Determine the number and type of solutions for the equation
5x^2−x−3=0

-Two different irrational-number solutions
-Two imaginary-number solutions
-One repeated rational-number solution
-One repeated irrational-number solution
-Two different rational-number solutions

Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

As given in the question,

Let 'x' represents the number of people

And 'y' represents the total cost

Linear relationship between number of people and total cost is:

y = mx + b

Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)

Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)

              = (58 - 52)/ (9 -6)

              = 6 / 3

              = 2

y = 2x + b

Now for, (x. y) = ( 12,64)

64 = 2(12) +b

⇒b = 64 - 24

⇒b = 40

Hence, required function is :

y = 2x + 40

a. Independent variable is the number of people.

Here it is x which represents the number of people.

True.

b. Initial value for the picnic is $40

y- intercept when x =0 ⇒ y = $40

True.

c. Rate of change is $8.67 per person.

No, rate of change is $2 per person.

d. Number of people increases as total cost of picnic increases

True .

e. If x = 4

⇒y = 2(4) + 40

     = 48 ≠46

False.

Therefore, function y = 2x + 40 represents that following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

The above question is incomplete, the complete question :

The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. a. The independent variable is the number of people.

b. The initial value (initial fee) for the picnic is $40.

c.  The rate of change is $8.67 per person.

d. As the number of people increases, the total cost of the picnic increases.

e.  If 4 people attended the picnic, the total cost would be $46.

Number of people               Total cost ($)

6                                                 52

9                                                 58

12                                               64

15                                               70

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The correct boolean expression to test for int x being a value between, including, 500 and 650, or int y not equal to 1000 is:

((x >= 500 && x <= 650)|| (y != 1000))

This expression uses the "&&" operator to test for x being greater than or equal to 500 and less than or equal to 650, and the "||" operator to test for y not being equal to 1000. The expression is using the correct comparison operators and logical operators to test for the desired conditions.

A boolean expression is a statement that evaluates to either true or false. It is commonly used in programming to control the flow of a program, as the result of a boolean expression can be used to determine whether a certain block of code should be executed or not.

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Answer:

Step-by-step explanation:

g(x) = 2*[tex]\sqrt{x}[/tex] + 4

Domain is the input  so what limits are there to the input?

for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m  a+bi,  but for now, just say  the input is  0 to ∞,  for now   The domain is  0 to ∞

Range is the output

so that is from 4 to ∞

Answer:

  a. translation 2 right and up 4

  b. g(x) = √(x -2) +4

  c. domain: x ≥ 2; range: y ≥ 4

Step-by-step explanation:

You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...

  translation right 2 units and up 4 units

Translation of function f(x) by h units right and k units up gives you ...

  g(x) = f(x -h) +k

Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...

  g(x) = √(x -2) +4

The domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.

  domain of g(x): x ≥ 2

The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.

  range of g(x): y ≥ 4

The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.

We should know that balance sheet is a summary of assets and liabilities and income and expenses of a  legal person.

We are told that the the balance sheet shows a bi-weekly net pay

This implies that a month has two bi-weeks.  therefore every income and expenses is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                      35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment              6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                        4%                                  $174.02

Miscellaneous              5%                                 $217.53

                                                                           $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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All of the values fall within 1.45 standard deviation of the mean.

From the information given, the mean price of the nonfiction books on a best-sellers list is $24.18 and the standard deviation is $3.98.

It should be noted that from the problem, the variable that is the farthest from the mean is $29.25.

Therefore, the z score will be illustrated as:

Z = (29.95 - Mean) / Standard deviation

Z = (29.95 - 24.18)) / 3.98

= 1.45

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The rows and columns of the positive integers greater than three are as shown. And the number 5018 is found in the third column.

When performing a permutation test, you repeatedly rearrange one of the variables without affecting the other variable (s). From the given table, we can start with column 4. Here, each row has about 6 numbers. That is singular row has numbers from columns 1 to 6 and an even row from columns 7 to 2.

Then subtract 5018 by 3. We get 5018-3=5015.

Divide this by 6,

5015/6 = 836.

So 5018 is located in an even row from 7 to 2.

Therefore, 5018 is located in the 836th row and 3rd column.

So the required answer is E) 3.

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The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.

We shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:

squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)

a² is common and can be cancel out

square root of (36a⁸/255a²) = square root of (36a⁶/255)

square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}

square root of (36a⁸/255a²) = 6a³/15

square root of (36a⁸/255a²) = 2a³ × 3/5 × 3

we divide through by the common factor 3

square root of (36a⁸/255a²) = 2a³/5

Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.

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The total number of fish in the lake would be = 60 fishes

The total of a data set is the addition of the various components that makes up a data set which gives a particular value.

On the first day the number of fish that was marked by the fisher man = 50 fishes.

On the second day the total amount of fishes that was caught = 80 fishes

The number of fishes that where among the 80 fishes that are marked= 20

Therefore the total amount of fishes in the lake = 80 - 20

= 60 fishes.

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Answer:

Step-by-step explanation:

40

We will see that the linear function h(x) is:

h(x) = -21x - 15

The slope is -21, and the y-intercept is -15.

Remember that a general linear function is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we start with the linear function:

f(x) = -7x + 9

First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:

g(x) =f(x + 2)

Replacing the actual function we will get:

g(x) = -7*(x + 2) + 9

Now we multiply the output of function g by 3 to get h(x), then:

h(x) = 3*g(x)

We will get:

h(x) = 3*[-7*(x + 2) + 9]

h(x) = -21*(x + 2) + 27

h(x) = -21x - 42 + 27

h(x) = -21x - 15

So we can see that the slope of function h(x) is -21, while the y-intercept is -15.

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The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.

The given triangle is a right-angle triangle.

It has two lengths. They are

length of the hypotenuse = 21

length of the adjacent or base = 13

Then, the third side i.e., the opposite side length is calculated by

(hyp)² = (opp)² + (adj)²

⇒ (21)² = (opp)² + (13)²

⇒ 441 = (opp)² + 169

⇒ (opp)² = 441 - 169 = 272

⇒ opposite side length = √272 = 16.49 ≅ 16.5

Therefore, the length of the third side is 16.5.

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The reason that is used to prove ΔFGH ≅ ΔJHK is SAS property

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.

According to the question,

Given : (1) ∠FGH and ∠JHK are right angles

(2) H is midpoint of GK

(3) GH ≅ JK

In ΔFGH and ΔJHK

Therefore ,  ΔFGH  ≅ ΔJHK using  SAS property

Hence , The reason use to prove ΔFGH ≅ ΔJHK is SAS

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Answer: 16

Step-by-step: 6 - (5(-2)=-10 then the - turns into + and your answer is 6 + 10

Answer:

The approximate period of the wave representing the airplane's path is 0.9 hours.

Step-by-step explanation:

The period of a wave is the time it takes for one complete cycle of the wave to occur. In the case of the airplane's path, this would be the time it takes for the airplane to complete one full oscillation, or "up and down" motion.

To find the period of the wave, we need to determine the value of x that corresponds to one complete cycle of the wave. In this case, the wave is defined by the function h(x) = 10000cos(0.0001x) + 20000.

To find the period, we can use the formula T = 2π/ω, where T is the period, π is the mathematical constant pi, and ω is the angular frequency of the wave. The angular frequency is related to the frequency of the wave, which is the number of cycles per second.

In this case, the angular frequency is given by the coefficient of the x term in the function, which is 0.0001. Plugging this value into the formula above, we get T = 2π/0.0001 = 200000π seconds.

Since one cycle of the wave corresponds to one complete oscillation of the airplane, the period of the wave is approximately 200000π seconds. This is a very large number, so it is usually more useful to express the period in minutes or hours. To convert to minutes, we can divide the period by 60, which gives us a value of about 3334 minutes. To convert to hours, we can divide the period by 3600, which gives us a value of about 0.9 hours.

In summary, the approximate period of the wave representing the airplane's path is 0.9 hours.

Ask me any questions you may have!

The amount of time it takes for a wave to complete one full cycle is known as the wave's period. This would be the amount of time needed for the plane to perform one full oscillation, or “up and down” motion, in the case of the flight path.

Finding the value of x that represents the wave's full cycle is necessary to calculate the wave's period. The equation h(x) = 10000cos(0.0001x) + 20000 in this instance defines the wave.

The formula T = 2/, where T is the period, is the mathematical constant pi, and is the wave's angular frequency, can be used to determine the period. The wave's frequency, or the number of cycles per second, and the angular frequency are connected.

We may convert the period to hours by dividing it by 3600, which gives us a number of approximately 0.9 hours.

Therefore, The wave that represents the course of the airplane has an approximate period of 0.9 hours.

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Answer:

10.5 oz

Step-by-step explanation:

The large pop and container are similar to the small pop and container.

Thus, we can use proportions to find how much the small container can hold, letting x represent the volume of the small container:

[tex]\frac{14}{8}=\frac{x}{6}\\ 8x=84\\ x=21/2=10.5[/tex]

Answer:

[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

The slope/gradient of a line is defined by this formula:

[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]

Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.

Two coordinates that this line passes through are (3, -2) and (-3, 2).

You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.

For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).

The gradient/slope is defined by [tex]m[/tex] in the following:

[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]

The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its centroid located at (5 , 3).

Centroid of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.

Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.

First, try to graph and visualize the triangle formed by the three vertices. (see photo)

From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.

One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.

To get the circumcenter, find the midpoint of the line BC.

midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]

M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]

M(xm ,ym) = (5 , 3)

Hence, the centroid is located at (5 , 3).

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Answer:

  B.  Incorrectly applied the distributive property

Step-by-step explanation:

You want to find Maria's error in her solution of -2(3x -5) = 40.

The solution can proceed as follows:

  -2(3x -5) = 40 . . . . . . . . given

  -6x +10 = 40 . . . . . . . . . use the distributive property

  -6x = 30 . . . . . . . . . . subtract 10

  x = -5 . . . . . . . . . . divide by -6

Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)

For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.

It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal  could be reffered to as  hundredths place however the remaining digits continue to fill in the place values until there are no digits left.

It should be noted that Decimal place value  can be described as the place values of all the digits in a given decimal number.

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The domain and the range of a function are the possible input and output values of the function.

The function is given as:

C = 130S + 3500

The domain

This is the possible S values of the function.

S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)

The value of S can be any value greater than 0

Hence, the domain of the function is [0, ∞)

The range

This is the possible C values of the function.

The function is given as:

C = 130S + 3500

When S = 0

C = 130(0) + 3500

C = 3500

The above means that:

C cannot be less than 3500

The value of C can be any value greater than 3500

Hence, the range of the function is [3500, ∞)

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SMPC should pay 136,992.36$ if it wants an 11 percent return. and the balance of the original loan after additional years 142,229.05$.

A monthly rate is a fee for services calculated over a thirty-day period.

Given, Your mortgage will be purchased by the Secondary Mortgage Purchasing Company (SMPC) from the nearby savings and loan. Your mortgage had an initial amount of $153,000 and was obtained five years ago with regular payments at a 10% interest rate. The loan was to be completely repaid over a 30-year period.

Payment Formula  =   PMT (monthly rate, month, -mortgage)

Present value formula   =  PV( monthly rate, month left, - payment, - repayment)

Loan value formula  = PV (monthly rate, month left, -payment)

a. formula   = PMT( 10%/12, 30*12, -153000)

Payment  =  $1342.68

Formula    =  PV(11%/ 12, (30-5)* 12, -1342.68)

Smpc pays  =  $136,992.36

b. Loan balance    =    139134.70$

Formlua   = PV(11%12,5*12, - 1342.68, -139134.7)

Smpc pays  = 142,229.05$

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-15 is an integer , rational and a real number

Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.

A negative number is not a natural number.

This means that -15 is a real number because real number comprises of rational and irrational number and rational numbers include negative numbers and they are called negative integers.

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The number of welcome packets that you will be able to fully complete in the time allotted would be = 14

The time allotted for the refilling of the whole welcome packets = 3 hours

To convert to mins = 3 × 60 = 180 mins.

To run each packet will take the following time:

5 minutes to print,

2 minutes to organize, and

5 minutes to proofread which is a total of 12mins

But for every 5 packets = 5×12+3 = 63 mins.

Therefore X packets = 180 mins.

Make X packets the subject of formula;

X packets = 5 × 180/63

= 900/63

= 14.2

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Answer:

94 percent.

Step-by-step explanation:

Since the tool set used to be worth 499, but is now worth 424.15, we divide the two prices.

             Calculation.

424.15/499 = 0.944654788.

We are figuring out the percent, so we need to round.

0.94465478 is about 0.94

0.94 IS EQUALVENT to 94%, so that is our answer.

Answer:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

Step-by-step explanation:

To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).

To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:

5 * 5x + 7 * 7y = 5 * 48

7 * x + 7 * y = 7 * 48

25x + 49y = 240

49x + 49y = 336

24x = 336 - 240

24x = 96

x = 4

Substituting this value for x in the first equation, we can solve for y:

5 * 4 + 7 * y = 48

20 + 7 * y = 48

7 * y = 28

y = 4

Therefore, there are 4 males and 4 females on the roller coaster ride.

P(D|FS)=.9529

If F and S are conditionally independent given D and ~D, then

P(FSD)= P(D)P(F|D)P(S|D)

P(FS~D) = P(~D)P(F|~D)P(S|~D)

P(F|~D) = 1 - P(~F|~D)

P(S|~D) = 1 - P(~S|~D)

P(~D) = 1 - P(D)

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D))

P(F|D) = P(S|D) = .9

P(~F|~D) = P(~S|~D) = .9

P(D = .2)

Then, P(FSD) = P(D)P(F|D)P(S|D) = .2*.9*.9 = .162

P(FS~D) = P(~D)P(F|~D)P(S|~D) = (1 - .2)(1 - .9)(1 - .9)= .008

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D)) = .162/(.162+.008) = 162/170=81/85 = .9529

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Answer:

The slope is same for both points.

Step-by-step explanation:

1st set of points: (1, 4) and (7, 2)

m = 2-4/7-1

m = -2/6

m = -1/3

2nd set of points: (7, 2) and (10, 1)

m = 1-2/10-7

m = -1/3

The slope is same for both points.

Answer:

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

Step-by-step explanation:

The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.

This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.

In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.

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Answer:228

Step-by-step explanation:

All you have to do is add 108 to 120.

0+8=8, 2+0=2, 1+1=2

   120

   108

+_____

   228