Squaring both sides of an equation is irreversible. Is Cubing both sides of an equation reversible? Provide numerical examples t

In detail: Based on the central limit theorem, the distribution appears normal due to the large sample size. The confidence interval is presented in the format: (Sample mean - margin of error, sample mean + margin of error). The sample mean, denoted as x, serves as the point estimate for the population mean. The confidence interval is computed as: mean ± z × σ/√n, where σ represents the population standard deviation. The formula transforms into confidence interval = x ± z × σ/√n, with specific values: x = $75, σ = $24. To find the z score, we subtract the confidence level from 100% which gives α as 1 - 0.96 = 0.04; halving this results in α/2 = 0.02, signifying the tail areas. To ensure we account for the center area, we have 1 - 0.02 = 0.98, corresponding to a z score of 2.05 for the 96% confidence level. The confidence interval becomes 75 ± 2.05 × 24/√64 = 75 ± 2.05 × 3 = 75 ± 6.15. The lower limit is 75 - 6.15 = 68.85, while the upper limit stands at 75 + 6.15 = 81.15. For n = 400, with x = $75 and σ = $24, the z score remains 2.05, resulting in the confidence interval calculated as 75 ± 2.05 × 24/√400 = 75 ± 2.05 × 1.2 = 75 ± 2.46. Subsequently, the lower bound becomes 75 - 2.46 = 72.54, and the upper limit adds up to 75 + 2.46 = 77.46. Lastly, when n = 400, x = $200, and σ = $80, the z score tied to a 94% confidence level is 1.88. Thus, the confidence interval is expressed as 200 ± 1.88 × 80/√400 = 200 ± 1.88 × 4 = 200 ± 7.52, giving us a margin of error of 7.52.

2/3 of 7/8
2/3×7/8=7/12

Answer:

The range of cheerleaders' heights lies within the interval [58, 74)

It includes all real numbers from 58 inches and above, but below 74 inches.

Step-by-step explanation:

we have

Separate the combined inequality into two distinct inequalities

-----> inequality A

-----> inequality B

Solve inequality A

Subtract 28 from both sides

Split by 4 on both sides

Reformulate

Address inequality B

Subtract 28 from both sides

Split by 4 on both sides

consequently

The height range of the cheerleaders is the interval [58, 74)

It consists of every real number starting from 58 inches and less than 74 inches

Answer:

55°

Step-by-step explanation:

The problem does not have a suitable diagram. Please check the attachment for the diagram.

Observing the diagram, it is evident that the triangle is isosceles, as it has two sides that are congruent (i.e., the same length). Since these sides are identical, the base angles are consequently also equal.

From the diagram, <EFG = <EGF

Since  <EFG  = 55°, it follows that  <EGF = y = 55°

Thus, the value of y is established as 55°

Response:

The number 40 can be found in Pattern B. Additionally, following the rule, each sequence will expand.

Detailed breakdown:

Let’s build each sequence. Recall that the guideline is to "add 15" to generate each sequence starting from the provided initial number.

Pattern A.

Pattern B.

Pattern C.

You can see that the number 40 appears in Pattern B. Moreover, per the rule, each pattern will show an increase.