The number of terms common to the two A.P.s 2+5+8+11+.......+98 and 3+8+13+18+....+198 are a. 33 b. 40 c. 7 d. None of these

Answers

Answer 1

Answer:

Step-by-step explanation:

To find the number of terms common to the two arithmetic progressions (APs), we can first determine the general terms of both sequences and then find their common terms.

The first AP has a common difference of 5, and the second AP also has a common difference of 5. We can write the general terms as:

First AP: a₁ = 2, a₂ = 2 + 5, a₃ = 2 + 2 * 5, ..., aₖ = 2 + (k - 1) * 5

Second AP: b₁ = 3, b₂ = 3 + 5, b₃ = 3 + 2 * 5, ..., bₖ = 3 + (k - 1) * 5

Now, we need to find when these two sequences are equal, i.e., aₖ = bₖ:

2 + (k - 1) * 5 = 3 + (k - 1) * 5

Simplifying this equation:

2 + 5k - 5 = 3 + 5k - 5

2 - 5 = 3 - 5

-3 = -3

The equation -3 = -3 is always true, which means that these two sequences are always equal for any value of k. Therefore, the number of terms common to the two APs is infinite, and the correct answer is:

d. None of these

Answer 2

Answer:

Final answer:

The number of terms common to the two arithmetic progressions is 7.

Explanation:

To find the number of terms common to the two arithmetic progressions (A.P.s), we need to compare the terms of each A.P. and count the number of terms that are the same.

The first A.P. is 2, 5, 8, 11, ..., 98. The common difference between the terms is 3.

The second A.P. is 3, 8, 13, 18, ..., 198. The common difference between the terms is also 5.

To find the common terms, we can use the formula:

Term = First Term + (n - 1) * Common Difference

For the first A.P., we have:
First Term = 2
Common Difference = 3

For the second A.P., we have:
First Term = 3
Common Difference = 5

We need to find the values of 'n' that make the terms of both A.P.s the same. By substituting the values into the formula, we can solve for 'n' and calculate the number of common terms.

The number of terms common to the two A.P.s is 7. Therefore, the answer is option c.

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Answers

The work is shown in the attachment

Find 12 1/2% of 96 men

Answers

$12(1)/(2)$ percent of 96 men is 12 men.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, $12(1)/(2)$ % of 96 men.

Here, $12(1)/(2)$ % =12.5%

Now, 12.5% of 96

12.5/100 ×96

= 0.125×96

= 12 men

Therefore, $12(1)/(2)$ percent of 96 men is 12 men.

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12 1/2 can be written as 25/2
25/2% of 96 men
25/2*100 *96
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20 points pls help someone

Answers

Answer: 5-6

Step-by-step explanation:

because it flips

The answer is 5-6

Hope this helps

X squared + ysquared-6y=-5

Answers

Standard Form of the circle:

$x^(2) +(y-3) ^(2) =14$

For y:

y=3 (+/-) $√(-x) ^(2) +14$

For x:

x= $\sqrt{-y ^(2) } +6y+5 and - √(-y) ^(2) +6y+5$

Suppose a normal distribution has a mean of 222 and a standard deviation of 16. What is the probability that a data value is between 174 and 238? Round your answer to the nearest tenth of a percent.A. 66.9%
B. 53.3%
C. 84.0%
D. 91.0%

Answers

P(174 < x < 238) = P(x < 238) - P(x < 174) = P[z < (238 - 222)/16] - P[z < (174 - 222)/16] = P(z < 1) - P(z < -3) = 0.84134 - 0.00135 = 0.83999 or 83.999%

Answer: 84.0% to the nearest tenth.

Factor : 49c^2 - 25d^6

Answers

49c^2 - 25d^6
(7c)^2 - (5d^3)^2
(7c + 5d^3)(7c - 5d^3)

The answer is: (7c + 5d^3)(7c - 5d^3).

Hello,

$49c^(2)-25d^(6)=(7c)^2-(5d^3)²=[7c-5d^3][7c+5d^3]$

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