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Semenov [28]
1 year ago
8

Spike is not a terribly bright student. His chances of passing chemistry are 0.35; mathematics, 0.40; and both, 0.12. Are the ev

ents "Spike passes chemistry" and "Spike passes mathematics" independent? What is the probability that he fails both subjects?
Mathematics
1 answer:
Feliz [49]1 year ago
8 0

Answer:

The events "Spike passes chemistry" and "Spike passes mathematics" are not independent.

The probability that he fails both subjects = 0.37

Step-by-step explanation:

The probability of Spike passing Chemistry = P(Chemistry) = 0.35

The probability of Spike passing Mathematics = P(Mathematics) = 0.40

The probability of Spike passing both Chemistry and Mathematics = P(Chemistry,Mathematics) = 0.12

For the events "Spike passes chemistry" and "Spike passes mathematics" to be independent, P(Chemistry,Mathematics) should be equal to P(Chemistry) * P(Mathematics)

But P(Chemistry) * P(Mathematics)=0.35*0.40 =0.14

So the two events are not independent.

The Probability that he passes Chemistry or Mathematics is given by P(Chemistry) + P(Mathematics) - P(Chemistry,Mathematics)

= 0.35+0.40-0.12=0.63

So the probability that he fails both subjects is the complement of this, namely (1 - 0.63) = 0.37

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Jackie ordered a set of wood and metal clothes pins. Of the 276 pins, 172 were wood. What percentage of the clothes pins were me
timurjin [86]

We know that 172 of them were wood, so the rest are metal. To find that number we do:

276 - 172 = 104 metal pins.

To find the percentage that they were metal, take the number of metal pins and divide by the total number of pins:

104/276 is about 0.3768.

Multiply this by 100:

37.68

So, the percent of metal pins is 37.68%.

8 0
2 years ago
A log is 16m long, correct to the nearest metre. It has to be cut into fence posts which must be 70cm long, correct to the neare
dmitriy555 [2]

Answer:

25 posts

Step-by-step explanation:

So the number of fence post would be the total length of the log divided by the length of each post. As the log is 16m and is corrected to the nearest metre, it could possibly be 16.499m. As for the post that is 70 cm long and corrected to the nearest 10cm, it may as well be 65 cm (or 0.65m) each post

So the max number of fence point once can possibly cut from the log would be

16.499 / 0.65 = 25 posts

5 0
1 year ago
The constant-pressure specific heat of air at 25°C is 1.005 kJ/kg. °C. Express this value in kJ/kg.K, J/g.°C, kcal/ kg. °C, and
Mice21 [21]

Answer:

In kJ/kg.K - 1.005  kJ/kg degrees Kalvin.

In  J/g.°C  -  1.005 J/g °C

In kcal/ kg °C  0.240 kcal/kg °C

In Btu/lbm-°F   0.240 Btu/lbm degree F

Step-by-step explanation:

given data:

specific heat of air = 1.005 kJ/kg °C

In kJ/kg.K

1.005 kJ./kg °C = 1.005 kJ/kg degrees Kelvin.

In  J/g.°C

1.005 kJ./kg °C \times 1000/1kJ \times (1kg/1000 g) = 1.005J/g °C

In kcal/ kg °C

1.005 kJ./kg °C \times \frac{1 kcal}{4.190 kJ} = 0.240 kcal/kg °C

For   kJ/kg. °C to Btu/lbm-°F  

Need to convert by taking following conversion ,From kJ to Btu, from kg to lbm and from degrees C to F.

1.005 kJ./kg °C \times \frac{1 Btu}{1.055 kJ} \times \frac{0.453 kg}{1 lbm} \times \frac{5/9 degree C}{1 degree F} = 0.240 Btu/ lbm / degree F

1.005 kJ/kg C =  0.240 Btu/lbm degree F

8 0
2 years ago
Brenda earns $1,700 per month after taxes. She is working on her budget and has the first three categories finished.
Zigmanuir [339]

Answer:

B

Step-by-step explanation:

Recommended for housing: 30%

X/100 = 612/1700

= 36%

Recommended for food: 10%

X/100 = 238/1700

= 14%

Recommended for transportation 15%

X/100 = 370/1700

= 21.8%

6 0
1 year ago
9. Ms. Ortiz sells tomatoes wholesale. The function p(x)=–80x2 + 320x – 10, graphed below,
labwork [276]

Answer:

<u>The correct answer is B. $310 at $2 per kilogram</u>

Step-by-step explanation:

1. Let's find out the maximum profit Ms. Ortiz can make with a loaf of tomatoes:

function p(x)=–80x² + 320x – 10

For x = 1, price per kilogram of tomatoes would be: 4 - x = 3

–80x² + 320x – 10, replacing with x = 1

-80 * 1² + 320 * 1 - 10 = -80 + 320 - 10 = 230

For x = 2 price per kilogram of tomatoes would be: 4 - x = 2

–80x² + 320x – 10, replacing with x = 2

-80 * 2² + 320 * 2 - 10 = -320 + 640 - 10 = 310

For x = 3, price per kilogram of tomatoes would be: 4 - x = 1

–80x² + 320x – 10, replacing with x = 3

-80 * 3² + 320 * 3 - 10 = -720 + 960 - 10 = 230

<u>The correct answer is B. $310 at $2 per kilogram</u>

7 0
1 year ago
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