if sinθ 1÷2 and θ is in quadrant , evaluate each expression. a) sin 2θ b) cos 2θ c) tan 2θ

The equation is n(n+1) = n + n+1 +29. The two consecutive integers are 6, 7 or -5, -4

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: the product of two consecutive integers is 29 more than their sum.

Let the first integer and second  integer be n and n+1 respectively

We can write the equation as:

n(n+1) = n + n+1 +29

n² + n = 2n + 30

n² + n - 2n - 30 = 0

n² + - n - 30 = 0

(n - 6) (n + 5) = 0

n - 6 = 0 or n + 5 = 0

n = 6 or n = -5

Thus, n+1 = 7 or n+1 = -4

Therefore, the two  integers are 6, 7 or -5, -4

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Answer: It will take Stephanie 20 minutes to run 2 miles.

Step-by-step explanation:

Since 3 miles is equal to 30 minutes, let us find the number of minutes run per mile

divide 30 by 3

10-It takes 10 minutes to run 1 mile

multiply 10 by the number of miles, which is 2

2x10=20

20 minutes

The vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively. Using the concept of function -

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predetermined domain and range. This specific sort of connection is what it is called.

Given that,

y = |4x +8| - 1

To get the vertex of y = |4x +8| - 1 as follows.

Where the absolute values are zeros are the vertex points of the absolute value function.

or, |4x +8| = 0

or, 4x +8= 0

or, 4x = -8

or, x = -2

Substitute the value into an original function,

y = |4(-2) + 8| - 1

y= 0 - 1

y = - 1

As a result, the vertex is at (-2, -1)

Remember that the domain is specified in the range of (-∞, ∞) while determining the range.

Given that |4x + 8| ≥ 0 , (absolute value is always 0 or positive)

The result of adding -1 to the inequality's two sides is

|4x + 8| - 1 ≥ - 1

But since |4x + 8| - 1 is identical to f(x) = y, we have y = f(x) - 1, which means that the range is specified for all values larger than -1.

So the range is -1 ≤ y < ∞

Thus,the vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively.

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The trigonometric equation is 5sin²x + 3sinx - 1 = 0.

What is a trigonometric equation?

A trigonometric equation is one that incorporates a variable-based trigonometric function. One illustration of a trigonometric equation is sin x + 2 = 1. This equation or one that is more complicated, such as sin2 x - 2 cos x - 2 = 0, can be used in the equations.

Here, we have

Given: (5/2)cos2x - 1/2 = 3sinx

We know that

cos2x = 1 - 2sin²x

Then our equation become

(5/2) (1 - 2sin²x) - 1/2 = 3sinx

5/2 - 5sin²x - 1/2 = 3sinx

2 - 5sin²x = 3sinx

-5sin²x + 2 - 3sinx = 0

5sin²x + 3sinx - 1 = 0

Hence, the trigonometric equation is 5sin²x + 3sinx - 1 = 0.

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Answer:

Step-by-step explanation:

if you send 12 messages a day.

and your sister sends and unkown number of texts per day but together you both send 26 number of total texts.

Then, suppose your sister sends X number of texts.

Then

X + 12 = 26

X = 26 - 12

X = 14

The measure for the exterior angle to the angle X of the triangle XYZ is 112.55°

In any triangle, an exterior angle is equal the sum of its two opposite interior angles is equals.

For the triangle XYZ, the exterior angle to the angle X is equal to the sum of the two opposite interior angles Y and Z

angle Y = 38.25° and angle Z = 74.3°

exterior angle to X = 38.25° + 74.3°

exterior angle to X = 112.55°

This implies that the angle X = 180° - 112.55° = 67.45°

and 67.45° + 38.25° + 74.3° = 180° which is true for the sum of interior angles of a triangle.

Thus, exterior angle to the angle X that is derived to be 112.55° is true for the triangle XYZ.

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Answer:

112.55

Step-by-step explanation:

i got it right

Solution:

Given:

(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])

[tex]\frac{-28yx}{-4y^{2}x^{4} }[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]

[tex]\frac{7}{x^{3} y}[/tex] + [tex]\frac{31}{4}[/tex]

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After dividing the given equation, the answer in the simplest form is [tex]\frac{7}{x^{3} y}- \frac{31}{4}[/tex]

What do you mean by simplest form?

A fraction with a denominator and numerator that are both relatively prime has the simplest form. It indicates that the fraction's numerator, which is the portion at the top of the fraction, and denominator, which is the portion at the bottom, do not share any factors other than one.

An amount that represents a fraction of a whole is called a fraction. A fraction's reduced form is another name for its simplest form. A fraction with a common factor of one, such as 34, has the simplest form. Although 2/4 can be further simplified and written as 12, it is not the most basic form. The fractions 12 and 2/4 are equivalent in this case, we can also say.

Given:

⇒(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])

⇒ [tex]\frac{-28yx}{-4x^{4}y^{2}}[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]

⇒     [tex]\frac{7} {x^{3} y}[/tex] - [tex]\frac{31}{4}[/tex]

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Answer:  1/12

Reason:

There's one side we want (rolling the "4") out of 12 sides total. Each side has a probability of 1/12 of occurring since each side is equally likely.

Answer:

A. The new maturity value of the loan would be $15,000

B. The maturity data of the loan would be June 20

Step-by-step explanation:

N/A

For an average intake of 2200 calories per day, the number of acres of land owned is 2.03

From the question, we have the following calories function that can be used in our computation:

C(x) = 270 ln(x + 1) + 1900

Also from the question, we have

Average intake of calories = 2200 inches

This means that

C(x) = 2200

So, we have the following equation

270 ln(x + 1) + 1900 = 2200

Subtract 1900 from both sides

270 ln(x + 1) = 300

Divide 270 from both sides

ln(x + 1) = 1.11

Take the exponent of both sides

x + 1 = 3.03

So, we have

x = 2.03

Hence, the number of acres is 2.03

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Answer:

3x + 12

Step-by-step explanation:

5x + 6(x - 2) - 8(x - 3) ← distribute parenthesis

= 5x + 6x - 12 - 8x + 24 ← collect like terms

==(5x + 6x - 8x) + (- 12 + 24)

= 3x + 12

For the given word problem, the cost to rent each chair is $5.25 and each table is $2.625

What is a word problem?

A word problem is a short passage presenting a "real-life" situation where an issue needs to be solved using math. The word problem for groups is a classic example, but there are numerous additional examples as well. This question is in many significant circumstances undecidable, which is a profound conclusion of computational theory.

Let C be the cost per chair

Let T be the cost per table

The total cost to rent 5 chairs and 6 tables is $53.

Then, 5C+6T=42 ................ (i)

The total cost to rent 3 chairs and 2 tables is $21.

Then, 3C+2T=21 ................. (ii)

Now, by solving both equations, multiply (ii) by 3 and subtract (i), we get

9C - 5C = 63 - 42

or, 4C = 21

or, C = $5.25

Then, T = (21-3*5.25)/2 = $2.625

Hence, the cost to rent each chair is $5.25 and each table is $2.625

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Answer:

[tex]\frac{1}{4}s^2[/tex]

Step-by-step explanation:

Use the formula for the area of a square and divide the result by 4.

Answer:

79.25

Step-by-step explanation:

What is the quotient of 3,487 divided by 44?

3,487/44 = 79.25

Answer:

y = -x or y= -2x+3 will work

the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.

A = [tex]\left[\begin{array}{ccc}9&5\\1&6\\\end{array}\right][/tex],  B =[tex]\left[\begin{array}{ccc}1&6\\3&-1\\\end{array}\right][/tex]

3A = [tex]\left[\begin{array}{ccc}27&15\\3&18\\\end{array}\right][/tex]

2B = [tex]\left[\begin{array}{ccc}2&12\\6&-2\\\end{array}\right][/tex]

3A + 2B = [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

Hence, the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

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1. Based on the profitability index per bunch, the combination of flowers to purchase each day is 10 Lilies, 10 Pansies, and 5 Orchids, costing $1,000.  On any other day, the florist can purchase 25 Roses.

2. The profitability index per bunch is as follows:

The profitability index can also be described as the profit investment ratio or value investment ratio.

The profitability index shows the ratio of the investment's payoff and the investment cost.

The profitability index is computed as the net present value added to the initial cost and divided by the initial investment.

The profitability index is the quotient of the present value of future cash flows and the initial investment cost.

                       NPV         Cost              Max.     Total     Total

                per bunch   per bunch    Bunches   NPV     Costs

Roses               $1             $21               25          $25     $525

Lilies               $10           $29                10        $100     $290

Pansies           $4            $33                10         $40      $330

Orchids         $20           $76                  5       $100      $380

Total budget per day = $1,000

Profitability index = (NPV + Cost)/Cost

Roses = 1.0476 ($1 + $21)/$21

Lilies = 1.345 ($10 + $29)/$29

Pansies = 1.121 ($4 + $33)/$33

Orchids = 1.270 ($20 + $74)/$74

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Answer:

Below

Step-by-step explanation:

from 800 to 1020 is  a  220/800 * 100% = 27.5% increase each year

P(t) = 800 ( 1 + .275)^t    

3300 = 800 ( 1+.275)^t

3300 / 800  = 1.275 ^t     LOG both sides

.615423 / LOG 1.275 = t   = 5.83 years

Option d is correct

y=β0+β1x1+β2x2+β3x3+........+βkxk+ε

Where y is the "independent" variable and 0 to k are the "regression" coefficients. In a "multiple linear regression" model, the "independent" variables are x1, x2, x3,..., xk, and the "residual" or "error" term is.

The "residual" for the regression model is calculated using the following formula.

Residual=y-ŷ

Where y is the "independent variable's" "actual" value and is the "independent variable's" "predicted" value.

The "difference" between the "actual" value of the "dependent" variables and the corresponding "predicted" value when employing the "multiple regression" model is referred to as the "residual" in the "residual" formula.

A statistical technique for evaluating the relevance of a "multiple regression" model is the "F test." Linear models are A linear model is a statistic that explains the “relationship” between “response” and “predictor” variables. Using the “multiple regression” model, the “predicted” value of the “response” variable is denoted by ŷ.

hence option 4 is correct

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I understand you mean:

What is a residual for a multiple regression model and the data that is used to create it? Select one:

1.A statistic that is used to evaluate the significance of the multiple regression model

2.A statistic that explains the relationship between response and predictor variables

3.The predicted value of the response variable using the multiple regression model

4.The difference between the actual value of the response variable and the corresponding predicted value (regression error) using the multiple regression model

Answer:

Part A:

Samuel: y=4x+18

Lewis: y=3x+30

Part B: 12 weeks

Part C: 66 rocks

Step-by-step explanation:

Part A:

X represents the number of weeks. With the current amounts, you add that to the equation.

Part B/C:

1. Have both equations equal to each other

4x+18 = 3x+30

2. Solve for x

x = 12

3. Substitute the given variable, x, into the equation y=4x+18

y=4(12)+18

4. Solve for y

y=66

x=12

y=66

The F ratio is 1.2.

What is statistic?

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

30/25 = 1.2

In an ANOVA, this statistic is used in the F test to test the hypothesis that the group means are not equal to one another. The F ratio is calculated as follows:

Fobs=MSB/MSW

30/25 = 1.2

Where MSB is the mean square between the groups and MSW is the mean square within the groups.

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Ginny charges $80 for an initial fee, and Bob charges $60 for an initial fee.  Bob charges less for an initial fee.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

f(x)=60x+80 is function that represents the charge to Ginny's customers, where x represents the number of hours of labor.

To find initial fee, put x = 0 in the given function.

Put x = 0 in f(x) = 60x + 80:

f(0) = (60×0) + 80

f(0) = 80

The initial fee is $80.

From the table,

When x = 0, cost = $ 60.

The initial fee is $60.

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the domain =  [1,∞) and range = [4 , ∞) for the given equation.

What is domain and range?

The set of all doable values that qualify as inputs to a operate is understood because the domain of the operate, or it may also be outlined because the entire set of values doable for freelance variables.

The set of all the outputs of a operate is thought because the vary of the operate or when subbing the domain, the whole set of all values attainable as outcomes of the variable.

Main body:

Given equation =

y=8x-4

as x is the number of days

and,y is the weight of the plant.

so x can not be negative

hence the domain of x = [1,∞)

As x is positive , y can not be negative as well.

Hence the domain =  [1,∞) and range = [4 , ∞)

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The quadratic function that models the path of the ball is given as follows:

y = -(x - 2)² + 9.

The graph of this quadratic function is given by the image shown at the end of the answer.

The ball is increasing, and then later it decreases, meaning that it is defined by a concave down quadratic function.

The ball has a positive height until 5 seconds, hence one of the roots of the quadratic function is of 5, that is, when x = 5, y = 0.

The vertex of the quadratic function is given as follows:

(2,9).

Hence the vertex form definition of the quadratic function is given as follows:

y = a(x - 2)² + 9.

When x = 5, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(5 - 2)² + 9

9a = -9

a = -1.

Hence the quadratic function is given as follows:

y = -(x - 2)² + 9.

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Answer: 3,-3  

Step-by-step explanation:

|6x-1| = 17

For absolute value problems there is always two solutions. They will both be the same number, one positive and one negative.

6x-1 = 17

Add 1 to both sides.

6x-1 +1 = 17+1

6x=18

Now, divide by 6.

6x/6=18/6

x = 3

The two answers that would be correct are 3,-3.

For both cases time needs to double the invested money is 7.7016 years

It is a mathematical expression define that interest can be compounded at any time even within any smallest period of time.

When annual interest rate is given in a data along with invested money, we can calculate the years required to get doubled money by using the formula A= Pe∧(rt)

A is the double money of the investment

P is the investment

r is the annual interest rate

t time in years

as per question A=2P, r=0.09

2P =Pe∧(0.09t)

2= e∧(0.09t)

㏑2=0.09t

t= 7.7016 years

hence, it takes 7.7016 years to get double money

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2,985/- need to deposit in an account.

To calculate the interest we use one type of formula which is

A=P(1+r/n)^(t n)------------------(1)

In the above formula:

A = Accrued amount.

P = Principal amount.

r = Annual nominal interest rate as a decimal.

n = number of compounding periods per unit of time.

t = time in decimal years.

I = Interest amount.

ln = natural logarithm.

Given That

A=4000 t=15 r=2% n=2

changing the r in % into decimal we get 0.02.

Now we substitute the values in the above Formula, and we get

A=P(1+r/n)^(t n)

4000=P(1+.02/2)^(15*2)

4000=P(1.01)^(30)

4000=P(1.34)

4000/1.34=P

2,985=P

Principal = $2,985

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The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

The mathematical expressions that we used to find unknown numbers are called Linear Equations. These can be formed by variables and constant terms according to given conditions. Here we use variables like x, y, z, etc to represent unknown variables.

Here we have,

Music company A charges a $ 15 membership fee and a $ 0.75 for each downloaded song

Music company B charges $ 0.90 for each downloaded song without the membership fee

Given question

a. For what number of songs will both companies charge the same amount?  

Let for x songs both companies will charge the same amount

Cost to download x songs from Company A

=> 15 + 0.75x

Cost to download x songs from Company B

=>  0.90x

As we assumed both costs are the same

=> 15 + 0.75x = 0.90x

=> 0.90x - 0.75 = 15

=> 0.15x = 15

-> x = 100

Therefore,

The number of songs that both companies will charge the same amount is 100.

b) You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money?  

Cost of 150 that charges company A =  15 + 150(0.75)  

= 15 + 150(0.75)  = 15 + 112.5 = 127.5  

Therefore,

Company A will charge $ 127.5 for 150 songs

Cost of 150 songs that charges company B = 150(0.90)

= $ 135  

Company B will charge $ 135 for 150 songs

Therefore,

Company B will charge $ 135 for 150 songs

Thus,

To pay the least amount of money we need to choose Company B.

Therefore,

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

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Dana Jones have amount after 7 years is $1560.97.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.

We have to find the amount after 7 years.

Consider, the formula

A = Pe^rt

where,

A is the amount after t years

P is the invested amount

r is the interest rate

t is the number of years

Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.

[tex]A = 1100e^0^.^0^5^(^7^)\\A= 1560.9743\\A = 1560.97[/tex]

Hence, Dana Jones have amount after 7 years is $1560.97.

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The dimensions of the poster with the smallest area are; 27.75 cm x 27.75 cm

Let "x" and "y" denote the length and the width of the poster.

We are told that the margin of a poster are 4 cm and the side margins are 4 cm.

The length of the print = x - 2(4) = x - 8

The width of the print = y - 2(4) = y - 8

The area of the print = length * width = (x - 8)(y - 8)

The area of the print is given as 390 square inches. Thus;

(x - 8)(y - 8) = 390

Making y the subject gives;

y = (390/(x - 8)) + 8

The area of the poster is; A = xy

Thus;

A = x[(390/(x - 8)) + 8]

A =  (390x/(x - 8)) + 8x

Minimizing the area gives;

A' = 8 - (3120/(x - 8)²)

Equating to zero gives;

8 - (3120/(x - 8)²) = 0

8(x - 8)² = 3120

(x - 8)² = 3120/8

(x - 8)² = 390

x = 27.75 cm

y = (390/(27.75 - 8)) + 8

y = 27.75 cm

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