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4 years ago

Find the magnitude and direction angle for the vector v = 3 cos 123°i + 3 sin 123°j.

1 answer:

8 0

The vector written in its generic form is given by:
v = lvl cos theta ° i + lvl without theta ° j
Where.
lvl: magnitude of the vector
theta: angle of the vector with respect to the x axis.
For this case we have the following vector:
v = 3 cos 123 ° i + 3 without 123 ° j
Where,
lvl = 3
theta = 123 °
Answer:
The magnitude and direction angle for the vector v is:
D. 3, 123 °

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4 years ago

Members of the millennial generation are continuing to be dependent on their parents (either living with or otherwise receiving

Morgarella [4.7K]

Answer:

$\bf H_0:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is 0.3

$\bf H_a:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is greater than 0.3

b) 34%

c) practically 0

d) Reject the null hypothesis.

Step-by-step explanation:

Since an individual aged 18 to 32 either continues to be dependent on their parents or not, this situation follows a Binomial Distribution and, according to the previous research, the probability p of “success” (depend on their parents) is 0.3 (30%) and the probability of failure q = 0.7

According to the sample, p seems to be 0.34 and q=0.66

To see if we can approximate this distribution with a Normal one, we must check that is not too skewed; this can be done by checking that np ≥ 5 and nq ≥ 5, where n is the sample size (400), which is evident.

We can then, approximate our Binomial with a Normal with mean

$\bf np = 400*0.34 = 136$

and standard deviation

$\bf \sqrt{npq}=\sqrt{400*0.34*0.66}=9.4742$

Since in the current research 136 out of 400 individuals (34%) showed to be continuing dependent on their parents:

$\bf H_0:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is 0.3

$\bf H_a:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is greater than 0.3

So, this is a right-tailed hypothesis testing.

According to the sample the proportion of "millennials" that are continuing to be dependent on their parents is 0.34 or 34%

Our level of significance is 0.05, so we are looking for a value $\bf Z^*$ such that the area under the Normal curve to the right of $\bf Z^*$ is ≤ 0.05

This value can be found by using a table or the computer and is $\bf Z^*$ = 1.645

Applying the continuity correction factor (this should be done because we are approximating a discrete distribution (Binomial) with a continuous one (Normal)), we simply add 0.5 to this value and

$\bf Z^*$ corrected is 2.145

Now we compute the z-score corresponding to the sample

$\bf z=\frac{\bar x -\mu}{s/\sqrt{n}}$

where

$\bf \bar x$ = mean of the sample

$\bf \mu$ = mean of the null hypothesis

s = standard deviation of the sample

n = size of the sample

The sample z-score is then

$\bf z=\frac{136 - 120}{9.4742/20}=16/0.47341=33.7759$

The p-value provided by the sample data would be the area under the Normal curve to the left of 33.7759 which can be considered zero.

Since the z-score provided by the sample falls far to the left of $\bf Z^*$ we should reject the null hypothesis and propose a new mean of 34%.

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Read 2 more answers

Find the value of each variable

aniked [119]

Answer:

Answer d)

$a= 10*\sqrt{3}$ $b=5*\sqrt{3}$ , $c=15$ , and $d=5$

Step-by-step explanation:

Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".

So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

$b=10*sin(60^o)= 10*\frac{\sqrt{3} }{2} = 5*\sqrt{3}$

where we use the fact that the sine of 60 degrees can be written as: $\frac{\sqrt{3} }{2}$

We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

$d=10*cos(60^o)=10* \frac{1}{2} = 5$

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

$sin(30^o)= \frac{b}{a} \\a=\frac{b}{sin(30)} \\a=\frac{5*\sqrt{3} }{\frac{1}{2} } \\a= 10*\sqrt{3}$

where we used the value of the sine function of 30 degrees as one half: $\frac{1}{2}$

Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

$c=10*\sqrt{3} * cos(30^o)=10*\sqrt{3} *\frac{\sqrt{3} }{2} \\c= 5*3=15$

Therefore, our answer agrees with the values shown in option d)

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3 years ago