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puteri [66]
3 years ago
13

8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm

on difference is -2 .​
Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Answer:

a₁ = 38

Step-by-step explanation:

Given AP, where:

  • 8a₈ = 12a₁₂
  • d = -2,
  • a₁ = ?

=============

<h3>Solution</h3>

aₙ = a₁ + (n-1)d

  • a₈ = a₁ + 7d = a₁ + 7*(-2) = a₁ - 14
  • a₁₂ = a₁ + 11d = a₁ + 11*(-2) = a₁ - 22

8a₈ = 12a₁₂

  • 8(a₁ - 14) = 12(a₁ - 22)
  • 2(a₁ - 14) = 3(a₁ - 22)
  • 2a₁ - 28 = 3a₁ - 66
  • 3a₁ - 2a₁ = -28 + 66
  • a₁ = 38
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Colin invests £2350 into a savings account. The bank gives 4.2% compound
marin [14]

Answer:

Answer:

£3692

Step-by-step explanation:

A = p(1 + r/n)^nt

Where,

A = future value

P = principal = £2350

r = interest rate = 4.2% = 0.042

n = number of periods = 1(annual)

t = time = 4 years

A = p(1 + r/n)^nt

= 2350(1 + 0.042/1)^1*4

= 2350(1 + 0.042)^4

= 2350(1.042)^4

= 2350(1.5789)

= 2770.42

A = £2770.42

Total years = 10

Remaining years = 10 – 4

= 6 years

Remaining 6 years

P = £2770.42

r = 4.9% = 0.049

n = 1

t = 6

A = p(1 + r/n)^nt

= 2770.42(1 + 0.049/1)^1*6

= 2770.42(1 + 0.049)^6

= 2770.42(1.049)^6

= 2770.42(1.3325)

= 3691.59

A = £3691.59

Approximately £3692

Thank you!

5 0
3 years ago
Which equation has a zero slope and y-intercept of -2?
slava [35]

Answer:

It is D

Step-by-step explanation:

6 0
3 years ago
1. How many variables are involved in the chi-square test?
GarryVolchara [31]

The result of the respective questions are:

  • This chi-square test only takes into consideration one variable.
  • The  type of chi-square test this is is a Goodness of Fit
  • df= 3
  • NO

<h3>How many variables are involved in the chi-square test?</h3>

a)

This chi-square test only takes into consideration one variable.

b)

The  type of chi-square test this is, is a Goodness of Fit

To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.

The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.

c)

Parameter

n = 4

Therefore

Degrees of freedom

df= n - 1

df= 4 - 1

df= 3

d)

In conclusion

Parameters

\alpha = 0.05

df = 3

Hence

Critical value = 7.814728

Test statistic = 6.6

Test statistic < Critical value, .

NO, the result of this test is not statistically significant.

Read more about Probability

brainly.com/question/11234923

#SPJ1

3 0
2 years ago
Question 11 (2.5 points)
Rama09 [41]

Answer:

D

Step-by-step explanation:

The answer is d, because a represents adults, and c represent children. It's $45 per adult, so $45a, and $30 per child, so $30c. a+c is equal to 10, because that's how many tickets were purchased. $45a+$30c=345, because $345 is the total amount spent on tickets.

3 0
3 years ago
Which number is between 6 1/8 and 64 squared?
lesya [120]

Answer:

Do you have a photo or picture of this question, I don't want to give you the incorrect answer because something was missing.

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