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2 years ago

Increase 14187.13 by 4.5%

1 answer:

7 0

If you increase a number by 4.5%, then you're adding 4.5% of that number to 100% of that number. So essentially you just multiply 14187.13 by 104.5%, or 1.045 to find the answer, which is 14,825.55.

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Fill in the missing digits to find the base 2 representation of 59.

Anna007 [38]

Answer:

111011

Step-by-step explanation:

Following the binary rule we can find the base 2 presentation of the decimal number 59.

To find the binary equivalence of 59 we use the sum of powers of 2.

$2^{0}=1$

$2^{1}=2$

$2^{2}=4$

$2^{3}=8$

$2^{4}=16$

$2^{5}=32$

$2^{6}=64$

Now we take our number and find out what the binary number will by taking our largest number closest to the number first.

59 = 32

We chose the number 32 since 64 will be a larger value than 59.

We then check how much we have to add to 32 to get 59.

59 = 32 + 27

We then look for the closest number to 27 in our powers of 2.

59 = 32 + 16

Now we check again for how much we need left to get a total of 59.

59 = 32 + 16 + 11

Now we repeat the same process of finding which value in the powers of 2 are closest to the number.

59 = 32 + 16 + 8 + 3

59 = 32 + 16 + 8 + 2 + 1

Now since we already have a total of 59, our binary number will be all the numbers present will have a value of 1 and the numbers now used will have a number of 0.

32 16 8 4 2 1

This can also be represented as:

2^5 2^4 2^3 2^1 2^0

Now we have to include the numbers that we skipped to get the total binary number.

32 16 8 4 2 1

1 1 1 0 1 1

This can be represented as:

59 = 32 16 + 8 + 0 + 2 + 1

1 1 1 0 1 1

3 0

2 years ago

Read 2 more answers

What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?

Y_Kistochka [10]

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=12\\
d=-10\\
a_{12}=13
\end{cases}
\\\\\\
a_{12}=a_1+(12-1)d\implies 13=a_1+(12-1)(-10)
\\\\\\
13=a_1-110\implies \boxed{123=a_1}$

$\bf \\\\
-------------------------------\\\\
\textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
a_n=\textit{value of the }n^{th}\ term\\
------------\\
n=12\\
a_1=123\\
a_{12}=13
\end{cases}
\\\\\\
S_{12}=\cfrac{12}{2}(a_1+a_{12})\implies S_{12}=\cfrac{12}{2}(123+13)$

and surely you know how much that is.

6 0

3 years ago

Does anyone know the answer to <br><br> -4 (-5) (9)

Grace [21]

Answer:180 I think

Step-by-step explanation:

3 0

2 years ago

Determine whether the set of all linear combinations of the following set of vector in R^3 is a line or a plane or all of R^3.a.

Temka [501]

Answer:

a. Line

b. Plane

c. All of R^3

Step-by-step explanation:

In order to answer this question, we need to study the linear independence between the vectors :

1 - A set of three linearly independent vectors in R^3 generates R^3.

2 - A set of two linearly independent vectors in R^3 generates a plane.

3 - A set of one vector in R^3 generates a line.

The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :

a. Let's put the vectors into the rows of a matrix :

$\left[\begin{array}{ccc}-2&5&-3\\6&-15&9\\-10&25&-15\end{array}\right]$ ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

$\left[\begin{array}{ccc}-2&5&-3\\0&0&0\\0&0&0\end{array}\right]$

We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).

We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).

At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.

b. Again, let's put the vectors into the rows of a matrix :

$\left[\begin{array}{ccc}1&2&0\\1&1&1\\4&5&3\end{array}\right]$ ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

$\left[\begin{array}{ccc}1&1&1\\0&1&-1\\0&0&0\end{array}\right]$

We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).

c. Finally :

$\left[\begin{array}{ccc}0&0&3\\0&1&2\\1&1&0\end{array}\right]$ ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

$\left[\begin{array}{ccc}1&1&0\\0&1&2\\0&0&3\end{array}\right]$

The set is linearly independent so the set of all linear combination of the set c. is all of R^3.

4 0

2 years ago

Hello, I dont understande this, can someone please explain what it is.

n200080 [17]

The required diameter of dwarf planet is $10^{6} m$ .

<h3>What is a statement?</h3>

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The given statement is the diameter of 3 planet is

planet A= $10^{9} m$ = 1000000000m