Josh wilson is traveling to california from south carolina for summer vacation. the states are approximately 2500 miles apart driving cross-country. he stops at his parent's house in oldham county, texas, which is (12x 106) miles away from south carolina and (5x + 685) miles away from california. determine if josh's parent's house in texas the midpoint between south carolina and california? justify your answer.

Given, distance between South Carolina and Texas =

Distance between Texas and California =

Let's assume, both the distance is same.

=>

=>

=>

Plug x = 113 in

Miles.

Similarly, miles

Since 2500 divided by 2 = 1250 miles, hence our assumption was correct, Texas lies between both the cities.

Yes, Josh's parent's house in Texas is the midpoint between South Carolina and California

Step-by-step explanation:

Let S represents South carolina C represents California and T represents Texas,

Given,

ST = 12x - 106,

TC = 5x + 685,

Also, SC = 2500 miles,

Suppose T is the midpoint of S and C,

⇒ ST = TC

12x - 106 = 5x + 685

7x = 791

⇒ x = = 113

So, ST =

Now,

⇒ 2 ST = SC

Hence, T is the midpoint of S and C.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;