Penny has 25 dimes. She likes to arrange them into three piles, putting an odd number of dimes into each pile. In how many ways would she do this?
Penny can arrange the 25 dimes into three piles in 6 different ways.
Explanation: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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When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will _.
Answer: Affect extremely.
Step-by-step explanation:
When a data set contains extreme values also known as outliers , then mean gets affected extremely.
For example : We have a data set with values : 1 , 2, 1,2,1, 2, 12
Here , 12 is much larger than the rest of the data values.
Mean of data : [tex]\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]=\dfrac{1 +2+ 1+2+1+2+12}{8}=\dfrac{21}{8}=2.625[/tex]
Mean excluding outlier :
[tex]=\dfrac{1 +2+1+2+1+2}{7}=\dfrac{9}{7}=1.28571428571\approx1.29[/tex]
We can see that with outlier the mean is way higher than the mean of the rest of the values.
Hence, When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will get affected.
ray is 23 years older than his sister Carol. in 20 years he will be twice as old as Carol. how old is each of them now?
The least common multiple of two numbers is 60 and one of the numbers is 7 than the other numbers what are the numbers justify the answers
A high rise building has a sink on the fourth floor located 2-feet above the floor. Each floor is 10-feet above the other. Calculate the psi at the sink where when the street pressure is 80 psi. The building does not have a pressure reducing device due to fire codes.
which choice correctly expresses the number below in scientific notation
the difference of 9 and the square of a number
How do I find out how many years it will take?
The San Andreas fault is a dextral (right-lateral) strike-slip fault that runs between Los Angeles and San Francisco. This means that Los Angeles is slowly approaching San Francisco. Assuming the average slip rate of 2.1 cm/year remains constant, in about how many years will Los Angeles be directly west of San Francisco? Los Angeles is presently 519 km from San Francisco. (Hint: 1 cm = 0.00001 km.)
Donna buys candy that costs $5 per pound. She will spend less than $30 on candy. What are the possible numbers of pounds she will buy?
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.
the shop has 1260 ounces of cranberry juice and 650 ounces of passion fruit juice.ifvthe juices are used to make crazy cranberry smoothies, which juice will run out first?how much of the other juice will be left over?
0.06 is 10 times as much as 0.600
Professor oger must choose between an extra writing assignment and an extra reading assignment for the upcoming spring break. for the writing assignment, there are two essay topics to choose from and three different mandatory lengths (30 pages, 35 pages, or 40 pages). the reading topic would consist of one scholarly biography combined with one volume of essays. there are five biographies and three volumes of essays to choose from. how many choices does she have? hint [see example 2.]
What does the "O" stand for in the S.T.O.P. method of refusal?
A.
Only try it once.
B.
Offer another idea.
C.
Offer a ride home.
D.
Organize a list of problems.
O stands for Offer another idea.
Option B is the correct answer.
What are abbreviations?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.
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Kira is saving money to buy a bike that costs $133 . She has $42 and will save an additional $7 each week. In how many weeks will she have enough money to buy the bike?
64 is 55% of what number
1. A pool company is trying out several new drains. Drain A empties a pool at a rate of 2 gal/min. Drain B empties a pool at a rate of 5 gal/min. One pool has 108 gal of water in it. Write an equation for each drain that shows the amount of time it takes to empty the pool. Then solve each equation showing your work.
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
If angle X has a measure of 40 degrees and angle Y is vertical to angle X what is the measure of angle Y?
simplify 12 divided (2+4)
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.
There is a sales tax of $6 on an item that costs $88 before tax and. The sales tax on a second item is $21. How much does the second item cost before tax
What can you say about the relationship between the row number and the second term in each row in pascal's triangle?
Final answer:
Pascal's Triangle demonstrates a pattern where the second term in each row relates to the row number raised to a specific power, with the power increasing by one as you move down the rows.
Explanation:
Pascal's Triangle is a mathematical concept that shows a triangular array of binomial coefficients. Each number in the triangle is the sum of the two directly above it.
The relationship between the row number and the second term in each row is that the second term in each row corresponds to the row number raised to the power of 1. For example, in the 3rd row, the second term is the row number (3) raised to the power of 1, which is 3.
As you move down the rows of Pascal's Triangle, the power to which you raise the row number to get the second term of each row increases by one. This pattern continues throughout the triangle.
Let x denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. suppose that for banner-tailed kangaroo rats, x has an exponential distribution with parameter λ = 0.01382. (a) what is the probability that the distance is at most 100 m? at most 200 m? between 100 and 200 m? (round your answers to four decimal places.)
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.
In 2 hours Cara read 48 pages. If she read he same number of pages each hour, how many pages did Cara read in one hour?
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.38 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
The total cost of the meal, rounded to the nearest cent, is approximately $82.30.
Explanation:
First, let's calculate the discount amount:
Discount = 15% of $78.38
= 0.15 * 78.38
≈ $11.76
Now, let's find the discounted meal cost:
Discounted meal cost = Original meal cost - Discount
= $78.38 - $11.76
≈ $66.62
Next, let's calculate the tip amount based on the original meal cost:
Tip = 20% of $78.38
= 0.20 * 78.38
≈ $15.68
Now, let's find the total cost of the meal, including the discounted amount and the tip:
Total cost = Discounted meal cost + Tip
≈ $66.62 + $15.68
≈ $82.30
So, the total cost of the meal, rounded to the nearest cent, is approximately $82.30.
Which best describes the dimensions of a line?
Square EFGH has vertices: E = (-1,1), F = (-1,2), G = (-2,1), H = (-2, 2). In which quadrant will the image of vertex E' be if the square is rotated 270° clockwise about the origin O?
Answer:
Quadrant III
Step-by-step explanation:
Did this lesson, just checked the answer key.
How do you solve 7/12 ÷ 2 5/8
Students in a class were asked to name their favorite flavor of ice cream. The results are shown in the circle graph. How many times more students prefer cookies and cream than prefer strawberry?
Cookies and Cream: 18%
Strawberry: 2%
Cookie Dough: 35%
Vanilla: 25%
Chocolate Chip: 20%
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.
The formula f 5280m can be used to convert a measurement of f feet to an equivalent measurement of m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?
4 miles?
5.3 miles?
111,513,600 miles?
132,620,600 miles?
I am having difficulty solving this problem
A poll conducted in 2013 found that 52% of u.s. adult twitter users get at least some news on twitter.40. the standard error for this estimate was 2.4%, and a normal distribution may be used to model the sample proportion. construct a 99% confidence interval for the fraction of u.s. adult twitter users who get some news on twitter, and interpret the confidence interval in context.
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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