The normal vector of the plane containing the lines is the cross product of (-12, 3, 6) and (4, -1, -2), which is (48, -66, 0).
The direction vector of a line is a vector that points in the direction of the line and the position vector of a line is a vector that represents any point on the line.
Let's start with line r1(t) = - (-12t, 3t + 1,6t + 5).
The derivative of r1(t) = - (-12t, 3t + 1,6t + 5) is (-12, 3, 6).
So, the direction vector of line r1(t) is (-12, 3, 6).
We repeat this process for line r2(t) = (4t – 4, -t + 4,5 – 2t).
The derivative of r2(t) = (4t – 4, -t + 4,5 – 2t) with respect to t is (4, -1, -2), so the direction vector of line r2(t) is (4, -1, -2).
If we plug in t = 0 into the line equation, we get the point
=> (4t – 4, -t + 4,5 – 2t) = (-4, 4, 5).
So, the position vector of line r2(t) is (-4, 4, 5).
So, we find the cross product of (-12, 3, 6) and (4, -1, -2). If the cross product is equal to the zero vector, then the lines are parallel.
If not, then the lines are not parallel.
The cross product of (-12, 3, 6) and (4, -1, -2) is (48, -66, 0).
Since the cross product is not equal to the zero vector, the lines are not parallel.
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If f(x) = 2x³ + x² - 3x + 4 , what is f'(2) ?
Answer:
f'(2) = 25
Step-by-step explanation:
differentiate f(x) using the power rule
[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant) = 0
f(x) = 2x³ + x² - 3x + 4
f'(x) = 3× 2x² + 2x - 3 = 6x² + 2x - 3 , then
f'(2) = 6(2)² + 2(2) - 3
= 6(4) + 4 - 3
= 24 + 1
= 25
Graph the piecewise function. You must graph on your own and not use a web-based program to graph. f(x)={(1/3 x-1 if " x≤0 -1/2 x+6 if 0
The graph for the piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6 is attached in the solution.
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals.
Given is a piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
Plotting the graph for:
f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
From the graph, we conclude that:
The graph of the given piecewise function is a straight line with two segments.
The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6.
The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.
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A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 18 m, and d = 3 m.)
W = __________ J
Answer:
Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.
Step-by-step explanation:
investigate whether the set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations. drag and drop yes or no into each box to show whether the set of polynomials in one variable is closed under the four basic operations. then complete the statement that explains whether polynomials are like whole numbers, integers, or rational numbers with respect to closure.
The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.
Whole numbers:
Addition: Yes
Subtraction: No (e.g. 5 - 7 = -2)
Multiplication: Yes
Division: No (e.g. 4 ÷ 2/3 is not a whole number)
Integers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (e.g. 4 ÷ 1/2 is not an integer)
Rational numbers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: Yes (provided the denominator is non-zero)
Polynomials:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (in general, polynomials cannot be divided by other polynomials)
Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.
However, they are not closed under division like rational numbers.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
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In 1976, a certain model of car cost $5,000. What would be the cost of that car in 1983 dollars? Express your answer rounded to the nearest cent.
The cost of car in the year 1983 is 2845
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The CPI (consumer price index) is a measure of the overall change in prices of goods and services over a certain period of time. It is given by:
CPI = (cost of market basket in a given year / cost of market basket in base year) * 100
Given that:
CPI = 56.9 in 1976, cost of market basket in a given year = x, cost of market basket in base year = $5000
Hence:
56.9 = (x/ 5000) * 100
x = 2845
The cost of car is 2845
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find the value of [tex](a-\frac{1}{a} )^2[/tex] and [tex](a-\frac{1}{a} )[/tex], when [tex]a^{2} +\frac{1}{a^2}=18[/tex]
Answer:
To find the value of (a - 1/a)^2 and (a - 1/a), we can start by squaring the given equation:
a^2 + 1/a^2 = 18
(a^2 + 1/a^2)^2 = 18^2
a^4 + 2 + 1/a^4 = 324
a^4 + 1/a^4 = 322
Now, to find (a - 1/a)^2, we can square the difference of a and 1/a:
(a - 1/a)^2 = a^2 - 2 + 1/a^2
We can substitute the value of a^4 + 1/a^4 = 322 into this equation:
(a - 1/a)^2 = 322 - 2
(a - 1/a)^2 = 320
To find (a - 1/a), we can take the square root of (a - 1/a)^2:
(a - 1/a) = √320
And, a^2 + 1/a^2 = 18, we can solve for a,
a^4 - 18a^2 + 1 = 0
(a^2 - 1)(a^2 - 18) = 0
a^2 = 1 or a^2 = 18
a = 1 or a = ±√18
So, in this case, the value of (a - 1/a)^2 is 320 and (a - 1/a) is √320.
Step-by-step explanation:
Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
A= -2,2
B=6,2
C=0,6
Step-by-step explanation:
we need to calculate the distances between the points as the side lengths of the triangle.
these side lengths must satisfy the Pythagoras principle :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.
the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.
this is then caked the distance formula, but it is all Pythagoras again.
AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =
= 8² + 0² = 8²
AB = 8
AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20
AC = sqrt(20)
BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52
BC = sqrt(52)
as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.
if this is a right-angled triangle, then
8² = sqrt(20)² + sqrt(52)²
must be true.
but
64 = 20 + 52 = 72
is wrong.
so, the segments do not form a right-angled triangle.
determine if ST is parallel to PR
Answer:
Step-by-step explanation:
Picture?
You didn’t give enough info. Are you able to provide more information? Or a picture?
According to the Anxiety and Depression Association of America (ADAA), approximately 8.7% of all adults suffer from a specific phobia, such as high bridges or old elevators. An experiment consists of selecting adults at random and asking them if they suffer from any kind of phobia. Is there any evidence to suggest the ADAA claim is false? Justify your answer. Because the probability that 35 people are selected before the first person with a phobia is chosen is 0.0453, there _____ evidence that the claim about the probability of people having a phobia being 8.7% is false.
The probability of 35 people being selected before the first person with a phobia being chosen does not provide sufficient evidence to suggest that the ADAA claim is false. To determine if the ADAA claim is false, we would need to perform a statistical hypothesis test to compare the sample proportion of adults with phobias to the ADAA estimate of 8.7%. This would involve collecting data on a random sample of adults, calculating the sample proportion of adults with phobias, and comparing it to the ADAA estimate of 8.7%.
If the sample proportion is significantly different from 8.7%, we can conclude that there is evidence to suggest that the ADAA claim is false. However, without performing a statistical hypothesis test, we cannot make a conclusion about the validity of the ADAA claim based solely on the probability of 35 people being selected before the first person with a phobia is chosen.
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The doctor orders 1000 mL D5RL to run at 100 ml/hr. How long will this IV infusion run?
This IV infusion will run for ____ hours.
(Round your answer to the nearest whole number.)
Answer: The IV infusion will run for 10 hours.
To find out, you divide the total volume of fluid (1000 mL) by the rate of infusion (100 mL/hr):
1000 mL / 100 mL/hr = 10 hours.
Rounding to the nearest whole number, the IV infusion will run for 10 hours.
Step-by-step explanation:
Answer:
The doctor orders 1000 mL of fluid to run at a rate of 100 mL per hour. To find out how long this IV infusion will run, divide the total volume of fluid by the flow rate:
1000 mL / 100 mL/hr = 10 hours
So, the IV infusion will run for 10 hours.
class 10r sat a test
the mean mark was 70%
there are thirty students in class 10r, 20 of whom are boys
the mean mark for the boys in the test was 62%
work out the mean of the girls
Answer:
15% tell me if im wrong
Step-by-step explanation:
simplify!!
(-2x^2-3x+4)+(-4x^2+x-2)
Answer:
number b is the write answer
Step-by-step explanation:
-2x²-3x+4-4x²+x-2
-2x²-4x²-3x+x+4-2
-6x²-2x+2
Fred’s fish tank is shown below how many cubic feet of water will he need to fill in his fish tank l=8.3ft W=11.5ft H=6
Answer:
611.05
Step-by-step explanation:
To find the number of cubic feet of water needed to fill Fred's fish tank, we need to calculate the volume of the tank. The volume of a rectangular prism (such as a fish tank) can be found by multiplying the length, width, and height together. Using the given measurements, the volume of Fred's fish tank would be:
8.3 ft * 11.5 ft * 6 ft = 611.05 cubic ft
So, Fred will need 611.05 cubic ft of water to fill his fish tank.
Find the slope of the line described by the table.
M =
The slope of the line describes by the table is 0.1.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The table represents Bike ride, where x represents the number of minutes in 'x' and y represents the number of kilometers.
We know, slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (1.0 - 0.5)/(10 - 5).
Slope(m) = 0.5/5.
Slope(m) = 0.1
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The population of 6 different states is shown below. Order the populations from the source to the target in order of GREATEST to LEAST value.
Florida: 1.98 x 10^7
Arizona: 6,730,000
Washington: 7.06 x 10^6
New York: 19,700,000
California: 3.88 x 10^7
Massachusetts: 6.74 x 10^6
Ordering the populations of the 6 different states, written in scientific notations, in order of the greatest to the least value is as follows:
California: 3.88 x 10^7Florida: 1.98 x 10^7New York: 19,700,000Washington: 7.06 x 10^6Massachusetts: 6.74 x 10^6Arizona: 6,730,000.What is scientific notation?Scientific notation is the standard way of writing very long or short numbers in their shorthand forms.
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10, with the following parts: coefficient, base, and exponent.
For instance, New York's population is 19,700,000 and can be written in scientific notation as 1.97^7.
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ANSWER ASAP OR MY MOM WILL BE MAD CUZ SHES ABOUT TO LOOK AT MY WORK IN MATH
25% of 84 is what value?
3
20
21
59
phil bikes a distance of x miles at a rate of 15 miles per hour. how many hours did the trip take?
Answer:
Below
Step-by-step explanation:
The equation you need to remember is:
rate X time = distance re-arrange to
time = distance / rate sub in the numbers given to get
time = x / 15 hours
Three friends are participating in a relay race where they each need to eat a hotdog as fast as they can. The first friend, Monica, starts eating as soon as the timer starts. When she finishes eating the hot dog, her team earns one point. Then, the next friend, Richard, starts eating the second hotdog. As soon as he finishes eating, the team earns another point. Finally, Andrew starts eating the third hotdog. As soon as he finishes eating the team earns their third point.
The graph below shows the points the team has (y) in relation to the time in minutes (x):
Use this information to answer the following questions:
How many points does the team have 1 minute into the competition?
How many points does the team have 5 minutes into the competition?
After how many minutes, does the team have 3 points?
The required solutions are as follows,
(a) The team has zero points in 1 minute of the competition.
(b) The team has two points in 5 minutes of the competition.
(c) After 8 minutes, the team has 3 points.
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,
From graph,
As at 0 seconds the race started and Monia finished eating a hot dog at 3 minutes. so 1 to 2.9 minutes of race point is zero.
Scorecard with time is given as
1 to 2.9-minute score = 0
3 to 4.9-minute score = 1
5 to 7.9 minutes score = 2
after 8 minutes score = 3
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At an amusement park, the straight water slide is 42m long and drops 20m. What angle does the slide ma with the horizontal?
The angle formed 28.42 degree between the slide and the drop.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
length of water slide is 42m. (Hypotenuse)
and length of drop = 20 m (Perpendicular)
Using Trigonometry
sin [tex]\theta[/tex] = P/ H
sin [tex]\theta[/tex] = 20 / 42
sin [tex]\theta[/tex] = 10 /21
sin [tex]\theta[/tex] = 0.476
[tex]\theta[/tex] = [tex]sin ^{-1[/tex] (0.476)
[tex]\theta[/tex] = 28.42 degree.
Hence, the angle is 28.42 degree.
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The number of households in the U.S. that own homes is 79.4 million, or 63.5% of all households. Find the total number of households to the nearest hundredth of a million.
Answer:
125 million
Step-by-step explanation:
[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]
a square has an perimeter of 56 ft what is the length of each side?
Answer:
14ft
Step-by-step explanation:
Perimeter of a square = 4s where s = side length
Here, we are given the perimeter, and we want to find the side length. To do so we plug in the perimeter and solve for s
Perimeter = 56
So 56 = 4s
==> divide both sides by 4
14 = s
A square with a perimeter of 56 feet has a side length of 14 feet
Which decimal is greatest, .54, .504, or .45?
Answer:
The correct solution is .54
Step-by-step explanation:
Think about this like counting change.
0.54 is the largest amount. Next would be 0.504 (which in change would be close to 0.50 rounded down), lowest amount would be 0.45
he radius of a circle is tripled. Which of the following describes the effect of this change on the area? The area is multiplied by 1/9 . The area is multiplied by 9. The area is multiplied by 3. The area is multiplied by 1/3.
Tripling the radius of a circle results in a nine-fold increase in its area.
The radius of a circle is a critical component in determining its size. Tripling the radius of a circle means that the size of the circle has increased three times its original size.
The area of a circle can be calculated using the formula
=> A = πr²,
where A represents the area of the circle, π is Pi, and r is the radius. When the radius of a circle is tripled, the value of r becomes 3 times its original value, meaning the formula becomes
=> A = π(3r)² = π * 9r² = 9πr².
Therefore, the new area of the circle is nine times the original area of the circle.
Complete Question:
The radius of a circle is tripled. Which of the following describes the effect of this change on the area?
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Andrea is buying some new shirts and sweaters. She is able to buy 6 shirts and 7 sweaters for $212 or she is able to buy 10 shirts and 8 sweaters for $258. How much does a shirt cost? How much does a sweater cost?
Answer:
Sweater: $26
Shirt: $5
Step-by-step explanation:
Systems of Equations:We can set up two linear equations to form a systems of equations which will allow us to solve for the price of a shirt and sweater.
The first step we want to take is assigning the shirt and sweater to an unknown, so I'll just refer to the price of a shirt as: [tex]S_h[/tex] with the little subscript "h" and I'll refer to the price of a sweater as: [tex]S_w[/tex] with the little subscript "w".
Now the next main thing to understand is we can calculate the total price of something by multiplying the price of an individual item by the quantity. So if I buy an apple for $10, but I buy 10 of them, then the total price would be 10 * 10 or $100. So when Andrea buys 6 shirts, the price of that can be represented as: [tex]6S_h[/tex] and when Anrea buys 7 sweaters the price of that can be represented as: [tex]7S_w[/tex], adding these together should equal 212, since it gives us that buying 6 shirts and 7 sweaters costs a total of $212.
Using this logic with the other case where she buys 10 shirts and 8 sweaters for $258, we can set up the two equations:
[tex]6S_h + 7S_w=212\\10S_h+8S_w=258[/tex]
From here we can use substitution to solve this equation. So let's solve for the [tex]S_h[/tex] on the top equation.
[tex]6S_h+7S_w=212[/tex]
Froom here subtract [tex]7S_w[/tex] from both sides and then divide by 6
[tex]S_h=\frac{212-7S_w}{6}[/tex]
Now we can plug this into the second equation:
[tex]10(\frac{212-7S_w}{6})+8S_2=258[/tex]
Simplifying the division and multiplication on the left side we get:
[tex]\frac{1060}{3}-\frac{70}{6}S_w+8S_w=258[/tex]
From here we can combine the like terms
[tex]\frac{1060}{3}-\frac{22}{6}S_w=258[/tex]
we can simplify the fraction a bit more
[tex]\frac{1060}{3}-\frac{11}{3}S_w=258[/tex]
Now subtract 1060/3 from both sides
[tex]\frac{-11}{3}S_w=\frac{-286}{3}[/tex]
Now divide both sides by -11/3
[tex]S_w=26[/tex]
Now from here we can substitute this back into any equation to solve for the shirt price. Let's use the equation where we solved for the price of the shirt but we just needed to know the price of the sweater.
[tex]S_h=\frac{212-7S_w}{6}[/tex]
Now let's plug in 26 for the sweater price.
[tex]S_h=\frac{212-7(26)}{6}[/tex]
Simplify this and we get:
[tex]S_h=5[/tex]
and now we know the shirt and sweater price!
which equation can be solved to find one of the missing side lengths in the triangle? triangle a b c is shown. angle a c b is 90 degrees and angle c b a is 60 degrees. the length of side c b is a, the length of c a is b, and the length of hypotenuse a b is 12 units.cos(60o)
The equation cos (60°) = a/12 can be used to find one of the missing side lengths in the triangle.
Trigonometric identities are equations that are true for all values of the angles in a right triangle. They express the relationships between the angles and sides of a triangle and are used to simplify trigonometric expressions or to prove that two expressions are equal.
One of the trigonometric identities is the SOH CAH TOA.
SOH: sin θ = opposite/hypotenuse
CAH: cos θ = adjacent/hypotenuse
TOA: tan θ = opposite/adjacent
Since angle CBA is 60°, the adjacent side is a, the opposite side is b, and the hypotenuse is 12 units, then:
cos θ = adjacent/hypotenuse
cos (60°) = a/12
Rearranging the equation, we can solve one of the missing side lengths, which is a.
a = 12cos(60°)
Hence, we can use the equation cos (60°) = a/12 to find the length of side a.
The problem seems incomplete, it must have been...
"Which equation can be solved to find one of the missing side lengths in the triangle? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.
cos(60°) = 12/a
cos(60°) = 12/b
cos(60°) = b/a
cos(60°) = a/12"
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En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor
The Percentage of bags with correct weight will be 84%
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, the following can be gotten:
Total number of bags = 2500
Bags with correct weight = 2100
Bags with lower weight = 275
Bags with higher rate = 125
Percentage of bags with correct weight will be:
= 2100 / 2500 × 100
= 84%
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solve 10 + x ≥ 14. then graph the solution.
Answer:
x ≥ 4
Step-by-step explanation:
Just treat the equation like you would a regular algebraic equation.
10 + x ≥ 14
10 + x - 10 ≥ 14 - 10
x ≥ 4
As for graphing it, I'm not really sure if you want a proper graph or a number line.
For a number line, put a closed dot on a 4
The market for cast iron marble urns has the supply and demand functions below.
Supply: p = 15 + 0.1q
Demand: p= √650- 5q
(a) Find the point of equilibrium for this market.
(b) Find the Consumers' surplus for this market.
(c) Find the Producers' surplus for this market.
By applying supply and demand concept, it can be concluded that:
a. Point of equilibrium for this market will be reached when p = 20 and q = 50
b. Consumers' surplus for this market when -150 < q < 50
c. Producers' surplus for this market when 50 < q < 130
Demand is the number of goods purchased or requested in the market at a certain price and time, while supply is the number of goods sold or offered in the market at a certain price and time.
Point of equilibrium will be reached when supply and demand are in balance.
We have the following supply and demand functions:
Supply: p = 15 + 0.1q
Demand: p= √(650- 5q)
A. The point of equilibrium occurs when supply and demand are in balance:
15 + 0.1q = √(650- 5q)
(15 + 0.1q)² = 650 - 5q
225 + 3q + 0.01q² = 650 - 5q
0.01q² + 3q + 5q + 225 - 650 = 0
0.01q² + 8q - 425 = 0
q² + 800q - 42500 = 0
q² + 800q + 160000 - 202500 = 0
(q + 400)² - 202500 = 0
(q + 400)² = 202500
q + 400 = 450
q = 50
As we know q, we can calculate the p:
p = 15 + 0.1q
= 15 + 0.1 * 50
= 20
B. The Consumers' surplus when demand > supply:
√(650- 5q) > 15 + 0.1q ⇔ q < 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Consumers' surplus for this market when -150 < q < 50
C. The Producers' surplus when supply > demand:
15 + 0.1q > √(650- 5q) ⇔ q > 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Producers' surplus for this market when 50 < q < 130
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During the time interval 4 St ≤ 8, the rate at which the number of wolves in a forest is changing, in wolves per week, can be modeled by the function
E(t) = 31 cos(0.11t?), where t is measured in weeks.
What is the rate at which the number of wolves in the
forest is changing at timet = 7? You may use a
calculator and round to the nearest thousandth. Indicate units of measure.
For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)
Here t is the time measured in weeks.
The time value is given as t = 7
Substitute the value of t in the equation -
E(t) = 31 cos (0.11t)
Apply the arithmetic operation of multiplication -
E(7) = 31 cos (0.11 × 7)
E(7) = 31 cos (0.77)
E(7) = 31 × 0.7179
E(7) = 22.2549
Therefore, the rate value is obtained as 22.2549.
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Is the following statement true or false? the mean of a random sample equals the mean of the population from which it was drawn.
The claim that the average of a random sample is the same as the average of the population from which it was taken is False.
Is the sample mean the same as the population mean?The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.
Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.
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