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kykrilka [37]
3 years ago
6

Trig question above plz plz plz help

Mathematics
1 answer:
alukav5142 [94]3 years ago
7 0
The answers are:
1. B
2.C
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Which of the following differential equations has the slope field below
Nookie1986 [14]

The differential equation that has the given slope is: dy/dx = -xy.

<h3>How to find the differential equation that models the situation?</h3>

We have to look at the slope, given in the graph of the solution of the differential equation, and represented by dy/dx. From the graph, we have that:

  • In quadrants I and III, in which x and y have the same signal, the differential equation is decreasing, hence the slope is negative.
  • In quadrants II and IV, in which x and y have different signals the differential equation is increasing, hence the slope is positive.

The differential equation that is negative when x and y have the same signals and positive when they do not have is given by the following option:

dy/dx = -xy.

More can be learned about differential equations at brainly.com/question/14423176

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6 0
1 year ago
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The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?
densk [106]

The radius of the sector is 10.27 miles

<h3>How to find the radius of a sector?</h3>

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

  • r = radius
  • ∅ = central angle

Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

8280 = 25πr²

divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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4 0
1 year ago
Hypothesis Testing
Yuri [45]

Answer:

<u>Problem 1</u>: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

<u>Problem 2</u>: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

<u>Problem 1:</u>

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = <em>proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement</em>

So, Null Hypothesis, H_0 : p \leq 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, H_A : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is <u>One-sample z-test</u> for proportions;

                       T.S.  =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of adult Americans who were worried about having enough saved for retirement = \frac{156}{295} = 0.53

           n = sample of adult Americans = 295

So, <u><em>the test statistics</em></u> =  \frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }

                                    =  1.03

The value of z-test statistics is 1.03.

<u>Also, the P-value of the test statistics is given by;</u>

              P-value = P(Z > 1.03) = 1 - P(Z \leq 1.03)

                           = 1 - 0.8485 = <u>0.1515</u>

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, <u><em>so we insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

<u>Problem 2:</u>

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let \mu = <em>mean daily volume in Google stock</em>

So, Null Hypothesis, H_0 : \mu = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, H_A : \mu \neq 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                       T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, <u><em>the test statistics</em></u> =  \frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }  ~ t_3_4

                                    =  -7.606

The value of t-test statistics is -7.606.

<u>Also, the P-value of the test statistics is given by;</u>

              P-value = P(t_3_4 < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, <u><em>so we sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

8 0
2 years ago
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