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3 years ago

Can someone help, thanks!

Mathematics

1 answer:

Marina86 [1]3 years ago

4 0

Answer:

16, 10

Step-by-step explanation:

There are 4 quarts in a gallon, so 4 gallons has 16 qt.

There are 2 pints in a quart, so 5 quarts has 10 pt.

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Alice searches for her term paper in her filing cabinet, which has several drawers. She knows thatshe left her term paper in dra

katen-ka-za [31]

You made a mistake with the probability $p_{j}$ , which should be $p_{i}$ in the last expression, so to be clear I will state the expression again.

So we want to solve the following:

Conditioned on this event, show that the probability that her paper is in drawer $j$ , is given by:

(1) $\frac{p_{j} }{1-d_{i}p_{i} } , if j \neq i,$ and

(2) $\frac{p_{i} (1-d_{i} )}{1-d_{i}p_{i} } , if j = i.$

so we can say:

$A$ is the event that you search drawer $i$ and find nothing,

$B$ is the event that you search drawer $i$ and find the paper,

$C_{k}$ is the event that the paper is in drawer $k, k = 1, ..., n.$

this gives us:

$P(B) = P(B \cap C_{i} ) = P(C_{i})P(B | C_{i} ) = d_{i} p_{i}$

$P(A) = 1 - P(B) = 1 - d_{i} p_{i}$

Solution to Part (1):

if $j \neq i$ , then $P(A \cap C_{j} ) = P(C_{j} )$ ,

this means that

$P(C_{j} |A) = \frac{P(A \cap C_{j})}{P(A)} = \frac{P(C_{j} )}{P(A)} = \frac{p_{j} }{1-d_{i}p_{i} }$

as needed so part one is solved.

Solution to Part(2):

so we have now that if $j$ = $i$ , we get that:

$P(C_{j}|A ) = \frac{P(A \cap C_{j})}{P(A)}$

remember that:

$P(A|C_{j} ) = \frac{P(A \cap C_{j})}{P(C_{j})}$

this implies that:

$P(A \cap C_{j}) = P(C_{j}) \cdot P(A|C_{j}) = p_{i} (1-d_{i} )$

so we just need to combine the above relations to get:

$P(C_{j}|A) = \frac{p_{i} (1-d_{i} )}{1-d_{i}p_{i} }$

as needed so part two is solved.

8 0

4 years ago

Calibrating a scale:

lana66690 [7]

Answer:

We conclude that the calibration point is set too high.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 1000 grams

Sample mean, $\bar{x}$ = 1001.1 grams

Sample size, n = 50

Alpha, α = 0.05

Population standard deviation, σ = 2.8 grams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778$

Now, $z_{critical} \text{ at 0.01 level of significance } = 2.326$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.

6 0

3 years ago

Simplify sqrt(3 + 2 sqrt 2) ...?

trasher [3.6K]

The answer is 1 + √2

sqrt(2) is $\sqrt{2}$
sqrt(3 + 2 sqrt 2) is $\sqrt{3 +2 \sqrt{2} }$
Now, let's simplify $\sqrt{3 +2 \sqrt{2} }$ .
We will use square of sum: (a + b)² = a² + 2ab + b²

$\sqrt{3 +2 \sqrt{2} } = \sqrt{1+2+2 \sqrt{2} }= \sqrt{1+2 \sqrt{2}+2 }= \\ 
= \sqrt{1^{2} +2*1* \sqrt{2} + (\sqrt{2} ) ^{2} } = \sqrt{(1+ \sqrt{2}) ^{2}} =1+ \sqrt{2}$

8 0

3 years ago

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A train travels 190 km in 3.0 hours and then 120 km in 2.0 hours. What is its average speed?

melisa1 [442]

The average speed it 310

3 0

3 years ago

Lola dice Argos mi perro tiene 10 kg menos que roco cuantos kilogramos tiene argos

Elena L [17]

Answer:

$A=R-10$