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emmasim [6.3K]
3 years ago
10

A drinks factory packed their drinks into red and yellow boxes. There were 24 more red boxes than yellow boxes. Each red box con

tained 60 packets of milk and each yellow box contained 75 packets of fruit juice. There were 120 fewer of milk than packets of fruit juice in all
boxes.

(a) How many yellow boxes were used ?
(b) How many packets of milk were packed into the the red boxes?

Mathematics
1 answer:
ira [324]3 years ago
3 0

Answer:

A) 128

B) 7800

Step-by-step explanation:

Trial and error until I got to 75 x 104 and 60 x 128 (which abides by the fact that there has to be 24 more red boxes) which equals 7800 and 7680 and if you take them away from each other you get 120

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If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.

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We have a population of N=25 skylight covers, were K=4 are defective.

We sample n=5 covers, and we will accept the lot if k=2 or fewer are defective.

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First, to be accepted, the sample can have 2, 1 or 0 defective covers, so the probability of being accepted is:

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Then, we can calculate the individual probabilities as:

P(k=0)=\dfrac{\dbinom{4}{0}\cdot \dbinom{25-4}{5-0}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{0}\cdot \dbinom{21}{5}}{\dbinom{25}{5}}\\\\\\P(k=0)=\dfrac{1\cdot 20349}{53130}=0.38

P(k=1)=\dfrac{\dbinom{4}{1}\cdot \dbinom{25-4}{5-1}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{1}\cdot \dbinom{21}{4}}{\dbinom{25}{5}}\\\\\\P(k=1)=\dfrac{4\cdot 5985}{53130}=0.45

P(k=2)=\dfrac{\dbinom{4}{2}\cdot \dbinom{25-4}{5-2}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{2}\cdot \dbinom{21}{3}}{\dbinom{25}{5}}\\\\\\P(k=2)=\dfrac{6\cdot 1330}{53130}=0.15

If we add this probabilities, we have:

P(accepted)=P(k\leq2)=P(k=0)+P(k=1)+P(k=2)\\\\P(accepted)=0.38+0.45+0.15=0.98

If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.

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Answer:

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half of this is 45 cube inch volume.

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3 years ago
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