All categories

2 years ago

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP

Mathematics

1 answer:

Ainat [17]2 years ago

7 0

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d } = 30

5(2a + 4d )d = 60

10a + 20d = 60

reduce to lowest term to easy calculation by dividing through by 10

a + 2d = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉ = ⁹/₂(2a + 8d ) = 69

9(2a + 8d ) = 30 + 69

18a + 72d = 99 x 2

18a + 72d = 198

divide through by 18 to reduce to lowest time

a + 4d = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

a + 2d = 6

a + 4d = 11

-2d = -5

d = ⁵/₂.

Now substitute for d to get a

a + 2(⁵/₂) = 6

a + 5 = 6

a = 6 - 5

a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

You might be interested in

29. Find CD.<br> 30. Find ZV.

Tems11 [23]

Answer:

for cd it's 12 I believe fs

8 0

2 years ago

Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2004 the company repor

GarryVolchara [31]

Answer:

$\mu_p -\sigma_p = 0.74-0.0219=0.718$

$\mu_p +\sigma_p = 0.74+0.0219=0.762$

68% of the rates are expected to be betwen 0.718 and 0.762

$\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696$

$\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784$

95% of the rates are expected to be betwen 0.696 and 0.784

$\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674$

$\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806$

99.7% of the rates are expected to be betwen 0.674 and 0.806

Step-by-step explanation:

Check for conditions

For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:

a) Independence : we assume that the random sample of 400 students each student is independent from the other.

b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.

c) np= 400*0.74= 296>10

n(1-p) = 400*(1-0.74)=104>10

So then we have all the conditions satisfied.

Solution to the problem

For this case we know that the distribution for the population proportion is given by:

$p \sim N(p, \sqrt{\frac{p(1-p)}{n}})$

So then:

$\mu_p = 0.74$

$\sigma_p =\sqrt{\frac{0.74(1-0.74)}{400}}=0.0219$

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

$\mu_p -\sigma_p = 0.74-0.0219=0.718$

$\mu_p +\sigma_p = 0.74+0.0219=0.762$

68% of the rates are expected to be betwen 0.718 and 0.762

$\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696$

$\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784$

95% of the rates are expected to be betwen 0.696 and 0.784

$\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674$

$\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806$

99.7% of the rates are expected to be betwen 0.674 and 0.806

5 0

3 years ago

Kenzie has. 4 pages of homework to do. If she can finish 1/3 of a page in one hour how many hours will her homework take?

Maru [420]

Answer:

It will take her 4 1/3 hours

Step-by-step explanation: so you know you needed to add 4 and 1/3 and you turn the 4 into 4/1 and 1/3 and since it adding you have to have the same denominator and you multiply 1x3 and if you do it on the bottom you have to do it on top so you also do 4x3 and 4x3 is 12 and one 1x3 is 3 and so you don't have to have to do it on the other fraction because now they have the same denominator now and now you add 12/3 + 1/3 and you shall get 13/3 and then you divide 13 divided by 3 and you shall get 4 1/3 and that shall be your answer.

hope it helps you!

5 0

3 years ago

It costs $200.00 to rent the mini-golf course, plus $7.25 per person. What would be the total cos

igor_vitrenko [27]

$417.50 should be the correct answer you just multiply the $7.25 to 30 and then add the $200.

7 0

2 years ago

Read 2 more answers

You are painting the root of a boathouse. You are going to place the base of a ladder 12 feet from the boathouse. How long does

jolli1 [7]

Answer:

37 ft

Step-by-step explanation:

The ladder forms a right triangle as it elan's against the wall of the boat house.

Thus, the length of the ladder can be determined using Pythagorean theorem.

c² = a² + b²

c = length of ladder

a = 35 ft

b = 12 ft

Plug in the values

c² = 35² + 12²

c² = 1,225 + 144

c² = 1,369

c = √1,369

c = 37

Therefore, to reach the roof of the boathouse, the length of the ladder = 37 ft

4 0

3 years ago

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP