24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.
Here,
Since there are 5 peoples,
let us fix the first person and remaining will be set according to that.
this can be arranged in,
(5-1)!=4!
=24 ways
When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.
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3 is divided by the difference of 4 and a number
Answer:
[tex] \frac{3}{4 - x} [/tex]
There are 728 calories in eight ounces of a certain ice cream. How many calories are there in two pounds? \text{1 pound}=\text{16 ounces} 1 pound=16 ounces Before you try that problem, answer the question below. How many ounces will you need to find the number of calories for?
Answer:
Step-by-step explanation:
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adioabiola
Ace
12K answers
42.2M people helped
Answer:
1,008 calories
Step-by-step explanation:
504 calories in eight ounces
How many calories are there in one pound
1 pound = 16 ounces
504 calories = 8 ounces
x calories = 1 pound
Recall, 1 pound = 16 ounces
504 calories : 8 ounces = x calories : 16 ounces
504 / 8 = x / 16
Cross Multiply
504 * 16 = 8 * x
8,064 = 8x
Divide both sides by 8
x = 8,064 / 8
= 1,008
x = 1,008 calories
Therefore, there are 1,008 calories in one pound
we are exploring the following model for fireflies flashing: a firefly flips a biological equivalent of a coin every second. if it comes up heads (probability of 0.1) it lights up for that second; otherwise it does not. for a given firefly, what is the average number of flashes over a minute? what is the spread (standard deviation) of that number? if we have 1000 fireflies in our field of view, what is the expected number of flashes we will see in 10 seconds? if each flash is .1 lumens and we want 40 lumens at least 70% of the time, how many fireflies do we need? we are monitoring 100 fireflies and determine that the number of flashes per minute per firefly is about 7. is this consistent with our model?
Given,
The probability of head ups of a firefly = 0.1 = 10%
The average flashes per minute = 10% of 60 seconds = 6 flashes.The average flashes per minute is 6.
If there is 1000 fire flies, number of flashes in 10 seconds.1 firefly 6 flashes per minute = 0.1 flash per second
Then,
1000 × 0.1 = 100 flashes per second
100 × 10 = 1000 flashes per 10 seconds
There will be 1000 flashes per 10 seconds.
How many fireflies are required if each flash produces.1 lumens, and we aim for 40 lumens at least 70% of the time?Each flash = 0.1 lumen
40 lumens = 4 flash
70/100 = 0.7
0.7 x 4 = 2.8 = 3 fireflies.
There is 3 fireflies required to produce 40 lumens
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force
area
A block exerts a force of 9 N on the ground.
Calculate the pressure the block exerts on the ground, in N/m², when
it is
a) flat on the ground, so that the area of its base is 0.04 m².
b) standing up on its side, so that the area of its base is 0.015 m².
pressure =
A block exerts a force of 9 N on the ground.
Calculate the pressure the block exerts on the ground, in N/m², when it is
a) 225N/m^2
b) 600N/m^2
Define pressure.
Force applied per unit area is the definition of pressure. P=FA, where F is the force acting perpendicular to the surface area A, is the formula used to calculate pressure mathematically. Having only magnitude and no directional vector properties, pressure is a scalar quantity. The pascal (Pa), or one newton per square meter (N/m 2), is the industry standard for measuring pressure.
Solution Explained:
Given, Force = 9N
For each part of the question we will use the formula
Pressure = Force / Area (Since, Force = Pressure X Area)
a) Here, Area = 0.04m^2
So using the formula, we have
P = 9/0.04 = 225N/m^2
b) Here, Area = 0.015m^2
So using the formula, we have
P = 9/0.015 = 600N/m^2
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What is the slope of the secant line that intersects the graph of f(x) = √4x+1 at x = = 0 and x = 6?
=
What is an equation of the line that passes through the points (-4, 5)(−4,5) and (-4, -2)(−4,−2)?
Answer:
∅
Step-by-step explanation:
set up your equation which will be [tex]\frac{-2-5}{-4+4}[/tex] which is undefined because denominator cannot be 0
Determine the total number of Fish food cubes that will fill the shipping box
I hate to leave you without an answer, but there isn't enough information to be able to answer your problem.
At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The equivalent ratios table is:
Toss Dollars
5 2
30 12
45 18
See the diagram in the attachment that shows the plotted points.
What are Equivalent Ratios?Equivalent ratios are ratios that have the same value when they are compared together.
For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.
Create an equation that models equivalent ratios that can be used to complete the table if:
x = toss
y = dollars
Therefore, given that 30 toss equals $12,
Constant of proportionality, k = y/x = 12/30
k = 2/5.
Plug in the value of k into y = kx:
y = 2/5x.
Therefore:
2 dollars (y = 2), will give:
2 = 2/5(x)
x = 10/2
x = 5 toss
45 tosses (x = 45) will need:
y = 2/5(45)
y = 18 dollars
The equivalent ratios table would be:
Toss | Dollars
5 2
30 12
45 18
The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.
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the mean cost of domestic airfares in the united states rose to an all-time high of $385 per ticket. airfares were based on the total ticket value, which consisted of the price charged by the airline plus any additional taxes and fees. assume domestic airfares are normally distributed with a standard deviation of $110. answer to four decimals. what is the probability domestic airfare is $250 or less.
The probability 11.1% of domestic airfares within the United States are $250 or less.
Define the term standard deviation?A square root of variance is used to calculate the standard deviation, a statistic that illustrates how distributed widely a dataset is in relation to its mean. By evaluating the deviation of each data point from the mean, the standard deviation may be approximated as the square root of variance.The formula for the z score is -
z = (x - μ)/σ
In which,
μ = mean = $385 per ticketσ = standard deviation = $110x = sample value = $250 or less.Substitute the value in formula.
P(x ≤ 250) = (250 - 385)/100
P(x ≤ 250) = -1.22
Select the p value from negative z score table;
P(x ≤ 250) = 0.111
P(x ≤ 250) = 11.1%
Thus, 11.1% of domestic flights within the United States are $250 or less.
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the physical examination records of the freshmen class of 1935 at university of toronto were examined in 1980 to see whether the freshman's record of bmi at the time of admission to the university were related to their chance of developing coronary heart disease in 1980. this is an example of:
A prospective research of men and women looked at body mass index, waist circumference, and the risk of coronary heart disease.
What is body mass index?Body Mass Index (BMI) is calculated by dividing a person's weight in kilograms (or pounds) by their height in meters squared (or feet). High body fatness may be indicated by a high BMI.BMI does not make a body fat or health diagnosis for a person, but it does screen for weight categories that may cause health issues.Calculate Adult BMI Using This WidgetBy including this widget on your website, anyone can determine their BMI. For the majority of persons, BMI is an accurate indication of body fatness. It is used to check for weight ranges that could cause health issues. The BMI and accompanying weight category are provided by this calculator. Adults who are at least 20 years old should use this calculator.Child and Teen BMI Calculator Widget from the CDCInclude this widget on your webpage. The CDC BMI-for-age growth chart is used to calculate BMI and the related BMI-for-age percentile. From the age of two to nineteen, kids and teenagers can use this calculator.For Schools: The Children's BMI ToolThis spreadsheet can be used by educators, daycare operators, and other experts to calculate BMI forLearn more about bmi here:
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the width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm. (a) what is the probability that a randomly chosen bolt has a width between 942 and 959 mm? (round your answer to four decimal places.) (b)
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
Define probability.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
Given,
The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.
Z = X - 951/10 ≈ N(0.1)
P(942 ≤ X ≤ 959)
P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)
P( -0.9 ≤ Z ≤ 0.8)
P(Z ≤ 0.8) - P(Z ≤ -0.9)
∅(0.8) - (1 - ∅(0.9))
∅(0.8) + ∅(0.9) - 1
0.788 + 0.859 - 1
0.647
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
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victoria deposited $5000 into a savings account that earns an annual simple interest rate of 0.3%. To the nearest tenth of a year, how long will it take for the account to reach $5500?
It will take 33.33 years for the account to reach $5500
What is simple interest?
Simple interest is defined as the direct crediting of cash flows related to an investment or deposit.
We know,
Victoria deposited into a savings account $5000
Annual simple interest rate of 0.3%.
Formula of Simple Interest
A = P(1 + rt)
5500 = 5000(1 + 0.003t)
5500 = 5000 + 15t
15t = 500
[tex]t = \frac{500}{15} = 33.33[/tex]
It will take 33.33 years for the account to reach $5500
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Explain+how+you+csn+use+similar+triangles+to+find+a+missing+measurement.++Write+a(n)+that+uses+the+missing+measurement+because+the+++are++
You can use similar triangles to find missing measures according to proportional relationships.
What are similar triangles?Similar triangles are two triangles that share these two features listed as follows:
Same angle measures.Proportional side lengths.The second feature, the proportional side lengths, is what is used to find the missing measures, as proportional relationships are built according to them.
When two triangles are similar, the equivalent side lengths have to be identified for the two triangles, and those are the sides that have the same angle measures.
Then, for the two triangles, the equivalent sides will have proportional lengths, and then these equations will involve a missing length. Then cross multiplication is applied and the equation can be solved for the missing length.
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Help me with these questions (all of them 1 to 19 )
Answer:
answer for 17 is 5+5+8which is 200 cm
Answer:
1 - 9p
2 - 4y
Step-by-step explanation:
1: 3p+2p+4p Since there all common terms you can just add them together! So it would be 9p!
2: 3y + (-y) + 2y
Lets make this easier to understand.
3y -1y + 2y (I added the one because the y technically is a 1.)
Since they are all like terms because they all have y it is pretty easy to solve now! So it would be 4y!
(WILL DO MORE LATER)
A shelf and bracket are shown below. The shelf is
perpendicular to the wall.
Note: The figure is not drawn to scale.
What angle (x), in degrees, does the bracket make
with the wall?
Using the concept of the sine function, the bracket made an angle of 51.37° with the wall.
What is a sine function?The sine of an angle is represented by the trigonometric function sin x, where x is the angle under consideration. The ratio between a right-angled triangle's perpendicular and the hypotenuse is known as the sine function. In other words, the hypotenuse is the ratio of the side opposite to the angle being discussed, and its value changes as the angle do. The sine function is used in physics to depict sound and light waves.
Use the trigonometric function sinθ = perpendicular/ hypotenuse
From the given figure, in accordance with ∠x
Perpendicular = 2.5 ft
Hypotenuse = 3.2 ft
So, sinx = 2.5/ 3.2
sinx = 0.78125
x = sin⁻¹(0.78125)
x = 51.37°
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Which number is greatest?
57
10
O 5. 84
51
√33, 5. 84,
0 5. 7
OV33
51
9
The greatest number among the given numbers is= 57
What are greatest numbers?largest and smallest number formation We are aware of how to list the numbers in both ascending and descending order. The highest number is created by placing the specified digits in ascending order, and the lowest number is created by placing them in descending order, as we have already learned.. A number has more places when the digit at the very left is in that position. Therefore, to increase the value of the number, the largest digit should be positioned at the very left of the number.The digit 0 is never written at the very leftmost position when one of the given digits is 0, but rather in the second place from the left to obtain the smallest number.learn more about greatest numbers click here:
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Isosceles and Equilateral Triangles !
find the volume of the frustum by calculating the radius
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
By the similar triangle, then the value of r is calculated as,
r/30 = 20/40
r = 15 cm
Then the volume of the frustum is calculated as,
V = 1/3 × (30/2)² × 40 - 1/3 × (15/2)² × 20
V = 1/3 × [9000 - 1125]
V = 1/3 × 7875
V = 2625 cm³
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
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Are the ratios 3:12 and 1:4 proportional? Show your work.
Explain:
Answer:
Yes
Step-by-step explanation:
3:12 both have a common factor of 3 you divide both sides by 3 to get 1:4
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The simplified form of the given fraction is, 2/3.
What is greatest common factor?
The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.
Consider, the given fraction [tex]\frac{48}{72}[/tex]
The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
So, from above the greatest common factor of 48 and 72 is 24.
Therefore,
[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]
Therefore, the simplified form of the given fraction is, 2/3.
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Find the nth term : 6, 12, 22, 36…
The nth term of the given sequence is 6n
The given sequence is 6, 12, 22, 36,....
The formula to find the nth term is
T(n) = a + (n-1)d ... (1)
Where n is the number of terms
a is first term
d is common difference
Here
n = n. a = 6,
d = 12 - 6 = 6
Substitute the values in equation (1)
T(n) = 6 + (n-1)6
⇒ T(n) = 6 + 6n - 6
⇒ T(n) = 6n
Hence the nth term of the given sequence is 6n
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If 2,000 mL can fit in a certain glass jar, how many liters can fit in 4.5 of these jars?
Answer: 9,000 mL
Step-by-step explanation:
If you multiply 2,000 by 4, you would get 8,000 & if you multiply .5 by 2,000, you get 1,000. If you add both the totals, you would end up with a final answer of 9,000 mL.
plss need help with this
Answer:
The solution is (-2, 4).
How do I find the measure of the triangles? Help.
Answer:
Step-by-step explanation: I am guessing that it is 180
The football team played 10 games and won 7 games. What was its winning percentage?
Answer: 70%
Step-by-step explanation:
Percentage is always out of 100. And 10x10 =100 so you do the same to 7 multiply it by ten then your answer is 70 which is 70%.
A seamstress usually sews 55 pieces per day. on a certain day,
she sews 77 pieces. what is the percent increase in the number
of pieces she sews on that day?
The percentage increase in the number of pieces she saws on that day is 40%.
Here it is given that a seamstress sews 55 pieces per day.
But on a certain day, 77 pieces were sewn.
We have to find the percentage increase in the number of pieces she sews on that day.
So first we have to find the increase in the number of pieces she sews.
Increase in the number = 77 - 55
= 22
The original number per day = 55
Formula to find the percentage increase in the number.
Percentage increase = Increase in number/ original number × 100
Now putting the values in the equation:
Percentage increase = 22 / 55 × 100
= 2/5 × 100
= 40%
Therefore there is a 40% increase in the number of pieces.
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the motel in the preceding example uses approximately600 bars of soap each day, and this tends to be fairly constant. lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. a service level of 90 percent is desired. the re-order point (rop) is:
The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
Define the term reorder point (ROP)?An exact level where the your stock has to be restocked is characterized as a reorder point (ROP). To put it another way, it advises you when to order so that you won't run out of supply.You'll need to be aware of the following factors in order to figure out the ROP for every item:Lead period: Days needed (in days) for the vendor to complete your orderSafeguard stock: The quantity of excess stock, if any, you maintain on hand to assist prevent stockoutsDaily usage: Average number of sales that particular item typically sees per day.ROP = (Daily usage x Lead period) + Safeguard stock
For the given question;
Lead time = 6 days
Safety stock = 2 days x 600 bars = 1200 bars
ROP = (600 x 6) + 1200 = 4800 bars.
Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
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How many zeros are in the graph for x^3+8x^2+11x-20? How you know they are the zeros? What does this tell us about the graph?
Answer:
There are 2 zeros. You know they are zeros because they are the only two points that intercept the x-axis. There is one touch zero and one bounce zero, meaning there are both even and odd multiplicities in the graph.
write a function that will standardize a multivariate normal sample for arbitrary n and d. that is, transform the sample so that the sample mean vector is zero and sample covariance is the identity matrix. to check your results, generate multivariate normal samples and print the sample mean vector and covariance matrix before and after standardization.
The function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.
Hence, the function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
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Solve S = 2πrh for h
Answer: [tex]h=\frac{S}{2πrh}[/tex]
Step-by-step explanation:
= Solve S = 2πrh:
= [tex]h=\frac{S}{2πrh}[/tex]
