Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.

Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:

Tony's car can travel 28 miles for each gallon of gas.
The average fuel cost at the time of their trip is $3 per gallon.
They plan to drive about 650 miles each day.
They estimate the average cost of a hotel each night is $85.
They will drive approximately 2,240 miles to get from Albuquerque to Boston.

Answer: 9 times

Step-by-step explanation:

Let the total number students be x.

Then the number of students liked cookies and cream = 18% of x= 0.18 x

The number of strawberry = 2% of x = 0.02 x

Clearly, 0.18 x> 0.02 x

The number of times more students prefer cookies and cream than prefer strawberry =[tex]=\frac{0.18x}{0.02x}=9[/tex]

Hence, The students prefer 9 times cookies and cream than prefer strawberry.

Answer:

George and Sue's money will grow due to both to their contributions and the simple interest that they accrue. Simple interest means that the interest they receive will be applied to the principle, but not the interest that has been accrued. This means that for every $10,000 they put in, they will receive $400 dollars in interest every year, and this number will not change with time.

Right now, they've deposited 10,000 every 7 years for a total of 70,000 dollars. Their annual interest therefore is 400 * 7 = 2800. With every 10,000 dollars they deposit, the yearly interest will grow by $400. This is different from compounding interest, in which annual interest will grow by more than $400 dollars every year since the rate will be applied to principle and all accrued interest.

Step-by-step explanation:

Answer:

B) 2x(5zy + 12y + 3z)

Step-by-step explanation:

First, all coefficient for each term are a pair number, therefor 2 is common factor for all these

[tex]10xyz + 24xy + 6xz=>2(5zxy + 12xy + 3xz )[/tex]

then, the variable X is present for each term of the funtion [tex](5zxy + 12xy + 3xz)[/tex], so, the variable X is a common factor to.

[tex]2(5zxy + 12xy + 3xz )=> 2x(5zy + 12y + 3z )[/tex]

For 99% confidence level, the interval will be (0.4582, 0.5818).

It can be interpreted as "45.82% to 58.18% of US adult will get information from twitter with a confidence of 99%".

Given information:

52% or 0.52 fraction of US adult twitter users get at least some news on twitter. It is the sample population in fractions.

The standard error is 2.4% or 0.024 fraction.

Normal distribution may be used to model the sample proportion.

Now, for 99% confidence level, the interval for the fraction of US adult who get some news on twitter will be,

[tex]I=\texttt{sample population}\pm 2.575\times \texttt{standard error}\\I=0.52\pm 2.575\times0.024\\I=0.52\pm 0.0618\\I=(0.4582, 0.5818)[/tex]

Therefore, for 99% confidence level, the interval will be (0.4582, 0.5818).

It can be interpreted as "45.82% to 58.18% of US adult will get information from twitter with a confidence of 99%".

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Answer:

Quadrant III

Step-by-step explanation:

Did this lesson, just checked the answer key.

O stands for Offer another idea.

Option B is the correct answer.

Abbreviations are shortened versions of words or phrases that are commonly used in written or spoken language.

They are created by taking the first letter (or sometimes multiple letters) of each word in a phrase and using them to form a shorter, more compact version of the phrase.

For example:

"ASAP" is an abbreviation for "as soon as possible" and "FYI" is an abbreviation for "for your information".

Abbreviations are often used to save time and space in writing and are common in fields such as science, medicine, and technology where complex terms and phrases are frequently used.

We have,

The "O" in the S.T.O.P. method of refusal stands for "Offer another idea."

Thus,

O stands for Offer another idea.

Learn more about abbreviations here:

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To determine the number of shelves that will display 2 cars each when 8 shelves display 1 car each, simply divide 8 by 2. The answer is 4 shelves.

To solve this problem, we'll use basic arithmetic. If each of the 8 shelves displays 1 car, then to display 2 cars on a shelf, we would need to combine pairs of shelves. This means we would take the 8 shelves, and divide by 2 cars per shelf to find the number of shelves needed for 2 cars each. So, 8 shelves divided by 2 cars per shelf equals 4 shelves.

Therefore, the answer is that 4 shelves will display 2 cars each if there were originally 8 shelves with 1 car each.

Answer: +2

Step-by-step explanation: When you're doing a problem like [tex]\frac{12}{2 + 4}[/tex], it's important to understand that a division bar has the same effect on a problem as a set of parentheses in that it groups terms together.

So this 2 + 4 can be thought of as being inside a set of parentheses just like it is in the original problem. Remember from your order of operations that before you do anything else, you must simplify what's inside the set of parentheses.

So the first thing we do here is add 2 + 4 to get 6 and this problem simplifies to [tex]\frac{12}{6}[/tex]. Now we can divide 12 by 6 which gives us +2.

The number of people who do not want plain hamburgers is 3+2+2 = 7, so 15-7 = 8 people want plain hamburgers. Each person wants 2 hamburgers, for a total of ...

... B: 16

plain hamburgers.

Jim and his dad will make 23 plain hamburgers.

To find the number of plain hamburgers Jim and his dad will make, we need to subtract the number of hamburgers with special toppings from the total number of hamburgers. There are 15 people in total, and each person wants 2 hamburgers, so Jim and his dad need to make 15 x 2 = 30 hamburgers in total.

Out of the 30 hamburgers, 3 people want hamburgers with cheese, 2 people want hamburgers with mustard, and 2 people want hamburgers with catsup. Therefore, the total number of hamburgers with special toppings is 3 + 2 + 2 = 7 hamburgers.

Subtracting the number of hamburgers with special toppings from the total number of hamburgers, we get 30 - 7 = 23 plain hamburgers. Therefore, Jim and his dad will make 23 plain hamburgers.

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The equations we can create is based from this equation:

time = volume of pool / rate

Drain A: time = 108 gal / (2 gal / min) = 54 min

Drain B: time = 108 gal / (5 gal / min) = 21.6 min

To solve this problem, we have to use the formula:

P = 1 - e^(-λx)

where λ = 0.01382, and x is the  distance

A. when x = 100

(P < or equal to 100) = 1 - e^(-0.01382 * 100)

(P < or equal to 100) = 0.75 

B. when x = 200
(P < or equal to 200) = 1 - e^(-0.01382 * 200)
(P < or equal to 200) = 0.94

C. when 100 < x < 200
P (100 < x < 200) = P ((x < 100) + P(x > 200)) 
P (100 < x < 200) = 0.75 + (1 – 0.94)

P (100 < x < 200) = 0.81 

Final answer:

The probabilities for a banner-tailed kangaroo rat to move at most 100 m, at most 200 m, and between 100 and 200 m are 0.7487, 0.9389, and 0.1903 respectively, when rounded to four decimal places.

Explanation:

The question deals with exponential distribution, which is a type of continuous probability distribution often used to model the time or space between events in a Poisson process. Given that the parameter λ (lambda) for the banner-tailed kangaroo rats is 0.01382, the mean (μ) can be calculated as the reciprocal of λ, so μ = 1/λ. In this case, μ = 1/0.01382. The cumulative distribution function (CDF) for an exponential distribution is  [tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex]

To find the probability that the distance is at most 100 m, we use the CDF:

[tex]P(X \leq 100) = 1 - e^{-(0.01382)(100)} = 1 - e^{-1.382} \approx 1 - 0.25132 = 0.74868[/tex]

For the distance at most 200 m:

[tex]P(X \leq 200) = 1 - e^{-(0.01382)(200)} = 1 - e^{-2.764} \approx 0.93894[/tex]

To find the probability that the distance is between 100 m and 200 m, we subtract the probability of being at most 100 m from the probability of being at most 200 m:

P(100 < X ≤ 200) = P(X ≤ 200) - P(X ≤ 100) = 0.93894 - 0.74868 = 0.19026

So, the probabilities are approximately 0.7487 for at most 100 m, 0.9389 for at most 200 m, and 0.1903 for between 100 and 200 m, when rounded to four decimal places.

The 'rem(m, n)' and 'mod(m, n)' methods in mathematics provide the remainder of the division operation m / n. When dealing with numbers in exponential form, you divide the base numbers and subtract the exponents to simplify the terms. An understanding of these operations is essential for solving more complex equations.

In mathematics, there are two ways to find the remainder of a division operation: rem(m,n) or mod(m,n). These functions take two numbers m and n, and return the remainder when m is divided by n.

For example, in the case of 106 divided by 103, you would first divide the 'base' numbers (10/10) which equals 1, and then subtract the exponents (6-3) which equals 3. So, the result is 103 or 1000. Another example is 4.5 x 109 divided by 103. Here, first you divide 4.5 by 1 (since 10/10 = 1) and then subtract 9-3 equals 6. Therefore, the answer is (4.5) x 106.

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