subject
Math, 25.02.2021 09:15 hajuyanadoy
Illustrate the following and determine the number of permutations. 1. Arranging 4 pots with different plants in a row
2. Forming a four-digit ATM pin.
3. Securing a motorcycle with a three-digit combination lock using the numbers 1, 2, 3 and 6
4. Displaying 3 identical small vases, 1 figurine, and a photo frame in a row
5. 3 girls sitting around a circular table
Answer:
1: 16
2: 4940
3: 24
4: 25
5: 9
Step-by-step explanation:
A permutation is a method of calculating the number of possible outcomes. It follows the following general formula;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
There (n) is the number of objects, and (r) is the number of objects selected.
1. Arranging 4 pots with different plants in a row
In order to solve this, one needs two pieces of information, the number of objects, and the number of objects selected. One is given the number of objects; (4), but when the problem states "in a row" it never specifies how many plants are in a row. Thus, let one assume that a "row" can have an infinite amount of space, but in this case, only (4) space will be used. Therefore there are (4) objects with (4) objects selected. However, the drawback is that the combination formula doesn't work when the two parameters (n) and (r) are the same. Hence, to solve this special case, one simply multiplies the two numbers to get the answers:
[tex]n*r\\\\=4*4\\\\=16[/tex]
2. Forming a four-digit ATM pin
One is given that there are (4) digits in the ATM pin, this is the number of objects selected. One is also given that number of objects, there are (10) digits including (0). Set up the permutation and solve;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
[tex]_1_0P_4=\frac{10!}{(10-4)!}\\\\=\frac{10!}{6!}\\\\=\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}\\\\=10*9*8*7\\\\=4940[/tex]
3. Securing a motorcycle with a three-digit combination lock using the numbers (1), (2), (3), and (6).
There are (4) digits to choose from on the lock. But there are (3) numbers that can be selected.
[tex]_4P_3=\frac{4!}{(4-3)!}\\\\=\frac{4!}{1!}\\\\=\frac{4*3*2*1}{1}\\\\=4*3*2*1\\\\=24[/tex]
4. Displaying 3 identical small vases, 1 figure, and a photo frame in a row.
There are (5) objects, and (5) spaces (read problem (1) for an explanation for the objects being put in a row). Thus, this is a special case; multiply the two numbers to get the result;
[tex]n*r\\=5*5\\=25[/tex]
5. 3 girls sitting around a circular table
There are (3) subjects, and (3) spaces in this problem. Apply the same logic applies to a row in this problem. Therefore, this is another special case; multiply the two numbers to get the result;
[tex]n*r\\=3*3\\=9[/tex]
Which statement describes the relationship between x and y?
As x increases, y decreases.
As x increases, y increases.
As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
Answer:
as x increases, y increases
Step-by-step explanation:
Answer:
B. as x increases, y increases
Step-by-step explanation:
Would appreciate I’m so far behind :/
Answer:
C
Step-by-step explanation:
Given the graph of f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Here the graph has been shifted 2 units to the right , then
f(x) = (x - 2)²
Given the graph of f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the graph has ben shifted 4 units up
Thus
f(x) = (x - 2)² + 4 → C
Graph the function F(x)=2^x-4
Answer:
The plotting are correct .
HOPE IT HELPED!!
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
118.6 and 42.3
The three inside angles of a triangle equal 180.
Subtract the two known angles from 180.
180 - 118.6 - 42.3 = 19.1
The third angle is 19.1
Suppose that x - y = 2 and 2x – 3y = 11. Then x + y =
Answer:
x + y = -12
Step-by-step explanation:
x - y = 2
2x – 3y = 11
-2x +2y = -4
2x – 3y = 11
-y = 7
y = -7
x = -5
x + y = -12
The angle A of a triangle ABC is 20% less than the sum of other two angles. If angle C is [tex]\frac{2}{3}[/tex] times angle B, then find the value of angle B.
Can someone help me with this math homework please!
OPTION C
The variable x represents the independent variable.
What’s the equation of the line that passes through the point (5,1) and has a slope of 1
Answer:
y = x + 4
Step-by-step explanation:
y = mx + b
y = 1x + b
5 = 1 + b
b = 4
y = x + 4
Someone tell me where everyone is going right please !!
Answer:
Step-by-step explanation:
( 2 , 3 ) , ( 6 , - 5) , ( - 1 , 3 ) - is a function
( 1 , 9 ) , ( -3 , - 2 ) , ( 1 , - 4 ) - is a function
( 7 , - 4 ) , ( 0 , 9 ) , ( 2 , - 2 ) - is a function
( 0 , 3 ) , ( 0 , 7 ) , ( 4 , 0 ) - is a function
( -6 , 5 ) , ( -5 , 6 ) , ( 8 , 2 ) - is a function
A rectangle has an area of 18 cm2
The lengths of the sides are whole numbers.
How long could the sides of the rectangle be?
Give all the examples you can think of
Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
In a group of 36 pupils, 10 play the flute only. 15 play the piano only. 4 play neither instrument. A student is selected at random. What is the probability the student plays both instruments?
Answer:
9
Step-by-step explanation:
First you would need to subtract all the irrelevant students.
So, subtract 4 from 36, which is 34.
34 - (10 + 15) =
34 - 25 =
9
The answer is 9 pupils.
As part of the math assignment, jane makes a graph pf her cookie function. Before handling it in, she compares it to the table. Do the table and the graph represent the same function
Answer:No
Step-by-step explanation:
A company is selling specialty ice cream. Their profit is modeled by the equation p(x) = x2 + 3, where x represents the number of cartons sold. Their cost to make the carton is represented by c(x) = -3x + 24, where x represents the number of cartons produced.
A. What does it mean to find the solution to this system?
B. What is the solution to the system? How did you find the solution?
C. What does the solution mean in context of the problem?
D. How do you solve this system when x does not stand for the same thing? What system are you referring to?
Answer:
The given function for the profit of the company is p(x) = x² + 3
The function for the cos of the company, c(x) = -3·x + 24
Where;
x = The number of cartons sold
A. To find the solution of the system means to find the number of cartons sold at which the profit and cost are equal
B. The solution of the system can be found by equating both functions as follows;
p(x) = c(x)
Therefore;
x² + 3 = -3·x + 24
∴ x² + 3 + 3·x - 24 = 0
x² + 3·x - 21 = 0
x = (-3 ± √(3² - 4×1×(-21)))/(2 × 1)
∴ x = (-3 ± √(93))/2
x = (-3 + √(93))/2 ≈ 3.32 or x = (-3 - √(93))/2 ≈ -6.32
Therefore, the possible solution is x = (-3 + √(93))/2 ≈ 3.32
C. The solution means that when the company sells about 3 cartons of specialty ice, the cost to make the carton and the profit from selling the cartons will be approximately equal
D. Part 1
To solve the system, we rewrite the functions using common variables, to obtain a consistent system of equations
Part 2 Inconsistent system of equations
When x does not stand for the same thing in both equations, we have an inconsistent system of equations and there are no solutions
Step-by-step explanation:
car travels at an average speed of 40 km/h for 0.5 hours.
How far did the car travel in km?
Given :-
A car travels at an average speed of 40 km/h for 0.5 hours.To Find :-
The distance travelled.Solution :-
We know that ,
→ Distance = Speed × Time
So that ,
→ Distance = 40 km/hr × 0.5 hr
→ Distance = 40km/hr × 1/2 hr
→ Distance = 20km .
Hence the required answer is 20km .
Prove: AAB
Step
Statement
Reason
Given
1
ABCD is a parallelogram
ABCD
Select a Reason!!
2
A
B
N
Which value is 10,000 times larger than 1,300?
Explain.
Which value is 10,000 times larger than 1,300?
answer= 1300×10000
= 13,000,000
Michelle did a survey in four butterfly parks and wrote the following observations:
Answer:
A. 55%
Step-by-step explanation:
First we should make these into fractions
A. 33/60
B. 36/78
C. 40/89
D. 24/59
these are the fractions, The question wants us to pick the Park with the Greatest Percentage, Not The Greatest Amount, so Lets look at these fractions A. 33/60 Is 55% B. 36/78 is 46% . C. 40/89 is 44% D. 24/59 is about 40%
I also remember doing this on a quiz!!
Find the measure of the missing angle using the exterior angle sum theorm
Answer:
r = 30°
Step-by-step explanation:
According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.
what are the lengths of SV and QT? no links.
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units
Which one of the following options is true when considering the expansion of
the binomial expression (x + y)6?
A. The first term of the expansion of (x + y)^6 is x3y3.
B. The coefficients of the expansion of (x + y) are: 1,6, 15, 15, 6, 1.
c. The expansion of (x + y)^6 will yield 7 terms.
D. The sum of the exponents of each term of the expansion of
(x + y)^6 is 5
Answer:
c The expansion of (x + y)^6 will yield 7 terms
Step-by-step explanation:
(x + y)^6 =
x^6 +6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6
so its a no on A
its a no on B because its missing a 20
its a yes on c
its a no on d because the sum is 6
so c
Is (-2,-4) a solution of the graphed inequality?
Choose 1 answer:
Yes
No
Answer:
Yes
General Formulas and Concepts:
Algebra I
Reading a coordinate graphCoordinates (x, y)Solving inequalitiesStep-by-step explanation:
When we plot (-2, -4) onto the graph, we can envision that the point is within the shaded region of the graphed line.
∴ (-2, -4) would be a solution.
What is the quotient of
Answer:
x^5+8x^4+17x^3-14x^2-84x-72
Step-by-step explanation:
if you were pouring juice into a cylindrical cup with a 2 inch radius and height of 8 inches. you want to fill it exactly half full, how many cubic inches of juice would you pour
Answer:
You would pour 50.3 in^3 of juice
Step-by-step explanation:
The term ‘cubic’ indicates volume
so in the context of this question, we are to calculate the volume of the cylinder, then we divide by 2
Mathematically, we have the volume of the cylinder as;
V = pi * r^2 * h
r = 2 inch
h = 8 inch
Since we are dividing the volume by 2 (exactly half full)
V = 1/2 * pi * 2^2 * 8
V = 50.3 in^3
The side of a rectangle legnth x+2 and width x-5. WHich equation describes the area A of the rectangle in terms of x?
Answer:
[tex] {x}^{2} - 3x - 10[/tex]
Step-by-step explanation:
Area= length× width
[tex](x + 2)(x - 5) \\ {x}^{2} + 2x - 5x - 10 \\ {x}^{2} - 3x - 10[/tex]
Does the point (1, 3) satisfy the equation y = 5x? yes no
Answer:
Nope
Step-by-step explanation:
we can graph y = 5x as y = 5 units up and one unit to the right
but for right now let me be specific on what i mean
Specifically:
y = 5x is a Slope-Intercept equation, the original Slope-Intercept equation would be y = mx + b but in this case, we don't have b so we're focusing now on y = 5x, but what are we suppose to do with 5x??? well 5x represents the slope of the line so to graph a slope, use rise over run = rise/run. so only 5 is being used so 5 = rise/run = 5/1.
------------------------------------------------------------------------------------
Answer: (1, 3) doesn't satisfy the equation
Answer:
No, it does not satisfy the equation
Step-by-step explanation:
Hi there!
We are given the equation y=5x and we want to know if the point (1,3) will satisfy the equation
If we substitute the values of a point into the equation, and the result is a true statement (ex. 2=2), then the point satisfies the equation
If we substitute the values of a point into the equation and the result is a false statement (ex. 0=7), then the point doesn't satisfy the equation
The reason for this is because when we plug the value of a point into an equation, we're seeing if the equation will pass through that given point.
So let's substitute 1 as x and 3 as y into y=5x
3=5(1)
multiply
3=5
The result is a false statement; therefore, the point doesn't satisfy y=5x
Hope this helps!
What is the solution for this equation:
Answer:
c) x=126
Step-by-step explanation:
tell me if I get it right
Sandra needs a new bicycle tire. Her tire has a circumference of about 113,04 inches. What is the radius of her tire?
Answer:
113,04 square root is 10.632027088 divided by Pi
3.38427933228
so the radius of her tire is 3.38
Hope This Helps!!!
The two figures shown are congruent. Which statement is true?
A). One figure is a translation image of the other.
B). One figure is a rotation image of the other.
C). Neither figure is a translation or rotation image of the other
Answer:
C
Step-by-step explanation:
They are the same without rotation and translation
which table represents a linear function graph 1. pleasee help also giving brainliest
Answer:
2 i think it is
Step-by-step explanation:
