A printer prints an average of 200 1/2 pages per hour approximately how many pages did it print in an 8 hour period

Response:

  a. height of the pyramid: 5√7 cm

  b. overall area: (100 +200√2) cm²

  c. volume: (500/3)√7 cm³

Step-by-step explanation:

b) Each triangular face is an isosceles triangle with a base measuring 10 cm and a side length of 15 cm. That side length serves as the hypotenuse of the right triangle formed when an altitude is drawn. The altitude length can be calculated using the Pythagorean theorem as...

  h = √(15² -5²) = √200 = 10√2... cm

The lateral area equals the combined area of the four triangular faces, each one having this altitude and a base of 10 cm

  LA = 4 × (1/2)bh = 2bh

  LA = 2(10 cm)(10√2 cm) = 200√2 cm²

Additionally, the area of the square base is calculated as...

  A = s² = (10 cm)² = 100 cm²

Thus, the total surface area of the pyramid can be expressed as...

  A + LA = (100 +200√2) cm².... overall surface area

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a)  The altitudes of opposite triangular faces along with a line drawn across the center of the base form another isosceles triangle. The height of this triangle corresponds to the pyramid's height. This height can also be derived with the Pythagorean theorem.

The altitude of the face acts as the hypotenuse of the right triangle, with half the base width being one side. The other side equates to the pyramid's height.

  height = √((10√2)² -5²) = √175 = 5√7

The pyramid's height is 5√7 cm.

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c) The volume is determined using the formula...

  V = (1/3)Bh

where B represents the base area (100 cm²) determined earlier, and h stands for the height (5√7 cm) calculated in section (a).

  V = (1/3)(100 cm²)(5√7 cm) = (500/3)√7 cm³.... pyramid volume

Response:

If there are "p" pounds of peanuts and "m" pounds of a mixture containing '20% peanuts and 80% almonds', then we can formulate the following equations:

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

The solution yields 5 lb peanuts and 5 lb mixture.

Detailed explanation:

In the mixture that Delaney desires to create, there will be

lb

= 6 lb of peanuts

Thus, there will be (10 - 6) lb

= 4 lb of almonds

If Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then based on the problem statement,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

From equation (2), we derive

m = 5 --------------(3)

From (1) and (3), we find that

p = (10 - 5) = 5

In each instance, when it sheds a shell, its size increases by a factor of 1 1/3. To determine the growth after the first molt, multiply 1 cm by 1 1/3 to get 1 1/3 cm. To find the next size, repeat the multiplication: 1 1/3 cm times 1 1/3 cm equals 16/9. This process will continue by multiplying by 1 1/3. We can express it mathematically as (initial size) * 1 1/3 *(number of shells) equals length or 1 cm * 1 1/3 * n equals L. Given that the final length is 10 cm, accordingly, 1 1/3 * n equals 10 cm, leading to n being 7.5 shells, which translates to either about 7 or 8 shells.

Answer:

The sequence decreases by 5

thus the subsequent numbers are

-13,-18,-23,-28

Answer:

Indeed, having 15 people recognize the brand would be considered unusual, as it lies beyond 2 standard deviations from the average.

Step-by-step explanation:

Examine the provided data.

The average recognition rate for the Yummy brand name among groups is 12.5, with a standard deviation of 0.58.

Mean = μ= 12.5  

σ = 0.58

n = 15

Thus, having 15 people recognize the brand would indeed be unusual, as it is outside of the 2 standard deviations from the mean.