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In a​ film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. He wittily​ replies, "Ah, but in 22 years time I shall only be twice her​ age." How old are the uncle and the​ woman?

Answer:

20,800

Step-by-step explanation:

10.00 per hour so 10x8=80

then 80x5=400

400x52=20,800

Answer:

Parallel

Step-by-step explanation:

So if they have the same slope but different y-intercepts, it would be parallel because the slope stays the same so the line doesnt change, just the starting point

For example use the following equations

y = x + 2  

y = x + 3  

In the graph, these equations are parallel

Answer:

20/27

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

30 is the answer to your question

The treatments used in this experiment were variations in price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end of aisle display, and twice the normal display space), with each combination being used three times.

In this experiment, the treatments are the different combinations of product price level and display level. There are three price levels (regular, reduced price, and at cost to supermarket) and three display levels (normal display space, normal display space plus end of aisle display, and twice the normal display space).

The treatments are the nine possible combinations resulting from these price and display levels. Each combination was tested three times during the experiment to assess its effect on the weekly sales of the particular supermarket product.

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(a) The general solution of the differential equation is y(t) = c1et + c2te t + c3cos(t) + c4sin(t). (b) The test function Y(t) is (A + Bt)e t (Ccost + Dsint) + Ecos(√3 t) + Fsin(√3 t) + G.

(a) Solution:Given differential equation isy(4) + y" - 6y' + 4y = 0

The characteristic equation of this differential equation is r4+7²-6r+ 4 = (r² - 2r + 1)(r² + 2r + 4)

Therefore the roots of the characteristic equation are r = 1, 1, -2i, 2i

Then the general solution is of the formy(t) = c1et + c2te t + c3cost + c4sint

where c1, c2, c3 and c4 are constants.

So, the general solution of the given differential equation is y(t) = c1et + c2te t + c3cos(t) + c4sin(t).

(b) Solution:The differential equation is y(4) + y" - 6y + 4y = 7e + te* cos(√3 t) - et sin(√3 t) + 5.

The characteristic equation of this differential equation isr4+7²-6r+ 4 = (r² - 2r + 1)(r² + 2r + 4)

The roots of the characteristic equation are r = 1, 1, -2i, 2i

Now, Y(t) can be of the following form:Y(t) = (A + Bt)e t (Ccost + Dsint) + Ecos(√3 t) + Fsin(√3 t) + Gwhere A, B, C, D, E, F and G are constants.

Therefore, Y(t) with the fewest terms to be used to obtain a particular solution of the given equation is(A + Bt)e t (Ccost + Dsint) + Ecos(√3 t) + Fsin(√3 t) + G.

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False. Counterexample: Let's consider a linear transformation T: R² → R² defined by T(x, y) = (x, 0). The subspaces V and W in R² are both the entire space R².

Now, let's take two linearly independent vectors v₁ = (1, 0) and v₂ = (0, 1) in V. However, their images under T are T(v₁) = (1, 0) and T(v₂) = (0, 0), which are not linearly independent in W. Therefore, the statement is false.

True. Justification: If there exists a nonzero vector x ∈ Rⁿ such that Ax = x, then x is an eigenvector of A corresponding to the eigenvalue 1. This is because if Ax = x, we can write it as Ax - x = 0, which can be rearranged as (A - I)x = 0, where I is the identity matrix. Since x is nonzero, the matrix (A - I) has a nontrivial null space, indicating that 1 is an eigenvalue of A. Therefore, the statement is true.

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False. Counterexample: Let's consider a linear transformation T: R² → R² defined by T(x, y) = (x, 0). The subspaces V and W in R² are both the entire space R².

Now, let's take two linearly independent vectors v₁ = (1, 0) and v₂ = (0, 1) in V. However, their images under T are T(v₁) = (1, 0) and T(v₂) = (0, 0), which are not linearly independent in W. Therefore, the statement is false.

True. Justification: If there exists a nonzero vector x ∈ Rⁿ such that Ax = x, then x is an eigenvector of A corresponding to the eigenvalue 1. This is because if Ax = x, we can write it as Ax - x = 0, which can be rearranged as (A - I)x = 0, where I is the identity matrix. Since x is nonzero, the matrix (A - I) has a nontrivial null space, indicating that 1 is an eigenvalue of A. Therefore, the statement is true.

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Answer:

Answer:

the left over piece is \(11 \frac{4}{5}\) inches

Step-by-step explanation:

The computation is shown below:

The total length of the strips is

\(= 11 \frac{3}{5} + 15 \frac{1}{5} + 9 \frac{2}{3} \\\\= \frac{58}{5} + \frac{76}{5} + \frac{47}{5}\\\\= \frac{58 + 76 + 47}{5}\\\\= \frac{181}{5}\\\\= 36 \frac{1}{5}\)

The left over piece would be

\(= 48 - 36 \frac{1}{5}\\\\= 48 - \frac{181}{5}\\\\= \frac{240 - 181}{5}\\\\= \frac{59}{5}\\\\= 11 \frac{4}{5}\)

Hence, the left over piece is \(11 \frac{4}{5}\) inches

It should be noted that the quotient of the division is 9r^2 + 2r - 5 and the remainder is -5

In this case, to solve this polynomial division, we can use either long division or synthetic division. Here, we'll use long division:

   9r^2 + 2r - 5

        ___________________________

r - 7  | 9r^3 - 73r^2 + 64r + 37

        - 9r^3 + 63r^2

        --------------------

                 - 10r^2 + 64r

                 + 10r^2 - 70r

                 ----------------

                          -6r + 37

                          -6r + 42

                          --------

                                -5

Therefore, the quotient is 9r² + 2r - 5 and the remainder is -5. Therefore: (9r³-73r² +64r +37)÷(r-7) = 9r^2 + 2r - 5 + (-5)/(r-7).

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Answer:

Solution is 34

Step-by-step explanation:

to find f(8) you plug in 8 for x in the equation

f(x)=4(8)+2=34

hope this helps.

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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The option is B. Emerson is painting the outside of a cube for a math project. he knows the area of each face is 145 square inches.

the place is the quantity that expresses the quantity of vicinity on the plane or on a curved floor. The area of a plane vicinity or aircraft location refers to the area of a shape or planar lamina, while surface location refers to the region of an open floor or the boundary of a three-dimensional object. the place can be understood as the quantity of material with a given thickness that might be necessary to fashion a model of the shape, or the amount of paint essential to cowl the surface with a single coat. it's by far the 2-dimensional analog of the period of a curve (a one-dimensional concept) or the volume of a stable (a three-dimensional idea).

The region of a form can be measured by using comparing the form to squares of a set size. within the global system of devices (SI), the standard unit of the region is the rectangular meter (written as m²), which is the place of a rectangular whose aspects are one meter long. A shape with an area of 3 square meters might have an equal area to 3 such squares. In mathematics, the unit square is defined to have area one, and the place of some other form or floor is a dimensionless real number.

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Answer:

see photo

Step-by-step explanation:

see photo, have a nice day!!

Answer:

x=133 y=-25

Step-by-step explanation:

I'll do both ways for you. So let's start with Substitution:

With the sub method, you have to set both equations equal to each other by setting them equal to the same variable. Since there is no coefficient in front of both x's in both equations, that variable will be easiest to solve for.

x + 2y = 83    &    x + 5y = 8

Solve for x.

x = 83 - 2y     &    x = 8 - 5y

Once you have solved for x, set each equation equal to one another and solve for y now.

83 - 2y = 8 - 5y

Isolate all variables to one side:

83 = 8 - 3y

Now subtract the 8 to fully isolate the y variable:

75 = -3y

Divide by -3:

-25 = y   Now that you have your first variable, plug it into one of the original equations and solve for x.

x + 2(-25) = 83

x - 50 = 83

x = 133

Now for the Elimination method. For this method you need to get rid of a variable by either subtracting/adding each equation together. Again, since you can subtract and x from both equations, you will be left with only the y variable to solve:

Put each equation on top of one another and subtract:

  x + 2y = 83

- (x + 5y = 8)

The x's will cancel out:

(x - x) + (2y - 5y) = (83 - 8)

Simplify:

-3y = 75

Solve for y

y = -25

Then, plug y = -25 into one of the original equations:

x + 5(-25) = 8

Solve for x:

x - 125 = 8

x = 133

Hope this helps!

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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Mapping the locations of robberies over the last year is best done with a choropleth map. A choropleth map is a type of map that uses different colors to represent different levels of a given variable across a geographic area. This would be the most appropriate mapping classification for visualizing the data distribution of robbery locations.

Graduated Symbol Classification

Mapping classification that is most appropriate in mapping robbery locations over the last year to get a sense of the data distribution is Graduated Symbol Classification.What is mapping?Mapping is the creation of maps, which are graphical representations of the Earth's surface or other physical entities. Mapping has many benefits in today's society, including in the areas of spatial analysis, cartography, and geographic information systems. Different types of maps can be created based on the goals of the cartographer, such as topographic maps, road maps, and weather maps.Graduated Symbol Classification:Graduated Symbol Classification is a technique in which different symbol sizes are utilized to represent different feature values of a specific thematic map variable. In this type of classification, the variable is divided into a few groups or classes, with each class having a specific range of values. The same symbol is used to indicate each class, but its size varies depending on the value of the variable.A graduated symbol map, in which a variety of symbols are used to represent different feature values, is one of the most efficient ways to display quantitative data. Graduated symbols are most commonly utilized for the following thematic maps: population density, magnitude of an earthquake, or frequency of an event.

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Answer:

0.08030

4000

Please Mark it as brainlist answer.

The probability density of a random variable is given in the form of a triangular shape with co-ordinates (0, 0), (0.5, 2), (1, 0). The probability that X is at least 0.5 is equal to the area under the curve of X when x  0.5. Option (c) 1/2 is the correct answer.

Given, probability density of a random variable x is given in the following figure.The probability that x is at least 0.5 can be calculated as follows:

From the given graph, it is observed that the probability density of a random variable is given in the form of a triangular shape with the following co-ordinates (0, 0), (0.5, 2), (1, 0).The probability density function of a continuous random variable X is represented by the area under the curve.The probability that X is at least 0.5 is equal to the area under the curve of X when x ≥ 0.5.

The total area under the curve is given as follows:

Area of triangle OAB = 1/2 × OA × OB

= 1/2 × 0.5 × 2

= 0.5

The probability that X is at least 0.5 can be calculated as follows:

Area under the curve for X when x ≥ 0.5= Area of triangle OCD

= 1/2 × CD × OD

= 1/2 × (1 – 0.5) × (2 – 0)

= 0.5

The probability that X is at least 0.5 is 0.5 or 1/2. Therefore, option (c) 1/2 is the correct answer.

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A line that intersects two or more lines at a distinct point is known as a transversal line.

A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important. Consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles are only a few examples of the several pairings of angles that can be formed when a transversal intersects two lines. Euclid’s parallel postulate states that if two lines are parallel, then comparable interior angles are equal, alternate interior angles are equal, and successive interior angles are supplementary.

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Answer:

a) QT = 8

b) QN = 24  

c) QP = 23

d) MP = 46

e) RT = 6

f) TP = 12

Step-by-step explanation:

Find the diagram attached

If T is the centroid of<MNP, then the following are true;

TN = 2QT

Given TN = 16

16 = 2QT

QT = 16/2

QT = 8

QN = QT + TN

QN = 8 + 16

QN = 24

MQ + QP = MP and MQ = QP

If MQ = 23

QP = 23

Recall that MP =  MQ + QP

MP = MQ + MQ

MP = 2MQ

MP = 2(23)

MP = 46

Similarly, TP = 2RT

RT = TP/2

Also RP = RT + TP

RP = RT + 2 RT

RP = 3RT

18 = 3RT

RT = 18/3

RT = 6

Recall that TP = 2RT

TP = 2(6)

TP = 12

Answer:

927.84

Step-by-step explanation:

The total cost of the antique clock that Janice bought is $927.82 approximately.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

For this case, we have:

Total cost = (discounted price of clock)'s price + sales tax of discounted price.

Let d = discounted price of the clock

Then, we have:

\(d = $967 - \text{5\% discount on 967} \\\\d = 967 - \dfrac{967}{100} \times 5 = \$918.65\)

1% sales tax on 'd' will be: \(\dfrac{d}{100} \times 1 = \$9.1865 \approx \$9.19\)

Thus, we get:

Total cost of the clock ≈ 918.65 + 9.19 = 927.82 (in dollars)

Thus, the total cost of the antique clock that Janice bought is $927.82 approximately.

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Answer: 2450 min or 40hr and 50 min

Step-by-step explanation:

We can use a proportion to set up this equation.

\(\frac{30 pages}{60 min} =\frac{1225 pages}{x min}\)

We cross muliply so get our equation.

\(30x=1225(60)\\\)

\(30x=73500\)

\(x=2450 min\)

It took Mike 2450 min to read 1225 pages. We can also use a proportion to write this in hours

\(\frac{60min}{1hr} =\frac{2450min}{x }\)

\(60x=2450\)

\(x=40 hr 50 min\)

Answer:

the second one

Step-by-step explanation:

If every individual in a population has an equal chance of being selected for a sample, the sample is said to be a "random sample" or a "simple random sample."

A random sample is a sampling technique used in statistics to gather data from a population. It is considered one of the most unbiased and reliable methods for selecting a sample. In a random sample, each individual in the population has an equal probability of being selected, regardless of their characteristics or attributes.

This equal chance of selection eliminates any systematic bias and ensures that the sample is representative of the population.

The process of obtaining a random sample involves assigning a unique identifier to each individual in the population and using a randomization method to select the desired number of individuals.

Random sampling can be conducted through various techniques, such as simple random sampling, where individuals are selected directly from the population using a random number generator or a randomization table.

The goal of a random sample is to reduce the potential for selection bias and increase the generalizability of the findings to the larger population. By giving every individual an equal opportunity to be included in the sample, researchers can make more accurate inferences and draw conclusions about the population as a whole.

This type of sampling method ensures that each member of the population has an equal opportunity to be included in the sample, making it a representative subset of the population.

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The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step