In 12144 ways the students can get first, second, or third place.
The permutation system is used to locate the special range of preparations that may be shaped through taking r matters from the n to be had matters. Permutations are beneficial to shape distinctive words, quantity preparations, seating preparations, and for al. of the conditions related to special preparations. As consistent with the permutation formula, the permutation of 'r' items taken from 'n' items is identical to the factorial of n divided through the factorial of distinction of n and r.
The formula for permutations is
nPr= n!/(n-r)!
From the given question let us consider,
n= 24 r=3
Now let us solve using formula
24P3= 24!/(24-3)!
=24*23*22*21......*2*1
=12144
Therefore there are 12144 ways.
To know more about Permutations visit:
brainly.com/question/1216161
#SPJ1
Evaluate each expression for the given value of the variable.
(x³ . x⁵ ; x=2)
After evaluating the expression x³ . x⁵, we get the result as 256.
We are given an expression:
x³ . x⁵
We can use the properties of exponents that if the base is same and two numbers are multiplied, then the powers get added.
So, the expression will become:
= x ³⁺⁵
Simplifying the expression, we get that:
= x⁸
Now, we need to evaluate the expression at x = 2
Put x = 2 in the expression, we get that:
= 2⁸
Evaluating it, we get that:
= 256
Therefore, after evaluating the expression x³ . x⁵, we get the result as 256.
Learn more about expressions here:
https://brainly.com/question/723406
#SPJ4
What is the quotient of (x³+2 x²-x+6) / (x+3) ?
(A) x²+5x+14
(B) x²-x+2
(C) x³+5x²+14x+42
(D) x²+x-2
The quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.
What is the Polynomial long division method?Polynomial long division is an algorithm in algebra for dividing a polynomial by another polynomial of the same or lower degree, which is a generalized version of the well-known arithmetic technique known as long division. It is simple to do by hand because it divides an otherwise complex division problem into smaller ones. It is sometimes faster to use a shorthand version called synthetic division, which requires less writing and fewer calculations. Polynomial short division (Blomqvist's method) is another abbreviated method.So, find the quotient of (x³+2 x²-x+6) / (x+3) using the Polynomial long division method:
(x³+2 x²-x+6) / (x+3) ⇒ R = 0 ⇒ quotient = x²-x+2As, (x²-x+2)(x+3) gives (x³+2 x²-x+6).Therefore, the quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.
Know more about the Polynomial long division method here:
https://brainly.com/question/24662212
#SPJ4
Solve the inequality −3s+7 ≤ 8 or −2s+4≥12
Answer: B
Step-by-step explanation:
WHAT IS THE RANGE OF THE FOLLOWING DATA 46, 67, 89, 13, 56, 90, 45, 66
For Grade 7
Answer:
Range = 77
Step-by-step explanation:
1. Reorder all the values in your data set from low to high.
13, 45, 46, 56, 66, 67, 89, 90
2. Subtract the lowest number from the highest number.
90 - 13 = 77
The scale of a map says that 4 cm represents 5 km. Type each answer in the boxes below. a. What distance on the map (in centimeters) represents an actual distance of 4 kilometers? 1$$ centimeters Correct answers: 13.2 0 out of 1 b. What is the actual number of kilometers that is represented by 5 centimeters on the map? 1$$ kilometers
The distance on the map that represents an actual distance of 4 kilometers is 3.2cm.
The actual number of kilometers that is represented by 5 centimeters on the map is 6.25 kilometers.
What are the distances?A scale drawing is a smaller version of a larger image. In this question, the map is a scale drawing of the city. The scale drawing is reduced using constant dimensions using a scale.
A scale gives the ratio of the length of the scale drawing to the actual diagram or object. In this question, every 4cm on the map represents 5km in the city.
The distance on the map = (4 x 4) / 5
16 / 5 = 3 1/5 cm = 3.2 cm
The actual distance = (5 x 5) / 4
= 25 / 4 = 6 1/4 = 6.25 kilometers
To learn more about scale drawings, please check: https://brainly.com/question/26388230
#SPJ1
answer please will mark brainliest
The Volume of the given Hemisphere is 1071.8 cm³ rounded to 1 decimal place whose radius is 8cm
The Volume of the sphere is given by the formula 4/3 πr³
The volume of hemisphere is half of sphere
So, The volume of hemisphere is 2/3 πr³
From the given figure it is clear that the radius of the hemisphere is 8cm
Here, we will use the value of π as 3.14 and not 22/7
So, Substituting the values in the formula of Volume of hemisphere
the Volume of hemisphere =2/3 π (8)³
=2/ 3× 3.14 × 512
= 1071.7867 cm³
Hence, the Volume of hemisphere 1071.7867 cm² or 1071.8 cm² rounded to 1 decimal place whose radius is 8cm
To know more about Volume of hemisphere - https://brainly.com/question/23178590
#SPJ1
Which function represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year?
(A) y=-15(25,000) x (C) y=25,000(0.85)x (B) y=25,000(0.15)x D) y=25,000(1.15) x
The function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.
Consider the compound interest formula:
y = P(1 + r/n)ⁿˣ
y here stands for the car's potential value.
P represents the value of the new car.
r is a measure of how quickly a car's value declines.
The number n indicates how frequently the car's value depreciates each year.
x represents the number of years.
Given P = 25000
r = -15% = -0.15 (Since the value of the car depreciates)
n = 1
x = x
Using the given values, we get the function as,
y = 25000(1 + (-0.15)/1)ˣ
⇒ y = 25000(1 - 0.15)ˣ
⇒ y = 25000(0.85)ˣ
Therefore, the function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.
Learn more about function here:
https://brainly.com/question/25638609
#SPJ4
What is the answer to this problem ?
The correct option for showing the interval (-∞, -7) is Option C.
What is Interval?
An interval includes all the numbers that come between two particular numbers.
The given interval is (-∞, -7).
Now, On the number line (-∞, -7) is shown as;
The interval is open interval.
Hence, At point -7 the graph is in open circle.
And, The graph is going left side.
Hence, The correct option for showing the interval (-∞, -7) is Option C.
Which is shown in figure.
Learn more about the interval visit:
https://brainly.com/question/28531287
#SPJ1
HELP .........................................
Answer: A and B
-3^4 = -3 × -3 × -3 × -3 = 81
When dealing with multiplying all negative numbers, the result is going to be positive.
-3^2 = -3 × -3 = 9
Step-by-step explanation:
Divide
81/9 = 9
Find an equivalent expression whose product is |+9|
A)(-3)^2 = -3 × -3 = 9
(-3)^4 = -3 × -3 × -3 × -3 = 81
81/9 = 9
A is correct, so we must find the next correct answer.
B)(-3)^6 = -3 × -3 × -3 × -3 × -3 × -3 = 729
(-3)^4 = -3 × -3 × -3 × -3 = 81
729/81 = 9
B is correct. Thus,
[tex]\frac{(-3)^4}{(-3)^2} = B)\frac{(-3)^6}{(-3)^4} = A)\frac{(-3)^2}{(-3)^4}[/tex]
Hope this helps, and have a great day.
PLEASE ANSWER RIGHT AWAY
8.723 x 10-¹⁰ =
An equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723
What is index form?The index form of a number is simply that number written as an exponential expression, or even as a single number that is raised to another number.
Index form is also known as standard form
Given the index form;
⇒ 8.723 x 10-¹⁰
⇒ 8. 723 × 10^ -(10)
This means that there 10 zero digits from the left end of the given decimal, it is expressed as;
0. 0000000008723
Thus, an equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723
Learn more about index form here:
https://brainly.com/question/15361818
#SPJ1
A box of oats cereal measures 24 cm long by 5 cm wide 25 cm high. A box of rice cereal measures 26 cm long by 4 cm wide by 28 mm high. Which box has the greater volume? How much greater?
Answer:
Box of oat:
24*5*25(all in cm)=3000 cm3
cereal:
26*4*2.8=291.2 cm3
oat is grater by 2708.8
Step-by-step explanation:
28mm was changed to 2.8 cm
Suppose the path of the jump changes so that the axis of symmetry becomes. X=2 and the height stays the same. If the path of the jump also passes through the point (5,5) , what quadratic function would model this path?
The quadratic function of the jump is y = -0.22x^2 +0.89x + 6.11 if the jump changes so that the axis of symmetry becomes X=2 , the height stays the same 7 and also passes through the point (5,5)
Quadratic function involving vertex is given by
y = a(x-h)^2 + k
Where (h,k) is the vertex which is given as (2,7)
y = a(x-2)^2 + 7
y = a(x-2)(x-2) + 7
y = a(x^2 -4x +4) + 7
Recall that
h = -b/2a
k = -(b^2 -4ac)/4a
2 = -b/2a
-b = 4a
b = -4a
Put b = -4a
k = -(b^2 -4ac)/4a
7= -(b^2 -4ac)/4a
7 = -((-4a)^2 -4ac)/4a
7 = -(16a^2 - 4ac)/4a
7 = (-16a^2 + 4ac)/4a
7 = -4a + c
c = 7 + 4a
The path of the jump also passes through (5,5)
y = ax^2 + bx + c
5 = a5^2 + b5 + c
5= 25a +5b + c
Put b = -4a in above
5= 25a +5(-4a) + c
5= 25a -20a+ c
5 = 5a + c
Put c = 7 + 4a
5 = 5a + 7 +4a
Collect like terms
5-7 = 5a + 4a
-2 = 9a
a = -2/9
Put a in
y = a(x^2 -4x +4) + 7
y = -2/9(x^2 -4x +4) + 7
y = (-2x^2 +8x -8)/9 +7
Multiple through by 9
9y = -2x^2 +8x -8 + 63
9y = -2x^2 +8x + 55
Dividing through by 9
y = -0.22x^2 +0.89x + 6.11
Therefore the equation of the jump is
y = -0.22x^2 +0.89x + 6.11.
To learn more about quadratic function. Click, https://brainly.com/question/28692589
#SPJ4
answer please will mark brainliest
The total surface area or surface area of the given sphere is 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm
The total surface area or surface area of a sphere is given by the formula 4πr²
From the given figure it is clear that the radius of the sphere is 2.6cm
Here, we will use the value of π as 3.14 and not 22/7
So, Substituting the values in the formula of Total surface area of a sphere.
the total surface area =4 π (2.6)²
4 × 3.14 × 6.76
= 84.9056 cm²
Hence, the total surface area or surface area of the given sphere is 84.9056 cm² or 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm
To know more about surface area of sphere - https://brainly.com/question/14692728
#SPJ1
look for relationships (an elevator decends at a constant speed what is the change in elevation after 19 seconds)
An elevator descends at a constant speed, the change in elevation after 19 seconds will be an elevation of distance
d= 19v where acceleration remains constant
What is elevation?Generally, An angle is created when a horizontal line and a line of sight are placed side by side.
In conclusion, This angle is known as the angle of elevation. If the line of sight rises above the horizontal line, the angle that is generated is known as an angle of elevation.
Read more about elevation
https://brainly.com/question/481548
#SPJ1
In the sentence 52 = 15∙3 + 7, 7 is the ________________.
In the sentence 52 = 15∙3 + 7, 7 is equal to 36.7
In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions represent the same mathematical object.
Someone or something that is equal to another has the same quantity, value, or rights as that other thing. One cup and eight ounces are equivalent, for instance. Equal pay for equal work performed by men and women is an illustration of equality.
If both operands have the same value, the equal-to operator (==) returns true; otherwise, it returns false. If the operands do not have the same value, the not-equal-to operator (!=) returns true; otherwise, it returns false.
Learn more about equal here
https://brainly.com/question/25716982
#SPJ9
The PTA at Greenville High School is having its annual dinner and auction to raise money for music and art programs. Last year, the event raised $42,890. This year, it raised 30% less. How much was raised this year?
The amount the PTA at Greenville High School raised this year is $30,023.
What is percentage?The percentages are also called the centesimal ratio, and are usually accompanied by the symbol “%”, which reads “percent”.
What percentage of the last year's funds are raised this year?The fact that the PTA at Greenville High School raises 30% less funds this year compared to last year means that the amount raised this year is 70% of last year's funds, in essence, 70% multiplied by last year's:
amount gives this year funds raisedfunds raised this year=funds raised last year*70%funds raised this year=$42,890*70%funds raised this year=$30,023Find out more about percentages on: brainly.com/question/18706090
#SPJ1
Cant submit till i find the right answer help me!!!!
Right Answers Only for crowns ratings and thankyous
You buy a 15-pound bag of bird seed. You fill a bird feeder with 5 pounds of seed. After 3 2 1/4 days, you add another pounds of seed to the feeder. How many pounds of bird seed are left in the bag?
Answer:
Step-by-step explanation:
5 pounds
The slope of line a is 2/3 . The slope of line b is 2/3 .
Which statement is true?
Responses
The lines are perpendicular.
The lines are neither perpendicular nor parallel.
The lines are parallel.
Since lines a and b have the same slope, then: the lines are parallel.
What are the Slopes of Parallel Lines?The slope of a line is the rise/run or change in y / change in x. When two lines lie parallel to each other, they will have equal slope value.
On the other hand, when two lines lie perpendicularly to each other, their slopes will be negative reciprocal.
For example, if a line has a slope of 2/3, the slope of the line that is parallel to it will be 2/3 also, while the slope of the line that is perpendicular to it will be -3/2.
Thus:
The slope of line a = 2/3
The slope of line b = 2/3
Therefore, since lines a and b have the same slope, then: the lines are parallel.
Learn more about the slope of a line on:
https://brainly.com/question/28086654
#SPJ1
Answer: the lines are parallel.
Work out m and c for the line: y = 2 x + 5
Answer:
m=2
Step-by-step explanation:
Kyle did not study for the first math test of the school year on the first test the ratio of the number he got correct to the number he got incorrect was 3:5 he was not happy with his grade so he decided to study for the next test. On the second test, the ratio of the ratio of number of problems he got correct to the number he got incorrect was 6:2. How many problems did he get corrector the second test if he got 10 incorrect on the first test
The problems he got correct on the second test is 12.
How many answers did he get correct?
Ratio expresses the relationship between two or more numbers. It shows the the number of times that one value is contained within other value(s). Ratio is used to compare two or more numbers. The sign used to represent ratio is :
The first step is to determine the total number of questions on the math test : (sum of ratios x answers gotten incorrect on the first test) / ratio of the answers gotten incorrect
(8 x 10) / 5 = 16
Answers gotten correct on the second test : (ratio of correct answers / sum of ratios) x total number of questions
(6/8) x 16 = 12
To learn more about ratios, please check: https://brainly.com/question/25927869
#SPJ1
Select the correct answer.
Statement 1: A citizen can vote if he or she is older than 18.
Statement 2: A citizen who is younger than 18 cannot vote.
How is statement 2 related to statement 1?
A.
The relationship between the statements cannot be determined.
B.
Statement 2 is the inverse of statement 1.
C.
Statement 2 is the converse of statement 1.
D.
Statement 2 is the contrapositive of statement 1.
Answer:
Statement 2 A supports statement 2 Best
Step-by-step explanation:
statement two is correct a citizen under the age of 18 cannot vote.
An inverse statement means the opposite of the original statement.
So, A would best support the answer.
I apologize if I am wrong in any way please kindly correct me.
Have a an amazing Day my fellow brainly users!
Answer:
A.
Statement 2 is the contrapositive of statement 1.
Step-by-step explanation:
Which of the following represents an algebraic expression?
4 + (5 - 2)
4x + 5y - 2
4x + 5 = 2
None of the above
Answer:
4x + 5y - 2
Step-by-step explanation:
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Evaluate each expression for x=-2,0 , and 2 .
(3/2)x
The value of given expression for x=0 is 1, x=-2 is 0.44 and x=2 is 2.25.
Given the expression is (3/2)ˣ.
Firstly, we will simplify the given expression (3/2)ˣ for x=0.
Substitute the value x=0 in given expression, we get
(3/2)ˣ =(3/2)⁰
As we know that something raise to power zero is 1.
So, we get
(3/2)ˣ =1
Now, we will simplify the given expression (3/2)ˣ for x=-2.
Substitute the value x=2 in given expression, we get
(3/2)ˣ =(3/2)²
Now, we will square the expression to simplify it, we get
(3/2)ˣ =9/4
(3/2)ˣ =2.25
Furthermore, we will simplify the given expression for x=-2.
Substitute the value x=-2 in given expression, we get
(3/2)ˣ =(3/2)⁻²
Now, we will square the given expression, we get
(3/2)ˣ =(9/4)⁻¹
Further, we will divide it above expression by 1 to remove negative sign, w eget
(3/2)ˣ =1/(9/4)
(3/2)ˣ =4/9
(3/2)ˣ =0.44
Hence, the value of expression (3/2)ˣ for x=0, 2 and -2 is 1, 2.25 and 0.44.
Learn more about the expression from here brainly.com/question/945593
#SPJ4
Find the distance between each pair of point
Answer:
6
Step-by-step explanation:
what is ∠ABD, ∠CBD, and ∠ABC??
The measure of angle ABD (m ∠ABD) is 44°
The measure of angle CBD (m ∠CBD) is 44°
The measure of angle ABC (m ∠ABC) is 88°
From the question, we are to calculate the measures of the given angles
From the given, information, we have that BD bisects ∠ABC
Thus,
m ∠ABD = m ∠CBD
From the given diagram,
m ∠ABD = (6x + 14)°
and
m ∠CBD = (3x + 29)°
Then,
(6x + 14)° = (3x + 29)°
Solve for x
(6x + 14)° = (3x + 29)°
6x + 14 = 3x + 29
Collect like terms
6x - 3x = 29 - 14
3x = 15
x = 15/3
x = 5
Put the value of x into the equations
m ∠ABD = (6(5) + 14)°
m ∠ABD = (30 + 14)°
m ∠ABD = 44°
Since
m ∠ABD = m ∠CBD
Then,
m ∠CBD = 44°
and
m ∠ABC = m ∠ABD + m ∠CBD
m ∠ABC = 44° + 44°
m ∠ABC = 88°
Hence, the m ∠ABD = 44°, m ∠CBD = 44°, and m ∠ABC = 88°
Learn more on Calculating measures of angles here: https://brainly.com/question/5371386
#SPJ1
HELP ME QUICK!!!!! i don't understand
2x+5=13
-21=7-4y
m/6-3=8
-4=d+3/5
Solve. Check for extraneous solutions. √√x+25 = √x+5
-1 is the extraneous solution
To know the value of x first we need to remove the square root of the equation
[tex]\sqrt \sqrt{x +25}[/tex] = [tex]\sqrt{x + 5}[/tex]
So to get the value we have to square both sides of the equation
[tex](\sqrt\sqrt{x +25})^{2}[/tex] = [tex](\sqrt{x + 5} )^{2}[/tex]
We get
[tex]\sqrt{x +25}[/tex]= x + 5
Now again we have to square both sides of the equation
x + 25 = [tex](x + 5)^{2}[/tex]
x + 25 =[tex]x^{2}[/tex] + 10x + 25( As we know [tex](a + b)^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] + 2ab )
[tex]x^{2}[/tex] + 9x = 0
x( x + 9) = 0
Therefore x = 0, -9
1 = [tex]\sqrt{-1}[/tex]
9 = [tex]\sqrt{81}[/tex]
The square root of 81 is 9 but the square root of -1 is an imaginary number
so the correct choice is " 9 is the solution of the equation " and -1 is the extraneous solution
To know more about the extraneous solutions refer to the link given below:
https://brainly.com/question/13198706
#SPJ4
Which of the following vectors has the greatest magnitude? Explain.
a= (3,4)b = (-4, 3)c = (4,-3)
The Magnitude of all the vectors is the same.
As you know, a vector is an object with both Magnitude and direction. To find the size of a vector, we need to calculate the length of the vector. Variables such as velocity, distance, force, and momentum are vector variables. But velocity, mass, distance, volume, temperature, etc., is a scalar quantities. A vector has both Magnitude and direction, while a scalar has only one Magnitude.
The Magnitude of a vector is the length of the vector. The Magnitude value of vector a is represented by ∥a∥.
The formula for its Magnitude is given below for a two-dimensional vector a= (a1, a2).
More vector-related questions are below:
https://brainly.com/question/13322477?referrer=searchResults
#SPJ4
Shannon buys a bag online for $32.00 including tax, and the shipping is $4.00. If she decided to buy more of the same bags and it doesn't change the shipping cost, how many can she buy with $100.00
8
3
6
7
Answer: 6
Step-by-step explanation:Shannon buys a bag online for $32.00 including tax, and the shipping is $4.00. If she decided to buy more of the same bags and it doesn't change the shipping cost, how many can she buy with $100.00