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3 years ago

Find the least common denominator for the fractions 3 4 and 1 12 . A) 8 B) 12 C) 16 D) 24

Mathematics

2 answers:

Aleks [24]3 years ago

6 0

B) 12. Both are divisible by that denominator, the it's the lowest number of which they are both factors.

OleMash [197]3 years ago

6 0

12 because they are both divisible

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Someone help me please

irinina [24]

Answer:

16/8 or 2

Step-by-step explanation:

1/8 ×?=16/8

?=16/8÷1/8

?=16/8 or 2

I hope that helps :)

8 0

3 years ago

Place parenthesis

ozzi

9514 1404 393

Answer:

7+(7–7) ÷(7+7•7)= 7

Step-by-step explanation:

The difference 7 - 7 provides an opportunity to zero out everything to its right. That's what we've done in this version:

7 +(7 -7) ÷ (7 +7×7) = 7 . . . our version of the equation

7 +0 ÷ (7 +49) = 7 . . . . . multiplication inside parentheses first

7 +0 ÷ 56 = 7 . . . . . . . . parentheses first

7 +0 = 7 . . . . . . . . . . . . division before addition

5 0

3 years ago

Which best describes the graph of a quadratic function witha discriminant of -7?

Anettt [7]

That means that it has 2 complex roots, and it has no x intercepts, means that it doesn't touch the x axis at all

6 0

3 years ago

Let C(n, k) = the number of k-membered subsets of an n-membered set. Find (a) C(6, k) for k = 0,1,2,...,6 (b) C(7, k) for k = 0,

vladimir1956 [14]

Answer:

(a) $C(6,0) = 1$ , $C(6,1) = 6$ , $C(6,2) = 15$ , $C(6,3) = 20$ , $C(6,4) = 15$ , $C(6,5) = 6$ , $C(6,6) = 1$ .

(b) $C(7,0) = 1$ , $C(7,1) = 7$ , $C(7,2) = 21$ , $C(7,3) = 35$ , $C(7,4) = 35$ , $C(7,5) = 21$ , $C(7,6) = 7$ , $C(7,7)=1$ .

Step-by-step explanation:

In this exercise we only need to recall the formula for C(n,k):

$C(n,k) = \frac{n!}{k!(n-k)!}$

where the symbol $n!$ is the factorial and means

$n! = 1\cdot 2\cdot 3\cdot 4\cdtos (n-1)\cdot n$ .

By convention 0!=1. The most important property of the factorial is $n!=(n-1)!\cdot n$ , for example 3!=1*2*3=6.

(a) The explanations to the solutions is just the calculations.

$C(6,0) = \frac{6!}{0!(6-0)!} = \frac{6!}{6!} = 1$

$C(6,1) = \frac{6!}{1!(6-1)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2\cdot 4!} = \frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!\cdot 3!} = \frac{5!\cdot 6}{6\cdot 6} = \frac{5!}{6} = \frac{120}{6} = 20$

$C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4!\cdot 2!} = frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,5) = \frac{6!}{5!(6-5)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,6) = \frac{6!}{6!(6-6)!} = \frac{6!}{6!} = 1$ .

(b) The explanations to the solutions is just the calculations.

$C(7,0) = \frac{7!}{0!(7-0)!} = \frac{7!}{7!} = 1$

$C(7,1) = \frac{7!}{1!(7-1)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,2) = \frac{7!}{2!(7-2)!} = \frac{7!}{2\cdot 5!} = \frac{6!\cdot 7}{2\cdot 5!} = \frac{5!\cdot 6\cdot 7}{2\cdot 5!} = \frac{6\cdot 7}{2} = 21$

$C(7,3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3!\cdot 4!} = \frac{6!\cdot 7}{6\cdot 4!} = \frac{5!\cdot 6\cdot 7}{6\cdot 4!} = \frac{120\cdot 7}{24} = 35$

$C(7,4) = \frac{7!}{4!(7-4)!} = \frac{6!\cdot 7}{4!\cdot 3!} = frac{5!\cdot 6\cdot 7}{4!\cdot 6} = \frac{120\cdot 7}{24} = 35$

$C(7,5) = \frac{7!}{5!(7-2)!} = \frac{7!}{5!\cdot 2!} = 21$

$C(7,6) = \frac{7!}{6!(7-6)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,7) = \frac{7!}{7!(7-7)!} = \frac{7!}{7!} = 1$

For all the calculations just recall that 4! =24 and 5!=120.

6 0

2 years ago

The value of the definite integral / 212x – sin(x) dx / 122x-sin(x) is

blondinia [14]

Hi there!

$\boxed{= 70 + cos(12) - cos(2) \approx 71.26}$

$\int\limits^{12}_{2} {x-sin(x)} \, dx$

We can evaluate using the power rule and trig rules:

$\int x^n = \frac{x^{n+1}}{n+1}$

$\int x = \frac{1}{2}x^{2}$

$\int -sin(x) = cos(x)$

Therefore:

$\int\limits^{12}_{2} {x-sin(x)} \, dx = [\frac{1}{2}x^{2}+cos(x)]_{2}^{12}$

Evaluate:

$(\frac{1}{2}(12^{2})+cos(12)) - (\frac{1}{2}(2^2)+cos(2))\\= (72 + cos(12)) - (2 + cos(2))\\\\= 70 + cos(12) - cos(2) \approx 71.26$

3 0

3 years ago