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3 years ago

14

A soft drink machine outputs a mean of 24 ounces per cup. The machine's output is normally distributed with a standard deviation

of 3 ounces. What is the probability of filling a cup between 21 and 28 ounces? Round your answer to four decimal places.

1 answer:

Arisa [49]3 years ago

7 0

Answer:

$P(21$

And we can find the probability with this difference

$P(-1$

And using the normal standard distribution or excel we got:

$P(-1$

Step-by-step explanation:

Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:

$X \sim N(24,3)$

Where $\mu=24$ and $\sigma=3$

We want to find this probability:

$P(21$

The z score is given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we got:

$P(21$

And we can find the probability with this difference

$P(-1$

And using the normal standard distribution or excel we got:

$P(-1$

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3 years ago

X + y = 30<br><br> 2x + 4y = 84<br><br> Substitution<br> or<br> Elimination<br> I

miv72 [106K]

Answer:

(X,Y)(18,12)

Step-by-step explanation:

x + y = 30

2x + 4y = 84

___________

2x+2y=60

2x+4y=84

_________

-2y=-24/-2y

y=12

2x+4(12)=84

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2x=84-48

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3 years ago

A plane rises from take off and flies at an angle 11° with the horizontal runway. When it has gained 750 feet find the distance

kogti [31]

Answer:

$D=3930.632298 \approx 3930.6miles$

Step-by-step explanation:

From the question we are told that

Angle $\theta=11\textdegree$

Height of plane $h =750feet$

Generally the equation for the total distance flown is mathematically given by

$D=\frac{h}{sin\theta}$

$D=\frac{750}{sin11}$

Therefore total distance flown is

$D=3930.632298 \approx 3930.6miles$

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3 years ago

What is the value of the exponential expression below? 36^1/2

Dmitry [639]

Answer:

6

Step-by-step explanation:

It's the square root of 36

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3 years ago

Solve the above que no. 55

aleksandr82 [10.1K]

Answer:

Let $\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)$ , we proceed to prove the trigonometric expression by trigonometric identity:

1) $\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)$ Given

2) $\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)$ $\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}$

3) $\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)$

4) $\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)$ $\sin^{2}A+\cos^{2}A = 1$

5) $\frac{1}{\sin^{2}A\cdot \cos^{2}A}$

6) $\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}$ $\sin^{2}A+\cos^{2}A = 1$

7) $\frac{1}{\sin^{2}A-\sin^{4}A}$ Result

Step-by-step explanation:

Let $\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)$ , we proceed to prove the trigonometric expression by trigonometric identity:

1) $\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)$ Given

2) $\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)$ $\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}$

3) $\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)$

4) $\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)$ $\sin^{2}A+\cos^{2}A = 1$

5) $\frac{1}{\sin^{2}A\cdot \cos^{2}A}$

6) $\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}$ $\sin^{2}A+\cos^{2}A = 1$

7) $\frac{1}{\sin^{2}A-\sin^{4}A}$ Result

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3 years ago