There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/10th


There are 42 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.

The first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:

So let's start by finding the first order maclaurin polynomial:

f(x)=f(0)+f'(0)x

so let's find each part of the function:

f(0)=arctan(0)

f(0)=0

now, let's find the first derivative of f(x)

f(x)=arctan(x)

This is a usual derivative so there is a rule we can use here:

[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]

so now we can find f'(0)

[tex]f'(0)=\frac{1}{(0)^{2}+1}[/tex]

f'(0)=1

So we can now complete the first order Maclaurin Polynomial:

f(x)=0+1x

which simplifies to:

f(x)=x

Now let's find the second order polynomial, for which we will need to get the second derivative of the function:

[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}[/tex]

so:

[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]

we can rewrite this derivative as:

[tex]f'(x)=(x^{2}+1)^{-1}[/tex]

and use the chain rule to get:

[tex]f''(x)=-1(x^{2}+1)^{-2}(2x)[/tex]

which simplifies to:

[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]

now, we can find f''(0):

[tex]f''(0)=-\frac{2(0)}{((0)^{2}+1)^{2}}[/tex]

which yields:

f''(0)=0

so now we can complete the second order Maclaurin polynomial:

[tex]f(x)=0+1x+\frac{0}{2!}x^{2}[/tex]

which simplifies to:

f(x)=x

Now let's find the third order polynomial, for which we will need to get the third derivative of the function:

[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}[/tex]

so:

[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]

In this case we can use the quotient rule to solve this:

Quotient rule: Whenever you have a function in the form , then it's derivative is:

[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]

in this case:

p=2x

p'=2

[tex]q=(x^{2}+1)^{2}[/tex]

[tex]q'=2(x^{2}+1)(2x)[/tex]

[tex]q'=4x(x^{2}+1)[/tex]

So when using the quotient rule we get:

[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]

[tex]f'''(x)=\frac{(2)(x^{2}+1)^{2}-(2x)(4x)(x^{2}+1)}{((x^{2}+1)^{2})^{2}}[/tex]

which simplifies to:

[tex]f'''(x)=\frac{-2x^{2}-2+8x^{2}}{(x^{2}+1)^{3}}[/tex]

[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]

now, we can find f'''(0):

[tex]f'''(0)=\frac{6(0)^{2}-2}{((0)^{2}+1)^{3}}[/tex]

which yields:

f'''(0)=-2

so now we can complete the third order Maclaurin polynomial:

[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}[/tex]

which simplifies to:

[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]

Now let's find the fourth order polynomial, for which we will need to get the fourth derivative of the function:

[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}+\frac{f^{(4)}(0)}{4!}x^{4}[/tex]

so:

[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]

In this case we can use the quotient rule to solve this:

[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]

in this case:

[tex]p=6x^{2}-2[/tex]

p'=12x

[tex]q=(x^{2}+1)^{3}[/tex]

[tex]q'=3(x^{2}+1)^{2}(2x)[/tex]

[tex]q'=6x(x^{2}+1)^{2}[/tex]

So when using the quotient rule we get:

[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]

[tex]f^{4}(x)=\frac{(12x)(x^{2}+1)^{3}-(6x^{2}-2)(6x)(x^{2}+1)^{2}}{((x^{2}+1)^{3})^{2}}[/tex]

which simplifies to:

[tex]f^{4}(x)=\frac{12x^{3}+12x-6x^{3}+12x}{(x^{2}+1)^{4}}[/tex]

[tex]f^{4}(x)=\frac{6x^{3}+24x}{(x^{2}+1)^{4}}[/tex]

now, we can find f^{4}(0):

[tex]f^{4}(x)=\frac{6(0)^{3}+24(0)}{((0)^{2}+1)^{4}}[/tex]

which yields:

[tex]f^{4}(0)=0[/tex]

so now we can complete the fourth order Maclaurin polynomial:

[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}+\frac{0}{4!}x^{4}[/tex]

which simplifies to:

[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]

you can find the graph of the four polynomials in the attached picture.

So the first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:

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Answer:     The answer is -2

Step-by-step explanation:

that is where the line starts

hope this helped

Answer:

x > -2

Step-by-step explanation:

The domain is the values that the input can take

x goes from -2( not including -2) to infinity

x > -2

Answer:

I'm not 100% on the interoperation of this question...

are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????

for this answer i will assume that you have 4 coins two nickels and 2 quarters

and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"

in that case I think the answer is 8

Step-by-step explanation:

1- N1 Q1 N2 Q2

2- N1 Q2 N2 Q1

3- N2 Q1 N1 Q2

4- N2 Q2 N1 Q1

5- Q1 N2 Q2 N1

6- Q2 N2 Q1 N1

7- Q1 N1 Q2 N2

8- Q2 N1 Q1 N2

[tex]2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)[/tex]

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

πr²h=πr²h

π(4.5)²*10=π(x/2)²4.9

Answer:

-7/8

Step-by-step explanation:

-5/8+x=-3/2

x= -3/2+5/8=-12/8+5/8= -7/8

Here are the complex numbers with their simplified differences

(7 -3i) - (6 - 4i) = 1 + i

(4 + 3i) - (6 +2i) = -2 - i

(4 + 5i) - (3 - 4i) = 1 + 9i

(5 + 4i) - (9 + i) = -4 + 3i

A complex number is when a real number and an imaginary number are added together

Complex numbers are usually in the form : a + bi

where a and b are real numbers and i is an imaginary number

An example of a complex number:

in this complex number : (7 -3i)

7 and 3 are real numbers while i is the imaginary number

How to simplify complex numbers

In order to simplify these set of complex numbers, remember that when there is a bracket in mathematics it signifies multiplication.

Here are the set of rules that guide multiplication :

1. When a negative value is multiplied by a positive value, the value becomes a negative value

For example, -1 x 1 = -1

2. When a positive value is multiplied by a positive value, the value remains a positive value

For example, 1 x 1 = 1

3. When a negative value is multiplied by a negative value, the value becomes a negative value

For example,-1 x -1 = 1

Solution to the questions:

Using the above information, the complex numbers can now be simplified

1. (7 -3i) - (6 - 4i)

this above equation becomes :

7 - 3i - 6 + 4i

add like terms together

7 - 6 - 3i + 4i  = 1 + i

2. (4 + 3i) - (6 +2i)

this above equation becomes :

4 + 3i - 6 - 2i

add like terms together

4 - 6 +3i - 2i = -2 - i

3. (4 + 5i) - (3 - 4i)

this above equation becomes :

4 + 5i - 3 + 4i

add like terms together

4 - 3 + 5i + 4i  = 1 + 9i

4. (5 + 4i) - (9 + i)

this above equation becomes :

5 + 4i -9 -i

add like terms together

5 -9 + 4i - i  = -4 + 3i

In order to solve for complex numbers remember that a bracket in mathematics means that a multiplication operation should be carried out. Also, pay cognisance to the rules guiding the multiplication of negative and positive numbers

Here is a similar question and answer on how to solve for complex numbers : https://brainly.com/question/1459664?referrer=searchResults

Answer:

y = 2

Step-by-step explanation:

I do not know how to explain how I got the answer

Answer:

y = 2

Step-by-step explanation:

- 14 + 6y = - 6y + 10

-14 - 10 = -6y - 6y collect the like terms

- 24/ -12 = - 12y/ - 12

2 = y

I hope this answers your question

Answer:

it is too long send me link of it

Answer: Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select? Erik, assume that Nita chooses 7. b. What number did the other player pick? 17

2. Should you use an equation or an inequality to represent the ways your player can

win? Why? (2 points: 1 point for an answer, 1 point for an explanation)

An algebraic statement that represents all the ways Eric will wins is

where

be the number that Eric thi

3. Imagine that Erik chose a 4 and Nita chose a 12. Would the winner be different if

Nita chose the 4 and Erik chose the 12? (2 points: 1 point for an answer, 1 point for

an explanation)

no because both nita and eric won. eric with a number less than than 10

and nita with a number more than 10.

4. Is it appropriate to use an absolute value inequality to represent how a player wins

this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)

they win it remains positive the negative will be losses which will be changed due to

absolute value

5. If your player is Erik, write an inequality that shows all of the ways that Erik will win

if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways

that Nita will win if Erik chooses 17.

Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for

the correct inequality)

Step-by-step explanation:

Answer:

here's the answer to your question

Answer:

for B : he spend 30 minutes jogging and 45 minutes riding his bike

Step-by-step explanation:

75-15=60

60/2=30

jogging (x) =30

30+15=45

riding bike (y) =45

hopefully it help you

Answer:

D

Step-by-step explanation:

We can go through each form of sampling and see where this scenario fits.

- Simple random sampling is simply taking a random percentage of the population. In this case, with the population being students in Carol's school, this would entail taking a random sample from her school. As her friends are not randomly selected, this does not fit

- Systematic random sampling means that every nth item is selected. For example, if Carol took every 10th person at her school, this would fit. However, as her friends are not selected by Carol choosing every 5th or 10th person at school (or something like that), this does not fit.

- Stratified random sampling means that different subgroups of the population are selected, and once those are selected, it is randomized to see who out of the subgroup is selected. For example, if Carol took all the men and women in her school and chose 50 random men and 50 random women, this would work. Although Carol's friends may define a subgroup of the population here, she is not asking anyone outside of that subgroup here, so this does not fit.

As none of these fit, the only answer left is D

If or whether Carol's sampling strategy was random and objective will determine if the survey's findings accurately reflect the population of pupils at her school. So, the correct option is D.

A statistical method known as random sampling is used to choose a representative sample of people or things from a bigger population. Every member of the population maintains an equal probability of being chosen in a random sample, and there is no systematic bias present in the selection procedure.

Which sample technique Carol employed is unclear given the facts in the question. Carol's poll would not be regarded as a random sample, and the findings might not be representative of the entire student body at her school if she simply asked 15 of her friends to respond.

Therefore, the correct option is D.

Learn more about Sampling, here:

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9514 1404 393

Answer:

  (x, y) ⇒ (y+1, 7-x) . . . rotation 90° CW about (4, 3)

or

  (x, y) ⇒ (y+1, x+1) . . . glide reflection across y=x; and translation (1, 1)

Step-by-step explanation:

The figure is apparently rotated 90° clockwise. This can be accomplished a couple of ways: (1) rotation 90° CW about some center; (2) reflection across the line y=x. Because of the symmetry of the figure, we cannot tell which of these is used.

Rotation

The center of rotation can be found by looking at the perpendicular bisectors of the segments joining a vertex and its image. One such segment has endpoints (1, 6) and (7, 6), so is a horizontal line with midpoint (4, 6). The perpendicular bisector of that is x=4.

Another segment joining a point with its image has endpoints (5, 6) and (7, 2). Its midpoint is (6, 4), and the slope of the bisector through that point is 1/2. It intersects the line x=4 at (4, 3), the center of rotation.

Rotation 90° CW about the origin is the transformation (x, y) ⇒ (y, -x), so rotation of (x, y) 90° about the point (4, 3) will be the transformation ...

  (x, y) ⇒ ((y -3) +4, (-(x -4) +3) = (y +1, 7 -x)

The transformation A to B is rotation 90° CW about (4, 3):

  (x, y) ⇒ (y +1, 7 -x).

__

Reflection

Simple reflection across the line y=x is the transformation (x, y) ⇒ (y, x). Applying that transformation, we see that an additional translation of 1 unit right and one unit up is required. The complete transformation is a "glide reflection", a reflection followed by a translation.

The transformation A to B is a glide reflection across the line y=x with a translation up 1 and right 1:

  (x, y) ⇒ (y +1, x +1).

Answer:

yall do school right now???and i forgot how to do these sorry

Answer:

18 = 2x-14

or, 2x =18+14

or, 2x =32

or, x=32/2

x=16

2(6x-7)=10

or, 12x-14=10

or, 12x=10+14

or, x=24/12

x=2

Answer:

t = 22 s

Step-by-step explanation:

If n is the number of strobe pulses

The first strobe pulse occurs at t = 0

t = 2(n - 1)

t = 2(12 - 1)

t = 2(11)

t = 22 s

Answer:

3/85

Step-by-step explanation:

that's the answer above

Answer:

Step-by-step explanation:

The measurement of the height is the dependent variable. The independent variable is the amount of fertilizer applied.

Answer:

at x-intercept, y = 0

4x = 28

x = 7

x intercept = (7,0)

at y-intercept, x = 0

y = 28

y intercept = (0,28)

Answer:

345/5=69

Step-by-step explanation:

345/5=69

355/5=71

Answer:

Answer:y=-2/9+3

Step-by-step explanation:

Answer:

Density = number of balls over volume of bag

The formula that can be used to calculate the density of the balls in the bag is Density = number of balls over volume of bag

"[tex]Density=\frac{Mass}{Volume}[/tex]"

"It is the measure of the matter inside a body."

For given question,

Amelia knows the number of balls in the bag and the volume of the bag.

She wants to calculate the density of soccer balls in a bag.

Here, mass = the number of balls in the bag

By using the density formula,

[tex]Density=\frac{number~of~balls}{volume~of~the~bag}[/tex]

Therefore, the formula that can be used to calculate the density of the balls in the bag is Density = number of balls over volume of bag

Learn more about the density here:

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Answer:

A

Step-by-step explanation:

By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)

Answer:

Hello the answer is A <!!

Answer:

c

Step-by-step explanation:

pi/ 3 * (180/pi)= 180/3

pi/3 = 60 degrees

9514 1404 393

Answer:

  2^6 = 64

Step-by-step explanation:

Each hour the initial value (1) is multiplied by 2 (again). So the number of times 2 multiplies the initial value is the number of passing hours (t).

The number of cells after t hours is ...

  c(t) = 1×2^t = 2^t

After 6 hours, this is

  c(6) = 2^6 = 64 . . . . cells after 6 hours

_____

Additional comment

As you know, multiplication simplifies repeated addition.

  x + x + x = 3x

In a similar way, exponentiation simplifies repeated multiplication.

 x·x·x = x³ . . . . (written as x^3 in plain text)

In this problem, we're repeatedly multiplying by 2. After we do that t times, the initial value is multiplied by 2^t.

Answer: width = 11 m

Concept:

Here, we need to understand how to find the area of a rectangle.

In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object.

A = w · l

w = width

l = length

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

w = w

l = w + 3

A = 154 m²

Given formula

A = w · l

Substitute values into the formula

154 = w · (w + 3)

Expand Parentheses (Distributive property)

154 = w² + 3w

Subtract 154 on both sides

154 - 154 = w² + 3w - 154

0 = w² + 3w - 154

Solve for the quadratic equation

(w - 11) (w + 14) = 0

w = 11 or w = -14 (Neglected because length cannot be negative)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)

A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)

Step-by-step explanation:

first everything is shifted down 8 units (x,y-8), so we get A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)

then you multiply by -1 A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)

Answer:

It would cost you 9.6 dollar .

I hope it is helpful mark me as brainlest and follow me for more good answer plz♥️♥️

I think because the angles are corresponding/opposite to each other u equate them to 180°