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3 years ago

Solving systems of equations using substitution -4x-y=16 Y=-8

Mathematics

1 answer:

Goshia [24]3 years ago

7 0

ᑕᒪIᑕK Oᑎ ᑭIᑕ ᖴOᖇ ᑭᖇOOᖴ

᙭= -2

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Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, nor

kenny6666 [7]

Answer:

a) 0.0167

b) 0

c) 5.948

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6.16 ounces

Standard Deviation, σ = 0.08 ounces

We are given that the distribution of fill volumes of bags is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) Standard deviation of 23 bags

$\displaystyle\frac{S.D}{\sqrt{23}} = \frac{0.08}{\sqrt{23}} = 0.0167$

b) P( fill volume of 23 bags is below 5.95 ounces)

P(x < 5.95)

$P( x < 5.96) = P( z < \displaystyle\frac{5.95 - 6.16}{0.0167}) = P(z < -12.57)$

$= 1 - P(z < 12.57)$

Calculation the value from standard normal z table, we have,

$P(x < 5.95) = 1 - 1 = 0$

c) P( fill volume of 23 bags is below 6 ounces) = 0.001

P(x < 6) = 0.001

$P( x < 6) = P( z < \displaystyle\frac{6 - \mu}{0.0167})$

Calculation the value from standard normal z table, we have,

$P( z \leq -3.09) = 0.001$

$\displaystyle\frac{6 - \mu}{0.0167} = -3.09\\\\\mu = 6 + (0.0167\times -3.09) = 5.948$

If the mean will be 5.948 then the probability that the average of 23 bags is below 6.1 ounces is 0.001.

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3 years ago

The circumference of a circle is like the ________ of a figure.

adelina 88 [10]

Answer:

The answer would be 'B. perimeter'.

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3 years ago

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nikdorinn [45]

Answer:

Step-by-step explanation:

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Find the equation of the line specified. The line passes through the points

marishachu [46]

Answer:

Step-by-step explanation:

substitute (2,1) and (5,4) into each equation

2-1=1 and 5-4=1 so c is correct

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3 years ago

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Barb is making a banner that is shaped like a trapezoid the height of the banner is 24 inches the top of the banner is it 14 inc

velikii [3]

Answer:

The length of the bottom side of the banner is 17 in.

Step-by-step explanation:

Given,

Area of the Banner = $372\ in^2$

Height of the Banner = 24 in

Top side of the Banner = 14 in

We have to find the length of the bottom side of the banner.

Solution,

Let the length of the bottom side of the banner be 'x'.

Since the banner is in the shape of trapezoid.

So according to the formula of area of trapezoid, which is;

Area of trapezoid = $\frac{1}{2}\times \textrm{sum of parallel sides}\times \textrm{distance between them}$

Here top and bottom sides are parallel and distance between them is equal to the height of the banner.

Now substituting the values, we get;

$\frac{1}{2}\times24\times(x+14)=372\\\\12(x+14)=372\\\\x+14=\frac{372}{12}\\\\x+14=31\\\\x=31-14=17\ in$

Hence The length of the bottom side of the banner is 17 in.

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3 years ago