A $55 gild ring costs $58.85 after sales tax is figured in. What is the sales tax percentage?

Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

EleoNora [17]

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

6 0

3 years ago

How do you know if two line segments are perpendicular?

Brut [27]

Perpendicular lines, when intersecting, will always create a right angle at the intersection point. A right angle is an angle that is exactly 90 degrees.

5 0

3 years ago

Read 2 more answers

What are the domain and range of the function 2 y x x    6 8 shown in the graph below?

Nat2105 [25]

Answer:

Missing information.

Step-by-step explanation:

However, the domain is all the x- values. The range is all the y-values (that do not repeat).

So when you look at your graph, find your x values and y-values and write them as set. That is your answer.

7 0

3 years ago

Please help with this problem.

larisa86 [58]

Answer:

60°, 120°

Step-by-step explanation:

$\frac{ {tan}^{2}x }{2} - 2 {cos}^{2}x = 1 \\ \\ \frac{ {tan}^{2}x - 4{cos}^{2}x }{2} = 1 \\ \\ {tan}^{2}x - 4{cos}^{2}x = 2 \\ \\ \frac{{sin}^{2}x}{{cos}^{2}x} - 4{cos}^{2}x = 2 \\ \\ \frac{{sin}^{2}x - 4{cos}^{4}x}{{cos}^{2}x} = 2 \\ \\ {sin}^{2}x - 4{cos}^{4}x = 2{cos}^{2}x \\ \\ 4{cos}^{4}x + 2{cos}^{2}x - {sin}^{2}x = 0 \\ \\ 4{cos}^{4}x + 2{cos}^{2}x + {cos}^{2}x - 1= 0 \\ \\ 4{cos}^{4}x + 3{cos}^{2}x - 1= 0 \\ \\ 4{cos}^{4}x + 4{cos}^{2}x - {cos}^{2}x - 1= 0 \\ \\4{cos}^{2}x({cos}^{2}x + 1) - 1({cos}^{2}x + 1) = 0 \\ \\ ({cos}^{2}x + 1)(4{cos}^{2}x - 1) = 0 \\ \\ ({cos}^{2}x + 1) = 0 \: or \: (4{cos}^{2}x - 1) = 0 \\ \\ {cos}^{2}x = - 1 \: or \: 4{cos}^{2}x = 1 \\ \\ {cos}x = \sqrt{ - 1} \: which \: is \: not \: possible \\ \therefore \: {cos}^{2}x = \frac{1}{4} \\ \\ \therefore \: {cos}x = \pm\frac{1}{2} \\ \\ \therefore \: {cos}x = \frac{1}{2} \: or \: {cos}x = - \frac{1}{2} \\ \\ \therefore \: {cos}x = {cos}60 \degree \: or \: {cos}x = {cos}120 \degree \\ \\ \therefore \:x = 60 \degree \: \: or \: \: x = 120 \degree$

6 0

2 years ago

4. Thoughtful Politicians [This problem setting is due to Prof. James Norris of Cambridge University.] In a group of 100 politic

kirill [66]

Answer:

Step-by-step explanation:

The focus is on Party 2, because as already said, Party 1 members NEVER change their minds on anything!

There are 60 politicians in Party 2. They change their minds completely-randomly every day.

Tomorrow, the politicians will vote on a proposition: Proposition 88, but today, 10 are in favor of it while 50 are against it.

Each member changes their mind based on the toss of a coin (a fair/unbiased coin; since it was not stated that the coin is biased). A fair coin has a 0.5 probability of landing HEADS and same 0.5 probability of landing TAILS.

What is the distribution of the number of members in Party II who will favor Prop 88 tomorrow?

The number of figures in the distribution will depend on the number of times the coin is tossed, between today and tomorrow.

<em>KEY: </em><em>Assuming the coin is tossed 12 times between today and tomorrow AND assuming that half of the time - 6 times - it landed HEADS and half of the time, TAILS (Head and Tail simultaneously).</em>

Beginning with HEADS, the distribution of the number of members who will favor the proposition tomorrow, is:

50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10

4 0

3 years ago