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Marina86 [1]
3 years ago
12

A square pyramid has a base area of 64 ft2. The pyramid’s total surface area is 224 ft2.

Mathematics
1 answer:
borishaifa [10]3 years ago
5 0

The area of each triangular face is 40 square feet

<em><u>Solution:</u></em>

Given that,

Square pyramid has a base area of 64 square feet

The pyramid’s total surface area is 224 square feet

The total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base

<em><u>Therefore, total surface area of square pyramid is given as,</u></em>

Total surface area = base area + 4(Area of traingular face)

Let "x" be the area of each traingular face

224 = 64 + 4(x)\\\\224 - 64 = 4x\\\\4x = 160\\\\x = 40

Thus area of each triangular face is 40 square feet

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Delta makes 12-volt car batteries. These batteries are known to be normally
blondinia [14]

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the sample size n =12 -volt car batteries</em>

<em>Let  'X' be a Random variable in a normal distribution</em>

<em>Given that mean of the normal distribution = 45 months</em>

<em>Given that the Standard deviation of the normal distribution = 8months</em>

<u><em>Step(ii):-</em></u>

Let  X₁ = 3 years = 12 × 3 = 36 months

Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125

Let X₂ = 4 years  = 12 × 4 = 48 months

Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375

<u><em>Step(iii)</em></u>:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

                   = P(Z≤0.375) - P(Z≤-1.125)

                   = 0.5 +A(0.375) - (0.5-A(1.125)

                   = 0.5 + 0.1480 - (0.5 -0.3708)

                  = 0.1480 + 0.3708

                 = 0.5188

<u><em>Final answer:-</em></u>

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

<em />

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Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\&#10;t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}
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Answer:

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Step-by-step explanation:

it is because 3/1 × 3×5

so which means 9/5

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