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2 years ago

Which expression is equivalent to this one? u · 5 + u · v A. u(5 + v) B. 5(u + v) C. v(5 + u) D. u · (5 + u) · v

1 answer:

4 0

We know: The distribution of multiplication by addition
and that means A is suitable
m*a+n*a= a*(m+n)=(m+n)*a
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A simple random sample of size n=40 from a population with mu = 74 and standard deviation= 7. Does the population need to be nor

Maurinko [17]

Answer:

Step-by-step explanation:

How does lack of sleep affect risk of injury

5 0

3 years ago

(+6) + (+4) + (+6) + (+5) simplify

Neporo4naja [7]

Answer: 21

1) simplify 6+4 to 10

10+6+5

2) simplify 10+6 to 16

16+5

3) simplify

21

3 0

3 years ago

[tex]cos {}^{4} α+sin {}^{4} α= \frac{1}{4} (3+cos4α) Prove:

asambeis [7]

Given:

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

To prove:

The given statement.

Proof:

We have,

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

$LHS=\cos^4 \alpha+\sin^4\alpha$

$LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2$

$LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha$ $[\because a^2+b^2=(a+b)^2-2ab]$

$LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha$ $[\because \cos^2 \alpha+\sin^2\alpha=1]$

$LHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

Now,

$RHS=\dfrac{1}{4}(3+\cos 4 \alpha)$

$RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]$

$RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]$ $[\because (a-b)^2=a^2-2ab+b^2]$

$RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]$

$RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]$

$RHS=1+2\cos^4 \alpha-2\cos \alpha$

$RHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

$LHS=RHS$

Hence proved.

8 0

3 years ago

Please help!! A. 170 B. 205 C. 230 D. 105

Damm [24]

Answer:

D. 105

Step-by-step explanation:

500-270, there's 230 total 2 head.

270-100 of one head, is 170 purple one head. 170+125 purple equals 295.

296 subtract from 500 total is 205 for total green.

205-100, 105 2 head.

8 0

2 years ago

Help #4-8 please thank you

Olin [163]

Answer:

#4: 130/60, simplified is 13/6 (divide numerator and denominator by 10)

#5: 110/130, simplified is 11/13 (divide numerator and denominator by 10)

#6: 5/12

#7: 4/12, simplified is 1/3 (divide numerator and denominator by 4)

#8: 12/4, simplified is 3, or 3/1 (divide numerator and denominator by 4)

Step-by-step explanation:

#4: Part 1 is 60 miles, and the whole trip is 60 + 20 + 50 = 130 miles

So while #1 was 60 over 130 for "60 to 130", now we'll put the 130 on top of the 60 for "130 to 60" as a spoken ratio

#5: I think they mean add part 1 to part 3, then compare to the whole.

so 60 + 50 = 110, and your answer is 110/130

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Punch: 3 pints Hawaiian punch, 4 pints of orange juice, 5 pints of ginger ale is the recipe. When you pour that all together, you have 3 + 4 + 5 pints of mixed punch as a total, or 12 pints.

#6: 5 pints of ginger ale to 12 pints of punch: 5/12

#7: 4 pints of orange juice to 12 pints of punch: 4/12

#8 12 pints of the whole drink to 4 pints of orange juice: 12/4

6 0

2 years ago