two equations have the same slope, but different points. This means that the lines are parallel to one another and will not intersect.
The answer is B: No solution
Answer: No solution.
Step-by-step explanation: I graphed the two given functions below. It looks like there is no solution to the given functions.
Hope this helps! :)
What’s 7 1/3 - 5 1/6 ?
Pls hurry !!!
6. If g(x)=-3x²-2 , find g(-2).
Answer:
g(-2) = -14
Step-by-step explanation:
We just need to substitute -2 for x
g(-2) = -3 * (-2)^2 - 2 = -3 * 4 - 2 = -12 - 2 = -14
Subtract 7x-9 from 2x² - 11.
O 2x²-7x-20
02x²-7x-2
O 2x²+7x-20
O 2x²+7x-2
The required, subtraction of 7x-9 from 2x² - 11 is 2x²-7x-2. Option B is correct.
What is arithmetic?Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To subtract 7x-9 from 2x² - 11, we need to distribute the negative sign across 7x and 9, and then combine like terms.
=2x² - 11 - (7x - 9)
= 2x² - 11 - 7x + 9
= 2x² - 7x - 2
Therefore, the answer is 2x²-7x-2.
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Find the vertex of the graph of f(x) = |0.25x − 0.75|. vertex ?
The vertex of the graph (3, 0)
What is Vertex of graph?
A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.
According to question
when f(x) = 0
that's the minimum point, the vertex, or the intersection of two lines, g(x) = 0.25x − 0.75 and h(x) = 0.75 - 0.25x
Therefore
find the intersection of Two line which are
⇒ y = x/4 - 3/4
⇒ 4y = x - 3 → First line
⇒ y = 3/4 - x/4
⇒ 4y = 3 - x → Second line
So x - 3 = 3 - x
2x = 6 ,
x = 3
And y = 0
hence the vertex of f(x) = (3, 0)
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A checkerboard is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Estimate the perimeter of the checkerboard.
The perimeter of the checker board 118.4 cm
Area of each square = 14 sq. cm.
What is the length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.
The square root of area is the length of one side
[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]
[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]
[tex]P=4 a[/tex]
[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]
[tex]\text { Perimeterofthecheckerboard }[/tex]
Therefor we get the perimeter of the checker board 118.4 cm
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How to calculate rate of change of y=4x-3
Answer:
4
Step-by-step explanation:
Answer:
The rate of change is 4
Step-by-step explanation:
The rate of change is the slope.
Since the equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
The slope is 4 and the y intercept is -3
Calculate two-thirds of three-quaters of one half
Answer:
0.25
Step-by-step explanation:
Step 1: Convert all fractions to decimals
Two-thirds = 0.6666
Three-quarters = 0.75
One-half = 0.5
Step 2: Multiply all fractions
0.6666 * 0.75 * 0.5 = 0.25
Step 3: The answer is 0.25
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Three-quarters of one half:
[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]
Two-thirds of "Three-quarters of one half":
[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]
Give expressions for the following:-
1) x is multiplied by -10 and then 5 is added to the result
2) 5 is multiplied by p and the result is subtracted from 26
3)y is multiplied by -5 and the result is added to 6
Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
