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Judging on the basis of experience, a politician claims that 57% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 25 randomly selected people in that area, and 18 of them reported having voted for an independent candidate. The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 57%. What value of the test statistic should you report?

Answers

Answer 1

Answer:

Answer: z= 1.51

Step-by-step explanation:

Test statistic for proportion is given by :-

$z=\frac{p-P}{\sqrt{(PQ)/(n)}}$

Where n is sample size ,p is the sample proportion , P Is the population proportion and Q =1 - P.

Given : P=57% = 0.57

Q= 1- P = 1-0.57=0.43

n = 25

$p=(18)/(25)=0.72$

Test statistic for proportion will be :-

$z=\frac{0.72-0.57}{\sqrt{(0.57*0.43)/(25)}}\approx1.51$

We should report the value of test statistic z= 1.51

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Find the limit of the formula given

Answers

Answer:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 1$

General Formulas and Concepts:

Algebra II

Natural logarithms ln and Euler's number e
Logarithmic Property [Exponential]: $\displaystyle log(a^b) = b \cdot log(a)$

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_(x \to c^+) f(x)$
Left-Side Limit: $\displaystyle \lim_(x \to c^-) f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_(x \to c) x = c$

L’Hopital’s Rule: $\displaystyle \lim_(x \to c) (f(x))/(g(x)) = \lim_(x \to c) (f'(x))/(g'(x))$

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

We are given the following limit:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)}$

Substituting in x = 0 using the limit rule, we have an indeterminate form:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 0^0$

We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:

$\displaystyle y = \lim_(x \to 0^+) x^\big{√(x)}$

Take the ln of both sides:

$\displaystyle lny = ln \Big( \lim_(x \to 0^+) x^\big{√(x)} \Big)$

Rewrite the limit by including the ln in the inside:

$\displaystyle lny = \lim_(x \to 0^+) ln \big( x^\big{√(x)} \big)$

Rewrite the limit once more using logarithmic properties:

$\displaystyle lny = \lim_(x \to 0^+) √(x)ln(x)$

Rewrite the limit again:

$\displaystyle lny = \lim_(x \to 0^+) (ln(x))/((1)/(√(x)))$

Substitute in x = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:

$\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = (\infty)/(\infty)$

Apply L'Hopital's Rule:

$\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}}$

Simplify:

$\displaystyle \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}} = \lim_(x \to 0^+) -2√(x)$

Redefine the limit:

$\displaystyle lny = \lim_(x \to 0^+) -2√(x)$

Substitute in x = 0 once more using the limit rule:

$\displaystyle \lim_(x \to 0^+) -2√(x) = -2√(0)$

Evaluating it, we have:

$\displaystyle \lim_(x \to 0^+) -2√(x) = 0$

Substitute in the limit value:

$\displaystyle lny = 0$

e both sides:

$\displaystyle e^\big{lny} = e^\big{0}$

Simplify:

$\displaystyle y = 1$

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Mr. Golv is practicing his jiu jitsu drill where he does 5 guard passes and 2 kimura arm locks. A guard pass takes G seconds, and a kimura arm lock takes K seconds. Which expressions can we use to describe the number of seconds it takes Mr. Golv to complete his jiu-jitsu drill 7 times?

Answers

Answer:

7(5G + 2K)
14K + 35G

Answer:

35g + 14k

Step-by-step explanation:

T = time D = drill

D(5G + 2K) = T

7(5g + 2k) = T

35g + 14k = T

35g + 14k is the answer.

Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

$(5^2)(7^2)(3^2)$

To find:

The value of the given expression.

Solution:

We have,

$(5^2)(7^2)(3^2)$

On simplification, we get

$(5^2)(7^2)(3^2)=(25)(49)(9)$

$(5^2)(7^2)(3^2)=11025$

Therefore, the value of the given expression is 11025.

Please Help! I'm lost, in a maze and I can't find my way out.

Answers

Show us the maze and we will help

A student is told to work any 8 out of 10 questions on an exam. In how many different ways can he complete the exam

Answers

Answer:

Step-by-step explanation:

Assuming the order in which he answers the questions matter the answer is the number of permutations of 8 in 10.

This is 10! / (10-8)!

= 1,814.400.

If the order does not matter then the answer is the number of combinations of 8 from 10:

This is 10!/8!*2!

= 45.

Two angels in a triangle are equal and their sum is equal to the third angle in the triangle. What are the measures of each of there interior angles?

Answers

Answer:

45°, 45°, 90°

Step-by-step explanation:

You have described an isosceles right triangle. The angle measures are ...

45°, 45°, 90°

_____

If x is the smaller angle measure, then the total of angles is ...

x + x + 2x = 180°

x = 180°/4 = 45°

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