find the solutions to the equation in the interval 0 ≤ theta ≤ ????/2 . enter your answers as a comma-separated list. 2cos(4theta) − 1

The standard form is  [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.

We have,

f ( x ) =  [tex]x^{2}[/tex]+ 9 x + 20        

g ( x ) = x + 5

Now we will simplify f ( x ) + g ( x ) f ( x ) + g ( x ).

On substituting the value of f ( x ) and g ( x ) in this equation, we get

( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5) ( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5)

Now we will simplify this equation,

( [tex]x^{2}[/tex]+ 10 x + 25 ) + ( [tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] + 20x + 5[tex]x^{2}[/tex] + 45x + 100 )

⇒ [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125

The standard form is  [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.

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Answer:

5 2/3

Step-by-step explanation:

because 17/3= 5 so 5 then they is 2 left so the answer is 5 2/3

Answer:

We can now solve for B(x2, y2):

-14 = -3 + x2 and 16 = 6 + y2

-11 = x2 ... and... 10 = y2

Therefore B(x2, y2) = (-11, 10)

Step-by-step explanation:

The information illustrated about the statistics 201 is a sample.

A sample is an analytical subset of a larger population in statistics. Researchers can conduct their studies more quickly and with more manageable data by using samples. If the sample size is large enough, there won't be any bias, but getting such a sample might be costly and time-consuming.

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

Since there are many students, a sample will be used.

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For the following questions, would you collect information using a sample or population

a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1500 students in the course over the past 5 years. you would like to know the average grade for the course

Answer:

631%

Step-by-step explanation:

Answer:

631%

Step-by-step explanation:

The mean of the sample (D) none of these alternatives is correct.

Therefore, the mean of the sample (D) none of these alternatives is correct.

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The correct question is given below:

The mean of the sample

a. is always smaller than the mean of the population from which the sample was taken

b. can never be zero

c. can never be negative

d. None of these alternatives is correct.

Answer:

3x-5

Step-by-step explanation:

It would take 7 years for  the initial investment of $200 to become $350

Which calculator is appropriate in this case?

The best calculator which addresses the case at hand is a financial calculator, since it is mandatory we make use of calculator to determine the number of years it takes for initial investment of $200 to grow to $350 with 8% interest compounded continuously, bearing in mind that we need to convert the interest rate to a discrete rate

Rd = (e^(Rc) - 1)

Rd=discrete annual rate=unknown

e=exponential value=2.7182818

Rc=continuous rate=8%

Rd=(2.1782818^(8%))-1

Rd=1.083287067-1

Rd=8.3287067%

I/Y=8.3287067=annual interest rate without the % sign

PMT=0(no annual additional investment)

PV=-200(initial investment)

FV=350(future value of investment)

CPT(press compute)

N=7

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The cargo plane flew approximately 1,760 km.

So, according to the information the equation formed will be:

Now, solve the equation for x:

Rounding off: 8

Therefore, the cargo plane flew approximately 1,760 km.

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Answer:

d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]

Step-by-step explanation:

4 liters of pure antifreeze is needed.

What is an linear equation in math?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let the amount of pure antifreeze required be x + 10 liters. Thus, total solution amount will be

0.30 (10) + 1.00(x) = 0.50 ( x + 10 )

     3.00 + x = 0.50x + 5.00

     0.50x = 2.00

          x = 4

Thus, 4 liters of pure antifreeze is needed.

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Answer:

21

Step-by-step explanation:

35x18 is 630/30 is 21.

Answer:

0=4    No solution

Step-by-step explanation:

you combine like terms like n, and n= 2n+8

then subtract 4 from both sides= 2n=2n+4

The total number of attendees who attended the seminar was 97. While the total cost and revenue generated are given to be $1455 each. This problem is solved using the knowledge of linear equations.

What is a linear equation?

It is the equation in which the degree of a variable is always one i.e. the greatest power of a variable is one. Linear equations consist of two major types, linear equations in one variable and linear equations in two variables. The general form of a linear equation in one variable is ax + b = 0, while for two variables is ax + by + c = 0

Calculation of the total number of attendees of seminar and total revenue generated

Let us assume x as the number of attendees and C(x) as the cost function for the company

According to the given conditions,

C(x) = 11x + 388

As the company pays $11 for every person, thus the total amount for x attendees is given by 11x, further $388 is added up to attain overall dollars.

Further, let the revenue be R(x) being equal to $15 per person i.e.

R(x) = 15x

The company will be breaking even when the cost and revenue are the same, R(x) = C(x)

15x = 11x + 388

15x - 11x = 388

4x = 388

x = 97

Thus, the total number of people attending the seminar is 97.

Now, calculate the total expense, C(x) and revenue, R(x)

C(x) = 11(97) + 388

= $1455

R(x) = 15(97)

= $1455

The cost and revenue are $1455 for each.

Hence, the total number of attendees who attended the seminar is 97. Total cost and revenue are given to be $1455 each.

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The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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Answer:

77 degrees

Step-by-step explanation:

180 - 103

The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

Given that,

M is the midpoint of AB and P is the midpoint of AM

Let's suppose AP = x

Then,

AB = AM + MB

Since M is the midpoint so AM =

MB = AM

AB = AM + AM = 2AM

Since P is the midpoint of A and M

So,

AP = PM

AM = AP + PM

So,

AM = 2AP = 2x

So,

MB = 2x

So,

AP = x and PB = 3x

PB = 3AP

Hence "The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP".

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A specific car accelerates consistently from zero to 22.4 m/s in 2.10 seconds during a test session. The car's uniform acceleration is 8.1356 meter/[tex]sec^{2}[/tex].

The rate at which an object's velocity with respect to time changes is known as acceleration in mechanics. Accelerations are vector quantities (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration.

For instance, a car accelerates in the direction of motion when it begins at rest (zero velocity in an inertial frame of reference) and moves at increasing speeds in a straight path. When a vehicle turns, its motion vector is altered and accelerates in the new direction. A linear acceleration is the acceleration of the car in the direction it is moving, and it is this acceleration that the occupants of the car feel.

Calculations:

Acceleration=([tex]\frac{change in speed}{change in time}[/tex])= (24 m/s) / (2.95 s) = 8.1356 meter/[tex]sec^{2}[/tex]

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Answer:

20

Step-by-step explanation:

Answer:

y = 3x - 6

Step-by-step explanation:

to find the answer we must first find the slope

the slope must be 3x because the two lines must be parallel

so

y = 3x + b

we must plug in x and y to find b

so

9 = 3(5) + b

9 = 15 + b

b = -6

that is your b

so

y = 3x - 6

that is your equation

Answer: I'd say C (y = 3x - 6)

Step-by-step explanation:

1. I mean, it is quite obvious as a parallel line needs to go the same way

2. But a parallel line doesn't mean the line is the same one, since the coordinate says that the other line passes through (5,9).

3. Also because looking at a graphing calc, you can see it for yourself, the equation on C is the correct answer

In two rectangles, the value of j and h are 2 and 4

The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc.

According to the question, we get the equations

The perimeter of rectangle = 2*[base + height]

Rectangle P

Perimeter = 20inches

Perimeter = 2*[j+4+h]

20= 2j+2h+8

2j+2h=12

J + h=6

J=6-h ………..  Equation 1

Rectangle Q

Perimeter = 30 inches

Perimeter = 2*[j+1+3h]

30=2j+6h+2

2j+6h=28

J+3h=14 ……….. Equation 2

Substitute equation (1) in equation (2)

(6-h) +3h=14

2h=8 = H=4

J=6-h

J=6-4 = J=2

Hence, the value of j and h is 2 and 4.

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The productivity of the painter is 0.66 up to two decimal places. It is attained by applying the knowledge of the division of two numbers and decimals to the provided problem.

What is decimal?

A decimal is a quantity that is distributed into two components, namely a whole and a fraction. A decimal number represents the numerical value lying in between the two integers. A decimal point (.) is used to segregate the fractional part from the whole part of a number.

E.g. 1.5, 0.06, 7.05, etc.

Calculation of the productivity of the painter

Productivity of the painter is obtained by dividing the number of houses painted by the number of days taken to paint them

The number of houses painted is 4

The number of days taken to paint 4 houses is 6 days

Productivity = 4 ÷ 6

                  = 0.666

Thus, the productivity of the painter is 0.66 up to two decimal places.

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The Mean number of points she scored per game is 8.

Mean is defined as the average value of the given set of data .

mean is calculated by dividing the (sum of all observations) with (total number of observations).

For Example , Smith scored 8,6,10 out of 10 in his three tests.

so the mean score of smith will be [tex]\frac{8+6+10}{3} =\frac{24}{3} =8[/tex].

In the given question

Points for each game = 8, 14, 4, 7, 6, 14, 4, and 7.

Sum of all the points = 64.

Total number of basketball games =8

[tex]Mean= \frac{Sum of all the points }{total number of games} \\ \\ Mean=\frac{64}{8} =8.[/tex]

Therefore , the mean number of points Swati scored per game is 8.

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Answer:

it is 8 the mean is 8

Step-by-step explanation:

Answer: 190,870,314

Step-by-step explanation:

It would be 190,870,314

The prime factors of 85 is 5 and 17

Prime factorisation:

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.

Factor:

the quantities that are multiplied to produce new quantities are called Factor.

Prime factors:

A prime factor is a factor that is a prime number and not a composite number.

85=5×17

Therefore,The prime factors of 85 is 5 and 17

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The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

[tex]\lim_{x \to c } F(x) = L[/tex]

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

[tex]F(x) = -x+8 ,x\leq 0[/tex]

[tex]F(x) = 4x+9 , if x > 0[/tex]

[tex]\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9[/tex]

[tex]\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8[/tex]

[tex]\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)[/tex]

So limit doesn't exist

For limit to exist

[tex]\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)[/tex]

must be satisfied

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This batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.

We are given that:

The total amount of cologne that we have = 48.5 ounce

Also,

Each bottle requires = 0.35 ounces of cologne.

We need to tell that how many bottles can this batch fill with 48.5 ounce of cologne.

We will do this by dividing the total amount of cologne with the cologne required per bottle.

So, we get that:

Number of bottles that can be filled = 48.5 ounces / 0.35 ounces.

Dividing the values, we get that:

Number of bottles that can be filled = 138.57

Number of bottles that can be filled = 138 bottles.

Therefore, this batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.

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Answer:a,8

when you do this in the graph its quite clear that in won't turn into a square so I think you should imagine it as a triangle.