The number of arrangements of the letters in mathematics such the last vowel in the arrangement is an i are 30,240.
To find the number of arrangements of the letters in "mathematics" such that the last vowel in the arrangement is an "i". Counting the vowels, we have three vowels that are a, e, and i.
Count the number of ways to arrange the three vowels in the word. This is a permutation problem, and we can use the formula for permutations of n objects taken r at a time, which is:
P(n, r) = n! / (n-r)!
So, putting the values,
P(3, 3) = 3! / (3-3)! = 3! / 0! = 6
There are 6 methods to arrange a, i and e in the word. Now, we have to arrange the consonants. There are 7 consonants in "mathematics", but we have already placed the last vowel as "i", so we only need to arrange the remaining 6 letters. This is again a permutation problem, and we can use the formula for permutations of n objects taken r at a time:
P(n, r) = n! / (n-r)!
Putting values,
P(7, 6) = 7! / (7-6)!
= 7! / 1!
= 5040
There are 5040 ways to arrange the remaining 6 letters in the word.
Finally, we can multiply the number of arrangements of the vowels and the number of arrangements of the remaining consonants to get the total number of arrangements that meet the given condition:
6 * 5040 = 30,240
Therefore, there are 30,240 arrangements of the letters in "mathematics" such that the last vowel in the arrangement is an "i".
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a circle centered at the origin has a radius of 12. What is the equation of the circle?
After looking through the sentence comparison examples, what do you think the guidelines are that tell you when to use the different forms of you?" Write down your thoughts about this grammar principle. Specifically, write down a "rule" that you think Spanish uses to explain the difference between tú and usted. Then check out the grammar pattern in the next link to see if your hunch was correct
The equation of a circle centered at the origin with a radius of 12, which is x² + y² = 144.
To find the equation of the circle, we use the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the center of the circle, and r is the radius.
In our problem, the center of the circle is at the origin, which means h = 0 and k = 0. The radius is given as 12, so we have r = 12. Substituting these values into the standard form equation, we get:
(x - 0)² + (y - 0)² = 12²
Simplifying, we get:
x² + y² = 144
Therefore, the equation of the circle centered at the origin with a radius of 12 is x² + y² = 144.
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The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Bus is the preferred transportation for 25 residents.
Bicycle is the preferred transportation for 48 residents.
Together, Streetcar and Cable Car are the preferred transportation for 42 residents.
Together, Walk and Streetcar are the preferred transportation for 165 residents.
The correct conclusion we can draw from the circle graph is an option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents."
As per the information provided, it is given that:
Bicycle is the preferred transportation for 8% of 300 residents, which is 0.08 x 300 = 24 residents.
Therefore, option (B) "Bicycle is the preferred transportation for 48 residents" is not correct, as it represents twice the actual number.
Option (A) "Bus is the preferred transportation for 25 residents" is not supported by the information in the graph, as the bus section represents 10% of the graph, but we don't know the actual number of residents who prefer the bus.
Option (C) "Together, Streetcar and Cable Car are the preferred transportation for 42 residents" is not correct, as the cable car section alone represents 27% of the graph, which is more than 42 residents.
Option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents" is supported by the information in the graph, as the walk section represents 40% of the graph, which is 0.4 x 300 = 120 residents, and the streetcar section represents 15% of the graph, which is 0.15 x 300 = 45 residents.
Therefore, the total number of residents who prefer walking or streetcar is 120 + 45 = 165.
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The area of a rectangular field is 4235 m2. If the width of the field is 55m, what is the length?
Answer:
The length of the rectangular field is 77 meters.
Step-by-step explanation:
We can use the formula for the area of a rectangle to solve this problem:
Area = length x width
We are given that the area is 4235 m² and the width is 55 m. We can substitute these values into the formula and solve for the length:
4235 = length x 55
To isolate the variable "length" on one side of the equation, we can divide both sides by 55:
4235/55 = length
Simplifying the right side gives:
77 = length
can you guys please help me on this?
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?
A.1.5 inches by 1 inch
B.2 inches by 1 inch
C.1 inch by 0.5 inches
D. 12 inches by 8 inches
Piper cut the corner off a piece of wood to use for a project. What is the area, in square feet, of the piece of wood that is left? 5 ft 8 ft 2.5 ft 2.5 ft .
Answer:
5(8) - (.5)(2.5)(2.5) = 40 - 3.125
= 36.875 square feet
Find the y-intercept of the line: x + 4y + 8 = 0
Answer:
y intercept is -2
Step-by-step explanation:
y intercept is when x is 0.
original equation:
If you want to make it into something solvable, you want to move everything but y to one side.
1. x+4y+8=0
2. 4y+8=-x
3. 4y=-x-8
4. y=-1/4x-2
5. Since this is a linear function, all you have to do to find the y intercept is plug x in with 0. (mentioned above)
6. y=-1/4(0)-2
7.y=-2
8. y int=-2
I NEED HELP!! what is going on with this problem???? A point in the figure below is chosen at random. Find the probability that the point lies in the region. Give answer as a percent.
The probability that the point lies in the region is 21.5%
How to determine the probabilityNote that percentage is the ratio of a number and 100.
From the information given, we have that;
The total area of the figure = 22(22 ×2)
expand the bracket
Total area = 22(44)
Total area = 968 units square
Area of the shaded area is expressed as;
= Total area - 2area of a circle
substitute the values
= 968 - 2πr/2²
=968 - 2(3.14 × 11²)
find the square
= 968 - 759. 88
= 208. 12 units square
The probability is;
Area of shaded are/total area × 100/1
208. 12/968 × 100/1
21. 5%
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discrete math steve wants to buy up to 20 bottles of orange juice. if there are 8 different brands he can choose from, how many ways can he buy the bottles?
The number of ways Steve can buy bottles of orange juice is equal to 1.3176 x 10¹⁸ ways.
Number of bottles of orange juice Steve wants to buy = up to 20
⇒ He can buy any number of bottles from 0 to 20, inclusive.
Number of available different brands = 8
For each number of bottles he decides to buy, he can choose from 8 different brands.
Use the sum rule of counting to find the total number of ways Steve can buy the bottles.
Number of ways
= number of ways to buy 0 bottles + number of ways to buy 1 bottle + ... + number of ways to buy 20 bottles
The number of ways to buy a specific number of bottles use the product rule of counting.
Number of ways to buy x bottles
= number of ways to choose a brand for each bottle is 8ˣ
Putting everything together, we get,
⇒ Number of ways = 8⁰ + 8¹ + 8² + ... + 8²⁰
This is a finite geometric series with a first term 'a' of 1 and a common ratio 'r' of 8.
Use the formula for the sum of a finite geometric series to simplify,
Sum = a ( 1 -rⁿ⁺¹)( 1 - 4)
Sum = (1 - 8²¹) / (1 - 8)
= (1 - 8²¹) / (-7)
= 1.3176 x 10¹⁸ ways.
Therefore, Steve can buy the bottles in 1.3176 x 10¹⁸ ways.
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suppose you want have a coin that you think might not be exactly fair, that is the probability of a head might be slightly different from 0.5. you would like to produce a 95% confidence interval for p, the true probability of a head. you decide that you would like the margin of error for your interval to be plus or minus 0.001 (that is plus or minus 0.1%). how many times, n, do you need to toss the coin to be sure your ci has this margin of error, or less?
We would need to toss the coin 46,316 times to be sure that our confidence interval has a margin of error of no more than plus or minus 0.001.
To calculate the sample size needed for our desired margin of error, we use the following formula:
n = (z² x p x (1-p)) / E²
where n is the sample size, z is the z-score corresponding to the desired level of confidence (in our case, 1.96 for 95% confidence), p is our estimate of the probability of a head, and E is the margin of error we want (in our case, 0.001).
Since we don't know the true probability of a head, we can use our best estimate based on past experience or a preliminary study. Let's assume we believe the probability of a head is 0.52.
Plugging in these values, we get:
n = (1.96² x 0.52 x 0.48) / 0.001² ≈ 46,316
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Let R(s, t) = F(u(s, t), v(s, t)), and assume the following are true.
u(1, 0) = 2
us(1, 0) = −2
ut(1, 0) = 6
v(1, 0) = 3
vs(1, 0) = 5
vt(1, 0) = 4
Fu(2, 3) = −1
Fv(2, 3) = 10
Find the values below.
Rs(1, 0) =
Rt(1, 0) =
Answer:
To find Rs(1,0) and Rt(1,0), we need to use the chain rule of partial differentiation.
Rs(1,0) can be found by computing the partial derivative of R with respect to s, while holding t constant and then evaluating the result at (1,0). Similarly, Rt(1,0) can be found by computing the partial derivative of R with respect to t, while holding s constant and then evaluating the result at (1,0).
Using the chain rule, we have:
Rs = Fu * us + Fv * vs
Rt = Fu * ut + Fv * vt
We are given the values of u, v, us, ut, vs, vt, Fu, and Fv at the point (1,0) and the values of u and v at the point (2,3). We can use these values to compute Rs(1,0) and Rt(1,0) as follows:
Rs(1,0) = Fu(2,3) * us(1,0) + Fv(2,3) * vs(1,0)
= (-1) * (-2) + (10) * (5)
= 52
Rt(1,0) = Fu(2,3) * ut(1,0) + Fv(2,3) * vt(1,0)
= (-1) * (6) + (10) * (4)
= 34
Therefore, Rs(1,0) = 52 and Rt(1,0) = 34
the picture is below I NEED HELP FAST IT'S DUE TOMMOROW
Answer:
I would say -F=0.4
Step-by-step explanation:
if F=-0.4 and -F is the opposite of F then the opposite of -0.4 is 0.4
In Ms. Talley's class, 9 out of 30 students have afterschool jobs. In Mr. William's class, 8 out of 25 students have afterschool jobs. Which statement is correct? Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is greater than 8 over 25. Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25. Ms. Talley's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25. Both classes have the same ratio of students with afterschool jobs.
Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25. Therefore, the second statement is correct.
Comparing the ratios of students with afterschool jobs in Ms. Talley's and Mr. William's classes.
Ms. Talley's class
Students have afterschool jobs = 9 out of 30
Ratio = [tex]\frac{9}{30}[/tex]
Mr. William's class
Students have afterschool jobs = 8 out of 25
Ratio = [tex]\frac{8}{25}[/tex]
Let us now compare the ratios:
9/30 = 0.3
8/25 = 0.32
Comparing the ratios, we can see that 0.32 is greater than 0.3.
As a result, compared to Ms. Talley's class, Mr. William's class has a higher percentage of students who have afterschool jobs.
Therefore, the correct statement is: Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25.
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Solve 3||y+6||=30.
Multiple choice question.
A)
{–16,4}
B)
{–12,8}
C)
{4,16}
D)
{–4,4}
Answer:
Step-by-step explanation:
||y + 6|| = 10
Next, we can consider the two possible cases:
Case 1: y + 6 ≥ 0
If y + 6 is non-negative, then the absolute value of y + 6 is just y + 6 itself. So we have:
y + 6 = 10
y = 4
Case 2: y + 6 < 0
If y + 6 is negative, then the absolute value of y + 6 is the opposite of y + 6, which is -(y + 6). So we have:
-(y + 6) = 10
y + 6 = -10
y = -16
Therefore, the solutions to the equation 3||y + 6|| = 30 are y = 4 and y = -16.
the distribution of total body protein in healthy adult men is normal with mean 12.3 kgand standard deviation 0.4 kg. if you take a random sample of 4 healthy adult men, what is theprobability that their mean total body protein is between 12.2 and 12.4 kg?
The probability that their mean total body protein is between 12.2 and 12.4 kg is 0.6826.
We know that the conveyance of the test mean is additionally ordinary with the mean breaking even with the populace mean and standard deviation rising to the populace standard deviation isolated by the square root of the test measure.
Let X be the whole body protein in sound grown-up men.
At that point, we have:
X ~ N(12.3, 0.4²) (populace conveyance)
X bar ~ N(12.3, 0.4²/4) = N(12.3, 0.2²) (dissemination of test cruel)
We need to discover P(12.2 ≤ X bar ≤ 12.4) for a test measure of n=4.
Utilizing standardizing the dispersion of the test mean, we have:
z = (X bar - μ) / (σ / √(n))
where μ = 12.3, σ = 0.2, n = 4
z = (12.2 - 12.3) / (0.2 / √(4)) = -1
z = (12.4 - 12.3) / (0.2 / √(4)) = 1
Employing a standard ordinary dispersion table, we are able to discover the likelihood:
P(-1 ≤ z ≤ 1) = P(z ≤ 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826
In this manner, the likelihood that the mean adds up to body protein of a test of 4 solid grown-up men is between 12.2 and 12.4 kg is 0.6826.
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What is the slope of the linear relationship shown on the graph?
Answer:
Step-by-step explanation:
A date in the month of October and a letter of the alphabet are chosen at random. How many outcomes are possible?
2. A bank account has $10,000 in it. The account pays a 6% interest rate compounded monthly. What was the principal amount in the account if it was opened 4 years ago?
Answer:
An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
If 15 people can do a piece of work in 6 days, how many days, to the nearest whole number, should 8 people take to do it? Assume that the rate of work is the same.
Answer:
20 days for 8 people to do the work Assuming that the rate of work is the same.
Twenty students volunteered to take a fitness test. We want to know if there is a convincing evidence of a positive linear relationship between speed (mph) and jump height. What is the p value of this test
Twenty students volunteered to take a fitness test. If there is a convincing evidence of a positive linear relationship between speed (mph) and jump height.
To find the p-value for this test, we need to perform a hypothesis test. Let's assume that the null hypothesis is that there is no relationship between speed and jump height (i.e., the slope of the regression line is zero), and the alternative hypothesis is that there is a positive linear relationship between speed and jump height (i.e., the slope of the regression line is positive).
We can use a simple linear regression model to test this hypothesis. Let x be the speed (in mph) and y be the jump height (in inches). We can fit a linear regression model to the data and obtain the estimated slope and intercept of the regression line, denoted by b1 and b0, respectively. We can also compute the standard error of the slope, denoted by SE(b1), and the t-statistic for testing the null hypothesis, given by
t = b1 / SE(b1)
Under the null hypothesis, this t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size (in this case, n=20).
To find the p-value for this test, we need to calculate the probability of observing a t-statistic as extreme as the one we computed, assuming that the null hypothesis is true. We can use a t-distribution table or a statistical software package to obtain this probability.
Assuming that the null hypothesis is true, if the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is convincing evidence of a positive linear relationship between speed and jump height.
Hence, we cannot provide an exact p-value without knowing the specific data values and the results of the regression analysis.
The given question is incomplete.
The complete question is "Twenty students volunteered to take a fitness test. The computer output below is a regression analysis of the relationship between x = how fast they can ran a mile (in mph) and y = how high they can jump (in inches).
(1) We want to know if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these. What is the P-value of this test?"
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PLS help with this question... I got a practice test today...
PLS reply ASAP..
The expressions with the options that will give 4^-12 are
A, C, and DHow to find the expressions that are equal 4^-12The expression is an exponent of negative integer. The options are simplified further to their simplest forms as shown below
A. 4^-10 * 4^-2
The equation is multiplied to give a result of 4^-12
B. (1/4^-3)^4
= (4^3)^4
= 4^12
C. (4^-16)^4
= 4^(-16+4)
= 4^-12
D. 4^3 / 4^15
= 4^(3 - 15)
= 4^-12
E. (4^-7 * 4^-2) / 4^3
= 4^(-7 + (-2) + 3)
= 4^6
Hence the expression that will result to 4^-12 are A, C, and D
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pls aswerrr
worth 30 pointsss
Answer:
divide d by 1
6.7÷1 so it will be the answer
to estimate the population parameter, will you construct a confidence interval to estimate a population proportion or a confidence interval to estimate a population mean? select the best answer option below.group of answer choiceswe will use a confidence interval to estimate a population mean becasue iat-score is quantitative variable.we will use a confidence interval to estimate a population mean becasue iat-score is categorical variable.we will use a confidence interval to estimate a population proportion becasue iat-score is quantitative variable.we will use a confidence interval to estimate a population proportion becasue iat-score is categorical variable. flag question: question 2question 25 ptsassuming conditions are met, which model should you use, a z-model or a t-model? select the best answer option below.group of answer choicesuse a t-model because the population standard deviation, , is known.a z-model because population standard deviation, , is known.a t-model because population standard deviation, , is not known.a z-model because the population standard deviation, , is not known.
The t-model is used to estimate the population means when the sample size is small or when the population standard deviation is unknown. It takes into account the variability in the sample and provides a more accurate estimate of the population mean.
To estimate a population parameter, we need to use a confidence interval. But the question is whether we should use a confidence interval to estimate a population proportion or a population mean. In this case, we need to consider the nature of the variable being measured. If the variable is quantitative, such as the IAT score, we should use a confidence interval to estimate a population means.
On the other hand, if the variable is categorical, such as gender or race, we should use a confidence interval to estimate a population proportion. Therefore, the correct answer is "We will use a confidence interval to estimate a population means because the IAT score is a quantitative variable."
Now, assuming that the conditions are met, we need to determine which model to use – a z-model or a t-model. This decision depends on whether we know the population standard deviation or not. If we know the population standard deviation, we should use a z-model. However, in most cases, we do not know the population standard deviation, so we need to use a t-model. Therefore, the correct answer is "a t-model because population standard deviation, sigma, is not known."
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a vehicle consumes 120l of fuel within a distance of 3000km. what is the rate of the fuel consumption in km/h?
Fuel consumption rate = Fuel used / Distance traveled
First, let's convert the fuel used from liters to milliliters (ml) for convenience in calculations:
Fuel used = 120 L = 120,000 ml
Now we can substitute the given values into the formula:
Fuel consumption rate = 120,000 ml / 3000 km
Simplifying this expression, we get:
Fuel consumption rate = 40 ml/km
This means that the vehicle uses 40 milliliters of fuel to travel 1 kilometer. To convert this to a more commonly used unit of fuel consumption, we can use the conversion factor of 1 L = 1000 ml:
Fuel consumption rate = 0.04 L/km
Finally, to find the rate of fuel consumption in km/h, we need to divide this value by the vehicle's speed in km/h. However, the problem does not provide information about the vehicle's speed, so we cannot determine the fuel consumption rate in km/h.
Step-by-step explanation:
Solve for a. 25° 55° a a = [? ]° 30°
We can determine that the necessary angle ∠a is 15° using the provided secant line.
A secant crosses a circle at precisely two points in a case of a circle.
Mathematicians refer to a line that cuts through the points P and Q of any arbitrary curve whose equation is y=f as a secant, from the Latin term secant, which means to cut (x).
So, we know that:
c = 55° and b = 25°
And, the formula is:
∠a = c - b/2
Now, substitute values as follows:
∠a = c - b/2
∠a = 55 - 25/2
∠a = 30/2
∠a = 15°
Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.
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Complete question:
The prices of backpacks are $37, $43, $41, $36, $44, and $70. Calculate the mean and median with and without the outlier. Round to the nearest tenth, if necessary. Then state whether the mean or the median best describes the center.
Answer: Mean: 40.2, Median: 41
Step-by-step explanation: 37, 43, 41, 36 and 44 added all together is 201 / 5 = 40.2 (70 is the outlier). The middle of 37 43 41 36 44 is 41, because the numbers lined up is 36, 37, 41, 43, 44 the middle is 41.
Lena bought a total of 20 postcards. She bought 6 more large postcards than small. Write a system of equations that represents the postcards Lena purchased. Solve the system by substitution. Interpret the solution.
The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Let x be the number of small postcards that Lena bought, and let y be the number of large postcards she bought.
From the problem statement, we know that:
Lena bought a total of 20 postcards, so x + y = 20.
Lena bought 6 more large postcards than small, so y = x + 6.
Now we can substitute the second equation into the first one to eliminate y:
x + (x + 6) = 20
Simplifying the equation, we get:
2x + 6 = 20
2x = 14
x = 7
So Lena bought 7 small postcards and y = x + 6 = 13 large postcards.
The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.
Interpretation: Lena bought more large postcards than small postcards, and the difference between the two is 6. Out of the 20 total postcards, 13 were large and 7 were small.
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pls help due soon if your right ill mark you brainliest asap
Answer:
D
Step-by-step explanation:
pls help me im rlly bad at math 819 divided by 63
Answer: 13
Step-by-step explanation: take 63 out of 819 and see how many times you can take it that out
Answer: It's 13, hop this helps!!!
Find the number which is obtained when 3 is multiplied by one less than the difference of 19 and 5
Answer: The number is 42
Step-by-step explanation:
difference of 19 & 5 = 19 - 5
= 14
One less than = 14-1
= 13
=> 13*3
= 39
