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4 years ago

8

Write an inequality that you can solve using the Division Property of Inequality where the direction of the inequality symbol mu

st be reversed.( >,<)

1 answer:

Verdich [7]4 years ago

7 0

4>2 then 1/4<1/2 if that is what you are wanting

You might be interested in

An insurance company selected a random sample of 500 clients under 18 years of age and found that 180 of them had had an acciden

Butoxors [25]

Answer:

a) The pooled proportion is p=0.3.

b) P-value = 0.000078

c) Lower bound = 0.0556

d) Upper bound = 0.1644

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the accident proportions differ between the two age groups .

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=500 has a proportion of p1=0.36.

$p_1=X_1/n_1=180/500=0.36$

The sample 2, of size n2=600 has a proportion of p2=0.25.

$p_1=X_1/n_1=150/600=0.25$ .

The difference between proportions is (p1-p2)=0.11.

$p_d=p_1-p_2=0.36-0.25=0.11$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{180+150}{500+600}=\dfrac{330}{1100}=0.3$

The standard error for the difference between proportions can now be calculated as:

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.3*0.7}{500}+\dfrac{0.3*0.7}{600}}\\\\\\s_{p1-p2}=\sqrt{0.00042+0.00035}=\sqrt{0.00077}=0.0277$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.11-0}{0.0277}=\dfrac{0.11}{0.0277}=3.964$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(t>3.964)=0.000078$

As the P-value (0.000078) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the accident proportions differ between the two age groups.

If we want to calculate the bounds of a 95% confidence interval, we start by calculating the margin of error.

For a 95% CI, the critical value for z is z=1.96.

Then, the margin of error is:

$MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0277=0.0544$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.11-0.0544=0.05561\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.11+0.0544=0.16439$

The 95% confidence interval for the population mean is (0.0556, 0.1644).

5 0

3 years ago

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma

Zina [86]

I'm assuming you meant:

$tan^{2}x + tanx - 30 = 0$
Let $u = tan(x)$

Thus, we can rewrite it into a quadratic.

$u^{2} + u - 30 = 0$
$(u + 6)(u - 5) = 0$
$u = -6 or u = 5$

Hence, $tan(x) = -6$ or $tan(x) = 5$
$x = tan^{-1}(-6)$ or $x = tan^{-1}(5)$

Rewriting it in general form, we get:
$x = \pi \cdot n + tan^{-1}(5), n \in Z$
$x = \pi \cdot n - tan^{-1}(6), n \in Z$

From there, you can find your solutions from $[0, 2\pi)$

6 0

4 years ago

Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

4 years ago

Solve the inequality.

Olegator [25]

Answer:

x = 14

x + 23 < 37 ( move constant to right-hand side and change its sign)

x<37-23 ( subtract numbers)

x < 14

3 0

3 years ago

Read 2 more answers

Rewrite 9*10^6+9*10+9 as a base ten

NARA [144]

The rewritten form of the expression in base ten as given in the task content is; 9,000,099.

<h3>What is the rewritten form of the number 9*10^6+9*10+9 as a base ten?</h3>

It follows from the task content that the number given in the task content is;

9*10⁶+9*10+9

= 9(10⁶ + 10 + 1)

= 9 (1,000,011)

= 9,000,099

Therefore, since base 10 numerals are 1,2,3,4,5,6,7,8, and 9, it follows that;

Ultimately, the rewritten form of the expression in base ten is; 9,000,099.

It therefore follows that the representation of the expression as a base ten is as represented above.

Read more on base ten;

brainly.com/question/27072175

#SPJ1

5 0

2 years ago