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Answer: y=pi-3

Step-by-step explanation:

2pi=2y+6

2pi-6=2y

(2pi-6)/2=y

pi-3=y

y=pi-3

hope this helped

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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Answer: 16

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

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 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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The total number of genes involved in fruit diameter in tomatoes is 4.

[tex]1/4^{n}[/tex] = ratio of F2 individuals expressing either extreme Phenotype

In the above equation, 'n' represents the number of genes involved.

The term 'extreme phenotype' refers to the phenotype of one of the parents from the P1 generation. In this case, it denotes the parents with fruit diameters of 8 cm and 16 cm. In the F2 generation, which consists of a total of 256 offspring, there is only 1 offspring that resembles either P1 parent.

The ratio of individuals expressing either extreme phenotype = Number of springs with either extreme phenotype / Total number of off spring.

ratio of F2 individuals expressing either extreme Phenotype = 1/256

Apply the value of 1/256 to the first equation.

That is, [tex]1/4^{n}[/tex]  = 1/256

1[tex]1/4^{4}[/tex] = 1/256

As shown above, the value of 'n' is 4.

Therefore, the total number of genes involved in fruit diameters is 4.

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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]

The slope over the interval 1 ≤  x < 3 is m = 3 / 2 .

Given :

the slope over the interval 1 ≤  x < 3

From the graph :

take two points which lies on the interval

( 1 , 0 ) and ( 3 , 3 )

slope :

Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line .

slope m = y2 - y1 / x2 - x1

= 3 - 0 / 3 - 1

= 3 / 3 - 1

= 3 / 2

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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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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.

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 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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-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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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.)

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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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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Answer:

x^2+3x-3

Step-by-step explanation:

(x^2+2x-1)+(x^2+x-5)

2x^2+3x-6

(3x^2+6x-9)-(2x^2+3x-6)

x^2+3x-3

hopes this helps

Answer:

[tex]x^2 + 3x - 3[/tex]

Step-by-step explanation:

The perimeter of a triangle, can be calculated as, the sum of the sides.

So let's first assume the third side is a polynomial, and more specifically, a quadratic in the form: [tex]ax^2+bx+c[/tex]. This assumption is denoted from the fact that the perimeter only has terms up to the degree of 2, also known as x squared. The answer is also a quadratic, so it isn't an unreasonable assumption that if we add two quadratics (the ones given), and add one more quadratic, we should still have quadratic.

So, the sum of the three sides can be expressed as: [tex](x^2 + 2x - 1) + (x^2 + x - 5) + (ax^2 + bx + c)[/tex]

We can combine like terms to get:

[tex](x^2+x^2+ax^2)+(2x+x+bx)+(-1-5+c)[/tex]

Now from here, we can combine like terms (add coefficients):

[tex](2+a)x^2 + (3+b)x + (-6+c)[/tex]

From here, we simply set this equal to the given perimeter of: [tex]3x^2 + 6x-9[/tex], which gives us the equation:

[tex](2+a)x^2 + (3+b)x+(-6+c) = 3x^2 + 6x - 9[/tex]

Now from here, the coefficients need to correspond for both quadratics to be equal to each other, so that means that the following must be true:
[tex](2+a)=3\implies a = 1\\(3 + b) = 6\implies b = 3\\(-6 +c) = -9 \implies c = -3[/tex]

We now plug this into the quadratic standard form to get:

[tex]x^2 + 3x - 3[/tex]

Which is our third side!

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:

[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]

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:

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]

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 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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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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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:

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.

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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The vertex of the parabola is at the point (7, 0) and since the vertex of this parabola is (7, 0), the equation of the parabola in graphing form is

The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. To find the vertex of the parabola y = (x - 3)(x - 11), you can average the x-intercepts of the parabola, which are the points where the parabola crosses the x-axis. The x-intercepts of this parabola are at x = 3 and x = 11, so the average of these two points is (3 + 11) / 2 = 7.

To write the equation of the parabola in graphing form, you can use the vertex form of a parabola, which is written as

where (h, k) is the vertex of the parabola and a is a coefficient that determines the direction of the parabola (whether it opens upwards or downwards). Plugging in the values for the vertex and the y-coordinate of the vertex (which is 0), we get

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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

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.