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Zepler
3 months ago
13

In a recent text message survey, 4,000 randomly selected teenagers were asked to cite their favorite Florida college football te

am. Twenty-two of 40 teenagers said the Florida Gators are their favorite team. A 99% confidence interval to estimate the true proportion of teenagers who like the Florida Gators is found to be (0.3474, 0.7526). Which of the following is a correct interpretation of the confidence level? (4 points)
Ninety-nine percent of all samples of this size would yield a confidence interval of (0.3474, 0.7526).

There is a 99% chance that the true proportion of teenagers who like the Florida Gators is (0.3474, 0.7526).

Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).

Ninety-nine percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who like the Florida Gators.

There is a 99% chance that randomly selected teenagers will be part of the 55% who like the Florida Gators.
Mathematics
1 answer:
lawyer [12.5K]3 months ago
3 0

Answer:

There is a 99% likelihood that the true percentage of teenagers liking the Florida Gators is within (0.3474, 0.7526).

Step-by-step explanation:

A 99% confidence interval estimating the true proportion of teenagers who favor the Florida Gators is calculated as (0.3474, 0.7526).

This indicates that we can be 99% confident the actual proportion of teenagers who like the Florida Gators falls within:

(0.3474, 0.7526)

In simpler terms, there is a 99% chance that the true proportion of teenagers who like the Florida Gators is contained in (0.3474, 0.7526).

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL
Leona [12618]

Answer:

KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47

Step-by-step explanation:

Given:

KL ║ NM,

LM = 45

m∠M = 50°

KN ⊥ NM  

NL ⊥ LM

To determine: KN and KL

1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,

LM = 45

m∠M = 50°

Consequently,

\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}

It is also true that

(angles LNM and M are complementary).m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}

2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,

NL=45\tan 50^{\circ}

m\angle KLN=m\angle LNM=40^{\circ} (alternate interior angles)

m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ} (angles KNL and KLN are complementary).

Thus,

\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08

and

\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47

3 0
2 months ago
Read 2 more answers
Doug purchased land for $8,000 in 1995. The year value of the land depreciated by 4% each year thereafter. Use an exponential fu
Leona [12618]

Answer:

Choice C. $6,012

Step-by-step explanation:

We know that

The formula to find the depreciated value is given by

V=P(1-r)^{t}

where

V stands for the depreciated value

P represents the original value

r corresponds to the depreciation rate in decimal

t refers to the Number of Time Periods

In this scenario, we have

t = 7 years

P = $8,000

r = 0.04

Plug these into the formula mentioned earlier

V = 8,000(1-0.04)^{7} = 6,012

Hope this assists you:)

4 0
3 months ago
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