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3 years ago

3/4, 1, 5/4 find the 22nd & 43rd terms

Mathematics

1 answer:

natali 33 [55]3 years ago

6 0

Answer:

6 and 45/4

Step-by-step explanation:

If the first three terms of your sequence are 3/4, 1, 5/4, the first term is obviously 3/4 and the common difference is 1/4. This is an arithmetic sequence.

We can write a general formula for the nth term of this sequence as follows:

a(n) = a(1) + (n-1)(1/4), or, since a(1) = 3/4,

a(n) = 3/4 + (n-1) / 4

Then a(22) = 3/4 + (22-1)/4, or 3/4 + 21/4, or 24/4, or just 6.

a(43) = 3/4 + (43-1)/4, or 3/4 + 42/4, or 45/4.

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The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3

Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is $258.75\ in^3$ .

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

$Volume = Length\times height\times width$

Substitute all given value in above formula.

$258.75 = (h-4)\times h\times 3$

Rewrite the equation as:

$258.75 = 3h(h-4)$

$258.75 = 3h^2-12h$

$3h^2-12h-258.75=0$

whole equation divided by 3.

$h^2-4h-86.25=0$

Use quadratic formula with $a = 1, b = -4,c=-86.25$

$h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}$

Put these a, b and c value in above equation.

$h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}$

$h=\frac{4\pm \sqrt{16+345}}{2}$

$h=\frac{4\pm \sqrt{361}}{2}$

$h=\frac{4\pm 19}{2}$

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$h=\frac{23}{2}$

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For negative sign

$h=\frac{-15}{2}$

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We take positive value of h.

Therefore, the height of the box h = 11.5 in

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3 years ago

In how many ways can you choose 2 side dishes out of 8

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Total number of ways to pick 2 out of 8 = (8 x 7) = 56 ways .

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That doesn't mean you can get 56 different sets of 2 side dishes.

For each different pair, there are 2 ways to choose them . . .
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