Select one of the factors of x3y2 + 8xy2 + 5x2 + 40.
a) (xy2 + 5)
b) (x2 + 4)
c) (xy2 − 5)
d) (x2 − 8)

At 8 hours of service, the two limousine rental companies charge the same amount.

Step-by-step explanation:

Given,

Initial fee of Executive Limousine rental = $200

Per hour charges of service = $40

Let,

x be the number of hours.

E(x) = 40x+200

Initial fee of Jet Limousine rental = $120

Per hour charges of service = $50

J(x) = 50x + 120

For the charges to be same;

E(x) = J(x)

[tex]40x+200=50x+120\\200-120=50x-40x\\80=10x\\10x=80[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]

At 8 hours of service, the two limousine rental companies charge the same amount.

Keywords: function, addition

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Answer:

The answer to your question is $43.15

Step-by-step explanation:

Current bill = 25, 789 kWh

Previous bill = 25, 350 kWh

Charge = $ 0.0983/ kWh

Process

1.- Subtract the current meter from the previous one

                   25, 789 - 25, 350 = 439 kWh

2.- Find the amount of the bill using a rule of three

                 $0.0983     -----------------   1 kWh

                      x             ----------------   439 kWh

                     x = (439 x 0.0983) / 1

                     x = $ 43.15

Answer:

-48

Step-by-step explanation:

Let me know if you need anything

Answer:

-48

Step-by-step explanation:

next in a row  is always equal previous one multiple by -2

-3*(-2)=6

6*(-2)=-12

-12*(-2)=24

24*(-2)=-48

Answer:

[tex]Jade's\,score=5*right\,answers[/tex]

Step-by-step explanation:

Because all the questions have the same point, we can find the weight (value) of each question dividing the total points by the total number of answers questions:

[tex]\frac{100}{20}= 5[/tex]

Now with the weight of each question the only thing we should to do is to multiply it by the number of the questions she got right:

[tex]Jade's\,score=5*right\,answers[/tex]

Let check if our equation works, if Jade got all the answers right, we expect she got a 100 score. Let verify on the equation

[tex]Jade's\,score=5*(20)=100[/tex], that's what we expected

If she got 10 right answers, we expect 50 score and if she got 0 right answers, we expect 0 score, let check again:

[tex]Jade's\,score=5*(10)=50[/tex]

[tex]Jade's\,score=5*(0)=0[/tex]

Again, we obtain the expected scores, so we can conclude our equation works.

To find Jade's score on the math test, calculate the points per question by dividing the total points (100) by the number of questions (20). Each question is worth 5 points. Jade's score is the number of questions she got right multiplied by 5 points.

To calculate Jade's score on a math test with 20 questions that is worth a total of 100 points, we can start by finding out how many points each correct answer is worth. Since the total points are evenly distributed among the questions, we divide the total points by the number of questions.

Each question is worth 5 points (100 points total ÷ 20 questions).

Let x represent the number of questions Jade got right. The equation to calculate Jade's score is then:

Score = 5 × x

To find Jade's score, we simply multiply the number of questions she got right by 5. For example, if Jade answered 16 questions correctly, her score would be 80 points (5 points/question × 16 questions).

The term quadratic comes from the word quadrate meaning square or rectangular. Similarly, one of the definitions of the term quadratic is a square. In an algebraic sense, the definition of something quadratic involves the square and no higher power of an unknown quantity; second degree. So, for our purposes, we will be working with quadratic equations which mean that the highest degree we'll be encountering is a square. Normally, we see the standard quadratic equation written as the sum of three terms set equal to zero. Simply, the three terms include one that has an [tex]x^{2}[/tex], one has an x, and one term is "by itself" with no [tex]x^{2}[/tex] or x.

Answer:

The graph of the inverse function is the same that the graph of the original function

Step-by-step explanation:

step 1

Find the equation of the function in the graph

Let

f(x) ---> the function in the graph

we know that

Is a linear function

take the points (0,6) and (6,0)

Find the slope of the linear function

[tex]m=(0-6)/(6-0)\\m=-1[/tex]

Find the the equation of the linear function in slope intercept form

[tex]f(x)=mx+b[/tex]

we have

[tex]m=-1[/tex]

[tex]b=6[/tex] ---> the y-intercept is given

substitute

[tex]f(x)=-x+6[/tex]

step 2

Find the inverse of the function f(x)

Let

y=f(x)

[tex]y=-x+6[/tex]

Exchange the variables (x for y and y for x)

[tex]x=-y+6[/tex]

Isolate the variable y

[tex]y=-x+6[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=-x+6[/tex]

[tex]f^{-1}(x)=f(x)[/tex]

In this problem the graph of the inverse function is the same that the graph of the original function

Graphing the inverse of a function is achieved by flipping the graph over the line y = x. In science, graphs of inversely proportional variables like P and V form a hyperbola, but these can be 'linearized' for clarity and accuracy. Often, a regression analysis is utilized to find the best fitting line within a set of data plots.

To graph the inverse of a function, you observe the function as a set of points in a 2D space (on a graph) and flip each point over the line y = x. This results in a new function, which is the inverse. When it comes to more specific functions like pressure and volume relationships, this is shown when plotting the inverse of the pressure (P^-1) versus the volume (V), or the inverse of volume (V^-1) versus the pressure (P).

Scientists often linearize data when graphs have curved lines because they're difficult to read accurately at low or high values. If you plot P (pressure) versus V (volume), you will get a hyperbola. This kind of function can be 'linearized' to make it easier to understand and interpret.

Finally, in many cases, such as plotting data points of inflation rate versus unemployment rate, the resulting graph can be analysed using a statistical process called regression. This helps to find the best fitting line for the set of data plots, which can often not perfectly fit the line.

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Answer:

145

Step-by-step explanation:

To find the number of boxes to reach the goal, divide the goal amount by the box amount:

[tex]650 \div 4.50 \approx144.444444[/tex]

Since you can't sell .444444 of a box, you must sell 145 boxes.

Answer:

Susan payed $30 for her purchase

Step-by-step explanation:

Chicken: $12.36 per package (x2) = $24.72

Broccoli: $1.98 per pound (x1/2)   =   $0.99      +

Milk: $3.49 per gallon (x1)             =   $3.49

-and no added sales tax             ____________

                                                           $29.20

If Susan got $0.80 in return, then she must have payed $30 to begin with.

Answer:

The amount of money that Susan use to pay for the items = $30

Step-by-step explanation:

2×(12.36)+0.5×(1.98)+(3.49)+(0.8) = 30.

:)

Answer:

c.Mean

Step-by-step explanation:

We have been given that the Sally is interested in taking a job in a city in which she's not familiar with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home.

We know that in a normal distribution all central tendencies (mean, mode, median) are equal.

When a very large or very small valued data point is added to data set, mean is mostly affected by that outlier.

We know that mode of a data set is the point that appears at-most in the data set, so outliers doesn't affect mode.

Median of a data set is less affected by outliers.

The price of the three bedroom homes owned by millionaires will be greater than prices of houses owned by people in the neighborhood.

Therefore, mean will be most influenced by three bedroom homes owned by millionaires.

Answer:the football team played 25 games in all

Step-by-step explanation:

Let x represent the total number of matches that the football team played.

The football team won 10 matches out of the total number of matches they played. if their win percentage was 40, it means that

10/x × 100 = 40

1000 = 40x

x = 1000/40 = 25

Answer:

[tex]\frac{5}{9}\approx0.556[/tex]

Step-by-step explanation:

A pair of dice is rolled so the outcome space will be.

[tex]S= \{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

Total number of elements [tex]=36[/tex]

Possible outcomes in which sum is less than [tex]6[/tex] or greater than [tex]8[/tex]

[tex]S_{1} = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}[/tex]

Number of element in this space [tex]=20[/tex]

P(sum is less than [tex]6[/tex] or greater than [tex]8[/tex])

[tex]=\frac{Favourable\ outcomes}{total\ outcomes} \\=\frac{20}{36}\\ =\frac{5}{9}[/tex]

Answer:There are 6 matches in each group

Step-by-step explanation:

The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. Assuming the teams are A, B, C and D.. The way the teams in the group play each other would be

AB, CD first group matches.

AC, BD second group matches.

AD, BC. Third group matches

Therefore, the number of matches in each group would be 6

Answer:

It would take 25 minutes for Patrick to complete the project alone.

Step-by-step explanation:

They did the project in 20 minutes, that is, 100% of the project, so:

[tex]x + y = 1[/tex]

In which x is the percentage that Patrick worked and y is the percentage that Stewart worked.

Patrick works four times as quickly as Stewart, so x = 4y.

So

[tex]x + y = 1[/tex]

[tex]4y + y = 1[/tex]

[tex]5y = 1[/tex]

[tex]y = 0.2[/tex]

-----------

[tex]x = 4y = 4*0.2 = 0.8[/tex]

Patrick did 80% of the project in 20 minutes. We can solve this problem by a simple rule of three, in which the time it would take for him to complete the project alone is 100%. So

20 minutes - 0.8

x minutes - 1

[tex]0.8x = 20[/tex]

[tex]x = 25[/tex]

It would take 25 minutes for Patrick to complete the project alone.

Patrick, who works four times as quickly as Stewart, would take 25 minutes to complete the project alone.

This question is about rates and can be solved using algebra. Let's denote the rate at which Stewart can do the work as S and the rate at which Patrick does the work as P. Since Patrick works four times as quickly as Stewart, P=4S. The rate at which they work together is S+P. According to the question, together they can complete the job in 20 minutes, so their combined rate is 1 job per 20 minutes or 1/20. Therefore, S + P = 1/20.

Substitute P=4S into the equation, we get S + 4S = 1/20, which simplifies to 5S = 1/20. Solve this equation, we find that S = 1/100. So Stewart alone would finish the job in 100 minutes. Since Patrick is four times faster, Patrick alone would complete it in 100/4 = 25 minutes.

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Answer:

19 revolutions per minute, for model 5.

Step-by-step explanation:

Consider the model shown below:

From the table:

The blade length for model 5 is 148 feet

Also the maximum blade tip speed is 200 miles per hour.

It is given that the tip of the blade travels 0.18 mile per revolution.

To find the number of revolution per hour simply divide the maximum speed of the blade with the revolution.

Number of revolutions per hour = [tex]\frac{200}{0.18}=1111.111[/tex]

We need to find the speed, in revolutions per minute, so divide the obtained revolution per hour with 60.

[tex]\frac{1111.11}{60} =18.52\approx19[/tex]

Hence, 19 revolutions per minute, for model 5.

Final answer:

To determine the speed in revolutions per minute for model 5, we need to know how far the blade tip travels in one minute. This would be divided by 0.18 miles, the distance per revolution, to find the RPM. Without the distance traveled in one minute, we cannot complete the calculation.

Explanation:

To calculate the approximate speed in revolutions per minute for model 5, where the tip of the blade travels 0.18 miles per revolution, we need to find how many revolutions it would complete in one minute. Assuming the tip travels at a constant speed, you would divide the distance it covers in one minute by the distance per revolution.

First, determine the distance traveled by the blade tip in one minute. Since no speed is given for one minute in the question, we cannot provide a direct answer; more information would be needed, such as the distance the blade tip travels in a given time frame. However, if we had information like this, we could proceed with a calculation:

Let's say the tip travels X miles in one minute. You would then divide X by 0.18 miles to find the number of revolutions per minute:

Revolutions per minute (RPM) = Distance in miles per minute / Distance per revolution

RPM = X miles / 0.18 mile

For example, if the tip travels 1.8 miles in one minute, then:

RPM = 1.8 miles / 0.18 mile = 10 RPM

Answer:

Step-by-step explanation:

1. Correct. Corresponding vertices are (A, D), (B, E), and (C, F). The triangle names must list corresponding vertices in the same order. Thus the answer is the one you have chosen.

__

2. Look again. As in the first problem, corresponding vertices are in the same order. Line segment EF is named by the first two vertices in the triangle name, so the corresponding segment is LM, also named by the first two vertices of that triangle's name.

Segment FG is named by the last two vertices of the triangle's name, so the corresponding segment in the other triangle is also named by the last two vertices of the triangle's name: MN. Corresponding segments are proportional, so EF/LM = FG/MN.

__

3. Correct. Segment DB is congruent to itself. The halves of the bisected angle at D are congruent to each other, and the segments DA and DC are shown as congruent. Hence, SAS is an appropriate choice for showing congruence of the triangles.

__

4. The 1:1 ratio of these similar triangles tells you they are congruent, so ...

  AC = EC

  4x -3 = 2x +6 . . . . substitute the given expressions

  2x = 9 . . . . . . . . . . add 3-2x

  EC = 9+6 = 15 . . . substitute for 2x in the expression for EC

The question asks for AE, which is 2 times the length EC, so is ...

 AE = 2·EC = 2·15 = 30 . . . . feet

___

The only indication that the units are feet is that the answer choice with the number 30 has feet as its units. (We should be seeing "(4x-3) feet" as the measure of AC, for example.)

Answer:

Step-by-step explanation:

cos(c+d)=cos c  cos d-sin c sin d   ...(1)

cos(c-d)=cos  c  cos d+sin c sin d  ...(2)

add (1) and (2)

cos (c+d)+cos (c-d) =2 cos c cos d  ...(3)

put c+d=x

c-d=y

add

2c=x+y

c=(x+y)/2

subtract

2d=x-y

d=(x-y)/2

substitute in (3)

[tex]cos~ x+cos~ y=2 cos (\frac{x+y}{2}) ~cos (\frac{x-y}{2})[/tex]

To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.

To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.

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1/2, or one half. since she cuts it into 2.

Answer:

$119.32

Step-by-step explanation:

Leiff decides to buy his video game, with a price tag of $128, at this site

he will get the 15% discount when he checks out.

100-15= 85%

Discounted price=85% of 128 is [tex]0.85 \cdot 128=108.8[/tex]

Leiff pays 5.3% sales tax on the discounted price

5.3% is 0.053

sales tax amount=0.053 times 108.8=5.7664

So we add the sales tax amount and shipping fee

[tex]108.8+5.7664+4.75=119.32[/tex]

So $119.32 is the total amount

The total of Leiff’s online purchase is $119.31.

To calculate the total of Leiff's online purchase, we need to first calculate the discount on the video game.

The discount is calculated by multiplying the original price of the video game by the discount rate.

Discount = $128 * 15%

= $19.20

The discounted price of the video game is the original price minus the discount.

Discounted price = $128 - $19.20

= $108.80

The sales tax is calculated by multiplying the discounted price of the video game by the sales tax rate.

Sales tax = $108.80 * 5.3%

= $5.76

The total cost of the video game, including the discount and sales tax, is:

Total cost = $108.80 + $5.76

= $114.56

The total cost of Leiff's online purchase is the cost of the video game plus the shipping fee.

Total cost = $114.56 + $4.75

= $119.31

Therefore, the answer is $119.31.

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Answer:the number of sixth graders is 28

Step-by-step explanation:

Total number of students in the school band is 70. 40% are sixth graders. 20% are seventh graders and the rest are eighth graders. This means that the percentage of eighth graders is 100 - (40+20) = 100 - 60 = 40%

This means that the number of sixth graders would be 40% of the total number of students in the school band. It becomes

40/100 × 70 = 0.4×70 = 28

Answer:the Vega's cell phone bill for March is $155

Step-by-step explanation:

Let x represent the number of talk time in minutes that the family uses for a month.

Let y represent the number of text messages that the family sends in a month.

Let z represent the total cost of using x talk time and sending y text messages in a month.

The cell phone plan costs $75 per month including taxes and fees. Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text. This means that the total cost of x minutes and y texts would be

z = 75 + 1(x - 1000) + 2(y - 400)

z = 75 + x - 1000 + 2y - 800

z = 75 - 1000 - 800 + x + 2y

z = x + 2y - 1725

Because of a family emergency,the family uses 1,050 minutes and 415 texts in March. The total cost would be

z = 1050 + 2(415) - 1725

z = 1050 + 830 - 1725 = $155

Answer:

  C

Step-by-step explanation:

The elements of the matrix need to match the coefficients in the equations.

Answer:

c.

Step-by-step explanation:

h

Answer:

On average the carnival gain on each play

= 0.04 dollars

Step-by-step explanation:

Given that a pond contains 100 fish: 78 purple, 21 blue, and 1 silver.

Fish            Purple     Blue          Silver    total

Frequency  78               21                 1    100

Prob          0.78      0.21             0.01      1

Revenue           0.4                0.8            13  

game fee 0.65        0.65            0.65  

Net revenue -0.25      0.15            12.35    

Net Rev*Prob -0.195      0.0315   0.1235   -0.04

Thus we get per player expected net revenue is -0.04

This would be gain for Carnival

Hence On average the carnival gain on each play

= 0.04 dollars

Final answer:

To calculate the carnival's average gain per play, determine the expected payoff for each fish type, subtract the cost to play, and sum these amounts. The carnival gains an average of $0.61 per play.

Explanation:

The student's question involves calculating the average gain for a carnival on each play of a carnival fishpond game. To find this, we need to determine what the carnival earns on average based on the probabilities of catching each type of fish (purple, blue, or silver) and the payoff for each.

Let's calculate the expected profit (gain) per play for the carnival. The probability and payoff for each type of fish are:

Purple fish: Probability = 78/100, Payoff = $0.40

Blue fish: Probability = 21/100, Payoff = $0.80

Silver fish: Probability = 1/100, Payoff = $13.00

The expected payoffs for the carnival from catching each type of fish are:

Purple: 78/100 * $0.40

Blue: 21/100 * $0.80

Silver: 1/100 * $13.00

Subtract the contestant's cost ($0.65) from each expected payoff to find the expected gain. Then, sum these expected gains to find the overall average gain for the carnival.

The carnival's expected gain is:

Expected Gain per Play = (78/100 * $0.40) + (21/100 * $0.80) + (1/100 * $13.00) - $0.65

Calculating:

Expected Gain per Play = ($0.3120) + ($0.1680) + ($0.1300) - $0.65

Expected Gain per Play = $0.61

This calculation shows that on average, the carnival gains $0.61 for each play of the fishpond game.

Answer:

Lines 'a' and 'c' are parallel. Line 'b' is non parallel to 'a' and 'c'.

Step-by-step explanation:

Picture is attached with the answer as a solution to it.

In the question it is give that line 'c' only intersect with line 'b' and not with, so the only way that two lines won't intersect here 'a' and 'c' is that lines are parallel. If the lines are not parallel then those lines will definitely meet.

Answer:

C. y = -3

Step-by-step explanation:

Line L is perpendicular to the y-axis, so line L is just a straight horizontally line going from left to right.

This mean that the x-coordinate they gave us is irrelevant since our flat line is going to pass through all possible x-values. The only thing we need to focus on the the y-value.

So we know that the line passes through (__, -3)

the equation y = -3 gives us a horizontal line that passes through (__, -3).

Therefore answer is C.

Answer A and B are wrong because they gave us vertical lines, we want horizontal lines. D and E are wrong because those are diagonal lines, we want flat horizontal lines.

Answer:

The proper time sequence of the three political parties/movements, from earliest to latest is as follow:

Step-by-step explanation:

Answer:

C. Darwin realized this also applied to plant and animal populations, and this struggle for existence resulted in an opportunity for natural selection to act on differences within populations.

Step-by-step explanation:

Thomas Malthus in his Malthusian theory of population concluded that since population increases geometrically and  resources only increase arithmetically, there will reach a point in time when the resources will be not be able to sufficiently cater for the population.

The Charles Darwin theory of Evolution is based on five key observations and conclusions drawn from them. These observations and inferences are summarized as:

Based off these observations, it is seen that there will be a struggle amongst the members of the specie for the limited resources.

From the last two observations, the species that survive then pass on their traits to their offspring and the cycle repeats itself with each subsequent generation being better evolved than the previous ones.

Thus, Darwin discovered that the Malthusian theory of population also applies to plant and animal populations where scarcity of resources gives room for natural selection to take place due to the variation within populations.

Answer:

  (3/4)(√3)r²

Step-by-step explanation:

The largest such triangle is an equilateral triangle. It will have a side length of r√3. The area can be found a number of ways, one of which is to use the formula for the area of an equilateral triangle of side length s:

  A = s²·(√3)/4

Using s=r√3, we get ...

  A = (3/4)(√3)r²

Answer:

[tex]2^{2005}[/tex]

Step-by-step explanation:

We are given [tex]f^{[2005]}(x) = \frac {1}{2}[/tex].

Hence, [tex]f(f^{[2004]}(x))=\frac{1}{2}[/tex].

Assume [tex]y=f^{[2004]}(x)[/tex].

Hence, [tex]f(y)=\frac{1}{2}[/tex] or [tex]y=\frac{1}{4}[/tex] or [tex]y=\frac{3}{4}[/tex].

So we can conclude that [tex]f^{[2004]}(x)=\frac{1}{4}[/tex] or [tex]f^{[2004]}(x)=\frac{3}{4}[/tex].

So we can find [tex]f(f^{[2003]}(x))=\frac{1}{4}[/tex] orf(f^{[2003]}(x))=\frac{3}{4}.

Assume [tex]z=f^{[2003]}(x)[/tex].

Hence, [tex]f(z)=\frac{1}{8}[/tex] or f(z)=\frac{7}{8} or f(z)=\frac{5}{8} or f(z)=\frac{3}{8}.

Therefore, we double the number of possible solutions for each iteration.

Thus, the number of solutions is [tex]2^{2005}[/tex].