Step-by-step explanation:
Lets understand the situation,
This means Each team can have 3, 4 or 5 people.And 21 people take part.
we have to find How many different possible arrangements of teams are there.
Solution:-Situation 1.
if 7 groups of people 3 Team7×3=21.situation 2.
if 4 groups of people 4 teams and 1 group of people 5 Team.(4×4)+(1×5)=21.Situation 3.
if 2 groups of people 3 Team and 3 group of people 5 Team.(2×3)+(3×5)=21.situation 4.
if 4 groups of people 3 Team and 1 group of people 4 Team And 1 group of people 5 team.(4×3)+(1×4)+(1×5)=21.
Solve each system by elimination.
5c - 4t = 8 , 14 + 4t = 3c
Using elimination method, the solution of the given system of equations is (-3, -23/4)
A system of equations can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations is:
5c - 4t = 8 ...... (1)
14 + 4t = 3c ...... (2)
Re-arrange equation (2) to
-3c + 4t = -14 ........ (3)
To eliminate variable t, add equation (1) to equation (3):
5c - 4t = 8
-3c + 4t = -14 +
2c = -6
c = -3
Substitute c = -3 into equation (1)
5c - 4t = 8
5 . (-3) - 4t = 8
-15 - 4t = 8
Add 15 to both sides:
-4t = 23
t = -23/4
Hence, the solution is (-3, -23/4)
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10 x 6 = 60 to find
the number of muffins in 10 boxes. Describe what each of
the factors represents in the multiplication equation.
Trent writes 10×6=60, then in multiplication equation 10 represents the quantity of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.
According to the statement
We have to find that the multiplication equation.
So, For this purpose, we know that the
The linear equation is defined as an equation that is written in the form of Ax+By=C.
From the given information:
Given,
Trent writes 10×6=60,
Here,
10 represents the quantity of muffin boxes
And
6 represents the numbers of muffins in each box
Then
60 represents the overall numbers of muffins
Hence, Trent writes 10×6=60, then within the multiplication equation 10 represents the amount of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.
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when you have a quadratic in the form of 2(x+1)(x+4), do you distribute the 2 to both parentheses, or just the first one {(x+1)}?
Answer:
2x²+10x+8
Step-by-step explanation:
you have to multiply the brackets first the multiply the 2 in
2(x+1)(x+4)
2(x²+4x+x+4)
2(x²+5x+4)
2x²+10x+8
If $5 = 4 pound and Rs 342 = $3, how many pounds will be equal to Rs 8,550?
The amount of Rs8550 will be equal to 60 pounds.
What is currency exchange?The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.
Given that $5 = 4 pounds and Rs 342 = $3, the amount RS 8550 will be calculated as below:-
$5 = 4 pounds
$1 = 4 / 5 pounds .............................( 1 )
Rs 342 = $3
$1 = 342 / 3 RS ..............................( 2 )
From the two equations:-
342 / 3 RS = 4 / 5 pounds
1 RS = ( 3 / 342 ) x ( 4 / 5 )
8550 RS = ( 8550 x 3 x 4 ) / ( 342 x 5 )
8550 RS = 60 pounds
Therefore, the amount of Rs8550 will be equal to 60 pounds.
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Find the value of x to the nearest tenth. 58.9=2 x
x = 29 is the value of x.
What exactly is meant by a value?A value in mathematics is a number that indicates the result of a calculation or function.So, in the preceding example, you might also tell your teacher that 5 x 6 equals 30 or that x + y equals 9 if x = 6 and y = 3.A value is another term for a variable or constant.To find the value of x:
Given: 58.9 = 2xSimplify the equation to find the value of x.So,
58.9 = 2xx = 58.9/2x = 29.45Now, rounding to the nearest tenths gives x = 29.
Therefore, x = 29 is the value of x.
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please help! will mark brainliest!
|x-1|+5=2
Answer:
No solution is what I got if you solve for x
Step-by-step explanation:
Hope this helps!!
if there are 12 gumdrops per scoop how much is each scoop
When there qre 240scoops and that there are 12 gumdrops per scoop, the number of gumdrop is 20 per scoop.
How to calculate the value?From the information, it was stated that there are 240scoops and that there are 12 gumdrops per scoop.
Therefore, the number in each scoop will be
= Total scoops /Number of gumdrop
= 240 / 13
= 20
Therefore, there are 20 gumdrops.
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There are 240scoops. If there are 12 gumdrops per scoop how much is each scoop
En que nos ayuda la proporción en matemáticas?
Answer:
Proportion says that two ratios (or fractions) are equal.
La proporción dice que dos razones (o fracciones) son iguales.
( translated )
Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly. Gerald invests half that amount into an account that pays twice Rodney’s interest rate. Which of the accounts will have the higher ending balance after 1 year? Explain.
In the account of Rodney's will have the higher ending balance after 1 year.
Given that:
Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly.
Gerald invests half that amount into an account that pays twice Rodney’s interest rate.
To find:
Which of the accounts will have the higher ending balance after 1 year?
So, according the question
We have,
For Rodney,
p = Principle = P
r = Interest rate = r
t = time expressed in year = 1 year
n = Number of periods in a year = 1
We, know that the formula to calculate the compound interest for new balance of Rodney ,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
Now, putting the values,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
B = [tex]P(1+\frac{r}{1} )^{1\times 1)[/tex]
B = [tex]P (1 + r )[/tex]
B = P + Pr
Now, For Gerald,
p = Principle = P/2 ( Invest half of the money from Rodney )
r = Interest rate = 2r ( Twice the rate of Rodney's)
t = time expressed in year = 1 year
n = Number of periods in a year = 1
We know that the formula to calculate the compound interest for new balance of Gerald ,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
Now, putting the values,
B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]
B = [tex]\frac{P}{2} (1+\frac{2r}{1} )^{1\times 1)[/tex]
B = [tex]\frac{P}{2} (1+ 2r)[/tex]
B = [tex]\frac{P}{2}[/tex] + Pr
Now compare the amounts of their accounts, so we can say that the amount of Rodney's account will have the higher ending balance after 1 year.
So, In the account of Rodney's will have the higher ending balance after 1 year.
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Hey, I am confused on this question. The question is, Find the median of the data set without the outliner. Then, find the median of the data set with the outliner.
Regina left her office downtown and traveled 3 blocks west and 5 blocks north. Write a translation vector to describe her route.
The translation vector will be as follows:
(x, y) → (x - 3, y + 5)
Regina travelled 3 blocks west and 5 blocks north.
What is meant by translation vector?The interpretation vector is the distance through which a particle should be moved (made an interpretation of) to be in the following unit cell. The image for an interpretation vector is television. The television ought to be indicated toward the finish of the math.
The distance that an atom must travel in order to transfer to the following unit cell is known as the translation vector. A translation vector is denoted by the letter Tv. At the conclusion of the geometry, the Tv should be provided. Real or fake atoms shouldn't follow a Tv, but symmetry information and other things are acceptable.
Let us consider the direction similar to map where north is positive y-axis , east is positive x-axis , west is negative x-axis and south is negative y-axis.
Therefore the translation vector will be as follows:
(x, y) → (x - 3, y + 5)
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5. A group of hikers walked 540 kilometers at a rate of 30 kilometers each day. How many days did they
hike for?
Answer: 18 Days
Step-by-step explanation: 30x18=540
Evaluate the discriminant for each equation. Determine the number of real solutions. x²+4 x+5=0 .
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
What is the discriminant of the quadratic equation?The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as
D = b² - 4ac
The type of roots will be given below.
D > 0, Real and Distinct rootsD = 0, Real and Equal rootsD < 0, Imaginary rootsThe equation is given below.
x² + 4x + 5 = 0
The discriminant of the given equation will be
D = 4² - 4 x 1 x 5
D = 16 - 20
D = - 4
D < 0
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
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The telephone company offers two billing plans for local calls. plan 1 charges 31$ per month for unlimited calls and plan 2 charges 13$ per month plus 0.09$ per call.use an inequality to find the number of monthly calls for which plan 1 is more economical than plan 2.
Using an inequality, Plan 1 is more economical than Plan 2 given that the number of monthly phone calls is greater than 200.
If Plan 1 charges 31$ per month for unlimited calls, then the total cost per month of using Plan 1 is also 31$.
Plan 1 = 31$
If Plan 2 charges 13$ per month plus 0.09$ per call, we can express the total cost per month of using Plan 2 as:
Plan 2 = 13 + 0.09x
where x is the number of monthly phone calls
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
If Plan 1 is more economical than Plan 2 then the monthly cost of Plan 1 is less than the monthly cost of Plan 2.
Plan 1 < Plan 2
31 < 13 + 0.09x
Solving for x.
31 - 13 < 13 + 0.09x - 13
18 < 0.09x
200 < x
x > 200
the number of monthly phone calls > 200
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Solve the equation. Check your solution.
2(x+4)=-5x-1
Due tomorrow pls help.
Answer:
-9/7
Step-by-step explanation:
Distribute
2x + 8 = -5x - 1
Get variables on left; constants on right
2x + 5x = -1 -8
Gather like terms and do the math
7x = -9
x = -9/7
A ladder of 18m reaches a point of 18 m below the top of vertical flagstaff. From the foot of the ladder the
angle of elevation of the flagstaff is 60°. Find the height of the flagstaff. And solve this question step by step solution.
The height of the flagstaff by suing trigonometric ratios is found to be 27 m.
Given,
Height of the ladder, AD = 18 m
The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m
Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °
Δ ACD is isosceles triangle.(Image is attached)
∠ ACB = ∠ CAD = 30 °
In △ ABD, by using the trigonometric ratios, we get that:
Sin 30 ° = BD / AD
1 / 2 = BD / 18
BD = 9 m
So, the height of the flagstaff will be:
BC = BD + DC =9 + 18 = 27 m
Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.
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Write a two-column proof.
Given: X is the midpoint of WY and VZ.
Prove: VW=ZY
The two-column proof are:
The angle WXV is congruent to angle YXZ
Triangle WXV congruent triangle YXZ
In this question, we are given;
X as the midpoint of line segment WY and line segment VZ
Therefore, it is correct for us to conclude that;
segment XZ is congruent to segment XV, segment XW is congruent to segment XY
Thus, angle WXV is congruent to angle YXZ
Triangle WXV congruent triangle YXZ
We then conclude that;
VW = ZY
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f(x) = 2x³5x² - 6x - 7
g(x)=2x-3
Find (f - g)(x).
A. (f-g)(x) = 2x³ + 5x² - 8x - 4
B. (f-g)(x) = 2x³ + 5x² - 4x - 4
C. (f-g)(x) = 2x³ +5x² - 4x + 4
D. (f-g)(x) = 2x³ +5x² - 8x +4
The expression which represents the function evaluation (f -g)(x) according to the task content is; (f -g)(x) = 2x³ +5x² -8x -4.
Which expression represents (f-g)(x) according to the functions given?It follows from the task content that the required function evaluation required is; (f -g)(x).
Given;
f(x) = 2x³ +5x² - 6x - 7
g(x)=2x-3
To find;
(f-g)(x).
Since; (f -g)(x) = f(x) - g(x), the resulting expression for (f -g)(x) is;
(f -g)(x) = 2x³ +5x² -6x -7 -2x +3
Collect like terms;
(f -g)(x) = 2x³ +5x² -6x -2x -7 +3
Hence, (f -g)(x) = 2x³ +5x² -8x -4
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4. Referring back to question 3. Determine the five vertices of the feasible region, given the constraints
2x + 6y ≤ 30
X ≤ 9
Y ≤ 3
X ≥ 0
y ≥ 0
Select all answers below that are vertices of the feasible region
A ( 0,0) F(0,9)
B(0,3). G(9,3)
C(9,3). H (9,2)
D ( 0,5). I ( 9,0)
E(6,3). J ( 3,6)
O( 0,0 ) A(9 , 0 ) D( 0,3 ) ( 9, 2) , ( 6 , 3 ) that are vertices of the feasible region.
What do math vertices mean?
The spots where two or more line segments or edges intersect are known as vertices in forms (like a corner). Vertex is the singular form of vertices. For instance, a cone only has one vertex whereas a cube has eight. Although vertices are occasionally referred to as corners, the term "vertex" is preferable when discussing 2D and 3D designs.The line 2x + 6y = 30
when x = 9 , 18 + 6y = 30
y = 2
So B = ( 9, 2)
So, C= ( b , 3 )
then , we can show O( 0,0 ) A(9 , 0 ) D( 0,3 )
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Use each recursive definition to write an explicit formula for the sequence. a₁=-5, an =a n₋₁-1
The explicit formula for the given sequence is a(n) = -5 + (-1)(n - 1).
What is termed as recursive definition?
A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.
The recursive formula for an arithmetic sequence is as follows.
a(1) = -5 and a(n) = a(n-1) -1
Remember that this formula provides us with two types of data.
1 is the first term.Add 4 to obtain any term out of its previous term. To put it another way, this same common difference is 4.Let's look for a formal formula again for sequence.
1) Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B:
A + B(n - 1)
2) As a result, the sequence's explicit formula is a(n) = -5 + (-1)(n - 1).
Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = -5 + (-1)(n - 1).
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Solve each system by elimination.
5x - 2y = -19 , 2x + 3y = 0
By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 3 and the second equation by 2.
5x - 2y = -19 ⇒ 15x - 6y = -57 (equation 1)
2x + 3y = 0 ⇒ 4x + 6y = 0 (equation 2)
Adding the two equations will eliminate the variable y.
15x - 6y = -57 (equation 1)
4x + 6y = 0 (equation 2)
19x = -57
x = -3
Substitute the value of x to any of the two equation and solve for y.
2x + 3y = 0 (equation 2)
2(-3) + 3y = 0
3y = 6
y = 2
Hence, the solution of the system of equations is (-3 , 2).
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Write the numbers in decreasing order. √14, √5/2, √9/16, 1,11
Given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex] in decreasing order are as follows:
[tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .
As given in the question,
Given numbers are as follow : [tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]
Approximate value of all given numbers
[tex]\sqrt{14} =3.74\\\\\sqrt{5/2}= 1.58\\ \\\sqrt{9 /16} = 0.75\\ \\1 =1.00\\\\11=11.00[/tex]
Arrange the given numbers in decreasing order :
11 > 3.74 > 1.58 > 1 > 0.75
[tex]\implies 11 > \sqrt{14} > \sqrt{5/2} > 1 > \sqrt{9/16}[/tex]
Therefore, given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex] in decreasing order are as follows: [tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .
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HELP MEEE, I NEED HELP FAST
if <3 measures 123°, what is the measure of <4?
Answer:57
Step-by-step explanation:180-123 I hope i have helped u have a wonderful day or night!
find all the roots of x^3-5x^2-7x+51 if one root is 4-i
Answer:
Hello,
Step-by-step explanation:
P(x)=x^3-5x^2-7x+51
Since the coefficients are all reals,
4+i (conjugate of 4-i) is also a root.
The polynomial est divisible by (x-4-i)(x-4+i)=(x-4)²+1=x²-8x+17
If we divide P(x) by x²-8x+17 we find the quotient (x+3) and the remainder 0
P(x)=(x+4)(x-4-i(x-4+i)
Roots are -4,4+i and 4-i
Answer:
All the roots are -3, 4-i and 4+i.
Step-by-step explanation:
If oine root is 4 - i then another one is 4 + i as complex roots occur as conjugate pairs.
(4 - i)(4 + i)
= 16 - i^2
= 17.
As the last term = 51 = 3 * 17
looks like the other root is 3 or -3.
By the Factor theorem
If x = 3 then f(3) = 0
f(3) = 27 - 5(3)^2 - 7(3) + 51
= 27 - 45 - 21 + 51 = 12 so 3 is not a root.
If x = -3:
f(-3) = -27 - 45 _ 21 + 51
= 0
So, x = -3 is a root.
Find the value of the variable and the measure of each labeled angle.
Answer:
x=2
angle 1= 27°
angle 2= 27°
Step-by-step explanation:
(x+6) =( 3x -36)
2x=42
x=21
Mr. Wong traveled 45 miles on a business trip. The cost to rent a car is 30.00 plus .75 per mile. How much did Mr. Wong pay for the car rental?
Mr. Wong paid 63.75 for the car rental.
The cost of rental car will be added one time to the total rent. The cost of trip will be calculated based on the distance covered.
So, forming the equation -
Total cost = 30 + 45 × 0.75
Performing multiplication on Right Hand Side of the equation to find the cost of business trip based on miles distance traveled
Total cost = 30 + 33.75
Performing addition on Right Hand Side of the equation to find the total cost based on one time rent of car and distance traveled
Total cost = 63.75
Hence, the total cost of car rental on business trip is 63.75.
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Y=2000( 4/5) ^x what is the decay factor or growth factor
The exponential function is y=2000(4/5)ˣ. 0.8 is the decay factor and 0.2 is the decay rate.
Given that,
The exponential function is y=2000(4/5)ˣ.
Parts of exponential function.
The general equation for an exponential growth function is :
y=a(b)ˣ
a is the initial value.
1. If b>1, growth. Then b is growth factor. r is the growth rate is b=1+r.
2. If 0<b<1, decay. Then b is decay factor. r is the decay rate is b=1-r.
Now, from the given y=2000(4/5)ˣ.
2000 is the initial value.
4/5=0.8 which is 0<0.8<1
So, 0.8 is the decay factor.
Decay rate r is
b=1-r
r=1-b
r=1-0.8
r=0.2
Therefore, 0.8 is the decay factor and 0.2 is the decay rate.
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REASONING Determine whether the following statement is true or false. If true, explain your reasoning. If false, provide a counterexample.
If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent.
"If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent."
The given statement true.
Briefing:When two angles become congruent, their degree measures are the same. The reverse of something like the Isosceles Triangle Theorem asserts that the sides of a triangle opposing congruent angles are also congruent.
What exactly is the isosceles triangle theorem and exactly how does it work?If two two triangles are congruent, then perhaps the sides opposite the congruent angles are equal, in accordance with the isosceles triangle theorem converse.
What is the mathematical definition of a theorem?Mathematics is defined by theorems. A theorem is a proposition that has been proven true by a rigorous proof, which is a type of logical argument.
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Complete the equation so that it has no solution.
3x + 2.5 = 12x – ___x + ____
Graph the following function by moving
the green and blue dots (if necessary).
Answer:
Reflect back on a time when you did something you later were at least somewhat uncomfortable with. Maybe it was something you said or did, but upon reflection you knew it wasn't the right thing to do. If you can't think of a real situation, you can create a hypothetical one.
[tex]\pink{ \rule{2pt}{99999pt}}[/tex]
