Hello please help i’ll give brainliest

True or false: f(x) represents a function.<br> A. True <br> B. False

pav-90 [236]

Answer:

A.) True

Step-by-step explanation:

A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.

8 0

2 years ago

Let [v1,v2,v3] be a set of nonzero vectors in r^m such that the (transpose of vi)*vj = 0 when i is not equal to j. show that the

babunello [35]

Let $\mathbf V$ be the $m\times3$ matrix whose columns are $\mathbf v_1,\mathbf v_2,\mathbf v_3$ , and let $\mathbf c$ be the vector whose components are the constants $c_1,c_2,c_3$ . Now consider the matrix equation

$\mathbf V\mathbf c=\mathbf 0$

Multiplying both sides by $\mathbf V^\top$ , we have

$\mathbf V^\top(\mathbf V\mathbf c)=(\mathbf V^\top\mathbf V)\mathbf c=\mathbf 0$

More explicitly, we're writing

$\mathbf V=\begin{bmatrix}\mathbf v_1&\mathbf v_2&\mathbf v_3\end{bmatrix}$

Multiply both sides by $\mathbf V^\top$ and the left hand side can be written as

$\mathbf V^\top\mathbf V=\begin{bmatrix}{\mathbf v_1}^\top\\{\mathbf v_2}^\top\\{\mathbf v_3}^\top\end{bmatrix}\begin{bmatrix}\mathbf v_1&\mathbf v_2&\mathbf v_3\end{bmatrix}=\begin{bmatrix}{\mathbf v_1}^\top\mathbf v_1&{\mathbf v_1}^\top\mathbf v_2&{\mathbf v_1}^\top\mathbf v_3\\{\mathbf v_2}^\top\mathbf v_1&{\mathbf v_2}^\top\mathbf v_2&{\mathbf v_2}^\top\mathbf v_3\\{\mathbf v_3}^\top\mathbf v_1&{\mathbf v_3}^\top\mathbf v_2&{\mathbf v_3}^\top\mathbf v_3\end{bmatrix}$

We're told that ${\mathbf v_i}^\top\mathbf v_j=0$ whenever $i\neq j$ , so we're left with

$\mathbf V^\top\mathbf V=\begin{bmatrix}\|\mathbf v_1\|^2&0&0\\0&\|\mathbf v_2\|^2&0\\0&0&\|\mathbf v_3\|^2\end{bmatrix}$

Each of $\mathbf v_1,\mathbf v_2,\mathbf v_3$ are nonzero, which means their norms are nonzero, which necessarily implies that $\mathbf c=0$ , and so the vectors $\mathbf v_1,\mathbf v_2,\mathbf v_3$ must necessarily be linearly independent.

6 0

3 years ago

Identify the mistake(s) in the work below:

xxTIMURxx [149]

Answer:

Step-by-step explanation:

4 0

2 years ago

A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives d

sergij07 [2.7K]

Answer:

There is evidence to show that the single-earner couples on average spend more time watching television together

Step-by-step explanation:

Given that a recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes.

$H_0: \bar x=\bar y\\H_a: \bar x > \bar y$

(Right tailed test where x stands for single earner and y for double)

Let us assume sample sizes are 500 each.

Difference -12.600

Standard error 1.066

95% CI -14.6913 to -10.5087

t-statistic -11.823

DF 998

Significance level P < 0.0001

Since p is less than alpha we reject null hypothesis.

There is evidence to show that the single-earner couples on average spend more time watching television together

4 0

3 years ago

What is the volume of a right rectangular prism that is 3 meters by 4.5 meters by 6 meters?

ddd [48]

This is the right rectangular prism which dimensions are:
W = 3 m , L = 4.5 m , H = 6 m
The volume of the prism:
V = W * L * H
V = 3 m * 4.5 m * 6 m = 81 m³
Answer:
The volume is 81 m³.

8 0

4 years ago