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Thepotemich [5.8K]

3 years ago

15

X^2=1/4 please help me

2 answers:

skelet666 [1.2K]3 years ago

5 0

X² = 1/4 ⇒√⇒ x₁ = 1/2, x₂ = -1/2

Zina [86]3 years ago

3 0

x= 1/2

If you take 1/2 times 1/2 you get 1/4, and 1/2 times 1/2 is the same as 1/2 squared.

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Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of

tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A Sample B

$x_A = 30$ $x_B = 50$

$n_A = 100$ $n_B =250$

Solving (a): Standard error using formula

First, calculate the proportion of A

$p_A = \frac{x_A}{n_A}$

$p_A = \frac{30}{100}$

$p_A = 0.30$

The proportion of B

$p_B = \frac{x_B}{n_B}$

$p_B = \frac{50}{250}$

$p_B = 0.20$

The standard error is:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}$

$SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}$

$SE_{p_A-p_B} = \sqrt{0.00274}$

$SE_{p_A-p_B} = 0.052$

Solving (a): Standard error using bootstrapping.

Following the below steps.

Open Statkey
Under Randomization Hypothesis Tests, select Test for Difference in Proportions
Click on Edit data, enter the appropriate data
Click on ok to generate samples
Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A Sample B

$x_A = 23$ $x_B = 57$

$n_A = 100$ $n_B =250$

$p_A = 0.230$ $p_A = 0.228$

So, we have:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}$

$SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}$

$SE_{p_A-p_B} = \sqrt{0.002475064}$

$SE_{p_A-p_B} = 0.050$

5 0

3 years ago

Tell whether the lines through the given points are parallel, perpendicular, or neither. (-3,1), (1,9), (-2-9), (-1,-7)

Brrunno [24]

Answer:

parallel

Step-by-step explanation:

all the details are in the attached picture.

4 0

3 years ago

Construct the line perpendicular to KL at point M.

guapka [62]

Based on the options given in the picture

The one that would be the result if we construct the line that perpendicular to KL at point M would be :

picture C

hope this helps

5 0

3 years ago

Read 2 more answers

Verify that (cos²a) (2 + tan² a) = 2 - sin² a....<br>

Sveta_85 [38]

Trigonometric Formula's:

$\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}$

$\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }$

Given to verify the following:

$\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )$

$\texttt{\underline{apply distributive method}:}$

$\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)$

$\texttt{\underline{simplify the following}:}$

$\rightarrow \sf 2cos^2 a + sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf 2(1 - sin^2a ) + sin^2 a$

$\texttt{\underline{distribute inside the parenthesis}:}$

$\rightarrow \sf 2 - 2sin^2a + sin^2 a$

$\texttt{\underline{simplify the following}} :$

$\rightarrow \sf 2 - sin^2a$

Hence, verified the trigonometric identity.

7 0

2 years ago

Read 2 more answers

Use long division to find the quotient of 405 and 27

asambeis [7]

27|405 27*1=27
- 27 27*5=135
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135
-135
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0

Answer is 6 :v

7 0

3 years ago