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iogann1982 [59]

3 years ago

10

A doctor's prescription calls for a daily intake containing 50 mg of vitamin C and 10 mg of vitamin D. Your pharmacy stocks two

compounds that can be used: one contains 80% vitamin C and 10% vitamin D, the other 40% vitamin C and 20% vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

1 answer:

blagie [28]3 years ago

8 0

Setup
0.8x + 0.4y = 50
0.1x + 0.2y = 10 - Multiply by -2 and add

get
0.6x = 30
x = 50 mg compound A

.1 (50) + .2y = 10
5 + .2y = 10
.2y = 5
y = 25 mg compound B

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Nata [24]

Answer:

<em>8 C sometimes</em>

<em>9 64x^8 y^11</em>

<em>10 c 1.28r^2/ t^9</em>

Step-by-step explanation:

<u>Algebraic Operations </u>

Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:

$\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}$

$\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}$

$\displaystyle x^{-n}=\frac{1}{x^n}$

Let's face the questions at hand

8. A number is raised to a negative exponent is negative?

Following the expressions recalled above, let's pick the expression

$\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}$

This is a negative power resulting in a positive number

Now we pick

$\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}$

This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result

<em>Answer: C sometimes </em>

9 simplify(4xy^2)^3(xy)^5

$(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5$

$=64x^3y^6x^5y^5$

$=64x^8y^{11}$

10 simplify(2t^-3)^3(0.4r)^2

$(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2$

$=8t^{-9} 0.16 r^2$

$=1.28t^{-9} r^2$

$\displaystyle \frac{1.28 r^2}{t^9}$

7 0

3 years ago

nadya68 [22]

Answer: Heyaa! :)

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<em>Slope: </em>−1

<em>y-intercept: </em>(0,−3)

<em>2. y=4x-5 =</em> 4

<em>Slope:</em> 4

<em>y-intercept: </em>(0,−5)

<em>3. 2x-y=-2 =</em> 2

<em>Slope:</em> 2

<em>y-intercept:</em> (0,2)

<em>4. x+y=4 =</em> 1

Slope: −1

<em>y-intercept:</em> (0,4)

<em>5. 3x+4y=-12 = - 3/4</em>

<em>Slope: </em>−3/4

<em>y-intercept: </em>

(0,−3)

Hopefully this helps<em> you!</em>

<em />

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4 0

2 years ago

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GrogVix [38]

Here is the order

- 6 2/3 ,- 1.3 , 29/8 , 7

5 0

3 years ago

6.<br> -20 + -2m<br> Can u help me

stellarik [79]

Answer

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Replace all occurrences of

+

−

with a single

−

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1

⋅

−

1

=

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−

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2

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4 0

3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago