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kirill115 [55]
2 years ago
15

To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade

of purple paint, how many gallons of red and blue paint should be used?
Mathematics
1 answer:
Gelneren [198K]2 years ago
4 0

Answer:

quantity of red paint =  12.5 gallons

quantity of blue paint =  7.5  gallons

Step-by-step explanation:

Ratio of red and blue paint : 5:3

in ratio

a:b = ax:bx

let the

quantity of red paint be 5x

quantity of blue paint be 3x

then quantity of purple paint = quantity of red paint  + quantity of blue paint

                                                  = 8x

given quantity of purple paint is 20 gallons

thus,

8x = 20

x = 20/8 = 2.5

thus,

quantity of red paint = 5x = 5*2.5 = 12.5 gallons

quantity of blue paint = 3x = 3x*2.5 = 7.5  gallons

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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y2 = 25 (a) Fin
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Answer:

(a) \frac{dy}{dt}=-3\frac{3}{4}

(b) \frac{dx}{dt}=3\frac{3}{4}

Step-by-step explanation:

x^{2} +y^{2}=25

Take \frac{d}{dt} of of each term.

\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\

For Question a

2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}

Given that x = 3, y = 4, and dx/dt = 5.

\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\   \\\frac{dy}{dt}=-3\frac{3}{4}

For Question b

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Given that x = 4, y = 3, and dx/dt = -5.

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Step-by-step explanation:

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The mapping diagram shows a functional relationship
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Answer:

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Step-by-step explanation:

Domain is the set of x values that make the function defined. Allowed x values for the function (mapping).

The Range is the set of y values that make the function defined. Allowed y values for the function (mapping).

  • Whenever we need to find f(a), suppose, then we look for "a" in the domain and see its corresponding value mapping in the range.
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Firstly, we need f(4), so we look for "4" in domain and see which number it corresponds to in range.

That is \frac{1}{2}

Thus,

f(4)=\frac{1}{2}

Next,

We want "x" value that gives us a "y" value of 4. We look for "4" in the range and see which value it corresponds to. That is "8". So,

f(8) = 4

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2 years ago
Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs. (a) The percentage of households in
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Answer:

a) The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

\hat p=\frac{7}{500}=0.014

And that represent the 1.4%.

b) And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

Step-by-step explanation:

Data given and notation  

n=500 represent the random sample taken    

X=7 represent the households with three or more large-screen TVs

\hat p=\frac{7}{500}=0.014 estimated proportion of households with three or more large-screen TVs

\alpha=0.05 represent the significance level (no given, but is assumed)    

z would represent the statistic (variable of interest)    

p= population proportion of households with three or more large-screen TVs

Part a

The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

\hat p=\frac{7}{500}=0.014

And that represent the 1.4%.

Part b

Yes is possible. We hav that np>10 and n(1-p)>10 so we have the assumption of normality to find the interval.

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

And replacing into the confidence interval formula we got:

0.014 - 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.00370

0.014 + 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.0243

And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

4 0
2 years ago
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