admin

2 months ago

Guest #4152

2 months ago

The correct answer is A.

The independent variable is time and the dependent variable is distance; this means the slope tells us how far she goes per minute. Since the slope is negative and we are referring to her distance from her house, this means the distance from her house is decreasing, which means she is getting closer to her house.

The independent variable is time and the dependent variable is distance; this means the slope tells us how far she goes per minute. Since the slope is negative and we are referring to her distance from her house, this means the distance from her house is decreasing, which means she is getting closer to her house.

Question

Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?

Solution 1

**Answer:**

**Justin got 7 rolls of quarters and 4 rolls of dimes.**

**Step-by-step explanation:**

Let the roll of quarters be x

Let the rolls of dimes be y

As total money received is $90, the equation becomes;

.....(1)

And he got 11 roll of coins, so equation becomes;

or .... (2)

Substituting the value of x from (2) in (1)

So, y = 4

As

So,

x = 7

**Hence, Justin got 7 rolls of quarters and 4 rolls of dimes.**

Solution 2

Well, it really depends but it could be 9 rolls of quarters, 5 rolls of quarters and 8 rolls of dimes, 4 rolls of quarters and 10 rolls of dimes, 3 rolls of quarters and 12 rolls of dimes, etc.

Question

The smith family is shopping for a new car and they are basing decision on color and style. Explain how many color choices and how many style choices they might have if there are 8 possible outcomes. Justify your answer

Solution 1

Either there are 2 color choices and 4 styles to choose

or 4 color choices and 2 styles to choose

or 4 color choices and 2 styles to choose

Solution 2

**Answer:**

Sample response: The Smith family has 2 choices to make, color

and style. By the fundamental counting principle, the product of the

number of choices of color and style must equal 8. So, there could be 1

color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles,

or 8 colors and 1 style.

**Step-by-step explanation:**

Question

sally made 10L of lemonade to sell for a fundraiser. if she puts 230ml of lemonade in each cup and sells each cup for fifty cents how much money can she make? how many ml of lemonade will remain? show work please

Solution 1

So 10L is equivalent to 10,000 mL (I moved the decimal place three to the right)

so now, divide 10,000 by 230 which is roughly 43 (it was a decimal, so what you're gonna have to do is, take 230 and multiply it by 43 to see what you get which is 9890. Now take 9890 and subtract it from 10,000 which gets you 110 mL).

So there is 110 mL left over.

So Sally sold 230 cups of lemonade, now multiply those 230 cups by 50 cents (or $0.50 (multiplying it by 0.50 will save you from having to move the decimal places over to the left)

230 x .50 = $115

so now, divide 10,000 by 230 which is roughly 43 (it was a decimal, so what you're gonna have to do is, take 230 and multiply it by 43 to see what you get which is 9890. Now take 9890 and subtract it from 10,000 which gets you 110 mL).

So there is 110 mL left over.

So Sally sold 230 cups of lemonade, now multiply those 230 cups by 50 cents (or $0.50 (multiplying it by 0.50 will save you from having to move the decimal places over to the left)

230 x .50 = $115

Question

harry buys a sofa set that costs$2,000.he pays for it with 12 month installments. how much will he pay each month? if he has to pay5%in interest how much will he pay in all for the sofa set?

Solution 1

Interest = 5% x 2000 = 0.05 x 2000 = $100

Total amount = $2000 + $100 = $2100

Month instalment = $2100 ÷ 12 = $175

**Answer: $175 each month. Total amount paid = $2100**

Total amount = $2000 + $100 = $2100

Month instalment = $2100 ÷ 12 = $175

Question

James filled 4 glasses with milk. Patrick filled 6 glasses with milk. Each glass held 8 ounces of milk. Which method explains a way to calculate the difference in the amount of milk each boy poured? A. Step 1 Multiply: 4 × 8. Step 2 Multiply: 6 × 8. Step 3 Add the products. B. Step 1 Divide: 8 ÷ 4. Step 2 Divide: 8 ÷ 6. Step 3 Add the quotients. C. Step 1 Multiply: 4 × 8. Step 2 Multiply: 6 × 8. Step 3 Subtract the products. D. Step 1 Divide: 8 ÷ 4. Step 2 Divide: 8 ÷ 6. Step 3 Subtract the quotients.

Solution 1

STEP 1:

multiply 4 glasses by 8oz

= 4 * 8

= 32 total ounces in 4 glasses

STEP 2:

multiply 6 glasses by 8oz

= 6 * 8

= 48 total ounces in 6 glasses

STEP 3:

subtract the difference of steps 1 & 2

= 48 ounces - 32 ounces

= 16 ounces difference

ANSWER: (C) Step 1 multiply: 4 × 8. Step 2 multiply: 6 × 8. Step 3 subtract the products

Hope this helps! :)

multiply 4 glasses by 8oz

= 4 * 8

= 32 total ounces in 4 glasses

STEP 2:

multiply 6 glasses by 8oz

= 6 * 8

= 48 total ounces in 6 glasses

STEP 3:

subtract the difference of steps 1 & 2

= 48 ounces - 32 ounces

= 16 ounces difference

ANSWER: (C) Step 1 multiply: 4 × 8. Step 2 multiply: 6 × 8. Step 3 subtract the products

Hope this helps! :)

Question

A number m minus 3 is more than -4

Solution 1

M= a number

> = more than/greater than

Expression:

m - 3 > -4

If you have to also solve:

m - 3 > -4

add 3 to both sides

m > -1

ANSWER: expression is m - 3 > -4;

expression solved for m is m > -1

Hope this helps! :)

> = more than/greater than

Expression:

m - 3 > -4

If you have to also solve:

m - 3 > -4

add 3 to both sides

m > -1

ANSWER: expression is m - 3 > -4;

expression solved for m is m > -1

Hope this helps! :)

Question

Your friend Zoe is very earnest about the benefits of her special diet. She believes that having kale for breakfast every day will lower your cholesterol. 4a. What's the best method for testing Zoe's claim: a survey, an observational study, or an experiment? Give at least one reason to support your answer. (4 points)
4b. Describe how you would set up a test to determine how much truth there is to Zoe's claims. In particular, what steps would you take to make sure the results were unbiased and valid?

Solution 1

- 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

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