All categories

3 years ago

1. What is the sum of the two vectors (-1,-4) and (3,5)?

Mathematics

1 answer:

mash [69]3 years ago

8 0

What is the sum of the two vectors (-1,-4) and (3,5)

to find the sum we add x component with x and y with y

(-1+3) , ( -4+5) = (2,1)

Hence option B is the correct option

2. Evaluate the following expression: -1(5,-1) + 2(1,1)

-1(5,-1) + 2(1,1) = (-5 , 1) + (2,2)

= ( -3 , 3)

Second option is the correct

3. Evaluate the following expression (1,4) -5(1,1)

(1,4) -5(1,1)

= (1,4) (-5,-5)

= (1-5 , 4-5)

= (-4,-1)

4. Let v=(8,-4) and w=(-4,2). Which of the following is true?

as we can see

(8,-4) = -2(-4,2)

v= -2w

and also the Y component of w is 2

5. Which of the following vectors are orthogonal to (-1,3)?

The orthogonal vector will be (3,1) as the dot product is zero

(-1,3).(3,1) = (-3+3) = 0

Hence Option third is the correct one

You might be interested in

A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet

brilliants [131]

Answer:

There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet (P-value = 0.15).

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the liquid diet yields a higher mean weight loss than the powder diet.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0$

The significance level is 0.05.

The sample 1 (powder diet group), of size n1=49 has a mean of 42 and a standard deviation of 12.

The sample 2 (liquid diet group), of size n2=36 has a mean of 45 and a standard deviation of 14.

The difference between sample means is Md=-3.

$M_d=M_1-M_2=42-45=-3$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{49}+\dfrac{14^2}{36}}\\\\\\s_{M_d}=\sqrt{2.939+5.444}=\sqrt{8.383}=2.895$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-3-0}{2.895}=\dfrac{-3}{2.895}=-1.04$

The degrees of freedom for this test are:

$df=n_1+n_2-1=49+36-2=83$

This test is a left-tailed test, with 83 degrees of freedom and t=-1.04, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.15) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet.

6 0

3 years ago

Read 2 more answers

I don’t quite understand what to do or how to solve it. Can someone explain please ?

Bess [88]

Answer:

True.

Step-by-step explanation:

Remember the vertical line test. Anywhere on that graph, you can draw a vertical line, and it will not touch the function two times. Because of this, it is true.

4 0

3 years ago

Which of the following graphs represents a function?

kirza4 [7]

The third graph represents a function.

In a function, every input (x value) has <em>exactly</em> one output (y value). If even a single input has zero or two outputs, the graph does not represent a function.

A good way of testing this is using a vertical line. As you move a vertical line from left to right across a graph, it should always be touching exactly one point on the graphed line.

In this case, every graph fails this vertical line test except for the third graph, so the third graph represents a function.

8 0

1 year ago

Read 2 more answers

Isabella solved the following equation: 4x − 2x + 8 = 6(x + 4) Step Work Justification 1 4x − 2x + 8 = 6x + 24 Distributive Prop

AnnZ [28]

Answer:

step 3 has incorrect justification.

Step-by-step explanation:

because it was combine like terms but 8 is still in left hand side. So,combine like terms 3 has incorrect justification.

7 0

3 years ago