90,175,087,309 in expanded form

x = number of pounds

5x<30

x<30/5

 so she can buy X<6 pounds

Answer:

The possible numbers of pounds she will buy is less than 6.

Step-by-step explanation:

Given : Donna buys candy that costs $5 per pound. She will spend less than $30 on candy.

To find : What are the possible numbers of pounds she will buy?

Solution :

Let x be the number of pounds.

Donna buys candy that costs $5 per pound.

i.e. cost of x candy is $5x.

She will spend less than $30 on candy.

i.e. [tex]5x<30[/tex]

Solve the inequality,

[tex]x<\frac{30}{5}[/tex]

[tex]x<6[/tex]

The possible numbers of pounds she will buy is less than 6.

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.

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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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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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

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:

Quadrant III

Step-by-step explanation:

Did this lesson, just checked the answer key.

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]

Penny can arrange the 25 dimes into three piles in 6 different ways.

Penny has 25 dimes and wants to arrange them into three piles, with an odd number of dimes in each pile. In order to do this, let's consider the possible combinations:

Possible combinations:
1. Pile A: 1 dime, Pile B: 1 dime, Pile C: 23 dimes
2. Pile A: 1 dime, Pile B: 3 dimes, Pile C: 21 dimes
3. Pile A: 1 dime, Pile B: 5 dimes, Pile C: 19 dimes
4. Pile A: 1 dime, Pile B: 7 dimes, Pile C: 17 dimes
5. Pile A: 1 dime, Pile B: 9 dimes, Pile C: 15 dimes
6. Pile A: 1 dime, Pile B: 11 dimes, Pile C: 13 dimes

Therefore, Penny can arrange the dimes into three piles in 6 different ways.

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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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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.

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.