One third of a number, decreased by 3/4 gives 1/3. What is the number?

The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable j

Bad White [126]

Answer:

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Step-by-step explanation:

Test if the proportion is less than 40%:

At the null hypothesis, we test if the proportion is of at least 0.4, that is:

$H_0: p \geq 0.4$

At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:

$H_1: p < 0.4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that $\mu = 0.4, \sigma = \sqrt{0.4*0.6}$

74 out of the 200 workers sampled said they would return to work

This means that $n = 200, X = \frac{74}{200} = 0.37$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}$

$z = -0.87$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.

Looking at the z-table, z = -0.87 has a p-value of 0.1922.

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

7 0

3 years ago

Why is the product of a rational number and an irrational number irrational

prohojiy [21]

Because u r adding irrational to rational its like if u add a whole number to a negative number u get deeper into negatives in this case irrational is the negative and rational is the whole

8 0

3 years ago

Need help with 7-10 please and thank you!!

Archy [21]

Answer:

#7: MK, LS and PR

#8: PN and PQ

#9: no

#10: no

Step-by-step explanation:

#7: lines MK, LS and PR are not intersecting each other, so these lines are parallel each other

#8: between lines PN and PQ is an right angle, so the lines PN and PQ are perpendicular

#9: lines PN and KM have an intesecting point, so they're not parallel

#10: there is no right angle between lines PR and NP

3 0

3 years ago

A semicircle with diameter PQ sits on an isosceles triangle PQR to form a region shaped like a two-dimensional ice- cream cone,

Ksivusya [100]

The limit of a(x)/b(x) as x approaches 0 is gotten as;

lim a(x)/b(x); x→0 = 0

The image showing the semi circle and isosceles triangle is missing and so i have attached it.

Formula for area of a semi circle is;

a(x) = A = ¹/₂πr²

Area of triangle is;

b(x) = A = ¹/₂ × base × height

From the image, ∠PQR = θ

Thus; a(x) = ¹/₂π(10 sin (θ/2))²

a(x) = ¹/₂π(100 sin² (θ/2))

Similarly;

b(x) = ¹/₂(20 sin (θ/2)) × (10 cos (θ/2))

b(x) = 100 sin (θ/2) cos (θ/2)

Thus;

a(x)/b(x) = ¹/₂π(100 sin² (θ/2)) ÷ 100 sin (θ/2) cos (θ/2)

100 will cancel out and the sin (θ/2) at the denominator will be eradicated

upon further simplification to give;

a(x)/b(x) = ¹/₂π(sin (θ/2)) ÷ cos (θ/2)

In trigonometry, we know that; tan θ = sin θ/cos θ

Thus;

a(x)/b(x) = ¹/₂π(sin (θ/2)) ÷ cos (θ/2) = ¹/₂π(tan (θ/2))

We want to find the limit as θ approaches zero.

Thus;

lim θ → 0 = ¹/₂π(tan (0/2))

⇒ ¹/₂π tan 0

⇒ 0

Read more at; https://brainly.in/question/9387458

3 0

2 years ago

Carl Cornfield has been wondering whether he should plant white corn this year. He decides to sample 100 customers. 38% say they

Brrunno [24]

Answer:

true

Step-by-step explanation:

8 0

3 years ago