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Misha Larkins [42]
3 years ago
8

A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first

term (ii) 6th term of the sequence​
Mathematics
1 answer:
EleoNora [17]3 years ago
8 0

Answer:

Step-by-step explanation:

r is the common ratio.

Third term minus first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

Fourth term minus second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

:::::

r²-1 = 48/a₁

a₁ = 6

:::::

a₆ = a₁r⁵ = 1458

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Solve the equation:<br><br> 5x-2=X+4
ElenaW [278]

Answer: x = 1.5

Step-by-step explanation:

5x - 2 = x + 4

Add 2 to each side

5x = x + 6

Subtract x from each side

4x = 6

Divide each side by 4

x = 1.5

6 0
3 years ago
Read 2 more answers
Describe two different ways to solve: -10=1/4(8y-12)
timurjin [86]
There are two ways to approach this question. The first is to divide both sides of the equation by 1/4, which is the same as multiplying by 4.
4*(-10)=4*(1/4)(8y-12)
-40=1(8y-12)
-40=8y-12
-40+12=8y-12+12
-28=8y
-28/8=8y/8
-3.5=y
Another method is to distribute 1/4 to each term within the parentheses.
-10=8y*(1/4) - 12*(1/4)
-10=2y - 3
-10+3=2y - 3 +3
-7=2y
-7/2= 2y/2
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I hope this is helpful!
3 0
3 years ago
paid after the grace period, on average, more than 4 times in 2018, what are the null and alternative hypotheses? Select the cor
Mila [183]

Answer:

<em>H</em>₀: <em>μ</em> = 4 vs. <em>H ₐ</em>: <em>μ </em>> 4

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by H ₐ.

In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.

The hypothesis can be defined as follows:

<em>H</em>₀: <em>μ</em> = 4 vs. <em>H ₐ</em>: <em>μ </em>> 4

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3 years ago
A parking lot has two entrances. Cars arrive at entrance I according to a Poisson distribution at an average of 3 per hour and a
olga_2 [115]

Answer:

P(X=3cars) = 0.052

P(X>3 cars) = 0.00638

Step-by-step explanation:

In total there are 7 cars per hour.

Using formulae for geometric Probability

P(X=3) = (7^3×e-7)/3! = 0.0521

P(X>3cars) = (7^2× e-7)/2! =

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7 0
2 years ago
Pls Help thanks :)<br><br><br><br> ......
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