The first pipe can fill 1/20 of the tank in one minute, while the second can fill 1/30 of the tank in one minute. Together, they can fill 1/20 + 1/30 = 1/12 of the tank in one minute.
Therefore, it would take the two pipes together 12 minutes to fill the tank. The answer is B. To solve this problem, we can use the concept of rates. One pipe can fill the tank in 20 minutes, so its rate is 1/20 of the tank per minute. The other pipe takes 30 minutes, so its rate is 1/30 of the tank per minute. When working together, their combined rate is (1/20 + 1/30), which simplifies to 1/12 of the tank per minute. Therefore, it would take the two pipes together 12 minutes to fill the tank. Your answer is B. 12 minutes.
To know more about rate click here
brainly.com/question/199664
#SPJ11
What are 2 facts about involving my number 12
The two facts about involving my number 12 are the following, twelve hours visible on a clock and and A dozen is a quantity that contains 12 quantities.
The word number twelve is the largest number with the most single-morpheme names in English. The number 12 is closely associated with heaven. The number 12 is often considered a symbol of growth and understanding. This number can help you achieve mental and emotional balance and harmony in your life. In mathematics, 12 (twelve) is the number after 11 and before 13. Twelve is a wonderful combination or divisible by 2, 3, 4 and 6. The truth or facts about the number 12 are :
12 Hours of SightThe dozen is the number with a 12 thing.There are 12 fields in total. One foot of is 12 inches.There are 12 months in a yearThere are 12 picture cards in the deck etc.For more information about number , visit :
https://brainly.com/question/25734188
#SPJ4
Evaluate the integral. Check your results by differentiation. (Use C for the constant of integration.) integral (x^3 + 3)^2(3x dx) Evaluate the integral. Check your result by differentiation. (Use C for the constant of integration.) integral 3x^4 dx/(2x^5 - 1)^4 IF integral f(x) dx = (2x - 14)^10 + C, find f(x). f(x) =
1. For the first integral, we will integrate the function (x^3 + 3)^2(3x dx):
∫(x^3 + 3)^2(3x) dx
To check the result, we differentiate with respect to x:
d/dx [(1/3)(x^3 + 3)^3 + C] = (x^3 + 3)^2(3x)
2. For the second integral, we will integrate the function 3x^4 dx/(2x^5 - 1)^4:
∫(3x^4) dx/(2x^5 - 1)^4
To check the result, we differentiate with respect to x:
d/dx [(-1/10)(2x^5 - 1)^(-3) + C] = 3x^4/(2x^5 - 1)^4
3. If ∫f(x) dx = (2x - 14)^10 + C, then to find f(x), we differentiate with respect to x:
f(x) = d/dx [(2x - 14)^10 + C] = 10(2x - 14)^9(2)
f(x) = 20(2x - 14)^9
1. To evaluate the integral (x^3 + 3)^2(3x dx), we can use the substitution u = x^3 + 3, which gives us du/dx = 3x^2 and dx = du/(3x^2). Substituting these into the integral, we get:
integral (x^3 + 3)^2(3x dx) = integral u^2 (du/ x^2)
= integral u^2/x^2 du
= integral (x^6 + 6x^3 + 9)/x^2 du
= integral (x^4 + 6x + 9/x^2) du
= (1/5) x^5 + 3x^2 - 9/x + C
To check our result by differentiation, we can take the derivative of the above expression with respect to x:
d/dx [(1/5) x^5 + 3x^2 - 9/x + C]
= x^4 + 6x + 9/x^2
= (x^3 + 3)^2
2. To evaluate the integral 3x^4 dx/(2x^5 - 1)^4, we can use the substitution u = 2x^5 - 1, which gives us du/dx = 10x^4 and dx = du/(10x^4). Substituting these into the integral, we get:
integral 3x^4 dx/(2x^5 - 1)^4 = integral 3/(10u^4) du
= (-3/30u^3) + C
= (-1/10(2x^5 - 1)^3) + C
To check our result by differentiation, we can take the derivative of the above expression with respect to x:
d/dx [(-1/10(2x^5 - 1)^3) + C]
= (3x^4)/(2x^5 - 1)^4
3. To find f(x) given that integral f(x) dx = (2x - 14)^10 + C, we can use the reverse power rule of integration, which states that if integral f(x) dx = F(x) + C, then f(x) = F'(x). Applying this to our given integral, we get:
f(x) = d/dx [(2x - 14)^10 + C]
= 10(2x - 14)^9(2)
= 20(2x - 14)^9
Therefore, f(x) = 20(2x - 14)^9.
Learn more about Integral:
brainly.com/question/18125359
#SPJ11
the branch of mathematics that analyses the strategic behavior of decision makers is known as _____
The branch of mathematics that analyses the strategic behavior of decision-makers is known as game theory.
The branch of mathematics that analyzes the strategic behavior of decision-makers is known as Game Theory.
Game theory is the study of the mathematical modeling of social interactions between agents. [1] It has applications in all areas of the social sciences, including logic, systems science, and computer science. It was originally focused on a two-player zero-sum game where each player's win or loss equals the other player's win or loss. In the 21st century, game theory applies to many social relationships; is now the subject of research on decision-making in humans, animals, and computers. The modern theory begins with the idea of a combination of competition in a two-player zero-sum game and its proof by John von Neumann.
Von Neumann's original proof of continuity in a linear system using Brouwer's fixed point theorem has become a standard in game theory and business mathematics. His research was based on the 1944 book Game Theory and Economic Behavior by Oskar Morgenstern, which deals with multiplayer cooperative games. The second edition of this book presents an axiomatic theory of expected utility that enables mathematical statisticians and economists to solve decisions in uncertainty.
Learn more about mathematics:
brainly.com/question/27235369
#SPJ11
let a be a denumerable set and let b = {x, y}. prove that a × b is denumerable
1. A is a denumerable set, which means it can be put into a one-to-one correspondence with the set of natural numbers.
2. B = {x, y}, a set with two elements.
Now, let's define A × B = {(a, b) | a ∈ A, b ∈ B}. Since A is denumerable, we can list its elements as {a1, a2, a3, ...}. We can create a one-to-one correspondence between A × B and the set of natural numbers by listing its elements as follows:
(a1, x), (a1, y), (a2, x), (a2, y), (a3, x), (a3, y), ...
Thus, we have established a one-to-one correspondence between A × B and the set of natural numbers, proving that A × B is denumerable.
To prove that a × b is denumerable, we need to show that there exists a bijection between a × b and the set of natural numbers. Since a is a denumerable set, we can list its elements as a sequence: a = {a1, a2, a3, ...}.
Now let's consider the set a × b = {(a1, x), (a1, y), (a2, x), (a2, y), (a3, x), (a3, y), ...}. We can list its elements in a similar way as a sequence: (a1, x), (a1, y), (a2, x), (a2, y), (a3, x), (a3, y), ...
To define a bijection between a × b and the set of natural numbers, we can use the following mapping: (a1, x) → 1, (a1, y) → 2, (a2, x) → 3, (a2, y) → 4, (a3, x) → 5, (a3, y) → 6, ...
In other words, we assign a unique natural number to each element of a × b by listing the elements in a zigzag pattern. This mapping is clearly one-to-one and onto, since every element of a × b is assigned a unique natural number, and every natural number corresponds to a unique element of a × b.
Therefore, we have shown that a × b is denumerable.
Learn more about the Natural Number:
brainly.com/question/1687550
#SPJ11
The number of moles of CH3COO- is equal to the number of moles of OH-. (aq) which have been added. The number of moles of CH3COOH.
Based on the information provided, the number of moles of CH3COO- is equal to the number of moles of OH- that have been added. This means that the two species are present in equal amounts in the solution. However, it is unclear how this information relates to the number of moles of CH3COOH. Without additional information, it is not possible to determine the number of moles of CH3COOH present in the solution.
Based on the information provided, we can deduce that the reaction occurring is the neutralization of acetic acid (CH₃COOH) with hydroxide ions (OH⁻). In this reaction, the number of moles of CH₃COO⁻ produced is equal to the number of moles of OH⁻ added. To determine the number of moles of CH₃COOH initially present, you would need additional information such as the initial concentration of CH₃COOH and the volume of the solution.
Learn more about Numbers:
brainly.com/question/17429689
#SPJ11
12) in her stats class last semester, bubbles earned a 80 on her final exam (m=85 and s=10). in her speech class she earned a 44 (m=50 and s=4). in which class did she do better?
According to the given information, Bubbles did better in her stats class.
To determine in which class Bubbles did better, we need to compare her scores in relation to the mean and standard deviation of each class.
In her stats class, Bubbles earned a score of 80, which is 5 points below the mean of 85. However, the standard deviation of the class is 10, which means that Bubbles' score is only 0.5 standard deviations below the mean (calculated by subtracting the mean from her score and dividing by the standard deviation: (80-85)/10 = -0.5).
In her speech class, Bubbles earned a score of 44, which is 6 points below the mean of 50. The standard deviation of the class is 4, which means that Bubbles' score is 1.5 standard deviations below the mean (calculated by subtracting the mean from her score and dividing by the standard deviation: (44-50)/4 = -1.5).
Comparing these results, we can see that Bubbles did relatively better in her stats class, as her score was only 0.5 standard deviations below the mean, compared to 1.5 standard deviations below the mean in her speech class. Therefore, Bubbles did better in her stats class.
To learn more about standard deviation visit : https://brainly.com/question/475676
#SPJ11
a circle has a radius that is decreasing at a rate of 18π mm per minute. what is the rate of change of the area of the circle when the radius is 4 mm?
The rate of change of the area of the circle when the radius is 4 mm and decreasing at a rate of 18π mm per minute is -144π^2 mm^2/min.
To find the rate of change of the area of the circle, we need to use the formula for the area of a circle, which is A = πr^2, where r is the radius of the circle.
We know that the radius is decreasing at a rate of 18π mm per minute, so we can write this as dr/dt = -18π.
To find the rate of change of the area, we need to take the derivative of the area formula with respect to time:
dA/dt = d/dt (πr^2)
Using the chain rule, we can write this as:
dA/dt = 2πr(dr/dt)
Substituting the given value for dr/dt and the given radius of 4 mm, we get:
dA/dt = 2π(4)(-18π)
Simplifying, we get:
dA/dt = -144π^2 mm^2/min
The rate of change of the area of the circle when the radius is 4 mm and decreasing at a rate of 18π mm per minute is -144π^2 mm^2/min.
To learn more about derivative visit:
brainly.com/question/30365299
#SPJ11
The image shown has two triangles sharing a vertex:
65°
y
K
L
65°
M
What is the measure of ZKML, and why? (4 points)
O, because AJHK ALMK
2
Oy+ 50 degrees, because AJHKAMLK
O115 degrees-y, because AJHK ALMK
Oy, because AJHK-ALMK
Note that in the triangles given above, the correct answer: the measure of ∠KML is y because ΔJHK ~ to Δ LMK. (Option D)
What is the explanation for the above response?
It can be inferred that the measure of ∠HKJ = ∠MLK = 90°
This means that both triangles not only share the same vertex but have two similar angles.
Thus, on the bases of the above, ∠KML is y because ΔJHK ~ to Δ LMK.
If two triangles share a common vertex and have two corresponding angles that are equal in measure, then the triangles are said to be "angle-sharing" or "sharing two similar angles." This is one of the criteria for the triangles to be similar.
In other words, if two triangles have two angles that have the same measure, then the third angle must also have the same measure, and the corresponding sides of the triangles are proportional in length.
Learn more about triangles at:
https://brainly.com/question/2773823
#SPJ1
The image shown has two triangles sharing a vertex:
What is the measure of ∠KML, and why?
y over 2 , because Triangle JHK is congruent to triangle LMK
y + 50 degrees, because Triangle JHK is similar to triangle MLK
115 degrees - y, because Triangle JHK is congruent to triangle LMK
y, because Triangle JHK is similar to triangle LMK
Use your knowledge of the instantiation and generalization rules for predicate logic natural deduction to determine which of the following statements are true. Check all that apply.
True or False?When using universal instantiation (UI) to instantiate a universal statement, the instantial letter must be a new constant that does not appear on any previous proof line.
True or False?If you have the statement (y)[My ⊃ (Ry • Cy)], you can obtain the expression Mk ⊃ (Ry • Cy) by universal instantiation (UI).
True or False?If you have the statement (x)[(Mx • ~Rx) ⊃ Cx], you can obtain the statement function (My • ~Ry) ⊃ Cy by universal instantiation (UI).
True or False?You can apply universal (UI) instantiation and existential instantiation (EI) only to statements on whole lines.
True or False?You can apply the instantiation and generalization rules to parts of whole lines, just like the propositional rules of replacement.
True or False?To use existential instantiation (EI) to instantiate an existential statement, remove the existential quantifier and replace each instance of the variable bound by the quantifier with a new (previously unused) constant.
True or False?When using universal instantiation (UI) to instantiate a universal statement, you can choose any constant or variable as the instantial letter.
True or False?If you have the statement Mk • ~Rk, you can obtain the statement (z)(Mk • ~Rz) by universal generalization (UG).
True or False?To use existential generalization (EG), you must introduce an existential quantifier in front of an expression, and you must replace every instance of a constant or free variable with a variable bound by the introduced quantifier.
If you have the statement Mk • ~Rk, you can obtain the statement (∃z)(Mk • ~Rz) by existential generalization (EG).
True or False?You can apply universal (UI) instantiation and existential instantiation (EI) only to statements on whole lines.
True or False?You can apply the instantiation and generalization rules to parts of whole lines, just like the propositional rules of replacement.
True or False?????To use existential instantiation (EI) to instantiate an existential statement, remove the existential quantifier and replace each instance of the variable bound by the quaifier with a new (previously unused) constant.
True or False?When using universal instantiation (UI) to instantiate a universal statement, you can choose any constant or variable as the instantial letter.
True or False?If you have the statement Mk • ~Rk, you can obtain the statement (z)(Mk • ~Rz) by universal generalization (UG).
True or False?To use existential generalization (EG), you must introduce an existential quantifier in front of an expression, and you must replace every instance of a constant or free variable with a variable bound by the introduced quantifier.
True or False?If you have the statement Mk • ~Rk, you can obtain the statement (∃z)(Mk • ~Rz) by existential generalization (EG).
The instantiation and generalization rules for predicate logic natural deduction to determine which of the following statements are true are:
If you have the statement Nh• ~Jh, you can obtain the statement (ay)(Nh • ~Jy) by existential generalization (EG).To use existential instantiation (EI) to instantiate an existential statement, remove the existential quantifier and replace each instance of the variable bound by the quantifier with a new (previously unused) constant.You can apply universal (UI) instantiation and existential instantiation (EI) only to statements on whole lines.Existential instantiation is the principle that, given the knowledge that xP(x) is true, leads us to infer that there is an element c in the domain for which P(c) is true. Here, c cannot be chosen arbitrarily; rather, c must be such that P(c) holds. Most of the time, all we know about c is that it exists. We may assign it a name (c) because it exists and move on with our argument.
Learn more about Instantiation:
https://brainly.com/question/29989933
#SPJ4
upper half plane zero imaginary part
The upper half plane is a region in the complex plane that consists of all complex numbers whose imaginary part is positive.
In other words, it is the set of complex numbers with a zero or non-negative imaginary part. Therefore, any point in the upper half plane has a non-zero imaginary part, and there are no points with a zero imaginary part in this region.
the upper half plane in the context of complex numbers, specifically focusing on the zero imaginary part. In the complex plane, the upper half plane refers to the set of complex numbers where the imaginary part is positive (greater than zero). If a complex number has a zero imaginary part, it lies on the real axis, which is the boundary between the upper and lower half planes.
Visit here to learn more about numbers : https://brainly.com/question/10547079
#SPJ11
—-------- Correct question format is given below —--------
(Q). Which numbers are consisted upper half region of complex plane?
The textbook say the answer is x=ab/a-b-c where have I gone wrong here and what is the correct way to do it?
Answer:
The working is attached below
Step-by-step explanation:
In the working you provided, you could’ve factored out a (a+b) from every single term before isolating x. This would simplify the expression to x = ab/a-b-c.
EDIT: your working was correct until the second last line, but you could have simplified further. I have attached an example of how to do that below as well.
4. Show that (- 2/5 + 4/9) + (- 3/4) = - 2/5 + \{4/9 + (- 3/4)\}
We have proven that the expressions
[tex]\frac{-2}{5} + \frac{4}{9} + (\frac{-3}{4} )[/tex] = [tex]\frac{-2}{5} + ( \frac{4}{9} + \frac{-3}{4} ) = \frac{-127}{180}[/tex]
What is an algebraic equation?
An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants.
The different properties of an equation are:-
1. Commutative Property
2. Associative Property
3. Distributive Property
4. Identity Property
=> Through the associative property of an equation, we know,
(-a + b) + (-c) = -a + {b + (-c)}
Thus, assume a= -2/5 , b= 4/9 and c= -3/4
[tex]\frac{-2}{5} + \frac{4}{9} + (\frac{-3}{4} )[/tex] = [tex]\frac{-2}{5} + ( \frac{4}{9} + \frac{-3}{4} )[/tex]
[tex]\frac{(-2*9) + (4*5)}{45}[/tex] + [tex]( \frac{-3}{4} )[/tex] = [tex]\frac{-2}{5} + ( \frac{ ( 4 *4) + ((-3)*9)}{36}[/tex]
[tex]\frac{-18 + 20}{45} + (\frac{-3}{4} ) =( \frac{-2}{5} )+ \frac{16 + (-27)}{36}[/tex]
[tex]\frac{2}{45} + (\frac{-3}{4}) = (\frac{-2}{5} ) + (\frac{-11}{36} )\\[/tex]
[tex]\frac{(2*4) + (-3)*45}{180} = \frac{(-2*36) + (-11*5)}{180}[/tex]
[tex]\frac{8 + (-13\\5)}{180} = \frac{-72 + (-55)}{180}[/tex]
[tex]\frac{-127}{180} = \frac{-127}{180}[/tex]
Therefore, LHS=RHS= -127 / 180.
To learn more about equations and its properties, click on the link given below
https://brainly.com/question/2061992
#SPJ1
shows two different processes by which 1.0 g of nitrogen gas moves from state 1 tostate 2. The temperature of state 1 is 31 ?C.
What is the pressure p1?
What are temperatures (in ?C) T2,T3, and T4?
Temperatures T2, T3, and T4 are unknown without more information about the processes involved. In general, different processes can result in different temperatures at each state.
To answer your question, I need more information about the processes and states involved. However, I can provide some general information using the given terms. There can be different processes by which 1.0 g of nitrogen gas moves from state 1 to state 2. These processes can involve changes in pressure, temperature, or volume. To find the pressure (p1) in state 1, we need to know the volume (V1) and temperature (T1) of the gas, and apply the Ideal Gas Law equation:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the Ideal Gas Constant (8.314 J/mol⋅K), and T is the temperature in Kelvin. To convert 31 °C to Kelvin, add 273.15 to get 304.15 K. To determine T2, T3, and T4, we need information about the processes between states 1 and 2, and how the pressure, volume, and temperature change during these processes. Once that information is provided, we can apply the appropriate gas laws to find the temperatures in each state.
To answer this question, we need to know more about states 1, 2, 3, and 4. Without that information, we can only provide a general answer: There are many different processes by which 1.0 g of nitrogen gas can move from state 1 to state 2. For example, it could be compressed slowly and isothermally, or it could be compressed quickly and adiabatically. The pressure p1 at state 1 is unknown without further information. Similarly, temperatures T2, T3, and T4 are unknown without more information about the processes involved. In general, different processes can result in different temperatures at each state.
Learn more about volume here: brainly.com/question/28058531
#SPJ11
suppose that b0, b1, b2, ... is a sequence defined as follows: b0 = 1 2 , b1 = 1 3 bk= bk−1 ·bk−2 for all integers k ≥2. prove that 0 < bn< 1 for all integers n ≥0.
To prove that 0 < bn < 1 for all integers n ≥0 in the given sequence b0, b1, b2, ..., we will use mathematical induction.
Base case: For n=0, we have b0=1/2 which is between 0 and 1. So the base case is true.
Inductive step: Assume that for some integer k≥0, 0 < bk < 1 is true. We need to show that this implies that 0 < bk+1 < 1 is also true.
Using the given formula, we have:
bk+1 = bk · bk-1
Since 0 < bk < 1 and 0 < bk-1 < 1 (from the induction hypothesis), we know that their product is also between 0 and 1.
Therefore, 0 < bk+1 < 1 for all integers k ≥0 by mathematical induction.
Thus, we have proved that 0 < bn < 1 for all integers n ≥0 in the given sequence b0, b1, b2, ...
Learn more about Mathematical Induction: https://brainly.com/question/29503103
#SPJ11
Find the equation of the hyperboloid of one sheet passingthrough the points(\pm 3,0,0),(0,\pm 8,0)and(\pm 6,0,7),(0,\pm 16,7)
=1
The equation of the hyperboloid is [tex](x^2/9) - (y^2/9) - ((z-7/2)^2/16) = 1[/tex]
How to find the equation of the hyperboloid?A hyperboloid of one sheet has the general equation:
[tex]((x-h)^2/a^2) - ((y-k)^2/b^2) - ((z-l)^2/c^2) = 1[/tex]
where (h, k, l) is the center of the hyperboloid and a, b, and c are the lengths of the semi-axes.
To find the equation of the hyperboloid passing through the given points, we first need to determine its center and semi-axes.
The center of the hyperboloid is the midpoint of the line segment connecting the points[tex](\pm 3, 0, 0)[/tex] and [tex](\pm 6, 0, 7)[/tex], which is (0, 0, 7/2).The semi-axes in the x-direction and y-direction are both 3, The semi-axis in the z-direction is 4, since the points [tex](0, \pm 8, 0)[/tex] and[tex](0, \pm 16, 7)[/tex] lie on the z-axis.Therefore, the equation of the hyperboloid is:
[tex]((x-0)^2/3^2) - ((y-0)^2/3^2) - ((z-7/2)^2/4^2) = 1[/tex]
Simplifying:
[tex](x^2/9) - (y^2/9) - ((z-7/2)^2/16) = 1[/tex]
So the equation of the hyperboloid of one sheet passing through the given points is [tex](x^2/9) - (y^2/9) - ((z-7/2)^2/16) = 1.[/tex]
Learn more about equation of hyperboloid
brainly.com/question/30880319
#SPJ11
Does (1, 2) make the equation y = 4x true?
Answer:
No, (1, 2) does not make the equation true.
Step-by-step explanation:
y = 4x
(x, y) = (1, 2)
2 = 4(1)
2 = 4 (false)
Answer: No
Step-by-step explanation:
If you plug in (1,2) to the equation you get: 2=4(2)
Which simplifies to 2=8 which is not true
Therefore, (1,2) does not make y=4x true.
After counting the total number of marbles in a bag, Jessica found that the bag held 25 marbles. Each
marble can be either red, green, or blue. If she knows that 20% of the marbles are green, how many green
marbles are in the bag?
Answer:
If 20% of the marbles are green, that means there are 0.2 x 25 = 5 green marbles in the bag.
Therefore, there are 5 green marbles in the bag.
Step-by-step explanation:
Using the graph above, choose the answer with the approximate lengths of sides UV and VW.
A: UV = 7.8
VW = 6
B: UV = 5
VW = 6
C: UV = 5.7
VW = 5
D: UV = 4
VW = 5
so uv distance = 5 ,vw distance 6 so from options option B is correct answer . we can solve by using graph
what is distance ?
Distance is a numerical measurement of the amount of space between two points, objects, or locations in a physical space. It is a scalar quantity that is typically measured in units such as meters, kilometers, feet, miles, or other distance units depending on the context.
In the given question,
from the graph we can measure distance between u and v by using units as 1 unit equals 1 cm
so uv distance = 4-(-1)=5
similarly
vw distance = 3-(-3)=6
so from options option B is correct answer .
To know more about distance , visit:
https://brainly.com/question/15172156
#SPJ1
The position of a car at time t is given by the function p (t) = t2 + 4t − 17. Where will the car be when it moves at a velocity of 10? Assume t ≥ 0.
Final Answer: The position of car is at 4.
Here position of car is given by p(t) = [tex]t^2+4t-17[/tex]
Velocity is rate of change of function so we will calculate derivative of
p(t).
[tex]dp/dt = 2t+4[/tex]
We want to find the position of car when it moves at a velocity of 10.
so dp/dt = 10
2t +4 = 10
2t = 6
t = 3
Hence at t = 3 the position of car will be determined.
p(3) = 3^2 + 4*3 -17
p(3) = 4.
To learn more about Velocity visit: https://brainly.com/question/17127206
#SPJ11.
Which is an equation of the line that passes through the point (0, 4) and is perpendicular to the line whose equation
is y = -1/2x + 3
Answer:
Step-by-step explanation:
yes
Two investment portfolios are shown with the amount of money placed in each investment and the ROR
Investment
Portfolio 1 Portfolio 2 ROR
Tech Company Stock $2,300
$1,575 2.35%
Government Bond
$3,100
$2,100
1.96%
Junk Bond
$650
$795
10.45%
Common Stock
$1,800 $1,900
-2.59%
Which portfolio has a higher total weighted mean amount of money, and by how much?
O Portfolio 1 has the higher total weighted mean amount of money by $24.08
O Portfolio 2 has the higher total weighted mean amount of money by $24.08.
O Portfolio 1 has the higher total weighted mean amount of money by
$18.90
O Portfolio 2 has the higher total weighted mean amount of money by $18.90
Thus, portfolio 1 has the higher total weighted mean amount of money by $370.
What is average mean?The average is calculated by summing a group of numbers and dividing by the number of those numbers.
For example,
The average mean of the numbers a, b, and c will be:
(a+b+c)/ 3
To calculate the means of both portfolio:
The means of the first portfolio is:
(2300 + 3100 + 650 + 1800)/ 4
= 1962.5
and the mean of the second portfolio is:
(1575 + 2100 + 795 + 1900) / 4
= 1592.5
So, it is clear that the first portfolio's average mean value is greater than from second.
Their difference = 1962.5 - 1592.5
= 370
Therefore, here first portfolio is greater than the second portfolio by $370.
To know more about weighted mean, visit:
brainly.com/question/15904675
#SPJ1
hey pls help but wrong answer will be reported. offering brainiest
Answer: h>7
Step-by-step explanation:
By 3 pm they have sold 125 glasses, and they need 300 total, so they need to sell 175 glasses more. At 25 glasses an hour, divide 175 by 25 to find the number of hours, which is 7. So they will need to be open for over 7 more hours to sell more than 300 glasses.
Answer:
C. h>7
Step-by-step explanation:
The fruit and juice bar sold 125 glasses of fruit punch by 3 p.m. To reach their goal of selling more than 300 glasses of fruit punch, they need to sell an additional 300 - 125 = 175 glasses of fruit punch.
We know that they sell 25 glasses of fruit punch per hour. Let's represent the number of hours they need to stay open past 3 p.m. as h. The total number of glasses of fruit punch they sell in h hours is 25h.
We need to find the value of h that satisfies the following inequality:
25h > 175
Dividing both sides by 25 gives us:
h > 7
Therefore, the fruit and juice bar needs to stay open for more than 7 hours past 3 p.m. to sell more than 300 glasses of fruit punch. The answer is option C: h > 7.
give an example of two 2×22×2 matrices aa and bb, neither of which is the zero matrix or the identity matrix, such that ab=baab=ba.
As we can see, AB = BA, so this example satisfies the condition. Note that neither A nor B is the zero matrix or the identity matrix.
It is possible to find many examples of 2×2 matrices A and B that satisfy the condition AB = BA. Here's one example:
A = [ 1 2 ]
[ 0 -1 ]
B = [ 3 0 ]
[ 4 5 ]
To check that AB = BA, we can compute:
AB = [ 1 2 ] [ 3 0 ] [ 3 4 ]
[ 0 -1 ] [ 4 5 ] = [ 0 -5 ]
BA = [ 3 0 ] [ 1 2 ] [ 3 6 ]
[ 4 5 ] [ 0 -1 ] = [ 4 -5 ]
As we can see, AB = BA, so this example satisfies the condition. Note that neither A nor B is the zero matrix or the identity matrix.
Visit to know more about matrix :-
https://brainly.com/question/30478774
#SPJ11
the census bureau includes nine states in what it defines as the northeast region of the united states. assume that the government is interested in tracking unemployment in these nine states and that the random variable of interest is the number of northeastern states with an unemployment rate that is less than 8.3%. what values may this random variable assume? (enter your answers as a comma-separated list.)
The northeast area consists of nine states, hence this variance can have any value between 0 and 9, inclusive.
The proportion of northeastern states having an unemployment rate lower than 8.3% is the random factor of interest. The random variable will have a value of 0 if the unemployment rate was higher compare to 8.3% in each of the nine states. The binomial distribution would have a value of 1 if only one state had an unemployment rate lower than 8.3%.
The random variable will assume on a value in the range if two states have a rate of unemployment lower than 8.3%, and so on, up to a limit result of 9 that all nine states include an poverty rate lower than 8.3%.The government can monitor the northeast region's economic conditions and make accurate policy decisions by keeping tabs on poverty in these nine states.
The government can recognize regions that might require extra assistance and initiatives to make their economic situation by knowing how many states had unemployment rates under a particular level.
Learn more about variance here:
https://brainly.com/question/13708253
#SPJ4
let u = {x | x is the name of one of the months in a year} j = {x | x is in u and x begins with the letter j} y = {x | x is in u and x ends with the letter y}. find n(j ∪ y).
First, we need to find the sets J and Y separately.
J = {January, June, July}
Y = {January, February, May, July, October, December}
Now, we can find the union of J and Y:
J ∪ Y = {January, February, May, June, July, October, December}
There are 7 elements in J ∪ Y, so n(J ∪ Y) = 7.
Hi! I'd be happy to help you with your question. To find n(j ∪ y), we need to determine the number of months in the union of sets j and y.
Set u contains all months of the year. Set j contains months starting with the letter "J," which are January, June, and July. Set y contains months ending with the letter "Y," which are January, February, and May.
The union of sets j and y, denoted by j ∪ y, is the set of all unique elements found in either set j or set y, or in both. In this case, j ∪ y = {January, June, July, February, May}. Therefore, n(j ∪ y) equals 5, as there are 5 unique elements (months) in the union of sets j and y.
Learn more about arithmetic here: brainly.com/question/11559160
#SPJ11
Let b ∈ R such that 0 < b < 1. Show that (nbn) converges to 0 by using the Binomial Theorem.
To show that (n * b^n) converges to 0 when 0 < b < 1 using the Binomial Theorem, we can consider the binomial expansion of (1+b)^n, where b is a positive real number less than 1. According to the Binomial Theorem, the expansion is:
(1+b)^n = C(n,0) * 1^(n-0) * b^0 + C(n,1) * 1^(n-1) * b^1 + ... + C(n,n) * 1^0 * b^n
Where C(n,k) represents the binomial coefficient, also written as nCk or "n choose k."
Since 0 < b < 1, (1+b) > 1, and thus, (1+b)^n is a strictly increasing sequence that diverges to infinity as n approaches infinity. Among the terms of the binomial expansion, the term C(n,1) * b represents n * b^n.
However, all other terms in the expansion have b raised to a power greater than 1 (b^2, b^3, ..., b^n), and since 0 < b < 1, these terms will decrease as the power of b increases. Thus, as n approaches infinity, the contribution of the term n * b^n to the sum (1+b)^n becomes insignificant compared to the other terms.
As a result, we can conclude that (n * b^n) converges to 0 as n approaches infinity when 0 < b < 1, using the Binomial Theorem.
Learn more about Binomial Theorem:
https://brainly.com/question/30946159
#SPJ11
Can a relation R on a be both symmetric and antisymmetric?
Yes, a relation R on a set A can be both symmetric and antisymmetric.
A relation R is symmetric if for every (a, b) in R, (b, a) is also in R. A relation R is antisymmetric if for every (a, b) and (b, a) in R, a = b.
For a relation to be both symmetric and antisymmetric, it must satisfy both conditions.
This can occur if the relation only contains ordered pairs with the same elements, such as (a, a) or (b, b), because they meet both the symmetric and antisymmetric criteria.
An example of such a relation is the identity relation, which consists of pairs (a, a) for every element a in the set A.
Learn more about symmetric and transitive : https://brainly.com/question/16886414
#SPJ11
Roller Coaster Project - Investigate Piecewise Functions Congratulations! You've graduated college as a Physics & Mathematics double major, and you've scored your dream job working at Six Flags to help them design new roller coasters. In the graph below, you will see that your boss has started developing the plan for a new roller coaster - THE TIGER - but needs you to finish the job. Answer the questions below based on the given piecewise function and the graph that is attached. Given: The function f(x) will model the roller coaster's height from the ground in feet over time, measured in seconds since the ride started. 5(2), -5x2 + 40x, 35, -5(x - 12)2 + 80, f(x)= 0 < x < 4 4
The total duration of the roller coaster ride is 16 seconds.
To answer the questions based on the given piecewise function and graph for the roller coaster project, we need to analyze the different parts of the function:
- For 0 < x < 4 seconds, the roller coaster starts at ground level and goes up to a maximum height of 10 feet before returning to ground level at 4 seconds. This is represented by the equation f(x) = 5(2).
- For 4 seconds ≤ x ≤ 5.5 seconds, the roller coaster drops down rapidly from the peak height to a depth of -5 feet (below ground level) at 5.5 seconds. This is represented by the equation f(x) = -5x2 + 40x.
- For 5.5 seconds < x < 12 seconds, the roller coaster rises gradually to a height of 35 feet at 12 seconds. This is represented by the equation f(x) = 35.
- For x ≥ 12 seconds, the roller coaster drops down from 35 feet to a depth of -5 feet (below ground level) at 14 seconds before rising back up to a peak height of 80 feet at 16 seconds. This is represented by the equation f(x) = -5(x - 12)2 + 80.
Now, let's answer some questions based on this information:
1. What is the maximum height of the roller coaster and when does it occur?
The maximum height of the roller coaster is 35 feet and it occurs at 12 seconds.
2. At what time does the roller coaster reach its lowest point?
The roller coaster reaches its lowest point at 5.5 seconds.
3. What is the peak height of the roller coaster and when does it occur?
The peak height of the roller coaster is 80 feet and it occurs at 16 seconds.
4. What is the total duration of the roller coaster ride?
The total duration of the roller coaster ride is 16 seconds.
By understanding the piecewise function and analyzing the graph, we can answer questions and make calculations related to the roller coaster project. Good luck with your dream job at Six Flags!
To know more about Equation visit:brainly.com/question/31420188
#SPJ11
A class contains 5 boys and 6 girls. Calculate how many ways are there to select 4 different students for unique awards such that at least one of the recipients is a girl?
There are 325 ways to select 4 different students for unique awards such that at least one of the recipients is a girl.
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
Now, coming to the question.
First, calculate the total number of ways to select 4 students from 11 (5 boys and 6 girls) without any restrictions.
This can be done using combinations:
C(11,4) = 11! / (4! * (11-4)!) = 330 ways.
Now, calculate the number of ways to select 4 boys out of 5, which means no girls are selected:
C(5,4) = 5! / (4! * (5-4)!) = 5 ways.
Subtract the number of ways with no girls from the total number of ways to get the number of ways with at least one girl:
330 - 5 = 325 ways.
Learn more about combinations:
https://brainly.com/question/11732255
#SPJ11
8) Amanda's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 adult tickets and 8 student tickets for a total of $140. The school took in $182 on the second day by selling 5 adult tickets and 8 student tickets What is the price each of one adult ticket and one student ticket?
Answer:
Let's call the price of one adult ticket "a" and the price of one student ticket "s".
From the information given, we can set up two equations:
2a + 8s = 140 (equation 1)
5a + 8s = 182 (equation 2)
We can solve this system of equations using elimination or substitution.
Let's use elimination. We'll start by multiplying equation 1 by 5 and equation 2 by -2:
10a + 40s = 700 (equation 1, multiplied by 5)
-10a - 16s = -364 (equation 2, multiplied by -2)
Adding these two equations eliminates the "a" term:
24s = 336
Dividing both sides by 24:
s = 14
Now we can substitute this value of "s" into either equation to solve for "a". Let's use equation 1:
2a + 8(14) = 140
2a + 112 = 140
2a = 28
a = 14
So the price of one adult ticket is $14 and the price of one student ticket is
