The vertices of a rectangle are plotted.

A graph with both the x and y axes starting at negative 7, with tick marks every one unit up to 7. The points negative 4 comma 2, 5 comma 2, 5 comma negative 3, and negative 4 comma negative 3 are each labeled.

What is the perimeter of the rectangle?

10 units
18 units
28 units
45 units

[tex]\cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x)=1 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x) \right)~~ = ~~12(1)} \\\\\\ 6(1-x)-4(2+x)+3(3-x)=12\implies 6-6x-8-4x+9-3x=12 \\\\\\ 7-13x=12\implies 7=13x+12\implies -5=13x\implies \cfrac{-5}{13}=x[/tex]

If they are equal, then the methods are consistent; if not, they yield different solutions, possibly due to varying techniques or assumptions.

Hi! Based on the information provided, it seems you are comparing two methods for finding the altitude of a triangle.

The previous activity gave an altitude of 9,000. If the new method also results in an altitude of 9,000, then both methods give the same solution.

To determine if they are the same, compare the calculated values from each method.

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Therefore, Mira's yearly taxable income is Rs. 12,60,600.

Income is the amount of money an individual or organization receives over a specified period, typically measured on a monthly or annual basis. This can include wages, salaries, bonuses, commissions, rental income, investment income, and any other sources of money that come in during a specific time period. Income is often used to measure an individual's or organization's financial success or stability and can be an important factor in determining one's ability to afford certain goods and services.

by the question.

To calculate Mira's yearly taxable income, we first need to determine her yearly basic salary, festival expenses, and provident fund deduction.

Yearly basic salary:

Mira's monthly basic salary is Rs. 55,000. So, her yearly basic salary is:

Rs. 55,000 x 12 = Rs. 6,60,000

Festival expenses:

Mira gets festival expenses equivalent to her monthly basic salary, which is Rs. 55,000. So, her yearly festival expenses are:

Rs. 55,000 x 12 = Rs. 6,60,000

Provident fund deduction:

10% of Mira's salary excluding allowance is deducted as provident fund. So, her monthly salary excluding allowance is:

Rs. 55,000 - Rs. 3,000 = Rs. 52,000

10% of Rs. 52,000 is Rs. 5,200, which is Mira's monthly provident fund deduction. So, her yearly provident fund deduction is:

Rs. 5,200 x 12 = Rs. 62,400

Now, to calculate Mira's yearly taxable income, we need to subtract her deductions from her gross income:

Yearly taxable income = Gross income - Deductions

Gross income = Yearly basic salary + Yearly festival expenses + Allowance

Gross income = Rs. 6,60,000 + Rs. 6,60,000 + Rs. 3,000 = Rs. 13,23,000

Deductions = Yearly provident fund deduction

Deductions = Rs. 62,400

Yearly taxable income = Rs. 13,23,000 - Rs. 62,400 = Rs. 12,60,600

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The area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A field of length l and width w has a perimeter of 320 yards.

As we know, the perimeter of the rectangle = 2(l + w)

2(l + w) = 320

l + w = 320/2

l + w = 160

The area of the rectangle = lxw

Let a is the area of the rectangle.

a = lw

Plug w = 160 - l in the above equation:

a = l(160 - l)

a = 160l - l²

The above expression represents the area of the rectangle in terms of l.

Thus, the area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

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Answer:

P-8+5

Step-by-step explanation:

When people get off, you lose them (duh), which means there will be negative people on the bus, so -8. Then +5

Answer:

The first one : p - 8 + 5

Hope this helps!

Step-by-step explanation:

8 people get off = - 8

5 more people get on = + 5

We can use trigonometry to solve this problem. Let h be the height of the radio tower. Then we have:

tan(69°) = h/60

Multiplying both sides by 60, we get:

h = 60 tan(69°)

Using a calculator, we find that:

h ≈ 178.37 feet

Therefore, the height of the radio tower is approximately 178.37 feet.

A quadratic functiοn f whose zeroes are 2 and 5 is f(x) = x² - 7x + 10.

A quadratic functiοn is a secοnd-degree pοlynοmial functiοn οf the fοrm:

f(x) = ax² + bx + c

where a, b, and c are cοnstants, and a is nοt equal tο 0. The graph οf a quadratic functiοn is a parabοla, which can οpen upwards οr dοwnwards depending οn the sign οf the leading cοefficient a.

The term ax² is the quadratic term, bx is the linear term, and c is the cοnstant term. The cοefficient a determines the shape οf the parabοla, while the cοnstants b and c determine its pοsitiοn and οrientatiοn.

Quadratic functiοns can have οne, twο, οr zerο real rοοts (alsο knοwn as sοlutiοns οr zerοs), which cοrrespοnd tο the x-intercepts οf the parabοla. The number and nature οf the rοοts depend οn the value οf the discriminant, which is given by b² - 4ac.

If the zeroes are x = 2 and x  = 5 then the solutions must be:

(x - 2)(x - 5)

Multiply them and make a quadratic function

⇒ (x - 2)(x - 5)

⇒ (x²  - 5x)- (2x - 5)

⇒ x² -5x - 2x + 5

⇒ x² -5x - 2x + 5

⇒ x² - 7x + 5

Comparing this to the form of the quadratic function f(x) = ax² + bx + c, we see that a = 1, b = -7, and c = 10. Therefore, the quadratic function with zeros at 2 and 5 is:

f(x) = x²- 7x + 10

So, the correct option is f(x) = x² - 7x + 10.

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The coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here , we need to find coordinates before using dilation. Then the coordinates are,

A=(-1,2) , B=(2,1) , C=(1,-1) and D=(0,0).

The scale factor = 0.5

For dilation coordinates we need to multiply coordinates by using scale factor. Then,

A = (-1,2) => (-1×0.5, 2×0.5) => (-0.5 , 1)

B = (2,1) => (2×0.5 , 1×0.5) => (1,0.5)

C = (1 , -1) => (1×0.5 , -1×0.5) => (0.5, -0.5)

D = (0 , 0) => (0×0.5 , 0×0.5) => (0,0)

Hence the coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

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Answer:

(24.5, 6.5)

Step-by-step explanation:

We can set up two equations:

x+y=31

x-y=18

Now, when we add the two equations, we get

2x=49

When we divide we get

24.5 for x.

Now we can plug this in the first equation:

24.5+y=31

minus 24.5 on both sides to get

y=6.5

Hope this helped!

~Cain

Answer:

The sum of two numbers is 31 and their difference is 18

what are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 31. In other words, x plus y equals 31 and can be written as equation A:

x + y = 31

The difference between x and y is 17. In other words, x minus y equals 17 and can be written as equation B:

x - y = 18

Now solve equation B for x to get the revised equation B:

x - y = 18

x = 17 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 31

17 + y + y = 31

17 + 2y = 31

2y = 13

y = 6

Now we know y is 6.5 .Which means that we can substitute y for 6.5 in equation A and solve for x:

x + y = 31

x + 6.5 = 31

X = 25.5

Summary: The sum of two numbers is 31 and their difference is 18. What are the two numbers? Answer: 25.5 and 6.5 as proven here:

Sum: 25.5 + 6.5 = 31

Difference: 25.5 - 6.5 = 19

The calculated length of the arc with the central angle and the radius is 2.2π inches

Given that we have the following values

Radius, r = 18 inches

Central angle, x = 22 degrees

The formula for the arc length of a circle is given as:

Arc length = (central angle / 360) x (2πr)

where r is the radius of the circle.

Substituting the given values, we get:

Arc length = (22/360) x (2π x 18)

So, we have the following

Arc length = (44/20)π

When evaluated, we have

Arc length = 2.2π or 6.91 inches

Rounding to the nearest hundredth, the arc length of the given arc is approximately 6.91 inches.

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Factor of equation 4x²-x-3 is (x-1)(4x+3)

Factorization, also known as factoring, is the process of breaking down a mathematical object (such as a number, polynomial, or matrix) into simpler pieces called factors. In number theory, factorization involves expressing a positive integer as a product of smaller integers (factors). For example, the number 12 can be factored as 2 × 2 × 3, where 2 and 3 are prime factors and the quadratic expression x² + 7x + 10 can be factored as (x + 2)(x + 5), which can be verified by expanding the product.

4x²-x-3

Simplifying the terms;

4x²-4x+3x-3

Taking x-1 common from the equation

4x(x-1)+3(x-1)

(x-1)(4x+3)

Hence, factor of 4x²-x-3 is (x-1)(4x+3)

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The complete question is;

Factorise 4x²– x – 3​

The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:

z = (x - μ) / σ

where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).

Plugging in the values, we get:

z = (428 - 400) / 60 = 0.467

Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.

Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.

Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

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Answer:

Step-by-step explanation:

im sorry im not sure

17 a 15 c to b

As per the unitary method,, Shana gets back $2 as change.

First, we need to find out how much money Shana paid for the almonds. We know that she paid with two $10 bills, so the total amount of money she paid is:

2 x $10 = $20

Next, we need to find out how much money Shana should have paid if she didn't have any change. We know that the cost of the almonds is $18, so if Shana paid without any change, she would have paid:

$18

Now, we can find out how much change Shana gets back by subtracting the amount she paid from the amount she should have paid:

$20 - $18 = $2

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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

[tex]P(X=x)[/tex] = (e^-μ * μ^x) / x!

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

Given that, total of 515 bombs hit the combined area of 573 regions.

The mean hits per region is;

μ = 515/573 = 0.898

We want to find the probability that a randomly selected region had exactly three hits, that is P(X = 3)

[tex]P(X=x)[/tex] = (e^(-μ) * μ^x) / x!

[tex]P(X=3)[/tex] = (e^(-0.898) * (0.898)^3) / 3!

[tex]P(X=3)[/tex] = 0.04915

Therefore, 4.915% probability that randomly selected region had exactly three hits.

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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

A subfield of statistics known as probability studies random events and their odds of happening. It is used to predict the future and determine the likelihood of events by dividing the number of favorable outcomes by the total number of possible outcomes.

The following formula gives the probability that X indicates the number of successes of a random variable in a Poisson distribution:

[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

As a result, 573 regions were struck by a total of 515 bombs.

The mean hits per region is;

[tex]\mu=\frac{515}{573}[/tex]

[tex]\mu= 0.898[/tex]

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]

[tex]P(X=3)=\frac{e^{-0.898}\times\ \(0.898^3 }{3!}[/tex]

p(X=3)= 0.04915

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

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Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1.

It should be noted that to determine which option is better in terms of decreasing total litres used, we need to calculate the total amount of fuel consumed in each case and compare them.

Option 1: For every 100 km traveled, the first vehicle consumes 23.5 litres of fuel.

For the same distance, the second vehicle consumes 11.7 litres of fuel.

Thus, the second vehicle would save 23.5 - 11.7 = 11.8 litres of fuel per 100 km traveled compared to the first vehicle.

So, the percentage reduction in fuel consumption would be:

(11.8 / 23.5) x 100 = 50.21%.

Option 2: For every 100 km traveled, the first vehicle consumes 11.7 litres of fuel.

For the same distance, the second vehicle consumes 4.7 litres of fuel.

Thus, the second vehicle would save 11.7 - 4.7 = 7 litres of fuel per 100 km traveled compared to the first vehicle.

So, the percentage reduction in fuel consumption would be:

(7 / 11.7) x 100 = 59.83%.

Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1. Therefore, replacing an 11.7 L/100 km vehicle with a 4.7 L/100 km vehicle is better in terms of decreasing the total litres used.

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Caleb's yearly expense for his internet service and Netflix subscription is $695.76.

To write an equation for Caleb's yearly expenses, we need to first determine his total monthly expense and then multiply it by 12 to get the yearly expense.

Caleb's monthly expense can be calculated as the sum of the internet and Netflix costs, which is:

$14.99 + $14.99 = $29.98

To include the initial setup fee of $28, we can add it to the monthly expense to get

$29.98 + $28 = $57.98

This is Caleb's total monthly expense, and to find his yearly expense, we can multiply it by 12

$57.98 x 12 = $695.76

Therefore, the equation for Caleb's yearly expense is

Yearly expense = 12 x (monthly internet cost + monthly Netflix cost + initial setup fee)

Yearly expense = 12 x ($14.99 + $14.99 + $28)

Yearly expense = $695.76

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The given question is incomplete, the complete question is:

Caleb got internet service at home from a company called "Inter-What??". The company charged him $28 to hook it up. Then joined Netflix. He pays $14. 99 a month to keep the internet connected and he also pays the same amount for Netflix. Write an equation and find the yearly expense

Answer:

6.28

Step-by-step explanation:

to find circumference of a circle you have to do 2×π×r

(a) The area of the top of the circular table is  1632.66 square inches.

(b) The area of the top of the square table is  1296 square inches.

(c) The circular tables is the most appropriate as it allow for better communication and interaction among all members, as everyone is facing towards the center of the table.

Assuming a family size of 6 persons, the minimum diameter of a circular table to seat all members can be calculated as follows:

Minimum circumference = (number of persons × 24 inches)

Minimum diameter = Minimum circumference / π

Minimum diameter = (6 × 24) / π

Minimum diameter ≈ 45.63 inches

The minimum length of the side of a square table can be calculated as follows:

Minimum perimeter = (number of persons × 24 inches)

Minimum length of side = Minimum perimeter / 4

Minimum length of side = (6 × 24) / 4

Minimum length of side = 36 inches

The area of the top of the circular table can be calculated as follows:

Area = π × (diameter/2)²

Area = π × (45.63/2)²

Area ≈ 1632.66 square inches

The area of the top of the square table can be calculated as follows:

Area = (length of side)²

Area = 36²

Area = 1296 square inches

Based on the calculations, the circular table has a larger surface area than the square table, and hence it would be more appropriate for the family size of 6. Additionally, circular tables allow for better communication and interaction among all members, as everyone is facing towards the center of the table.

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Yes, it's possible probability for there to be girls in the group with other hair colors.

How to calculate probability?

Let's say there are n girls in the group.

The probability of a girl having red hair is 1/6, so the number of girls with red hair would be n/6.

The probability of a girl having blonde hair is 2 times more than the probability of having red hair. This means the probability of a girl having blonde hair is (2/1) times the probability of having red hair, or 2/7. So the number of girls with blonde hair would be (2/7)*n.

The probability of a girl having brown hair is three times more than the probability of having red hair. This means the probability of a girl having brown hair is (3/1) times the probability of having red hair, or 1/2. So the number of girls with brown hair would be (1/2)*n.

So far, we have accounted for:

n/6 girls with red hair

(2/7)*n girls with blonde hair

(1/2)*n girls with brown hair

If we add these up, we get:

n/6 + (2/7)*n + (1/2)*n = 7n/42 + 12n/42 + 21n/42 = 40n/42

This means that we have accounted for 40n/42 of the girls in the group. The remaining 2n/42 girls could have other hair colors, such as black or gray.

Therefore, it's possible for there to be girls in the group with other hair colors besides red, blonde, and brown.

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As per the proportion, we need to replace 3.6 liters of the mixture with pure wine to get a concoction containing wine and spirit in equal proportion.

Let's start by understanding the given information. We have a concoction of 12 liters that contains wine and spirit in the ratio of 2:3. This means that out of every 5 liters of the concoction, 2 liters are wine and 3 liters are spirit.

We are asked to find 'x', the quantity of the mixture that needs to be replaced, such that the resultant mixture has wine and spirit in equal proportion. In other words, we need to find 'x' such that:

(2x + 2)/(12 + 'x') = 3(12 - 'x')/5(12 + 'x')

Let's simplify this equation using cross-multiplication:

5(2x + 2)(12 - 'x') = 3(12 + 'x')(12 - 'x')

Simplifying further:

10x² - 36x + 36 = 0

Dividing both sides by 2:

5x² - 18x + 18 = 0

We can solve this quadratic equation using the quadratic formula:

x = [18 ± √(18² - 4(5)(18))]/(2(5))

Simplifying:

x = [18 ± 6]/10

x = 1.8 or 3.6

Since we cannot replace a fraction of a liter, the only possible value of 'x' is 3.6 liters.

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Answer: 260:455

260 / 455 = .57

4 / 7 = .57

455 - 260 = 195

i think the answer is the second choice -3x +9

Answer:37.8541 or 37.9

Step-by-step explanation: round up from five

Answer:

About 37.8541, or 37.9

The probability of observing that the difference between the average height of the 6 waves in California and the average height of the 6 waves in Florida (California minus Florida) is greater than 0.5 feet is 0.55.

A beach in California has an almost normal distribution of wave heights, averaging 7.2 feet. The wave height distribution on a Florida beach is about normal, average 6.6 feet. Six waves are randomly selected from each beach and the heights are recorded.

Probability distributions generate the possible outcomes of any random event. It also defines the set of possible outcomes for any random experiment based on the underlying sample space. These parameters can be a set of real numbers or a set of vectors or a set of any entity. This is part of probability statistics.

A randomized experiment is defined as the result of an experiment whose outcome cannot be predicted.

Suppose if we toss a coin, we cannot predict whether the outcome will be heads or tails. The possible outcomes of a random experiment are called outcomes. The resulting set is called a sample point. With these experiments or events, we can always create tables of probability models based on variables and probabilities.

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Answer:

84%

Step-by-step explanation:

This is a pretty normal grading weight system. Think of a perfect score being 100. The grade earned may be a percent but think of it as 100/100.

So we can set up an equation to represent the missing grade earned in the "Final Exam" row.

0.4(x) + 0.3(80) + 0.2(90) + 0.1(100) = 85

The x represents the percent grade earned for the final exam, in order to achieve an 85% total.

Evalulate and solve the above equation for x to find its value.

0.4x + 24 + 18 + 10 = 85

0.4x = 33

x = 33/0.4

x = 82.5

The question asks for the minimum grade to achieve 85% total. This means that whatever choice we choice must be the least choice that is also greater than 82.5%. That answer is B, 84%.

The coordinates of B, considering the proportions in the context of the problem, are given as follows:

(4.33, 8).

The coordinates of B are obtained applying the proportions in the context of the problem.

BC is 50% longer than AB, hence point B is at one-third of the way from A to C, and thus the equation is given as follows:

B - A = 1/3(C - A).

The x-coordinate of B is then given as follows:

x - 1 = 1/3(11 - 1)

x - 1 = 3.33

x = 4.33.

The y-coordinate of B is then given as follows:

y - 3 = 1/3(18 - 3)

x - 3 = 5

y = 8.

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