For each lettered part, a through c, examine the two given sets of numbers. without doing any calculations, decide which set has

The smallest whole-number value for x that works is 7. The triangle’s sides can be defined as: a = x, b = 2x, and c = 15. Recognizing c as the longest side leads us to the condition for an acute triangle: c^2 must be less than a^2 + b^2. Inputting the known values, we solve for x and find that x must exceed 6.708. As a result, the least integer that satisfies this requirement is 7.

The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].

Step-by-step clarification:

We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.

For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.

The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;

                      P.Q.  =  

 ~

where,

= sample mean of mail-order sales = $74.50

= sample mean of internet sales = $84.40

= standard deviation for mail-order sales = $17.25

= standard deviation for internet sales = $21.25

= number of mail-order sales receipts = 16

= number of internet sales receipts = 9

Furthermore,  

 =   = 18.74

The actual mean difference between average mail-order and internet purchases is denoted by (

).

Thus, the 99% confidence interval for () is expressed as;

      = Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807.           =

          = [$-31.82, $12.02]

Therefore, the 99% confidence interval for the true mean difference between average mail-order and internet purchases is [$(-31.82), $12.02].

A. The quantity of 10-boards that Peter purchases is equal to n divided by 10. Consequently, each of the 10-boxes will receive two boxes of nails. After purchasing n boards, the formula for the number of boxes of nails Peter will have will be,

N = (2)(n/10)

When simplified,

N = n/5

b. If the total number of boards is 90, then,

N2 = (90/10)(2)(100 nails/box)
N2 = 1800

Final Answer: 1800

The process of subtracting polynomials resembles removing integers, as both involve regular subtraction. For instance, 3xy - 2xy results in 1xy. The same rules of subtraction apply when working with polynomials.

Answer:

1.4×10⁻⁵=0.000014

Step-by-step explanation:

Since the exponent of the 10 term is negative, shift the decimal point to the left by 5 positions;

1.4×10⁻⁵=0.000014