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olganol [36]
2 years ago
12

Suppose there is a 20% chance of rain on Monday and a 40% chance of rain on Tuesday. Assuming the weather on successive days is

independent, find
a. the probability it rains on Monday or Tuesday.
b. the conditional probability it rains on Tuesday given that it rained on Monday.
Mathematics
1 answer:
nadya68 [22]2 years ago
4 0

Answer:

a. 52%

b. 40%

Step-by-step explanation:

Let A represents the event of raining on Monday and B represents the event of raining in Tuesday,

Then according to the question,

P(A) = 20% = 0.2,

P(B) = 40% = 0.4,

Here, A and B are independent events,

So, P(A∩B) = P(A) × P(B),

⇒ P(A∩B) = 0.2 × 0.4 = 0.08

We know that,

P(A∪B) = P(A) + P(B) - P(A∩B)

a. The probability it rains on Monday or Tuesday, P(A∪B) = 0.2 + 0.4 - 0.08

= 0.52

= 52%

b. The conditional probability it rains on Tuesday given that it rained on Monday,

P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)} = \frac{0.08}{0.2}=0.4 = 40\%

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Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.
Ray Of Light [21]

Answer:

B. Geometric sequence.

g(n)=900\cdot (\frac{2}{3})^{n-1}

Step-by-step explanation:

We have been given that Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

The amount of contaminants remaining after each hour would be 2/3 of the previous hour amount as 1/3 of contaminants was filtered.

Since amount is not constant, therefore, the sequence would be geometric.

We know that explicit formula for geometric sequence is in form a(n)=a\cdot r^{n-1}, where,

a = First term,

r = Common ratio.

For our given scenario a=900 and r=\frac{2}{3}, so our required formula would be:

g(n)=900\cdot (\frac{2}{3})^{n-1}

Therefore, an explicit formula for the given geometric sequence would be g(n)=900\cdot (\frac{2}{3})^{n-1}.

8 0
2 years ago
joyce is helping her aunt create craft kits. her aunt has 138 pipe cleaners, and each kit will include 6 pipe cleaners. what is
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23 pipe cleaners cause 23 x 6= 138
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2 years ago
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A company produces breakfast cereal. The true mean weight of the contents of its cereal packages is 20 ounces, and the standard
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Answer:

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Step-by-step explanation:

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2 years ago
Parker is planning to build a playhouse for his sister.The scaled model below gives the reduced measures for width and height. H
kipiarov [429]

Answer:

The cross multiplication would be 10(350) = 22(x).

Step-by-step explanation:

We would first convert meters to centimeters.  There are 100 cm in a meter; this means 3.5 m = 3.5(100) = 350 cm.

The ratio of the height to base of the model is 10/22.  The ratio of the playhouse would then be x/350.  This gives us

10/22 = x/350

Cross multiplying, we would have 10(350) = 22(x).

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2 years ago
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A steel pipe 100 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If thee density of the steel is 7.8 g
ELEN [110]

Answer:

The mass of the pipe is 465\ g

Step-by-step explanation:

step 1

Find the volume of the steel pipe

The volume is equal to the area of outside circle minus the area of inside circle, multiplied by the length of the pipe

so

V=\pi [r2^{2}-r1^{2}]L

we have

r2=2/2=1\ cm ---> the radius is half the diameter

r1=1.8/2=0.9\ cm ---> the radius is half the diameter

L=100\ cm

\pi=3.14

substitute

V=(3.14)[1^{2}-0.9^{2}](100)=59.66\ cm^{3}

step 2

Find the mass

The mass is equal to the density multiplied by the volume

so

m=7.8(59.66)=465\ g

8 0
2 years ago
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