Complete each conversion by dragging a number to each box.


Numbers may be used once, more than once, or not at all.



1,20012012,00012


12,000 g =


kg



120 cm =


mm



1. 2 L =


mL



1,200 cm =


m



0. 12 m =


mm

The values of C1 and C2 back into f(x), we get the final expression. The function f(x) is given by \(f(x) = x^5 - x^4 + 2x^2 - 6x + 7\).  

]we get:3 = - 4(1)⁵ + 8(1)⁴ - 4(1)³ + 4(1) + C∴ C = 3 + 4 - 8 + 4 - 3 = 0

∴ f(x) = - 4x⁵ + 8x⁴ - 4x³ + 4x + 0

∴ f(x) = - 4x⁵ + 8x⁴ - 4x³ + 4x

Hence, the value of f(x) is - 4x⁵ + 8x⁴ - 4x³ + 4x.

The given function is f f . f ' ' ( x ) = 20 x 3 12 x 2 4 , f ( 0 ) =

7 , f ( 1 )

= 3

We need to find f(x).

Given function is f f . f ' ' ( x ) = 20 x 3 12 x 2 4 , f ( 0 ) = 7 , f ( 1 ) = 3

We know that f′(x) = f(x)f′′(x)

Differentiating both sides with respect to x,

we get: f′′(x) = f′(x) + x f′′(x)

Let's substitute the given values :f(0) = 7; f(1) = 3;

f′′(x) = 20x³ - 12x² + 4

From f′′(x) = f′(x) + x f′′(x),

we get: f′(x) = f′′(x) - x f′′(x)

= 20x³ - 12x² + 4 - x(20x³ - 12x² + 4)

= - 20x⁴ + 32x³ - 12x² + 4xf′(x)

= - 20x⁴ + 32x³ - 12x² + 4

Let's integrate f′(x) to get

f(x):∫f′(x) dx = ∫(- 20x⁴ + 32x³ - 12x² + 4) dx

∴ f(x) = - 4x⁵ + 8x⁴ - 4x³ + 4x + Cf(0) = 7

∴ 7 = C Using f(1) = 3.

Given:

\(f''(x) = 20x^3 - 12x^2 + 4\)

f(0) = 7

f(1) = 3

First, let's integrate f''(x) once to find f'(x):

f'(x) = ∫\((20x^3 - 12x^2 + 4)\) dx

= \((20/4)x^4 - (12/3)x^3 + 4x + C_1\)

=\(5x^4 - 4x^3 + 4x + C_1\)

Next, let's integrate f'(x) to find f(x):

f(x) = ∫\((5x^4 - 4x^3 + 4x + C_1)\) dx

=\((5/5)x^5 - (4/4)x^4 + (4/2)x^2 + C_1x + C_2\)

= \(x^5 - x^4 + 2x^2 + C_1x + C_2\)

Now, we'll apply the initial conditions to determine the values of the constants C1 and C2:

Using f(0) = 7:

7 = \((0^5) - (0^4) + 2(0^2) + C_1(0) + C_2\)

7 = \(C_2\)

Using f(1) = 3:

3 = \((1^5) - (1^4) + 2(1^2) + C_1(1) + C_2\)

3 = 1 - 1 + 2 + \(C_1\) + 7

3 = \(C_1\) + 9

\(C_1 = -6\)

Now, substituting the values of C1 and C2 back into f(x), we get the final expression for f(x):

\(f(x) = x^5 - x^4 + 2x^2 - 6x + 7\)

to know more about constant, visit

https://brainly.com/question/27983400

#SPJ11

Answer:

b and d option are correct

Answer:

B, D

Step-by-step explanation:

B, D

x cannot be in a root.  (A)

x cannot be in the denominator.  (C)

Answer:

true

Step-by-step explanation:

Answer:

True

Both slopes have to be negative reciprocals for the two lines to be perpendicular.

Hope this Helps!

Answer:

.44 repeating would be your decimal of dogs that weigh under 20 pounds.

Step-by-step explanation:

Answer:

.44

Step-by-step explanation:

Answer: x = 100

Step-by-step explanation:

With these base cases and the defined recurrence relation, you can recursively calculate the number of ways to deposit any given amount of dollars, considering the order of coins and bills.

To formulate a recurrence relation for the number of ways to deposit n dollars in a vending machine, where the order of coins and bills matters, we can break it down into smaller subproblems.

Let's define a function, denoted as F(n), which represents the number of ways to deposit n dollars. We can consider the possible options for the first coin or bill deposited and analyze the remaining amount to be deposited.

1. If the first deposit is a coin of value d, where d is a positive integer less than or equal to n, the remaining amount to be deposited will be (n - d) dollars. Therefore, the number of ways to deposit the remaining amount, considering the order, would be F(n - d).

2. If the first deposit is a bill of value b, where b is a positive integer less than or equal to n, the remaining amount to be deposited will be (n - b) dollars. Similar to the coin scenario, the number of ways to deposit the remaining amount, considering the order, would be F(n - b).

To obtain the total number of ways to deposit n dollars, we sum up the results from both scenarios:

F(n) = F(n - 1) + F(n - 2) + F(n - 3) + ... + F(1) + F(n - b)

Here, b represents the largest bill denomination available in the vending machine. You can adjust the range of values for d and b based on the available denominations of coins and bills.

It's important to establish base cases to define the initial conditions for the recurrence relation. For example:

F(0) = 1   (There is only one way to deposit zero dollars, which is to deposit nothing)
F(1) = 1   (There is only one way to deposit one dollar, either as a coin or a bill)

With these base cases and the defined recurrence relation, you can recursively calculate the number of ways to deposit any given amount of dollars, considering the order of coins and bills.

To know more about function click-
http://brainly.com/question/25841119
#SPJ11

To show that\(\( \vec{c} = \frac{2}{3}\vec{a} + \frac{1}{3}\vec{b} \)\) , we can use the concept of vector addition and scalar multiplication.

We know that point vector c lies on the line segment \(\( \overline{ab} \)\) and is twice as far from point vector b as it is from point vector a .We can express the position vector of point vector c as a combination of vector a and \( \vec{b} \) using scalar multiplication and vector addition.

The distance ratio between vector c and \( \vec{b} \) is \( \frac{2}{3} \) (twice as far from \( \vec{b} \) as vector a .

Similarly, the distance ratio between  vector c and vector a  is \( \frac{1}{3} \) (half the distance between \( \vec{b} \) and vector a

Using these distance ratios, we can express the position vector  vector c  as \(\( \vec{c} = \frac{2}{3}\vec{a} + \frac{1}{3}\vec{b} \).\)

Hence, we have shown as desired.

Learn more about vectors here :

https://brainly.com/question/30958460

#SPJ11

Answer:

i is always positive

Step-by-step explanation:

if be multiply 3 by 3 and get 9, then you multiply -2i by 2i and get -4i squared

9-4i^2 is now easy to solve unless we do now know the value of i, but since i is squared, i is always positive

Answer:

13

Step-by-step explanation:

Assuming this is (3-2i)(3+2i)

Use the FOIL method

First:       3(3) = 9

Outter:   3(2i) = 6i

Inner:     -2i(3) = -6i

Last:        -2i(2i) = -4i²

Add all of them together:

    9 + 6i - 6i - 4i²

=   9 - 4i²   =    9  - 4(-1)   =   9 + 4  =  13

*NOTE that i² = -1

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

Find out more information about geometric sequence here:

brainly.com/question/11266123

Answer:

x=y/m-6

Step-by-step explanation:

According to the exponential function,

a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ

b) The number of rabbits in 1870 is 6.5

c) According to your model, the first pair of rabbits introduced into Australia is 19th century

Here we have given that during the 19th century, here rabbits were brought to Australia.

And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.

And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.

Then the exponential function can be written as,

=> f(rabbits) = 65000(√500/13)ˣ

When we plot these on the graph then we get the graph like the following.

Through the graph we have identified that the value of rabbits in 1870 is 6.5

to know more about Exponential function here.

https://brainly.com/question/14355665

#SPJ4

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

Learn more about proportional relationships here: brainly.com/question/10424180

#SPJ1

The ways to select the players from the total is 167960

From the question, we have

Total number of players, n = 20

Numbers to selection, r = 11 players

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 20 and r = 11

Substitute the known values in the above equation

Total = ²⁰C₁₁

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 20!/(11! * 9!)

Evaluate

Total = 167960

Hence, the number of ways is 167960

Read more about combination at

brainly.com/question/11732255

#SPJ1

The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

Learn more about Distribution at:

brainly.com/question/28021875

#SPJ4

Answer:

1,11,111 I don't know how I know it I just know it

Triangle AFC is the triangle that appears to be consistent with triangle AFD.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. There is an obtuse angle, or angle AFD, same like in the give triangle AFD.

Therefore, the opposite triangle must have an obtuse angle in order to be a congruent triangle. Only triangle AFC, out of the three that are given, has an acute angle. Additionally, they both support the same side, increasing the likelihood of congruence. There is no obtuse angle in the triangles BFC and DFE.

Learn more about congruent Visit: brainly.com/question/2938476

#SPJ4

Answer:

The correct answer:

C. 7

3(2) + 1 = 6 + 1 = 7

Step-by-step explanation:

So the question is 3x+1. We are given the information that x=2. Therefor we would plug in 2 to where x is. 3(2)+1. Now we would multiply first for 6+1. Add to get 7. 7 would be our answer giving us C.

Answer:

3. x=16

4. x=51

Step-by-step explanation:

3. 3x-8=x+24

2x=32

x=16

4. 2/3(x+27)= 180-(3x-25)

2/3x+18=180-3x+25

11/3x=187

11x=561

x=51

Step-by-step explanation:

Excercise 3:

By Alternate Exterior angles,

(x + 24)° = (3x - 8)°.

=> 2x = 32, x = 16.

Excercise 4:

By C-angles,

2/3 * (x + 27)° + (3x - 25)° = 180°.

=> 2x/3 + 18 + 3x - 25 = 180

=> 11x/3 = 187

=> x = 187 * (3/11) = 51.

Answer:

The radius is 6.

Step-by-step explanation:

If you have a diameter, you simply divide it by 2. so 12/2 is 6. Hope it helps :)

In total, Menaha traveled 97km 1000m (97.1km).

Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.

Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)

and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres

And the car distance is 11,480 metres.
When added together,

the total distance is 97,000 metres (97km).

To know more about distance click-
https://brainly.com/question/23848540
#SPJ4

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

Option (a) False:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

Option (b) False:

It is true that AB invertible implies \($(A B)^{\top}$\) is invertible but this does not imply B is invertible (not a valid statement).

Option (c) False:

A B is invertible does not mean \($A=B^{-1}$\). Since \($A=B^{-1}$\) implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

Option (d) True:

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

For more questions on matrices

https://brainly.com/question/13424110

#SPJ4

Answer:

It will option C this is correct answer 6n-20

Answer:

c

Step-by-step explanation:

Answer:

$102

Step-by-step explanation:

if Tommy spent 7 dollars on pie, that means he had more money than that amount before.

So before he spent 7 dollars, he had those 7 dollars.

Add 7 with 95

95 + 7 = 102

Answer:

Step-by-step explanation:

Price assuming he bought all large flags: \(20*8=160\)

Amount of money more: \(160-112=48\)

Difference of price in both flags: \(20-12=8\)

Medium Flags: \(48\div8=6\)

Large Flags: \(8-6=2\)

----------------------------------

The reason why this works, is because the amount of money more comes from the difference between both flags.

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

Learn more about number here

https://brainly.com/question/10547079

#SPJ4