Suppose the supply for a certain textbook is given by p=1/4 q^2 and demand is given by p=-1/4 q^2+40, where p is the price and q is the quantity.
(a) How many books are demanded at a price of $5?
(b) How many books are supplied at a price of $5?
(c) Graph the supply and demand functions on the same axes.
Answers
Approximately 11.83 books are demanded at a price of $5 and approximately 4.47 books are supplied at a price of $5.
(a)To find the quantity of books demanded at a price of $5, we need to substitute the price value (p) into the demand function and solve for the quantity (q).
Given:
Demand function: p = -1/4 q^2 + 40
Price (p) = $5
Substituting the price value into the demand function:
5 = -1/4 q^2 + 40
To isolate q^2, we subtract 40 from both sides:
-35 = -1/4 q^2
Now, let's solve for q^2:
q^2 = (-35) / (-1/4)
q^2 = (-35) * (-4)
q^2 = 140
Taking the square root of both sides to solve for q:
q = √(140)
q ≈ 11.83
Therefore, approximately 11.83 books are demanded at a price of $5.
(b) To find the quantity of books supplied at a price of $5, we need to substitute the price value (p) into the supply function and solve for the quantity (q).
Given:
Supply function: p = 1/4 q^2
Price (p) = $5
Substituting the price value into the supply function:
5 = 1/4 q^2
To isolate q^2, we multiply both sides by 4:
20 = q^2
Now, let's solve for q:
q = √(20)
q ≈ 4.47
Therefore, approximately 4.47 books are supplied at a price of $5.
(c) Graph the supply and demand functions on the same axes:
To graph the supply and demand functions on the same axes, we will use the price (p) on the vertical axis and the quantity (q) on the horizontal axis.
Let's plot the points for both the supply and demand functions and then connect them to visualize the graph.
Supply function: p = 1/4 q^2
Demand function: p = -1/4 q^2 + 40
Here is the graph:
|
40 | *
| *
| *
| *
| *
| *
| *
| *
5 | * *
| * *
|________________________________________
0 | 4.47 | 11.83 q
Supply Dema
The horizontal axis represents the quantity (q) of books, and the vertical axis represents the price (p). The supply curve is upward sloping, indicating that as the quantity increases, the price also increases. The demand curve is downward sloping, indicating that as the quantity increases, the price decreases. The intersection of the supply and demand curves represents the equilibrium point where the quantity supplied equals the quantity demanded.
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Related Questions
What is 75% of 85$?
Pls help
Answers
Answer:63.75 :)
Step-by-step explanation:
Answer:
$63.75
Step-by-step explanation:
85 x 75/100
85/1 x 3/4
255/4 - > $63.75
- You should already know how to do this yourself as this is very easy and basic question.
Population density is the number of people per unit of area. The population density of a certain region is 45 people per square kilometer. If the region covers 31 square kilometers, what is the population of the region?
Answers
The population of the region is 1395 people.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
The population density of a certain region is 45 people per square kilometer.
This means,
1 square km = 45 people
Multiply 31 on both sides.
31 square km = 31 x 45 people
31 square km = 1395 people
Thus,
The population of the region is 1395 people.
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what is the answer to this?
Answers
which of the following equations are perpendicular
Answers
A cargo ship left port a and is headed across the ocean to shipping port b. After one month, the ship stopped at a refueling station along a path described by a vector with components leftanglebracket 14, 23 rightanglebracket. After another month, on the same path, the ship reached port b, twice the distance from port a as the fueling station. What are the characteristics of the vector representing the path of the ship?.
Answers
Answer:
Step-by-step explanation:
The vector representing the path of the ship from port A to the refueling station has components <14, 23>, and the vector representing the path from the refueling station to port B has twice the magnitude as the vector from port A to the refueling station.
To find the characteristics of the vector representing the path of the ship from port A to port B, we can add the two vectors together.
The sum of two vectors <a, b> and <c, d> is given by <a+c, b+d>. Therefore, the vector representing the path of the ship from port A to port B is given by:
<14, 23> + 2*<14, 23> = <14+214, 23+223> = <42, 69>
The vector representing the path of the ship from port A to port B is <42, 69>. This vector has a magnitude of √(42^2 + 69^2) = √(1764 + 4761) = √(6525) = 81 and a direction given by the angle theta, where tan(theta) = 69/42.
I hope this helps! Let me know if you have any other questions.
Answer: D. components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 53.85
Step-by-step explanation:
Does anyone know angles?
Answers
Answer:
1: Vertical
2: Adjacent
3: Adjacent
4: Complementary
5: Vertical
6: Vertical
Step-by-step explanation:
sorry if any of them are wrong its been a little since i did that worksheet ^w^
The elongation α
of a planet is the angle formed by the planet, earth, and sun. it is known that the distance from the sun to venus is 0.723au
(see exercise 65 in section 6.2 ). at a certain time the elongation of venus is found to be 39.4∘.
find the possible distances from the earth to venus at that time in astronomical units (au).
Answers
The distance from the earth to venus is an illustration of the sine ratio
The distance from the earth to venus at that time is 1.12 au
How to determine the possibe distance?See attachment for the diagram that illustrates the complete question.
Start by calculating the angle V using the following sine ratio
SE/sin(V) = VS/sin(E)
This gives
1/sin(V) = 0.723/sin(39.4)
Take the inverse of both sides
sin(V)/1 = sin(39.4)/0.723
Evaluate the quotient
sin(V) = 0.8779
Take the arcsin of both sides
V = 61.4
Calculate the measure of angle S
<S + <V + <E = 180
This gives
<S = - <V - <E + 180
Substitute known values
<S = -61.4 - 39.4 + 180
<S = 79.2
The distance (VE) is then calculated using the following sine ratio
VE/sin(S) = VS/sin(E)
This gives
VE/sin(79.2) = 0.723/sin(39.4)
Multiply bot sides by sin(79.2)
VE = sin(79.2) * 0.723/sin(39.4)
Evaluate the product
VE = 1.12
Hence, the distance from the earth to venus at that time is 1.12 au
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Which of the following is not true of a normal curve?a. It is skewed.b. It is a probability distribution.c. Its total area contains 100% of the cases.d. The mode, median, and mean are identical.
Answers
The statement that is not true of a normal curve is a. It is skewed.
A normal curve, also known as a bell curve or Gaussian distribution, is a symmetric probability distribution.
This means that it is not skewed, and it has a shape that is roughly like a bell. The curve is defined by its mean and standard deviation, which determine its center and spread. The total area under the curve represents 100% of the cases or observations in the distribution. The area under the curve between any two points represents the proportion of cases falling between those points. The mode, median, and mean are identical in a normal curve, which means that they all represent the center of the distribution. The mode is the most frequently occurring value, the median is the middle value, and the mean is the arithmetic average of all the values.In summary, a normal curve is a symmetric probability distribution that is not skewed, and its total area contains 100% of the cases.
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HELP ASAP PLEASE
What is the equation of p(x) in vertex form? p(x) = 2(x − 1)2 − 2 p(x) = 2(x + 1)2 − 2 p(x) = 3(x − 1)2 − 2 p(x) = 3(x + 1)2 − 2
Answers
Answer:
p(x)=-2*p*x+4*x+-4=1*-2*p*x+4*x+4=1*-2*p*x+6*x+-6=6*x+4*1*1
Step-by-step explanation:
suppose that y follow a multivariate normal distribution. then, what are the mean and covariance matrix of y ?
Answers
The value of mean, variance and covariance matrix is illustrated in following solution as
\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)
What is mean and covariance?The mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions. with \bar{x} and \bar{y} denoting the means of X and Y, respectively.
Mean and variance is a measure of central dispersion. Mean is the average of given set of numbers. The average of the squared difference from the mean is the variance. Central dispersion tells us how the data that we are taking for observation are scattered and distributed.
To find the mean, variance and covariance matrix of a random vector
\(\left[\begin{array}{ccc}X\\X'\\\end{array}\right]\) X~ U(0,1)
\(E(X')=\int\limits^1_0 {r} \, dr = \frac{1}{r+1}\)
where, r = 1 , 2, 3...
Now,
\(E(X) = \frac{1}{2}\\ \\E(X^2) = \frac{1}{3}\\ \\E(X^3) =\frac{1}{4}\\\)
\(E(X^4)=\frac{1}{5}\)
So, cov(X , X') =
\(E(X^3)-E(X).E(X')\\\\=\frac{1}{4} -\frac{1}{2}.\frac{1}{3}\\ \\ =\frac{1}{12}\)
\(Var(X) = E(X^4) -E'(X')\\\\\frac{1}{5}-\frac{1}{9}\\ \\ \frac{4}{45}\)
Hence,
\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)
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The given question is incomplete, complete question is:
suppose y follows a γ(α, β) distribution. find the mean and variance covariance matrix of the random vector x x2 , where x
What is -5/2 times -41
Answers
The solution of the mathematical statement is 102.5
How to evaluate the expression?From the question, we have the following mathematical statement that can be used in our computation:
"What is -5/2 times -41"
This means that
-5/2 times -41
Express as numbers
So, we have
-5/2 * -41
Divide 5 by 2
So, we have
-2.5 * -41
Evaluate the product
102.5
Hence, the result is 102.5
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In triangle, STU, ST = 52, and TU = 39. What is the range of values for the length third side? With decent explanation please.
A)-13 < SU < 13
B) -13 < SU < 91
C) 13 < SU < 52 (It's not this one, I promise you all it is not)
D) 13 < SU < 91
Answers
Answer:
D
Step-by-step explanation:
given 2 sides of a triangle then the third side SU is in the interval
difference of 2 known sides < SU < sum of 2 known sides , that is
52 - 39 < SU < 52 + 39
13 < SU < 91
Ms. Burnham is playing Jeopardy against Mr. Lafferty. Mr. Lafferty incorrectly answers questions worth 50 points five times in a row. What is his score so far?
Answers
Answer:
-250
Step-by-step explanation:
assuming he starts at 0 pts -50 * 5 = -250
Write an equation in slope-intercept form.
Answers
Given:
The table of values.
To find:
The equation in slope intercept form.
Solution:
From the given table it is clear that the line passes through the points (5,17), (8,41) and (12,73).
Consider any two points from the table, i.e., (5,17) and (8,41). So, the equation of line is
\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)
\(y-17=\dfrac{41-17}{8-5}(x-5)\)
\(y-17=\dfrac{24}{3}(x-5)\)
\(y-17=8(x-5)\)
\(y=8x-40+17\)
\(y=8x-23\)
Therefore, the equation of line in slope intercept form is \(y=8x-23\).
Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle
Answers
No, the tangents cannot intersect outside the circle.
When tangents intersect outside a circle, the measure of the angle they form is one half the difference of the intercepted arcs. Since the tangents are at the endpoints of the same diameter, both intercepted arcs would have to measure 180 degrees.
tangent
a tangent is the line drawn from an external point and passes through a point on the curve.
One real-life example of a tangent is when you ride a bicycle, every point on the circumference of the wheel makes a tangent with the road.
curve
A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it.
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For the preceding problem you should find that there are significant differences among the three treatments. Onee reason for the significance is that the sample variances are relatively small. The following data have the same sample means that appeared in the preceding question, but the SS values within each sample are doubled
Calculate the sample variance for each of the three samples These values are the variances in the previous question (12.00, 13.00, and 8.00)
Answers
The SS value for the first, second and third sample is 24, 26 and 18 respectively. Upon dividing the SS value by the sample size minus one, sample variance can be derived.
In the previous question, there were significant differences among the three treatments, partially due to the relatively small sample variances. Now, with the SS (sum of squares) values within each sample doubled, we need to calculate the new sample variances. The values provided in the previous question were 12.00, 13.00, and 8.00.
To calculate the sample variance for each of the three samples, we utilize the formula for variance, which is the sum of squared deviations from the mean divided by the sample size minus one.
For the first sample with a previous variance of 12.00, if the SS value is doubled, the new SS value would be 24.00. To calculate the new sample variance, we divide this SS value by the sample size minus one.
Similarly, for the second sample with a previous variance of 13.00, the doubled SS value would be 26.00. Again, we divide this SS value by the sample size minus one to calculate the new sample variance.
Lastly, for the third sample with a previous variance of 8.00, the doubled SS value would be 16.00. We divide this SS value by the sample size minus one to obtain the new sample variance.
By performing these calculations, we can determine the new sample variances for each of the three samples, which will reflect the changes resulting from the doubled SS values within each sample.
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Help me with this question this was supposed to be due yesterday!
Effects of Shifting, Adding and Removing Data
Pamela works at the zoo. She was looking at some data showing the weight of their 4 giraffes. The mean of weight of the giraffes was 1,800 pounds and the median weight was 2,000 pounds. Then gets a baby giraffe that weighs 500 pounds. How would the addition of the baby giraffe affect the mean and median?
Chose one:
• Both the mean and median increased.
• Both the mean and median decreased.
• The mean increased, but the median decreased.
• The median increased, but the mean decreased.
Answers
Answer: Both the mean and median decreased.
Step-by-step explanation:
The addition of the 500 lb baby elephant will have a huge impact on the mean, since you'll be finding the average (adding all numbers then dividing). So the only logical answer would be the chosen. The median will most likely either decrease or stay the same, but since staying the same isn't an option for the median, it's most likely going to be decrease.
[I do apologize in advance if it's wrong, and next time try submitting work on time :)) Hope I helped!]
what are the answers please help!
Answers
Answer: A, C, D
Step-by-step explanation:
A) Correct. They factored out 5.
C) Correct. They factored out 10.
D) Correct. They factored out -5.
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant’s research indicates that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.
a. Find the expected number of repairs for this freezer per year.
b. Find the standard deviation of the number of repairs per year.
c. What are the mean and standard deviation of the restaurant’s annual expense with the service contract for the freezer?
Answers
(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.
What is Standard Deviation?Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.
(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.
E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)
= 0.33
(b) Standard deviation of number of repairs per year can be calculated as,
SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)
= √ (0.5611)
= 0.749
(c) Mean of the restaurant's annual expense with service contract is,
Mean = Expected cost = $125 + ($35 × 0.33) = $136.55
Standard deviation of the restaurant's annual expense with service contract is,
SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217
Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.
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For questions 1-2, find the distance and midpoint of the segments given the endpoints. 1. AB with A(3, 4) and B(-1, 10) Midpoint
Answers
Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:
\(d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)then, we have the following:
\(\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}\)1. Expresa cada función cuadrática f en la forma f(x)-yo = p(x – xo) x ϵ R, donde xo , yo , p ϵ R son elegidos apropiadamente. Indica las coordenadas
del vértice de la parábola, el mínimo o máximo de la función f, sobre todo R. Traza la gráfica de f.
a) f(x)= 2x2 + 3x -5, ϵ R,
b) f(x)= -3x2 + 7x +9, ϵ R,
c) f(x)= - x +1, ϵ R,
AYUDA LE DARE CORONA PLIS
Answers
Answer:
Step-by-step explanation:
1. Express each quadratic function f in the form f (x) -yo = p (x - xo) x ϵ R, where xo, i, p ϵ R are appropriately chosen. Indicate the coordinates
of the vertex of the parabola, the minimum or maximum of the function f, especially R. Draw the graph of f.
a) f (x) = 2x2 + 3x -5, ϵ R,
b) f (x) = -3x2 + 7x +9, ϵ R,
c) f (x) = - x +1, ϵ R,
HELP YOU GIVE YOU CORONA PLIS
Show that, when SI units for µ0 and ε0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.
Answers
The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.
The equation mentioned in the question is as follows; The SI units of magnetic permeability and permittivity of free space are Henry/meter and farad/meter respectively. In order to prove that the units given by the right-hand side of the equation are m/s, we need to perform the following steps: Substitute the values of magnetic permeability and permittivity of free space in the equation. Let's substitute µ0 and ε0 values in the above equation, we get; In order to perform this step, we need to know the units of each component in the equation. A unit of force is Newton, and a unit of charge is Coulomb. A magnetic field has the unit Tesla. Let's find out the units of the right-hand side component of the above equation. We can now rearrange the equation to make it simpler.!)
The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.
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Which of the following is not a criteria for the construction of a triangle?
A
ASA
B
SAS
C
SSS
D
AAA
Answers
Answer:
D) AAA
Step-by-step explanation:
an archaeologist uncovers 26 artifacts from a site. the types of artifacts are shown. an artifact is randomly selected for display. a bar-graph titled archeological artifacts. the horizontal axis represents tools, pottery, and coins. the vertical axis represents number of artifacts and ranges from 0 to 16, in increments of 2. number of artifacts of tools is 14. number of artifacts of pottery is 7. number of artifacts of coins is 5. what is the probability that a piece of pottery is selected? express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. or about %
Answers
The probability of selecting a piece of pottery is 7/26, and when converted to a percentage and rounded to the nearest whole percent, it is approximately 27%.
An archaeologist uncovers 26 artifacts from a site. The types of artifacts are shown below. The horizontal axis represents tools, pottery, and coins. The vertical axis represents the number of artifacts and ranges from 0 to 16, in increments of 2. The number of artifacts of tools is 14. The number of artifacts of pottery is 7. The number of artifacts of coins is 5.
What is the probability that a piece of pottery is selected?The total number of artifacts at the site = 26
Number of pottery artifacts = 7
Probability of selecting a piece of pottery = Number of pottery artifacts/Total number of artifacts
Probability of selecting a piece of pottery = 7/26
If we want to express this probability in a percentage, we can convert it by multiplying it by 100.
Thus,Probability of selecting a piece of pottery = 7/26 = 0.269 = 26.9% (rounded to the nearest whole percent)
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PLEASE HELP ME WITH THIS ASAP, I’m really confused.
Answers
Answer:
scalene triangle for the first
equilateral triangle for the second
isosceles triangle for the 3rd
Answer:
The first is a scalene triangle. No two sides on a scalene trinagle will have the same length.
The second is an equilateral triangle. Equilateral literally means "equal sides".
The third is an isosceles triangle. These triangle will have perfect symmetry.
A student is instructed to square a binomial, and gets the result shown. Choose the correct description of the student's work.
(x3)x9
Answers
The student's work is incorrect. The correct answer is x^6.The student's work is incorrect because they multiplied the binomial by 9 instead of squaring it.
The student has incorrectly multiplied the binomial by 9 instead of squaring it. To square a binomial, we need to multiply the first term by itself, then multiply the second term by itself, and then add the products together. In this case, the first term is x^3 and the second term is 9. So, the correct answer is x^6.
How to square a binomial:
Square the first term. In this case, x^3 * x^3 = x^6.
Square the second term. In this case, 9 * 9 = 81.
Add the products together. x^6 + 81 = x^6.
Therefore, the correct answer is x^6. The student's work is incorrect because they multiplied the binomial by 9 instead of squaring it.
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without using symmetry, determine a definite integral that represents the area of the region enclosed by r = 1 sin θ .
Answers
The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ
To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.
In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.
The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.
By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.
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What is the surface area?
in
- 5 in
Answers
Answer:
94 ft
Step-by-step explanation:
A dude ranch in Texas charges each customer y dollars to gohorseback riding based on the equation y=10x+20, where xrepresents the number of hours they go horseback riding.5. How much will it cost for one person to go horseback riding for 3hours?6. How much will it cost for a family of 4 to go horseback riding for2 hours?7. What does the y intercept mean in the equation?
Answers
Answer:
(a)$50
(b)$160
Explanation:
The equation that represents the charge per customer is:
\(\begin{gathered} y=10x+20 \\ x=\text{number of hours they go horseback riding.} \end{gathered}\)Part 5
When one person goes horseback riding for 3 hours.
x=3
\(\begin{gathered} y=10(3)+20 \\ =30+20 \\ =\$50 \end{gathered}\)Part 6
If one person goes horseback riding for 2 hours:
\(\begin{gathered} y=10(2)+20 \\ =20+20 \\ =\$40 \end{gathered}\)Since they are a family of 4, the cost will be:
\(\begin{gathered} 4y=4\times40 \\ =\$160 \end{gathered}\)Part 7
In the equation:
\(y=10x+20\)The y-intercept, $20 represents the cost of entry to the ranch. It means that even if a person does not go horseback riding, they will still pay the $20.
Use propositional logic to prove that the argument is valid. Do not use truth tables (A + B) ^ (C V -B) ^(-D-->C) ^ A D Please use the following substitute operators during your quiz: ^: &
v: I
¬: !
-->: ->
Answers
To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:
(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D
We will represent the proposition as follows:
P: (A + B)
Q: (C V -B)
R: (-D --> C)
S: A
T: D
From the given premises, we can deduce the following:
P ^ Q (Conjunction Elimination)
P (Simplification)
Now, let's apply the rules of disjunction elimination:
P (S)
A + B (Simplification)
Next, let's apply the rule of disjunction introduction:
C V -B (S ^ Q)
Using disjunction elimination again, we have:
C (S ^ Q ^ R)
Finally, let's apply the rule of modus ponens:
-D (S ^ Q ^ R)
C (S ^ Q ^ R)
Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.
To learn more about Simplification : brainly.com/question/28261894
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