a man finds the angle of depression of a packed car to be 40 degree from floor 25m high in a high multi storey building.find the distance of car from the foot of the building and the man by using scale drawing
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Type of Attention Impact on Encoding Process

1. Sustained attention Facilitates thorough encoding of information.

2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.

3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.

4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.

5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.

1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.

2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.

3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.

4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.

5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.

Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.

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P=A/(1+r)T

Step-by-step explanation:

1) p(1+r)=A/T

2)P=A/(1+r)T

Answer:

P=A/(T+Tr)

Step-by-step explanation:

A = P(1+r)T

Multiply P and T

A=PT(1+r)

Clear the bracket by multiplying all bracketed terms by PT

A=PT+PTr

A=P(T+Tr)

Divide both sides by (T+Tr)

A/(T+Tr)=P(T+Tr)

P=A/(T+Tr)

The minimum amount of vinyl needed for the liner is 481 sq. feet.

An open cylinder is a type of cylinder in which one of its circular surfaces has been removed. Thus its area can be determined as:

area of an open cylinder = πr^2 + 2πrh

where r is the radius, and h is the height.

The area of the swimming pool that will be covered by vinyl liner resembles an open cylinder. So that;

area of the open swimming pool = πr^2 + 2πrh

                                                 = πr(r + 2h)

r = diameter/ 2

 = 18/ 2

r = 9 feet

area of the open swimming pool = 3.14*9(9 + 2*4)

                                                    = 28.26*17

                                                    = 480.42

The minimum amount of vinyl needed for the liner is 481 sq. feet.

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1) Total cost = 1246.67 + 7.60 production volume.

2) The variable cost per unit produced is $7.60.

3) The coefficient of determination is 0.96 or 96%.

4) The estimated total cost is $5,046.67.

Explanation :

1)

The estimated regression equation that could be used to predict the     total cost for a given production volume is:

Total cost = 1246.67 + 7.60 production volume

2)

The variable cost per unit produced is given by the slope of the line. The slope of a regression line is represented by the value of the dependent variable for one unit of the independent variable, which represents the increment in the volume of production by a unit change in the value of the total cost.

So, the variable cost per unit produced is $7.60.

3)

The coefficient of determination is 0.96 or 96%. This implies that the percentage of the variation in total cost that can be explained by production volume is 96%.

4)

For Volume = 500 units predict the total cost as follows:

Total Cost = 1246.67+ 7.60 production volume

               = 1246.67 + (7.60 × 500)

               = 1246.67 + 3800

               = 5046.67

Thus, the estimated total cost is $5,046.67.

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Disclaimer : The complete question is given below

Question : An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. In the Microsoft Excel Online file below you will find a sample of production volumes and total cost data for a manufacturing operation. Conduct a regression analysis to explore the relationship between total cost and production volume and then answer the questions that follow.Production Volume Total Cost

(Units) ($)

400 4,000

450 5,000

550 5,400

600 5,900

700 6,400

750 7,000

1. Use the data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.

2. What is the variable cost per unit produced

3. Compute the coefficient of determination what percentage of the variation in total cost can be explained by production volume

4. The company production schedule shows 500 units must be produced next month what is the estimated total cost of this operation.

The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is

(a) Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 is ±1.711.

To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.

(a) Ha: μ ≠ 0 (two-tailed test)

The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = 1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = -1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 (two-tailed test)

To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

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An inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

\(r = \sqrt{x^2+y^2}\)

​

Therefore,

\(m\frac{d^2x}{dt^2} =-|F|cos \theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and cos⁡θ = \(\frac{x}{\sqrt{x^2+y^2} }\)

Similarly using,

\(r = \sqrt{x^2+y^2}\)

we get,

 \(m\frac{d^2y}{dt^2} = -|F|sin\theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and sinθ = \(\frac{y}{\sqrt{x^2+y^2} }\)

Therefore we showed that holds

\(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\)

Hence the answer is an inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

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The solutions to the equation cos(2θ)sin^2(θ) = 0 in the interval [0, 2π) are θ = 1.0122 radians, 5.2708 radians, 3.2695 radians, 7.528 radians

We can use the double-angle identity for cosine to rewrite cos(2θ) as 2cos^2(θ) - 1. Substituting this into the equation, we get:

2cos^2(θ) - 1 · sin^2(θ) = 0

Expanding the left-hand side using the identity sin^2(θ) = 1 - cos^2(θ), we get:

2cos^2(θ) - 1 · (1 - cos^2(θ)) = 0

Simplifying and factoring, we get:

2cos^4(θ) - 2cos^2(θ) + 1 = 0

This is a quadratic equation in cos^2(θ), so we can use the quadratic formula:

cos^2(θ) = [2 ± sqrt(4 - 8)] / 4

cos^2(θ) = [1 ± i]/2

Since cos^2(θ) must be a real number between 0 and 1, we can only take the positive square root:

cos(θ) = sqrt([1 + i]/2)

To find the two solutions in the interval [0, 2π), we need to use the half-angle formula for cosine:

cos(θ/2) = ±sqrt[(1 + cos(θ))/2]

Substituting cos(θ) = sqrt([1 + i]/2), we get:

cos(θ/2) = ±sqrt[(1 + sqrt([1 + i]/2))/2]

We can simplify this expression using the fact that sqrt(i) = (1 + i)/sqrt(2):

cos(θ/2) = ±[(1 + sqrt(1 + i))/2]

Taking the positive and negative square roots gives us two solutions:

cos(θ/2) = (1 + sqrt(1 + i))/2, θ/2 = 0.5061 radians or 2.6354 radians

cos(θ/2) = -(1 + sqrt(1 + i))/2, θ/2 = 1.6347 radians or 3.764 radians

Multiplying each solution by 2 gives us the final solutions in the interval [0, 2π):

θ = 1.0122 radians, 5.2708 radians, 3.2695 radians, 7.528 radians

Therefore, the solutions to the equation cos(2θ)sin^2(θ) = 0 in the interval [0, 2π) are:

θ = 1.0122 radians, 5.2708 radians, 3.2695 radians, 7.528 radians

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Answer:

Exercise 2.

He spent $9.

Exercise 3.

2, 4, 6, 8, 10.

Answer: 2. 9

3. 7 9 11 13 15

Step-by-step explanation:

Answer:

-4x -y :)

Step-by-step explanation:

Probability of the number being part of A∩B= 2/9

The Venn diagram, a style of diagram that illustrates the logical connection between sets, was created by John Venn in the 1880s. The examples are used to illustrate fundamental set connections and introduce basic set theory in the fields of probability, logic, statistics, linguistics, and computer science.

A Venn diagram is a type of visual representation that uses circles to show the relationships between various items or constrained groups of objects. Circles that coincide and those that intersect have certain properties in common. Venn diagrams are helpful for visually illustrating the relationship and differences between two ideas.

The probability of an occurrence is a figure used to indicate the likelihood that the event will occur. It is expressed as a figure between 0 and 1, or between 0% and 100%, when expressed as a percentage. The likelihood that the occurrence will occur increases with the probability.

In this question,

A∩B= 4,9

Probability of the number being part of A∩B= 2/9

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Answer:

105

Step-by-step explanation:

Work out the difference between the highest value and the lowest value in

the list:  -55, 45, -30, 25, -90

The lowest value will be the largest negative number in the list: -90

The highest value will be the largest positive number in the list: 45

the difference between -90 and 45:

-90 - 45 = 105

The answer would be 73.86

0.29 km is equal to 290,000 mm when rounded to two significant figures.

Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).

Step 1: Multiply 0.29 km by the conversion factor:

0.29 km x 1,000,000 = 290,000,000 mm

Step 2: Round the result to two significant figures:

Since the original value, 0.29 km, has two significant figures, we round the result to match.

290,000,000 mm becomes 290,000 mm.

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The maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

To find the maximum rate of change of the function f(x,y) = 4x1x2y2 - 7y2 at the point (-2,5), we need to calculate the gradient vector and evaluate it at that point. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the calculations.

The gradient vector of a function represents the direction of the steepest increase at any given point. To find the maximum rate of change, we need to calculate the magnitude of the gradient vector at the point (-2,5).

The gradient vector of f(x,y) = 4x1x2y2 - 7y2 is given by:

∇f = (∂f/∂x1, ∂f/∂x2, ∂f/∂y)

To calculate the partial derivatives, we differentiate each term of the function with respect to the corresponding variable:

∂f/∂x1 = 4x2y2

∂f/∂x2 = 4x1y2

∂f/∂y = -14y

Substituting the values x1 = -2, x2 = 5, and y = 5 into the partial derivatives, we can evaluate the gradient vector at the point (-2,5):

∇f(-2,5) = (4(-2)(5)^2, 4(-2)(5), -14(5))

         = (-200, -40, -70)

The magnitude of the gradient vector represents the maximum rate of change of the function at the given point:

Magnitude = |∇f(-2,5)| = √((-200)^2 + (-40)^2 + (-70)^2)

                       = √(40000 + 1600 + 4900)

                       ≈ √46500

                       ≈ 215.60

Therefore, the maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

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The probabilities of each outcome are:P(X = 0) = (6 C 0) * 0.10^0 * 0.90^6 = 0.5314.

Assuming that 10% of people are left-handed, we are to find the probability of each outcome when 6 people are selected at random. The question does not specify if replacement is allowed or not, so we will assume replacement is not allowed. We can use the binomial probability formula to solve the problem.

The binomial probability formula for n independent trials is:P(X = k) = (n C k) * p^k * q^(n-k)where n is the total number of trials, k is the number of successful trials, p is the probability of success, and q is the probability of failure. Also, (n C k) = n!/[k! * (n-k)!] is the binomial coefficient, which gives the number of ways k successes can be selected from n trials.

Let X be the number of left-handed people selected. Then X follows the binomial distribution with parameters n = 6 and p = 0.10 (the probability of selecting a left-handed person). Using the binomial formula, we can find the probability of each outcome:P(X = 0) = (6 C 0) * 0.10^0 * 0.90^6 = 0.5314 (rounded to four decimal places)P(X = 1) = (6 C 1) * 0.10^1 * 0.90^5 = 0.3352P(X = 2) = (6 C 2) * 0.10^2 * 0.90^4 = 0.1130P(X = 3) = (6 C 3) * 0.10^3 * 0.90^3 = 0.0202P(X = 4) = (6 C 4) * 0.10^4 * 0.90^2 = 0.0018P(X = 5) = (6 C 5) * 0.10^5 * 0.90^1 = 0.0001P(X = 6) = (6 C 6) * 0.10^6 * 0.90^0 = 0.0000 (rounded to four decimal places).

Assuming that 10% of people are left-handed, we want to find the probability of each outcome when 6 people are chosen at random. Let X be the number of left-handed people chosen. Then X follows the binomial distribution with parameters n = 6 and p = 0.10. The probability of X = k is given by:P(X = k) = (n C k) * p^k * (1-p)^(n-k)where (n C k) = n!/[k! * (n-k)!] is the binomial coefficient.

The probabilities of each outcome are:P(X = 0) = (6 C 0) * 0.10^0 * 0.90^6 = 0.5314 (rounded to four decimal places)P(X = 1) = (6 C 1) * 0.10^1 * 0.90^5 = 0.3352P(X = 2) = (6 C 2) * 0.10^2 * 0.90^4 = 0.1130P(X = 3) = (6 C 3) * 0.10^3 * 0.90^3 = 0.0202P(X = 4) = (6 C 4) * 0.10^4 * 0.90^2 = 0.0018P(X = 5) = (6 C 5) * 0.10^5 * 0.90^1 = 0.0001P(X = 6) = (6 C 6) * 0.10^6 * 0.90^0 = 0.0000 (rounded to four decimal places) .

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Answer:

b

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

-64,24,58,76,99

Step-by-step explanation:

thats the answer

Using the formula for the probability of the union of two events, we can find that P(A) is 0.6 given that P(A ∪ B) = 0.9, P(B) = 0.8, and P(A ∩ B) = 0.7.

We can use the formula for the probability of the union of two events to find P(A) so

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Substituting the given values, we have

0.9 = P(A) + 0.8 - 0.7

Simplifying and solving for P(A), we get:

P(A) = 0.8 - 0.9 + 0.7 = 0.6

Therefore, the probability of event A is 0.6.

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The price of a gallon of milk relative to a pound of butter is 1.25.

The price of a loaf of bread relative to a gallon of milk can be calculated by finding the ratio of the price of a loaf of bread to the price of a gallon of milk.

This ratio can be calculated as follows:

Price of loaf of bread / Price of gallon of milk

= $1.50 / $3.00

= 0.5

Therefore, the price of a loaf of bread relative to a gallon of milk is 0.5.

The price of a gallon of milk relative to a pound of butter can also be calculated by finding the ratio of the price of a gallon of milk to the price of a pound of butter.

This ratio can be calculated as follows:

Price of gallon of milk / Price of pound of butter

= $3.00 / $2.40

= 1.25

Therefore, the price of a gallon of milk relative to a pound of butter is 1.25.

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The total capacity of the tank is 272.675 cubic meters.

Given that,

A storage tank consist of a hemisphere and a cylinder which share a common base.

The base of both hemisphere and cylinder will be the same circle with the same radius.

Also, we have,

Height of the tank = 16.5 m

Base diameter of the cylinder = 4.7 m

Radius of the base of the cylinder = 4.7 / 2 = 2.35 m

Radius of the hemisphere = 2.35 m

Height of the cylinder = Total height of the tank - Height or radius of the hemisphere

Total capacity of the tank = Volume of hemisphere + Volume of cylinder

                                          = 2/3 π r³ + π r² h

                                          = 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)

                                          = 8.652π + 78.143π

                                          = 272.675 cubic meters

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The width of the rectangle is 8 units.

The length of the rectangle is 11 units.

Let's assume the width of the rectangle as "w."

According to the given information, the length of the rectangle is 5 units less than 2 times the width, which can be represented as "2w - 5."

The perimeter of rectangle is given by the formula: 2(length + width). In this case, it is stated that the perimeter is 22 units more than twice the width, which can be expressed as "2w + 22."

Now we can set up an equation based on the given information:

2(2w - 5 + w) = 2w + 22

Simplifying the equation:

2(3w - 5) = 2w + 22

Expanding and collecting like terms:

6w - 10 = 2w + 22

Subtracting 2w from both sides:

6w - 2w - 10 = 2w - 2w + 22

4w - 10 = 22

Adding 10 to both sides:

4w - 10 + 10 = 22 + 10

4w = 32

Dividing both sides by 4:

w = 8

Therefore, the width of the rectangle is 8 units.

To find the length, we can substitute the value of the width back into the expression for the length:

Length = 2w - 5 = 2 * 8 - 5 = 16 - 5 = 11

Therefore, the length of the rectangle is 11 units.

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To prove that 12 | n^2 - 1 for all values where n = 6k + 1, we can use modular arithmetic.

First, let's simplify n^2 - 1:

n^2 - 1 = (6k + 1)^2 - 1
= 36k^2 + 12k
= 12(3k^2 + k)

So we need to show that 12 divides (3k^2 + k) for all values of k.

We can use modular arithmetic to prove this. Let's consider k modulo 3:

If k ≡ 0 (mod 3), then 3k^2 + k ≡ 0 (mod 3).
If k ≡ 1 (mod 3), then 3k^2 + k ≡ 4 (mod 3).
If k ≡ 2 (mod 3), then 3k^2 + k ≡ 2 (mod 3).

So in all cases, 3k^2 + k ≡ 0 (mod 3) or 3k^2 + k is divisible by 3.

Now let's consider k modulo 4:

If k ≡ 0 (mod 4), then 3k^2 + k ≡ 0 (mod 4).
If k ≡ 1 (mod 4), then 3k^2 + k ≡ 0 (mod 4).
If k ≡ 2 (mod 4), then 3k^2 + k ≡ 2 (mod 4).
If k ≡ 3 (mod 4), then 3k^2 + k ≡ 0 (mod 4).

So in all cases, 3k^2 + k is divisible by 4 if k is even, and if k is odd then 3k^2 + k is divisible by 2.

Therefore, 3k^2 + k is always divisible by 12, and so n^2 - 1 = 12(3k^2 + k) is always divisible by 12 when n = 6k + 1.

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Answer:

290 inches

Step-by-step explanation:

The algebraic expression that represents the total cost of signing the lease is as follows:

Total cost = r(2) + r(1) + D + C + r(12) * 0.07

Explanation: Given that Larry is renting an apartment that will cost r dollars per month. He must pay a D dollars application fee and C dollars for a credit application. His security deposit is two months rent and he must also pay the last month's rent upon signing the lease. His broker charges 7% of the total year’s rent as the fee for finding the apartment. Larry must pay the first month's rent and the last month's rent upon signing the lease. Therefore, the total cost of signing the lease will be:

r(2) + r(1) + D + C + r(12) * 0.07

r(2) represents the security deposit of two months rent, r(1) represents the last month's rent that he must pay upon signing the lease, and r(12) represents the yearly rent payable.

r(12) * 0.07 is the broker's fee for finding the apartment.

Conclusion: The algebraic expression that represents the total cost of signing the lease is as follows:

Total cost = r(2) + r(1) + D + C + r(12) * 0.07

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The shapes that matches the characteristics of this polygon are;

A quadrilateral is a four-sided polygon, having four edges and four corners.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

From the given diagram of the polygon we can conclude the following;

The shapes that matches the characteristics of this polygon are;

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Answer:

$ 16800

Step-by-step explanation:

Simple Interest Value = Principal × Interest Rate × Time

0.05 × 16000 × 1 = $ 800

(Money invested + Interest = Total money in the account)

16000 + 800 = 16800

Trivia's Bank account will have $16800 at the end of one year.

The equation written is m + 16 + 7 = 40 and the amount of money Melis has left is $17.

As mentioned, assuming the amount of money left be m. Sum of left money and spent money will be equal to earned amount of money. Representing this as equation -

m + 16 + 7 = 40

Performing addition on Left Hand Side of the equation

m + 23 = 40

Rewriting the equation

m = 40 - 23

Performing subtraction on Right Hand Side of the equation

m = 17

Thus, Melia is left with $17 from her earnings.

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Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

Answer:

10/7

Step-by-step explanation:

5x+2x=10

7x=10

x=10/7