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Aleksandr [31]
3 years ago
5

Find S12 for the series 2 + 5 + 8 +...

Mathematics
2 answers:
Svetllana [295]3 years ago
7 0
Hi, I'm pretty sure by S12 you mean the sum of all the 12 terms in the series 2 + 5 + 8 + .....

Then, first you find the pattern:
5 -2 = 3
8 -5 = 3
This is an arithmetic series with a common difference of 3. Next, we find the last term, or the 12th term.

A12 = A1 + (n - 1)d
A12 = 2 + (12 - 1)3
A12 = 35

Since, we know the first and last terms of the series, we could find the sum by this formula:

S = (n/2)*(A1 + A12)
S = (12/2) * (2 + 35)
S = 222

The answer is 222.
olga55 [171]3 years ago
4 0
2+5+8+11+14+17+20+23+26+29+32+35
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The sum of two numbers is 12. One number is prime and the other is composite. What are the numbers?
kompoz [17]
9 and 3. Because 9 is a composite number (3*3 = 9) and 3 is a composite number (1*3 = 3).

4 0
3 years ago
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Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coheren
Leno4ka [110]

Answer:

A simple way to mentally subtract is to simplify the numbers, subtract, then subtract or add for the simplified answer.

Step-by-step explanation:

A simple way to mentally subtract is to simplify the numbers, subtract, then subtract or add for the simplified answer. For this 304 - 81 is easier as 300 - 80. Make note that we took away 4 from 304 and 1 from 81. Now we just subtract mentally, and 300 - 80 = 220. If we took 4 from 304, this means that our answer should be 4 less, since 4 less would be 304 - 80 = 216. If we took 1 from 81, then we add 1 back to get the equation 304 - 81 = 217.

304 - 81 = ?

300 - 80 = 220

304 - 80 = 216

304 - 81 = 217

7 0
3 years ago
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Which function is the inverse of f(x) = 2x + 3 ?<br> Help
bearhunter [10]

Answer:

The inverse is 1/2x -3/2

Step-by-step explanation:

y =2x+3

Exchange x and y

x = 2y+3

Solve for y, subtracting 3 from each side

x-3 = 2y+3-3

x-3 =2y

Divide each side by 2

(x-3)/2 = 2y/2

1/2x - 3/2 =y

The inverse is 1/2x -3/2

7 0
3 years ago
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A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small
True [87]

Answer:

95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.

Step-by-step explanation:

Confidence interval is given by mean +/- margin of error (E)

Eggs from small nest

Sample size (n1) = 60

Mean = 37.2

Sample variance = 24.7

Eggs from large nest

Sample size (n2) = 159

Mean = 35.6

Sample variance = 39

Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11

Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93

Difference in mean = 37.2 - 35.6 = 1.6

Degree of freedom = n1+n2 - 2 = 60+159-2 = 217

Confidence level = 95%

Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132

E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79

Lower limit = mean - E = 1.6 - 0.79 = 0.81

Upper limit = mean + E = 1.6 + 0.79 = 2.39

95% confidence interval for the difference in average mass is (0.81, 2.39)

3 0
2 years ago
The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round
Andrews [41]

Answer:

Shorter leg = 2.5 ft.

Longer leg = 6.5 ft.

Step-by-step explanation:

a^2 + b^2 = c^2

Because the hypotenuse = 7 ft, a^2 + b^2 = 49

To represent the two legs, we can use x and x+4.

x^2 + (x+4)^2 = 49

Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.

Then, using the quadratic formula, we find that x = 2.5.

Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.

5 0
2 years ago
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