A tire manufacturer is measuring the margin of error in the thickness of their tires to make sure it is within safety limits. Overall, the tires' thickness is normally distributed with a mean of 0.45 inches and a standard deviation of 0.05 inches. What thickness separates the lowest 5% of the means from the highest 95% in a sample size of 65 tires

Z = -1.65

Step-by-step explanation:

The main objective is to compute the data for the Z value and determine the of the sample distribution

Given that;

the tires' thickness is normally distributed  with a mean μ = 0.45 in

standard deviation σ = 0.05 in

sample size  =  65 tires

Also; we are being told that the  thickness separates the lowest 5% of the means from the highest 95%

∴

P(Z < Z) =0.05

From the Z- table

P(Z < -1.645) = 0.05

Z = -1.65

Similarly;

Let consider  to be the sample mean;

Then:

mean

standard deviation

= 0.00620174

By applying the Z-score formula:

x =  μ + ( Z × σ )

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x