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3 years ago

What is the mean in 74,75,80,76,75,81,78?

Mathematics

2 answers:

Svetlanka [38]3 years ago

8 0

Answer:

Step-by-step explanation:

Add all the numbers up, then divide it by how many numbers there are in the set.

Lena [83]3 years ago

7 0

Answer:

Step-by-step explanation:

put them in order so it'd be 74,75,75,76,78,80,81 then add them together is 539 then divide 539 and 7 and your answer is 77

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NEED HELP ! 20 POINTS

prohojiy [21]

If $z=1-i$ , then $|z|=\sqrt{1^2+(-1)^2}=\sqrt2$ and $\arg z=-\dfrac\pi4$ because $z$ lies in the fourth quadrant.

By DeMoivre's theorem,

$z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i$

so the answer is B.

8 0

2 years ago

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

Setler79 [48]

Answer:

The First Option

Step-by-step explanation:

y - 7 = -1/4(x - 4)

6 0

2 years ago

Read 2 more answers

Determine if the columns of the matrix form a linearly independent set. Justify your answer. [Start 3 By 4 Matrix 1st Row 1st Co

Volgvan

Answer:

Linearly Dependent for not all scalars are null.

Step-by-step explanation:

Hi there!

1)When we have vectors like $v_{1},v_{2},v_{3}, ...$ we call them linearly dependent if we have scalars $a_{1},a_{2},a_{3},...$ as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.

$a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...a_{m}\vec{v_{m}}=0$

When all scalar coefficients are equal to zero, we can call them linearly independent

2) Now let's examine the Matrix given:

$\begin{bmatrix}1 &-2 &2 &3 \\ -2 & 4 & -4 &3 \\ 0&1 &-1 & 4\end{bmatrix}$

So each column of this Matrix is a vector. So we can write them as:

$\vec{v_{1}}=\left \langle 1,-2,1 \right \rangle,\vec{v_{2}}=\left \langle -2,4,-1 \right \rangle,\vec{v_{3}}=\left \langle 2,-4,4 \right \rangle\vec{v_{4}}=\left \langle 3,3,4 \right \rangle$ Or

Now let's rewrite it as a system of equations:

$a_{1}\begin{bmatrix}1\\ -2\\ 0\end{bmatrix}+a_{2}\begin{bmatrix}-2\\ 4\\ 1\end{bmatrix}+a_{3}\begin{bmatrix}2\\ -4\\ -1\end{bmatrix}+a_{4}\begin{bmatrix}3\\ 3\\ 4\end{bmatrix}=\begin{bmatrix}0\\ 0\\ 0\end{bmatrix}$

2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.

Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.

$\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ -2 &4 &-4 &3 \\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )R_{1}\times2 +R_{2}\rightarrow R_{2}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &0 &9 &0\\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\ R_{2}\Leftrightarrow R_{3}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &1 &-1 &4 \\ 0 &0 &9 &0 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )$ $\left\{\begin{matrix}1a_{1} &-2a_{2} &+2a_{3} &+3a_{4} &=0 \\ &1a_{2} &-1a_{3} &+4a_{4} &=0 \\ & & &9a_{4} &=0 \end{matrix}\right.\Rightarrow a_{1}=0, a_{2}=a_{3},a_{4}=0$

$S=\begin{bmatrix}0\\ a_{3}\\ a_{3}\\ 0\end{bmatrix}$

3 0

3 years ago

What is the perimeter of the trapezoid below?

Lisa [10]

Answer:

40 cm

Step-by-step explanation:

<em>Diagonal side: use pythagorean</em>

8^2 + 6^2 = 10^2 => the side is equal to 10

add up w/ 3 others side is 8, 8 and 14

So it is 10 + 8 + 8 + 14 = 40

5 0

3 years ago

TWENTY POINTS.

earnstyle [38]

Answer: 54 feet or 648 inches.

Step-by-step explanation:

1. You know that 1 inch on the doll house corresponds to 1/2 foot for life-sized objects. Therefore, you can calculate the width of the full-sized house that it's modeled after, as following:

$width=\frac{108in*1/2ft}{1in}\\width=54ft$

2. Then, the width in feet is: 54 feet.

3. And the width in inches is:

(Keeping on mind that 1 feet=12 inches)

$\frac{54ft*12in}{1ft}=648in$

4 0

3 years ago