The different ways of arranging these categories will be 720.
What is the factorial of n?The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as,
n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1
We have the group letter (A-F). Then the number of letters is given as,
n = 6 (A, B, C, D, E, F)
Then the different ways of arranging these categories will be given as,
⇒ 6!
⇒ 6 x 5 x 4 x 3 x 2 x 1
⇒ 720
The different ways of arranging these categories will be 720.
More about the factorial of n link is given below.
https://brainly.com/question/16003649
#SPJ1
What type of function is represented in the table? exponential linear quadratic logarithmic.
The type of function represented in the table is exponential.
The table shows an exponential function, which is a function that increases or decreases by a constant rate over a period of time. The table shows a relationship between the x-values and the y-values, where the y-values increase or decrease by a constant factor as the x-values increase. In this particular table, the y-values increase by a factor of two as the x-values increase by one. This type of function is common in mathematics and can be used to model a variety of real-world phenomena, such as population growth, compound interest, and radioactive decay.
Learn more about exponential function: https://brainly.com/question/11464095
#SPJ4
Nicole is saving money. Nicole started with $5 and added $15 every week. Find the rate of change.
Answer:
The Mathman guy is wrong, the answer is actually 15.
Step-by-step explanation:
because from the equation that you gave, nicole started with $5 and added $15 every week
thus let y represent the total money and x represent the number of week after x week
nicole save: 15x
because at the beginning he has $5
so, y = 15x + 15
y = mx+c m is the slope c is the y intercept
so slope = 15
so we reach to the conclusion that the rate of change is 15
The Browns are buying a new living room set for $1,875. They made a down payment of $250 and financed the rest. How much did the Browns finance?
Answer:
$1,625
Step-by-step explanation:
Write an equivalent expression to the following: 5y + 35 HINT: Think distributive property.
what is the least number of terms required to compute pi as 3.14
The least number of terms required to compute pi as 3.14 is approx 400.
The series is π = 4 - 4/3 + 4/5 - 4/7 + .................
We have to determine the least number of terms required to compute pi as 3.14.
We can write the series as
π = 4(1 - 1/3 + 1/5 - 1/7 + .................)
The general equation of this series is
π = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]
Now let S = π. So
S = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]
From the Alternating series theorem
|S - S(n)| ≤ 4/(2n+1)
Hence, the accuracy should be
4/(2n+1) ≤ 1/2 × 10^{-2}
Multiply by 2 on both side, we get
8/(2n+1) ≤ 10^{-2}
We can write 10^{-2} as 1/100. Now the expression is
8/(2n+1) ≤ 1/100
Multiply by 100 on both side, we get
800/(2n+1) ≤ 1
Multiply by 2n+1 on both side, we get
800 ≤ 2n+1
Subtract 1 on both side, we get
2n ≥ 799
Divide by 2 on both side, we get
n ≥ 399.5
Hence, approx 400 terms need to compute pi as 3.14.
To learn more about Alternating series theorem link is here
brainly.com/question/14446730
#SPJ4
The complete question is:
What is the least number of terms required to compute pi as 3.14 using the series:
π = 4 - 4/3 + 4/5 - 4/7 + .................
How does the square root function differ from the cube root function?
The square root function contains a variable under the square root sign. The cube root function contains a variable under the cube root sign.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varying quantities and other variables.
A variable under the square root sign is present in a square root function, and a variable under the cube root sign is present in a cube root function.
Zero has a square root of zero, and one has a square root of one. Keep in mind that the graph only contains points where x and y are positive. For instance, using the imaginary number i is necessary when taking the square root of a negative number.
The square root function is f(x) = √x
For positive values, the graph resembles the square root graph, but cube roots can also be negative, making this equation infinite for all real numbers. Recall that a negative number will result from being multiplied an odd number of times.
The cube root function is f(x) = ³√x
To learn more about function, click on the below link:
https://brainly.com/question/23567345
#SPJ4
Chritine had already knitted 15 row of a carf. She knitted r more row over the weekend. Chooe the expreion that how the number of row Chritine ha knitted in all
"15 + r" is the expression that represents the total number of rows knitted by Christine. Thus, option B is correct.
To find the total number of rows Christine has knit, we need to add the number of rows she knit over the weekend (represented by the variable "r") to the number of rows she had already knit (15).
This can be done by using the expression:
15 + rThis expression states that the total number of rows is equal to the initial number of rows (15) plus the additional rows knit over the weekend (represented by the variable "r"). The value of "r" could be any number, so the expression "15 + r" could represent any total number of rows.
For example, if Christine knit 5 more rows over the weekend, the expression "15 + 5" would equal 20, so Christine has knit a total of 20 rows.
This question should be provided as:
Christine had already knit 15 rows of a scarf. She knitted r more row over the weekend. Choose the expression that shows the number of rows Christine has knitted in all.
A. 15B. 15 + rC. 15 - rD. r - 15Learn more about math expression here: brainly.com/question/1859113
#SPJ4
PLEASE HELP I NEED IT FAST
3. Mr. Sanchez’s class sold fruit pies for $1.45 each and Mr. Kelly’s class sold bottles of fruit juice for $1.25 each. Together, the classes sold 53 items and earned $70.85 for their school. (a) Write and solve a system of equations that model the problem. Show all your work. (b) Which class earned more money? (c) How much more money did that class earn?
Sanchez made more money by 3.93$
Please help need this done asap
Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.
what is triangle ?Since that it has three sections and two vertices, a triangular qualifies as a polygon. It corresponds to the essential geometric patterns. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. Because when three principles are not linearly related, a unique plane composite triangle in Geometric shapes are discovered. Triangles are polygons because they have three sections and three corners. The points where it three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
given
m∠ELG = 124°
m∠ELD = 2x
Thus:
m∠ELG + m∠ELD = 180° (linear pair)
Substitute
124 + 2x = 180
2x = 180 - 124
2x = 56
x = 56/2
x = 18
Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Exponential Functions
The exponential growth factor of the given function is 7.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
The slope of the line that represents a linear relationship is equal to the growth factor. When the relationship is shown as an equation in the form y = mx + b, the growth factor is also equal to the value of m.
Given exponential function is
y = 4 * 5⁷.
Now compare the given function with y = P₀e^k
P₀ = 4
e = 5
k = 7
The growth factor is 7.
To learn more about exponential Functions, click on the below link:
https://brainly.com/question/29004772
#SPJ1
How do you convert 162 Pound (lb) to Kilogram (kg)?
To convert 162 pounds to kilograms, you can use the following conversion factor 1 pound = 0.453592 kilograms
How do you convert 162 Pound (lb) to Kilogram (kg)?The conversion factor of 1 pound to 0.453592 kilograms is based on the definition of the kilogram as being equal to approximately 2.20462 pounds.To convert from pounds to kilograms, simply multiply the number of pounds by the conversion factor of 0.453592.For example, 162 pounds is equal to 162 x 0.453592 = 73.48776 kilograms.This conversion factor is commonly used in various industries, such as sports, health, and trade, to convert weights between pounds and kilograms.It's important to keep in mind that this conversion factor is an approximation and may not be entirely accurate in all situations.For more precise conversions, it's best to use a conversion calculator or a reference guide that provides exact conversion factors.
To learn more about pounds to kilogram refer:
brainly.com/question/30400939
#SPJ4
Corey ram around a rengtanguler soccer field that measures 38.50 m by 27.345 m. How far did Corey run
Corey ran 131.69 meters around a rectangular soccer field.
What is rectangular perimeter?The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
Given:
Corey ran around a rectangular soccer field that measures 38.50 meters by 27.345 meters.
Corey ran = Perimeter of rectangle =2 (38.50 + 27.345)
Corey ran = 131.69 meters.
Therefore, Corey ran 131.69 meters.
To learn more about the rectangular perimeter;
https://brainly.com/question/22109593
#SPJ1
When 256 i multiplied by a poitive power of 10 the number of zero in the product i related to the power of 10. Explain how the number of zero relate to the power of 10
If you multiply 256 by 10 powered by k, then the number of zeros in the product is k
How to find integer?In this case, we have the number 256, but in reality, every INTEGER number multiplied by 10 empowered by n, the number of zeros will be equal to n.This is because, when multiplying by 10, a zero would be put. Now when multiplying to 10 * 10 = 10 ^ 2, it would have 2 zeros in the final product, and so on until leading to 10 ^ n, the result would have n zeros in the final product.Let x be any integer, if you multiply x by 10 you will have to add one zero at the right of x. If you multiply by 10 again, you will have to add a second zero at the right, thus if you multiply by 100, you will have to add 2 zeros. If you multiply by 1000 = 10*10*10 = 10³ you will have to add 3 zeros and so on.Therefore, if you multiply 256 by 10^k, then you will have to add k zeros to 256, and as a consequence, the amount of zeros in the product is equal to the power of 10 we are multiplying.
To learn more about integer refers to:
brainly.com/question/15459916
#SPJ4
Which expression represents the final cost of 1 sweatshirt 2 T shirts and 1 pair of pants
The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.
The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants can be represented by the following formula:
Final Cost = Sweatshirt Cost + (2 x T Shirt Cost) + Pants Cost
For example, if the cost of a sweatshirt is $20, the cost of a T shirt is $10, and the cost of a pair of pants is $30, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be:
Final Cost = $20 + (2 x $10) + $30
Final Cost = $20 + $20 + $30
Final Cost = $70
Therefore, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.
Learn more about Final Cost here:
https://brainly.com/question/19075809
#SPJ4
Complete question:
What is the Final Cost of 1 Sweatshirt, 2 T-Shirts, and 1 Pair of Pants?
How do you write intervals of increase and decrease?
For a real-valued function f, it is said that the interval's value increases for every x and y where f (x) f (y) (x). and the interval is referred to as declining if its value is f (x) f (y) for every x y.
What is meant by intervals?An interval is described numerically in mathematics. An interval is any set of numbers that fall between two distinct integers.This range includes all real values that fall between those two. Any kind of number you can think of exists.The distance between the upper and lower class limits is known as the class interval. For instance, the first class's class interval is 30 - 26 = 4, which is a size of 4. Similar to the first class, the second class's class interval measures 31 minus 35, or 4. A range of numbers between two given numbers that contains all of the real numbers in that range is known as an interval.To learn more about intervals, refer to:
https://brainly.com/question/27998402
#SPJ4
complete the table. please answer
The complete points of each x for the given linear function are:
(-2, 2)(0, 4)(2, 6)(6, 10)(8, 12)Please refer to the attached graph for the graph of the function.
From the question, we have a linear function of:
y = x + 4
x points given are:
x = -2x = 0x = 2 x = 6x = 8Let's try to find the output of y and the (x,y) point for each given x-point:
x = -2
y = (-2) + 4
y = 2 --> (-2, 2)
x = 0
y = (0) + 4
y = 4 --> (0, 4)
x = 2
y = (2) + 4
y = 6 --> (2, 6)
x = 6
y = (6) + 4
y = 10 --> (6, 10)
x = 8
y = (8) + 4
y = 12 --> (8, 12)
Those points are used to make a graph as attached below.
Learn more about Linear Function here: brainly.com/question/29205018
#SPJ1
Sand sells at 8. 5 cents per pound. How much would you save by buying a 100 pound sack at $8. 25?.
Answer:
25 cents
Step-by-step explanation:
Sand sells at 8.5 cents per pound, an hundred-pound bag of this price would total $8.50 (8.5 * 100).
This is 25 cents more than buying a hundred-pound bag for 8.25, meaning you would save [25 cents]
Guys its that time, I neeed help
The slant height,
x = 5 meters.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
A right circular cone is 4 meters tall and have a radius 6/2 = 3 meters.
Applying the Pythagoras' theorem,
The slant height = √{(3)² + (4)²}.
The slant height = √25
The slant height = 5 meters.
Therefore, the slant height = 5 meters.
To learn more about the Pythagoras theorem;
https://brainly.com/question/343682
#SPJ1
A group of adult males has foot lengths with a mean of 27. 41 cm and a standard deviation of 1. 31 cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 24. 2 cm significantly low or significantly high? Explain
The adult male foot length of 24.2 cm is significantly low as it falls outside of the range of 26.10 cm to 28.72 cm.
The range is just the difference between the greatest and smallest data points in a set.
The square root of the variance is the standard deviation.
The standard deviation measures how far apart the data is from the mean.
The range is a less useful measure of variance than the standard deviation.
The range of data is a measure of variance that indicates the difference between the dataset's maximum and least observation.
It is based only on two observations, the maximum and minimum.
The range rule of thumb states that approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% of the data falls within two standard deviations of the mean.
So, the lower limit separating significantly low values will be:
27.41 - 1.31 = 26.10 cm
And the upper limit separating significantly high values will be:
27.41 + 1.31 = 28.72 cm.
For more questions on Range and Standard deviations
https://brainly.com/question/30373365
#SPJ4
how many arrangements are there of all the letters of sociological
As per the concept of permutation, there are 362,880 possible arrangements of the letters of "sociological."
In mathematics and combinatorics, the number of arrangements of a set of objects is calculated using a formula called permutation.
When it comes to the word "sociological," there are 9 letters, and we want to calculate the number of arrangements that can be made using all 9 letters.
To find the number of arrangements, we can use the formula for permutation.
In this case, it would be
=> 9!
which is equal to
=> 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Complete Question:
How many arrangements are there of all the letters of word "sociological" calculate it by using the permutation method?
To know more about permutation here.
https://brainly.com/question/1216161
#SPJ4
Line C has a slope of -8/3. Line D is parallel to line C. what is the slope of line C?
Since line C has a slope of -8/3 and line D is parallel to line C, the slope of line C is equal to -8/3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂
This ultimately implies that, the slope of the two lines are equal and the same:
Slope of line C = Slope of line D
-8/3 = -8/3.
Read more on slope here: brainly.com/question/3493733
#SPJ1
a boat takes 2 hours to travel 28.62 km down a river, then 4.4 hours to return. how fast is the river flowing?
To travel downstream, a boat needs 2 hours while to travel back upstream, it needs 4 hours. The river flows at speed of 3.58 3.58 km/hour
The relation between distance and speed is given by:
distance = speed x travelled time
In the problem, let:
vb = boat speed
v = river speed
Then, when the boat travels downstream:
28.62 = (vb + v) x 2
2vb + 2v = 28.62 ... (Equation 1)
When the boat travels upstream:
28.62 = (vb - v) x 4
Divide both sides by 2:
14.31 = (vb - v) x 2
2vb - 2v = 14.31 ... (Equation 2)
Substract equation 1 by equation 2
2vb + 2v = 28.62
2vb - 2v = 14.31 _
4v = 14.31
v = 3.58
Hence, the speed of water = 3.58 km/hour
Learn more about speed here:
https://brainly.com/question/17146782
#SPJ4
A Spanish class has a total of 41students. The number of females is 13less than the number of males. How many males and how many females are in the class?
Answer:
42-13 =28 so there are 28
how to subtracting mixed fractions with like denominators?
Subtracting mixed numbers with the same denominators
Follow the steps to subtract mixed numbers with the same denominators:
Step 1– Subtract the wholes.
Step 2– Converting the fractions into improper fractions.
Step 3– Subtract the fraction.
Step 4– Swap the improper fraction into a mixed number.
Step 5– Write down the mixed number with wholes and the fraction.
Example- [tex]5\frac{7}{3} - 3\frac{2}{3}[/tex]
Subtract 3 from 5.
5 – 3 =2
Subtract the fractions:
[tex]\frac{7}{3} - \frac{2}{3}[/tex]
Write the fraction with the whole.
[tex]5\frac{7}{3} - 3\frac{2}{3} = 2\frac{5}{3}[/tex]
Read more about fractions:
https://brainly.com/question/17220365
#SPJ4
4. Alexander has a square-shaped basket of apples. The
basket covers the area of 36 squared feet. Find the length of any
side of the basket?
The length of any side of the square basket would be 6 feet.
What are Square roots and length?
In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.
The word "length" refers to the size of an object or the separation between two points. For instance, the length of a ruler is indicated below and indicates how long the ruler is.
You can find this by finding the square root of 36, which is 6.
The length of any side of the square basket would be 6 feet.
Learn more about the equation here,
brainly.com/question/14198272
#SPJ4
Need help
How do you solve this?
a) class interval that contains the median is: 2 ≤ h ≤ 3
b) An estimate for the mean numbers of hours: 23
What is median?In statistics, the median is the value that, when placed in order, falls in the centre of the supplied collection of data. Either descending or ascending order can be used to arrange the data or observations. The median of 2,3,4, for instance, is 3. The median is a form of average that is used to determine the center value in mathematics. The middle pair must be identified, added, then divided by two in order to calculate the median value in a list of even integers.
To find median class calculating cumulative freq. (cf) of less than type first:
Number of hours(h) frequency(f) cf
0 ≤ h ≤ 1 4 4
1 ≤ h ≤ 2 8 12
2 ≤ h ≤ 3 11 23
3 ≤ h ≤ 4 7 30
N/2 = 30/2
Where, N = ∑f
N = 15 ∑cf > N/2
so, median class is 2 ≤ h ≤ 3 since cf 23 is corresponding to this class.
Therefore class interval that contains the median is: 2 ≤ h ≤ 3.
To know more about median refer to:
https://brainly.com/question/26177250
#SPJ1
Drag the values into the boxes to classify each number as rational or irrational.
Answer:
A rational number is any number that can be expressed as a whole number, a fraction, or as a non repeating decimal. Otherwise, it is an irrational number.
19/5: it is a rational number because it is in fraction form
√12: this is an irrational number
√49: this is a rational number because when you simplify this you will get the answer 7, that is a whole number.
0.3425563758: This is a decimal, hence, this is rational.
4/25 : it is a fraction so it is a rational number.
√1/8: this is an irrational number
√0.6¯: this is an irrational number
during the super bowl game, a survey of 5108 randomly selected households finds that 44% of them have television sets tuned to the super bowl (based on data from nielsen media research). what is the sample?
Since the statistical survey was done with 5108 randomly selected households it can be concluded that the sample is 5108 randomly selected households.
In order to draw conclusions about the population as a whole a sample of data can be chosen.
A sample is a subset of a larger population that represents the larger population that is chosen for analysis.
In this instance, the sample consists of 5108 homes that were chosen at random for the survey to determine the proportion of homes with televisions tuned to the Super Bowl.
In order to accurately represent the number of households that watched the Super Bowl, a sample size of 5108 was used.
It should be also noted that Nielsen Media Research is a market research company that specializes in measuring media audiences, including television viewership.
Learn more about statistics:
https://brainly.com/question/29342780
#SPJ4
The position y (in meters) of a submarine after x minutes is y = -8x - 12. Interpret the slope
Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.
What is slope ?
The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
he equation of the position y (in meters) of a submarine after x minutes can be represented as:
y = -8x - 12
Where x is the time in minutes and y is the position in meters. To solve for y, we can substitute a specific value of x and calculate the corresponding value of y.
For example, if we substitute x = 0, we can find the initial position of the submarine:
y = -8 * 0 - 12
y = -12
So, the initial position of the submarine is -12 meters.
In general, the slope of the line represented by this equation is -8, meaning that for every one unit increase in x (i.e., one minute), the position of the submarine decreases by 8 meters.
Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.
To learn more about slope visit : brainly.com/question/3605446
#SPJ4
The position y (8 meters per minute) of a submarine after x minutes is y = -8x - 12,
given that:
The position y (in meters) of a submarine after x minutes is y = -8x - 12
The slope of the equation y = -8x - 12 represents the rate of change of the position of the submarine. It tells us the amount by which the position of the submarine changes for each unit change in time that is (minutes).
In this case, the slope is -8, which means that for each 1-minute increase in time, the position of the submarine decreases by 8 meters. This indicates that the submarine is descending at a rate of 8 meters per minute. Hence our result is 8 meters per minute.
Learn more about Interpret the slope here:
https://brainly.com/question/29075872
#SPJ4
let f(x) = 3x-2x^2 for 0
The solution is of the function 3f(x) +2g(x) is:
=> -5x-2
Now, According to the question:
Algebra of functions:
Algebra of functions means the operations of the functions, specifically the arithmetic operations. Algebra of functions mainly deals with the following four arithmetic operations of functions:
Addition of functionsSubtraction of functionsMultiplication of functionsDivision of functionsThe function given as:
f(x) = -3x, g(x) = 2x-1 are the two functions
then by the algebra of two functions(adding two functions) we can find the value of 3f(x) + 2g(x)
Now find
3f(x) = 3(-3x) = -9x -----------(i)
2g(x) = 2(2x-1)
= 2(2x)-2(1)
2g(x) = 4x-2 ----------(ii)
Now, add the above two equation (i) and (ii)
3f(x) + 2g(x) = -9x + 4x - 2
= -5x-2
Learn more about Algebra of function at:
https://brainly.com/question/28841704
#SPJ4
The given question is incomplete, complete question is:
Let f(x) = -3x and g(x) = 2x-1
Find the following: 3f(x) +2g(x)
0 6x +4
0 -5x - 2
O There is no correct answer given.
O 8x -8
O 5x+1