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3 years ago

Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,3,-1), R(-4,2,-2), S(-8,5,-3).

Mathematics

1 answer:

-BARSIC- [3]3 years ago

4 0

Answer:

Step-by-step explanation:

Co-ordinate of point P(0,0,0)

Q (-4,3,-1)

R (-4,2,-2)

S (-8,5,-3)

$\vec{PQ}=$

$\vec{PS}=$

Area of Parallelogram $=|\vec{PQ}\times \vec{PS}|$

$Area=\begin{vmatrix}i &j &k \\ -4 &3 &-1 \\ -8 &5 &-3 \end{vmatrix}$

$A=|\hat{i}(-9+5)-\hat{j}(-12-8)+\hat{k}(-20+24)|$

$A=|-4\hat{i}+20\hat{j}+4\hat{k}|$

$A=\sqrt{(-4)^2+(20)^2+(4)^2}$

$A=\sqrt{432}$

$A=20.78\ unit^2$

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Question 3 A study was performed to determine whether men and women differ in their repeatability in assembling components on pr

Fed [463]

Answer:

There is no sufficient evidence to support the claim that men and women differ in repeatability for this assembly task

Step-by-step explanation:

Given

Let subscript 1 represent men and 2 represent women, respectively.

$n_1 = 25$

$n_2 = 21$

$s_1 = 0.98$

$s_2 = 1.02$

$\alpha = 0.02$

Required

Determine if here is enough evidence

First, we need to state the hypotheses

$H_o: \sigma_1^2 = \sigma_2^2$

$H_1: \sigma_1^2 \ne \sigma_2^2$

Next, calculate the test statistic using:

$F = \frac{s_1^2}{s_2^2}$

$F = \frac{0.98^2}{1.02^2}$

$F = 0.923$

Calculate the rejection region;

But first, calculate the degrees of freedom

$df_1 =n_1 - 1$

$df_1 =25 - 1$

$df_1 =24$

$df_2 = n_2 -1$

$df_2 = 21 - 1$

$df_2 = 20$

Using the F Distribution: table

$c = \frac{\alpha}{2}$

$c = \frac{0.02}{2}$

$c = 0.01$

At 0.01 level (check row 20 and column 24), the critical value is:

$f_{0.01,24,20} = 2.86$ --- the upper bound

At 0.01 level (check row 24 and column 20), the critical value is:

$f_{0.01,20,24} = 2.74$

Calculate the inverse F distribution.

$f_{0.99,20,24} = \frac{1}{f_{0.01,20,24}} = \frac{1}{2.74} =0.365$ ---- the lower bound

The rejection region is then represented as:

$0.365 < Test\ Statistic < 2.86$

If the test statistic falls within this region, then the null hypothesis is rejected

$F = 0.923$ --- Test Statistic

$0.365 < 0.923 < 2.86$

The above inequality is true; so, the null hypothesis is rejected.

This implies that, there is no sufficient evidence.

7 0

3 years ago

If DM=35, what is the value of r? Where DG is r+5 and GM is 3r-14

AlekseyPX

R=17.5
DG=22.5
GM=38.5

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3 years ago

Katrina wants to estimate the proportion of adults who read at least 10 books last year. to do so, she obtains a simple random

Vaselesa [24]

E=Z*sqrt (p(1-p)/N), where E= error margin, p=proportion, N=sample size

Katrina's margin error at 85% confidence interval: E=1.96*sqrt (p(1-p)/100) = 0.196 sqrt (1(1-p))

Mathew's margin error at 99% confidence interval: E= 2.58*sqrt (p(1-p)/400) = 0.129 sqrt (p(1-p))

Since both obtained same estimate of proportion (that is, value of p), it can be seen that Mathew's estimate will have a small error (That is, 0.129 is smaller than 0.196). This can be attributed to larger sample size although a wider confidence (99%) interval was considered.

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3 years ago

If the 16 boys in the classroom is 40% what is the percent of girls

notsponge [240]

Answer:

60%

Because the reaming percent has to add up to 100. 60 plus 40 is 100

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3 years ago

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egoroff_w [7]

Answer:

Step-by-step explanation:

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3 years ago