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Serggg [28]
3 years ago
14

A G.P has its 3rd term and 7th term as 45 and 3645 respectively. what is the product of its 2nd and 4th

Mathematics
1 answer:
Ede4ka [16]3 years ago
3 0

Answer:

2,025

Step-by-step explanation:

Given:

Third term ar² = 45

Seventh term ar⁶ = 3,645

Find:

ar x ar³

Computation:

From 7th term / 3rd term

ar⁶ / ar² = 3,645 / 45

r⁴ = 81

r = 3

So,

ar² = 45

a(3)² = 45

a = 5

So,

ar x ar³

(5)(3) x (5)(3)³

2,025

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3 years ago
11) Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random
Alekssandra [29.7K]

Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.

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3 years ago
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6 0
3 years ago
F(n) = 93 + 4(n − 1)
Lunna [17]

Answer:

f(1) = 93, f(n) = f(n-1) +4

Step-by-step explanation:

The value of f(1) is:

f(1) = 93 +4\cdot (1-1)

f(1) = 93

The values for n and n-1, are respectively:

f(n-1) = 93 + 4\cdot (n-2)

f(n) = 93 + 4\cdot (n-1)

After some algebraic manipulation, the following expression is obtained:

f(n) = 93 + 4\cdot (n-2) + 4

f(n) = f(n-1) +4

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