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3 years ago

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A powdered drink mix calls for a ratio of powder to water of 1:8. If there are 32 cups of powder, how many total cups of water a

re needed? Explain

1 answer:

Kruka [31]3 years ago

7 0

256 are needed because 32x1=32 that means the ratio would be 32:256 because 8 x 32 = 256
The final ratio would stay the same as 1:8 though because it would be simplified.
Hope this helped.

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Use the graph of f "(x) below to state x-coordinates of the inflection points for the graph of f(x).

Kipish [7]

0 an 4 are the answers ok

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3 years ago

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Help me please I’m not sure about this

frutty [35]

easy, 36/6=6

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2 years ago

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Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the

dem82 [27]

Answer:

I = 91.125

Step-by-step explanation:

Given that:

$I = \int \int_E \int zdV$ where E is bounded by the cylinder $y^2 + z^2 = 81$ and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and $y^2 + z^2 = 81$

∴ $z^2 = 81 - y^2$

$z = \sqrt{81 - y^2}$

Thus, z lies between 0 to $\sqrt{81 - y^2}$

GIven curve x = 0 and y = 9x

$x =\dfrac{y}{9}$

As such,x lies between 0 to $\dfrac{y}{9}$

Given curve x = 0 , $x =\dfrac{y}{9}$ and z = 0, $y^2 + z^2 = 81$

y = 0 and

$y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9$

∴ y lies between 0 and 9

Then $I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0$

$I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}$

I = 91.125

4 0

3 years ago

If x = 1 is a common root of ax² +ax + 2 = 0 and x² + x + b = 0 , then ab =

vodka [1.7K]

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0 x² + x + b = 0

a*1² +a*1 + 2 = 0 1² + 1 + b = 0

a +a + 2 = 0 1 + 1 + b = 0

2a + 2 = 0 2 + b = 0

2a = - 2 b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

6 0

3 years ago

Event v occurs 28% of the time on Tuesdays.

vampirchik [111]

Answer:

68%

Step-by-step explanation:

Probability of occurrence of Event v = P(v) = 28% = 0.28

Probability of occurrence of both Events v and Event w together = P(v and w) = 19% = 0.19

We have to find what is the probability that event w occurs with event v given that event v occurs on a Tuesday. This is a conditional probability. In other words we have to find what is the probability of event w given that event v occurs of Tuesday. i.e we have to find P(w|v)

The formula to calculate this conditional probability is:

$P(w|v) = \frac{P(v \cap w)}{P(v)}$

Using the given values, we get:

$P(w|v) = \frac{0.19}{0.28}\\\\ P(w|v) = 0.68\\\\ P(w|v) = 68\%$

Therefore, the probability that even w will occur with event v given that event v occurs on Tuesday is 68%

7 0

2 years ago