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2 years ago

10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

Mathematics

2 answers:

Tanya [424]2 years ago

5 0

Answer:

-13

Step-by-step explanation:

"Arithmetic sequence" is a big clue, because it means you add on the same amount every time the term number goes up by 1, then add on the same amount to the numbers in the sequence (the list of numbers) see image There are of course formulas to find these missing numbers, but also, crunch it out sometimes so that it makes sense. And when the numbers in the question get crazy you can fall back on the formulas.

9966 [12]2 years ago

4 0

$a_{5}=a+4d=11\\a_{10}=a+9d=41$

Solve the above equations,

$a_{10}-a_{5}=41-11\\a+9d-a-4d=30\\5d=30\\d=6\\a=11-24=-13$

First term is -13.

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Two numbers are in the ratio 3:5. If one of them is greater than the other by 10,Find the smaller number.

alisha [4.7K]

Answer:

smaller number = 15

Step-by-step explanation:

Let the two numbers be 5x and 3x respectively.

According to the question —

5x — 3x = 10

2x = 10

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Thus the smaller number is 3 × 5 = 15

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3 years ago

Read 2 more answers

Find the dimensions of the rectangle with area 289 square inches that has minimum perimeter, and then find the minimum perimeter

nalin [4]

<span>To minimize the perimeter you should always have a square.
sqrt(289) = 17
The dimensions should be 17 X 17

To see , try starting at length 1, and gradually increase the length.
The height decreases at a faster rate than the length increases, up until you reach a square.

Or if you want to use algebra, Say the width is 17-x
Then the length is 289/(17-x)

Now, this is bigger than 17+x, as shown here:
289/(17-x) > 17+x
289 > 289 - x^2
which is true.
so the perimeter would be bigger than 2 * (17- x + 17 + x) = 2 * (2 * 17) = 4 * 17

Again, the dimensions should be a square. 17 X 17.</span>

4 0

3 years ago

uppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for

vodka [1.7K]

Answer:

The answer is "294.2075".

Step-by-step explanation:

Given:

$\hat{p} = 0.5 \\\\1 - \hat{p} = 1 - 0.5 = 0.5\\\\E = 4\% = 0.04\\\\$

At $83\%$ confidence level the z is ,

$\alpha = 1 - 83\% = 1 - 0.83 = 0.17\\\\\frac{\alpha}{2} = \frac{0.17}{2} = 0.085\\\\Z_{\frac{\alpha}{2}} = Z_{0.085} = 1.3722\\\\n = (\frac{Z_{\frac{\alpha}{2}}}{E})^2 \times \hat{p} \times (1 - \hat{p})\\\\$

$= (\frac{1.3722}{0.04})^2 \times 0.5 \times 0.5\\\\= (34.305)^2 \times 0.5 \times 0.5\\\\= 1,176.83 \times 0.5 \times 0.5\\\\= 1,176.83 \times 0.25\\\\=294.2075$

5 0

3 years ago

Any suggestions or answers

Studentka2010 [4]

your answer should be c.

A water balloon holds roughly 1.5 oz. of water

and pat has 19 water balloons to fill.

Multiply 1.5 and 19 and you get 28.5, or about 30 oz.

hope i helped!

3 0

3 years ago

Please help me this is very important due today

alexdok [17]

Answer:

I'd say D) a worried young man

4 0

3 years ago

10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term? ​

10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?