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3 years ago

15

The axis of symmetry is located at x=A.

itle=" \frac{1}{6} " alt=" \frac{1}{6} " align="absmiddle" class="latex-formula">
B.6
C.2
D.3

1 answer:

adell [148]3 years ago

7 0

D is the correct answer for the symmetry

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Choose the correct numbers from the box below to complete the subtraction sentence that follows

maw [93]

Answer:

umm there isn't a subtraction sentence

Step-by-step explanation:

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2 years ago

Write a variable expression for this amount a number x decreased by 6

ANEK [815]

I'm not exactly sure what you're asking but <em />I'll give it a go.
A = x -6

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3 years ago

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. At a clothing store, 12 people purchased blue sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 purchased

DedPeter [7]

Answer:

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

P(A)= the probability that they purchased a green sweater
P(B)= the probability that they purchased a gray sweater
Mutually exclusive events

You know:

8 purchased green sweaters
4 purchased gray sweaters
number of possible cases= 12 + 8 + 4+ 7= 21

So:

$P(A)=\frac{8}{31}$

$P(B)=\frac{4}{31}$

P(A⋂B) = 0

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= $\frac{8}{31}+ \frac{4}{31}$

P(A∪B)= $\frac{12}{31}$

<u><em>The probability that they purchased a green or a gray sweater is </em></u> $\frac{12}{31}$ <u><em></em></u>

5 0

3 years ago

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

There are 2 leaves along 3 in. of an ivy vine. There are 14 leaves along 15 in. of the same vine. Which equation models the numb

Hunter-Best [27]

Doing a bit of guess and check, we can notice that the amount of leaves is one less than the number of inches of vine. Writing it out, we get x-1=y (the amount of inches-1=the amount of leaves)

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3 years ago

Read 2 more answers