admin

2 months ago

Guest #4079

2 months ago

- The best method to test Zoe's claim is an observational study, as with this method it is possible to observe if the claim presents some truth to it. Observational studies are often used in testing claims like Zoe's as they allowed to have a great access to the variable that are behind a claim of that type, and so they are also more accessible.

- The set up I would use is an observational study of a great number of people, over a long period of time, that have to have kale for breakfast every day, with a measurement of their cholesterol over the time. the great number and the long period of study assured that the variable subject of study is statistically represented in an optimal way.

- The set up I would use is an observational study of a great number of people, over a long period of time, that have to have kale for breakfast every day, with a measurement of their cholesterol over the time. the great number and the long period of study assured that the variable subject of study is statistically represented in an optimal way.

Question

1. Using the formula for the probability of one event or another event, calculate the probability of drawing a card from a standard deck that is either a jack or a club. Write out the formula and show your work. Write the final answer as a fraction in simplified form. (10 points) Bonus question for extra credit: What is the probability of drawing two cards from a deck, without replacing the first card, and either getting two red cards or two aces? Hint: the probability of getting two aces is the probability of the first card being an ace, times the probability of the second card being a different ace. Show your work, and write your answer as a fraction in reduced form.

Solution 1

A standard deck has 52 cards.

A standard deck has 4 jacks.

A standard deck has 13 clubs.

From this, we can derive the following:

The probability of drawing a jack is 4/52 or 1/13

The probability of drawing a club is 13/52 or 1/4

But since the problem asks for drawing jack or club, therefore we should add the 2 probabilities, making 17/52. This is not the final answer yet. We know that there is a jack of clubs, therefore we need to subtract 1 from the probabilities since jack of clubs were considered in the 2 categories of probability.

With that being said, the probability of drawing a club or a jack is 16/52 or**4/13**

Bonus Question:

The first thing you need to do here is find the probability of each scenario. First let's do what is given, the probability of drawing 2 aces. Since there are 4 aces in a deck of 52, we can easily say that the probability of drawing an ace is 4/52. However for our second draw, the probability of drawing a different ace is 3/51. This is so since we already drew a card that is an ace, hence we need to subtract one from the total aces (4-1) and from the total cards in the deck (52-1). In getting the probability of drawing two aces, we need to multiply the said probabilities: 4/52 and 3/51, resulting to 1/221.

For the second scenario, the drawing of 2 red cards, we just use the same concept but in this, we are already considering the 2 red cards in the first scenario, therefore the chance of drawing a red on our first draw is 24/52. For our second, we just need to subtract one card, therefore 23/51. Multiply these two and we will get 46/221.

Now, the problem asks for the chance of drawing either 2 reds or 2 aces, therefore we add the probabilities of the 2 scenarios:

**46/222 + 1/221 = 47/221**

Summary:

First Scenario:

4/52 + 3/51 = 1/221

Second Scenario:

24/52 + 23/51 = 46/221

Chances of drawing 2 red cards or 2 aces:

1/221 + 46/221 =**47/221**

A standard deck has 4 jacks.

A standard deck has 13 clubs.

From this, we can derive the following:

The probability of drawing a jack is 4/52 or 1/13

The probability of drawing a club is 13/52 or 1/4

But since the problem asks for drawing jack or club, therefore we should add the 2 probabilities, making 17/52. This is not the final answer yet. We know that there is a jack of clubs, therefore we need to subtract 1 from the probabilities since jack of clubs were considered in the 2 categories of probability.

With that being said, the probability of drawing a club or a jack is 16/52 or

Bonus Question:

Summary:

4/52 + 3/51 = 1/221

Second Scenario:

24/52 + 23/51 = 46/221

Chances of drawing 2 red cards or 2 aces:

1/221 + 46/221 =

Question

The Eiffel Tower is about 301 m tall Cooper is making a scale model of the using the scale 750 meters : 1 meter to the nearest 10th of a meter, what will be the height of the scale model

Solution 1

Assuming the scale is 750:1, you can set up the following proportion:

Cross multiply the values.

750x = 301

Divide both sides by 750 to solve for x.

x =

Converted to a decimal and rounded to the nearest tenth, the scale model will be**0.4 meters tall.**

Cross multiply the values.

750x = 301

Divide both sides by 750 to solve for x.

x =

Converted to a decimal and rounded to the nearest tenth, the scale model will be

Question

The probability of Jaden making a free throw is 15%. Predict the number of free throws that he can expect to make if he attempts 40 free throws.

Solution 1

We have been given that the probability of Jaden making a free throw is 15%.

Now, we have to predict the number of free throws that he can expect to make if he attempts 40 free throws.

In order to find the total number of free throws, we will find 15% of 40.

Therefore, the number of free throws should be

**Therefore, the number of free throws that he can expect to make if he attempts 40 free throws is 6.**

Solution 2

6 divided by 40 is 15 percent so the answer is 6

Question

the price of a cup of coffee has risen to 2.80 today yesterday price was 2.45 find the percentage increase round to the nearest tenth of a percent

Solution 1

Percentage increase can be found by the following equation:

(new cost / old cost) - 1 = percentage increase

Plug the values in.

(2.80/2.45) - 1 = percentage increase

1.1428 - 1 = 0.1428

Convert the decimal to a percentage.

0.1428 = 14.28%

Rounded to the tenth spot, the percentage increase is**14.3%.**

(new cost / old cost) - 1 = percentage increase

Plug the values in.

(2.80/2.45) - 1 = percentage increase

1.1428 - 1 = 0.1428

Convert the decimal to a percentage.

0.1428 = 14.28%

Rounded to the tenth spot, the percentage increase is

Question

What is an rational number between 9.5 and 9.7 and include decimal approximation to the nearest hundredth

Solution 1

On of the solutions could be 9.65

Question

The sum of a number and two more than twice the number is less than 50 (write in number form and solve)

Solution 1

N+2n+2 < 50

Combine like terms 3n+2< 50

Subtract 2 from both sides 3n<48

Divided both sides by 3

n<16

Combine like terms 3n+2< 50

Subtract 2 from both sides 3n<48

Divided both sides by 3

n<16

Question

A beach club made profits of $39,100 in May and $59,200 in August. What is the rate of change in the average monthly profit for this time period?

Solution 1

6,700 per month subtract 59200 from 39,100=20100

Divide by 3 because that’s the differences in month

20100 divide by 3 is 6700

Divide by 3 because that’s the differences in month

20100 divide by 3 is 6700

Question

a rectangular porch has dimentions of (x+12) and (x+5) feet. If thr aria of the porch floor is 120 square feet, what is its length and width?

Solution 1

We have (x+12)·(x+5) = 120; where x > 0;

Then, x^2 + 17x + 60 = 120;

x^2 + 17x - 60 = 0;

The solutions are x1 = +3 and x2 = -20;

Then, x = 3 is the correct solution.

Finally, x + 12 = 15 feet (length) and x + 5 = 8 feet (width).

Then, x^2 + 17x + 60 = 120;

x^2 + 17x - 60 = 0;

The solutions are x1 = +3 and x2 = -20;

Then, x = 3 is the correct solution.

Finally, x + 12 = 15 feet (length) and x + 5 = 8 feet (width).

Question

Y=2x-1
3y=6x-5
Please help

Solution 1

I gotchu this time buddy so substitute 2x-1 for the second equation: 3(2x-1)=6x-5

Distribute 3x :6x-3=6x-5

Subtract 6x from both sides

-3=-5 which is not true so the answer is no solution

Distribute 3x :6x-3=6x-5

Subtract 6x from both sides

-3=-5 which is not true so the answer is no solution

Question

The graph of linear equation A passes thru the points (-7,4) and (3,-10), while the graph of linear equation B passes thru the points (-7,4) and (5,11). which of these is a solution to the system of equations consisting of linear equation A and B a. (-7,4)
b. (3,-10)
c. (5,11)
d. (7,4)
show work and i need really bad

Solution 1

We want to find the solution for the** system of linear equations** such that we know some points of the** lines. **We will see that the correct option is A:** (-7, 4).**

When we have a **system of equations** the solutions are the points where the graphs of the equations **intercept**.

Here we know that we have two lines:

- Line A passes through (-7, 4) and (3, - 10)
- Line B passes through (-7, 4) and (5, 11).

So we already can see that both **lines **pass through the point (7, -4), meaning that the lines do **intercept **at that point, so the solution of the **system** is that point (we know that we don't have more solutions because lines __intercept only once__).

So the correct option is A: **(-7, 4)**

If you want to learn more about **systems of equations**, you can read:

Solution 2

Is it A since it passes thru both equations

Mathematics
2647929

History
842281

English
748681

Biology
586256

Social Studies
406852

Chemistry
368373

Business
348603

Physics
324927

Health
199835

Spanish
130075

Geography
112100

Computers and Technology
106146

Arts
77164

Advanced Placement (AP)
23675

World Languages
23213

French
22589

Engineering
19607

Law
17108

Medicine
13966

SAT
10987

German
3389

High School
3423409

Middle School
2092250

College
1518097