Answer:
4
Step-by-step explanation:
a term is simply separated by either a + or a - which means the terms here is 4x,2x,3x and 5
Answer:
4
Step-by-step explanation:
There are 4 terms in the equation 4x+2x(3x-5).
4x,2x,3x and 5
What are the solutions to the quadratic equation (5y + 6)2 = 24?b
ANSWER
The exact solution are:
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
EXPLANATION
The given quadratic equation is
[tex] {(5y + 6)}^{2} = 24[/tex]
We use the square root method to solve for y.
We take square root of both sides to get:
[tex] \sqrt{{(5y + 6)}^{2}} = \pm\sqrt{24} [/tex]
This gives us:
[tex]5y + 6 = \pm 2 \sqrt{6} [/tex]
Add -6 to both sides to get:
[tex]5y = - 6 \pm 2 \sqrt{6} [/tex]
Divide through by 5:
[tex]y = \frac{ - 6 \pm2 \sqrt{6} }{5} [/tex]
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
The pentagon on the left is a reflection of the pentagon on the right.
The pentagon is reflected over line ____.
Answer:
A
Step-by-step explanation:
If you reflect over line A both pentagons are equally spaced in proportion to the line
The pentagon is reflected over the line A.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
Here given are two pentagons on left and right.
The pentagon on the left is a reflection of the pentagon on the right.
This means that both the pentagons should be proportionally spaced from the line.
If we consider the line of reflection as B, the the pentagon on the right is nearer to the line compared to that on the left.
If we consider line D as the line of reflection, then pentagon on the left is nearer to the line compared to that on the right.
So if line A is the line of reflection, the both pentagons are equally spaced from the line.
Hence line A is the line of reflection.
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Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from his starting point? Express your answer as a decimal to the nearest hundredth.
Answer:
1.25 mi
Step-by-step explanation:
Think of this in terms of a graph in the x-y axis
Bill starts out at point (0,0)
He walks 1/2 mile south (i.e 0.5 miles in the -y direction) and ends up at (0,-0.5)
Next he walks 3/4 mile (0.75 miles) in the +x direction and ends up at (0.75, -0.5)
Then he continues to walk 1/2 mile (0.5 miles) in south in the -y direction and ends up at (0.75, -1).
His final distance from the starting point (0,0) from his end point (0.75,-1) is simply the distance between the 2 coordinates (see picture for formula).
hence,
D = √ (0.75 -0)² + (-1 - 0)²
D = √ (0.75)² + (-1)²
D = 1.25
Answer:
1.25 M
Step-by-step explanation:
The office manager at a small law firm has taken a survey on how many cups of coffee each person drinks per 5-day work week. A table of her results is below.
Employee Cups per Week
1 29
2 13
3 27
4 26
5 9
6 15
7 17
8 19
9 25
10 32
11 14
On average, how many cups of coffee does each person at the firm drink per hour, assuming a 10-hour work day?
Answer:
A person drinks 4.52 cups per hour
Step-by-step explanation:
No of work days = 5
No of hours in day = 10
No of hours in week = 10*5= 50 hours
Total cups consumed = 226
No of cups consumed per hour = Total no of cups/ Total week hours
= 226/50
= 4.52 cups/ hour
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
The equation that represents the line passing through the points (-1, 2) and (3, 1) is [tex]\[ x + 4y = 7 \][/tex]
The correct option is (B).
To find the equation of the line that passes through the points (-1, 2) and (3, 1), we need to determine the slope of the line and use the point-slope form of the equation of a line, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
First, let's calculate the slope [tex]\( m \)[/tex] using the two given points [tex]\( (x_1, y_1)[/tex]= [tex](-1, 2) \) and \( (x_2, y_2) = (3, 1) \)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's compute the slope.
The slope \( m \) of the line that passes through the points (-1, 2) and (3, 1) is [tex]\( -0.25 \)[/tex].
Next, we'll use one of the points and the slope to write the equation of the line in point-slope form and then convert it to slope-intercept form[tex]\( y = mx + b \)[/tex]. Let's use the point (-1, 2) to find the equation of the line.
The equation of the line in slope-intercept form is [tex]\( y = -0.25x + 1.75 \)[/tex].
Now let's convert this to the standard form of the line equation, [tex]\( Ax + By = C \),[/tex] and compare it with the given options.
To get the standard form, we will multiply through by 4 to eliminate the decimals and then rearrange the terms:
[tex]\[ y = -0.25x + 1.75 \][/tex]
[tex]\[ 4y = -x + 7 \][/tex]
[tex]\[ x - 4y = -7 \][/tex]
This standard form equation needs to be matched with one of the given options by comparing coefficients. Let's do this by checking which of the given options has the same ratio of coefficients for[tex]\( x \) and \( y \)[/tex] as the equation we found.
The equation that represents the line passing through the points (-1, 2) and (3, 1) is given by option B, which is:
[tex]\[ x + 4y = 7 \][/tex]
Choose the equation that represents a line that passes through points (-1,2) and (3,1)
A. 4x-y=6
B.x+4y=7
C. x-4y =-9
D.4x+y=2
find the sum of these polynomials (x^6 + x + 9) + (7x^6 + 5) =
Answer:
8 x^6 + x + 14
Step-by-step explanation:
Simplify the following:
7 x^6 + x^6 + x + 5 + 9
Grouping like terms, 7 x^6 + x^6 + x + 5 + 9 = (x^6 + 7 x^6) + x + (9 + 5):
(x^6 + 7 x^6) + x + (9 + 5)
x^6 + 7 x^6 = 8 x^6:
8 x^6 + x + (9 + 5)
9 + 5 = 14:
Answer: 8 x^6 + x + 14
For this case we must find the sum of the following polynomials:
[tex]x ^ 6 + x + 9\ and\ 7x ^ 6 + 5[/tex]
We have:
[tex](x ^ 6 + x + 9) + (7x ^ 6 + 5) =[/tex]
We eliminate parentheses:
[tex]x ^ 6 + x + 9 + 7x ^ 6 + 5 =[/tex]
We add similar terms:
[tex]x ^ 6 + 7x ^ 6 + x + 9 + 5 =\\8x ^ 6 + x + 14[/tex]
Finally we have that the sum of the polynomials is:[tex]8x ^ 6 + x + 14[/tex]
Answer:
[tex]8x ^ 6 + x + 14[/tex]
(PLEASE ANSWER QUICK) (10 points )
WHICH OF THE FOLLOWING IS THE FUNCTION FOR THE GRAPH SHOWN?
Answer:
C. y=x^2-6x+8
Step-by-step explanation:
We have to check each functions in options with the given point
So,
The point is (3,-1)
For A:
[tex]y = x^2+6x+8\\Putting\ the\ point\\-1 = (3)^2+6(3)+8\\ -1=9+18+8\\-1 \neq 35[/tex]
For B:
[tex]y=x^2-2x-8\\-1 = (3)^2-2(3)-8\\-1=9-6-8\\-1\neq -5[/tex]
For C:
[tex]y = x^2 - 6x+8\\-1 =(3)^2-6(3)+8\\-1= 9-18+8\\-1=-1[/tex]
The given point satisfies the third function. Therefore, Option C is the correct answer ..
HURRY PLEASE NEED IT NOW! What is the simplified value of the expression below? -1(2x + 3) -2 (x - 1)?
Answer:
-4x-1
Step-by-step explanation:
-1(2x + 3) -2 (x - 1)
Distribute the -1 and the -2
-2x - 3 -2 x +2
Combine like terms
-4x-1
[tex]\huge \boxed{-4x-1}[/tex], you can use the distributive property of [tex]\displaystyle a(b+c)=ab+ac[/tex].
Multiply from left to right.
[tex]\displaystyle 1\times(2x+3)=2x+3[/tex]
[tex]\displaystyle -(2x+3)-2(x-1)[/tex]
[tex]\displaystyle -(2x+3)=-2x-3[/tex]
[tex]-2(x-1)=-2x+2=-2x-3-2x+2[/tex]
[tex]\Large\textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle-2x-3-2x+2=-4x-1[/tex]
[tex]\large \boxed{-4x-1}[/tex], which is our answer.
In a survey, 250 adults and children were asked whether they know how to
swim. The survey data are shown in the relative frequency table.
Total
Can swim
0.34
Cannot swim
0.06
Adults
Children
0.48
0.12
Total
Answer:
82%
Step-by-step explanation:Because O.34 + O. 48 = .82 and .82 • 1OO=82
So 82% Can swim
i got it right on Aoex
The percentage of people cannot swim is 18%.
What is the relative frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
Given that, in a survey, 250 adults and children were asked whether they know how to swim.
From table cannot swim = 0.06+0.12
= 0.18
In percentage = 0.18×100
= 18%
Therefore, the percentage of people cannot swim is 18%.
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Use the diagram to answer the questions. What is the area of the circle in terms of pi? π units² What is the measure of the central angle of the shaded sector? ° What is the area of the shaded sector rounded to the nearest whole number? units²
The radius of the circle is 11, so the area is
[tex]A=\pi r^2 = 121\pi[/tex]
The central angles of the shaded and non-shaded regions sum up to 360 degrees, so the central angle of the shaded region is
[tex]360-217=143[/tex]
The area of the shaded region is in proportion with the area of the whole circle: if the whole area is given by a sector of 360°, the area of a 143° sector will be given by
[tex]A_{360}\div A_{143} = 360\div 143[/tex]
Since we know that the whole area is [tex]121\pi[/tex], we can solve for the area of the 143° sector:
[tex]121\pi\div A_{143} = 360\div 143 \iff A_{143}=\dfrac{121\pi\cdot 143}{360} \approx 151[/tex]
Answer:
121
143
151
Step-by-step explanation:
What is the area of a rectangle with vertices at (1, 7) , (5, 3) , (3, 1) , and (−1, 5) ?
Enter your answer in the box.
units²
Answer:
Area = 16 units²
Step-by-step explanation:
Points to remember
Distance formula
The distance between two points (x1, y1) and (x2, y2) is given by
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the length and breadth of rectangle
Let the points be (1, 7) , (5, 3)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(5 - 1)² + (3 - 7)²]
= √[(4)² + (-4)²]
= √32 = 4√2
If the points be (5, 3) , (3, 1)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(3 - 5)² + (1 - 3)²]
= √[(-2)² + (-2)²]
= √8 = 2√2
Length = 4√2 and breadth = 2√2
To find the area of rectangle
Area = Length * Breadth
= 4√2 * 2√2
= 16 units²
Answer:
16 units
Step-by-step explanation:
i have answered ur question
(x^2y^3) = (xy^a)^b
In the equation above, a and b are constants, and the
equation is true for all x > 0 and y > 0. What is the
value of a ?
The correct answer is C, 3/2
Thanks!
Answer:
C. [tex] \frac{3}{2} [/tex]
Step-by-step explanation:
To find the value f b, we need to compare the exponents.
The given exponential equation is:
[tex]( {x}^{2} {y}^{3} )^{3} = ( {x} {y}^{a} )^{b}[/tex]
Recall and apply the following rule of exponents.
[tex] ( {x}^{m} )^{n} = {x}^{mn}[/tex]
We apply this rule on both sides to get:
[tex]{x}^{2 \times 3} {y}^{3 \times 3} = {x}^{b} {y}^{ab}[/tex]
Simplify the exponents on the left.
[tex]{x}^{6} {y}^{9} = {x}^{b} {y}^{ab}[/tex]
Comparing exponents of the same variables on both sides,
[tex]b = 6 \: and \:\: ab = 9[/tex]
[tex] \implies \: 6b = 9[/tex]
Divide both sides by 6.
[tex]b = \frac{9}{6} [/tex]
[tex]b = \frac{3}{2} [/tex]
Which equation correctly describes the relationship between segment lengths in the given figure?
A. (FP)(GP) = (EP)(DP)
B. (FD)(FG) = (EG)(ED)
C. (FP)(FG) = (EP)(ED)
D. (FP)(DP) = (EP)(GP)
Answer: Choice A
Step-by-step explanation:
-
Answer: (FP)(GP) = (EP)(DP)Find the distance between (0,4) and (3,-1)
Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, -4) and (x₂, y₂ ) = (3, - 1)
d = [tex]\sqrt{(3-0)^2+(-1+4)^2}[/tex]
= [tex]\sqrt{3^2+ 3^2}[/tex]
= [tex]\sqrt{9+9}[/tex]
= [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex] ≈ 4.24 ( to 2 dec. places )
Roofing material costs $84.52 per square (10ft×10ft). The roofer charges $55.75 per square for labor, plus $9.65 per square for supplies. Find the total cost for 26.3 squares of installed roof. Round to the nearest cent.
Answer:
$1720.00
Step-by-step explanation:
55.75 + 9.65 = 65.40
65.40 x 26.3 = 1720.02
Which system of equations is equivalent to the following system?
2x + 4y = 14
4x + y = 20
A.2x + 4y = 14
-16x – 4y = -80
B.2x + 4y = 14
- 4x + y = -20
C.4x + 8y = -28
4x + y = 20
D.-2x - 4y = 14
4x + y = 20
Answer:
A
Step-by-step explanation:
Given :
2x + 4y = 14 ---------- eq 1
4x + y = 20 ---------- eq 2
if you multiply eq 2 by -4 on both sides, you get
-4 (4x + y = 20) = -4 (20)
-16x -4y = -80 --------- eq3
we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.
Answer:
A.Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&(2)\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{multiply both sides by (-4)}\end{array}\right\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-16x-4y=-80&(2)\end{array}\right\to \boxed{A.}[/tex]
B.
[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{change the signs}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-4x-y=-20&\text{it's different to (2)}\end{array}\right[/tex]
C.
[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{multiply both sides by 2}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}4x+8y=28&\text{different to (1)}\\4x+y=20&(2)\end{array}\right[/tex]
D.
[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{change the signs}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}-2x-4y=-14&\text{different to (1)}\\4x+y=20&(2)\end{array}\right\\\\A.[/tex]
Which ordered pairs make both inequalities true? Select two options.
y < 5x + 2 y>=1/2x+1
(-1,3)
(0,2)
(1,2)
(2,-1)
(2,2)
Answer:
The points C(1,2) and E(2,2) make both inequalities true
Step-by-step explanation:
we have
[tex]y < 5x+2[/tex] -----> inequality A
The solution of the inequality A is the shaded area below the dashed line
[tex]y\geq \frac{1}{2}x+1[/tex] ------> inequality B
The solution of the inequality B is the shaded area above the solid line
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
Remember that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities and the point lie on the shaded area of the solution
Plot the points and verify if lie on the shaded area
Let
[tex]A(-1,3),B(0,2),C(1,2),D(2,-1),E(2,2)[/tex]
see the attached figure
The points C(1,2) and E(2,2) lie on the shaded area
Note
The points A(-1,3) and B(0,2) satisfy inequality B but don't satisfy inequality A
The point D(2,-1) satisfy inequality A but don't satisfy inequality B
therefore
The points C(1,2) and E(2,2) make both inequalities true
Answer:
c and e
Step-by-step explanation:
Algebra 2 help please ASAP
Answer:
The option A,D and E are correct.
Step-by-step explanation:
Given: 2x^3-250x^2
Factor : 2x^2(x-125)
So, GCF = 2x^2
Now a = 1 and b= 5
we know that a^3-b^3 = (a-b)(a^2+ab+b^2)
(x)^3 - (5)^3 = (x-5)(x^2+5x+25)
So, the option A,D and E are correct.
Consider the function f(x)=|x+3|−5 and its graph, which follows.
An absolute value function with vertex (negative 3, negative 5). It passes through (negative 8, 0) & (2, 0).
Suppose the function is transformed by the function g(x) = −1/5f(x).
Please graph response
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x+3\right|-5[/tex]
Obtain the function g(x)
[tex]g(x)=-\frac{1}{5} f(x)[/tex]
substitute
[tex]g(x)=-\frac{1}{5} [\left|x+3\right|-5][/tex]
[tex]g(x)=-\frac{1}{5}\left|x+3\right|+1[/tex]
using a graphing tool
The graph in the attached figure
The vertex is the point (-3,1)
The x-intercepts are the points (-8,0) and (2,0)
The y-intercept is the point (0,0.4)
Answer:
n
Step-by-step explanation:
A marble is randomly selected from a bag containing 15 black, 12 white, and 6 clear marbles. Find P(not clear). Round
to the nearest percent if necessary.
A.18%
B.82%
C.64%
D.88%
Answer:
A 18%
Step-by-step explanation:
I believe it should be A because there is no specific type a marble specified therefore if you do
12/33--> 0.36 times 100= 36 % which isn't an option
15/33->0.45 times 100= 45 % which also isn't an option
6/33= 0.18 times 100= 18% this is the only option given
Answer:
B. 82%
Step-by-step explanation:
From the question; A marble is randomly selected from a bag containing 15 black, 12 white, and 6 clear marbles. Find P(not clear).
To find p(not clear), we use this formula;
P(not clear) = 1 - p(clear)
To proceed we first have to find p(clear) and the minus it from 1
But,
probability = Required outcome/ all possible outcome
In the question, since what we are looking for now is probability of clear, so our 'required outcome' is the number of marble which is 6,
all possible outcome is the number of all the marbles; 15 + 12 + 6 = 33
We can now proceed to find the probability of clear marble, hence;
probability = Required outcome/ all possible outcome
p(clear marble) = 6/33
Now, we go ahead to find the probability of 'not clear marble'
P(not clear) = 1 - p(clear)
= 1 - 6/33
= 1 - 0.181818
=0.818182
P(not clear) = 0.818182
But the question says we should round our answer to the nearest percent, so we will multiply our answer by 100%
p(not clear) = 0.818182 × 100%
p(not clear) = 82% to the nearest percent
is this a parallelogram? Just checking
Answer:
Step-by-step explanation:
Yes it’s parallel because the lines do not meet
a car sales for 25,000 if the rate of depreciation is 15% what is the value of the car after 7 years round to the nearest hundred
Answer:
$8,000 to the nearest hundred.
Step-by-step explanation:
A depreciation of 15% means that after each year the car is worth 0.85 of it's value the previous year.
So after 7 years the values of the car is 25,000(0.85)^7
= 8,014
The value of a car that depreciates at a rate of 15% per year after 7 years is $10,400, after rounding to the nearest hundred.
The question is asking for the value of the car after 7 years when it depreciates at a rate of 15% per year. To find the car's value after each year, we can multiply the current value at the end of each year by 85% (which is 100% - 15%), because the car is losing 15% of its value. The formula to calculate the depreciation is P(1 - r)^t, where P is the initial principal (the initial value of the car), r is the depreciation rate, and t is the time in years.
Using this formula, the car's value after 7 years would be: $25,000 x (1 - 0.15)^7. Calculating this gives a value of $25,000 x 0.417709 = $10,442.73.
After rounding to the nearest hundred, the value is approximately $10,400.
Use the rules of exponents to evaluate or simplify. Write without negative exponents.
3 • 4 0 =
a0
Using the rule that any non-zero number raised to the power of zero equals one, the equation 3 • 4^0 / a^0 simplifies to 3.
Explanation:The problem seems to be a little bit confusing, so let's format it more clearly. I believe that you're looking to simplify: 3 • 4^0 / a^0.
There's a rule in mathematics stating that any number raised to the zeroth power equals one. In other words, if x is a non-zero number, then x^0 = 1. In this case, 4^0 = 1 and a^0 = 1.
Apply that rule to your problem and it becomes 3 • 1 / 1, or simply 3.
So, according to the rules of exponents, the simplified form of 3 • 4^0 / a^0 is 3.
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latoya got home from work shopping at 4:30.she spent hour and 15 minutes at the mall. Then she did her grocery shopping for 30 minutes. what time did she start shopping
Answer: 2:45
Step-by-step explanation:
1 hour and 15 minutes plus 30 minutes equal an hour and 45 minutes. We subtract 1 hour and 45 minutes from 4:30 and get 2:45.
So she started shopping at 2:45.
A retail shop accepts only cash or checks suppose that 45% of its customers carry cash 44% carry checks and 31% carry both cash and checks what is the probability that a randomly chosen customer at the top of the shop is carrying cash or checks are both
Answer:
Step-by-step explanation:
The number of customers carrying cash=45% = 0.45
The number of customers carrying checks= 44% =0.44
The number of customers carrying both = 31% = 0.31
So,
To find the probability we will write the expression:
cash+checks-cash or checks(both)=cash and checks
0.45+0.44-both=0.31
0.45+0.44-0.31=both
0.58=both....
How many different pairs of parallel edges are there on a rectangular solid?
Answer:
18
Step-by-step explanation:
A rectangular prism has four parallel edges along its length, four parallel edges along its width, and four parallel edges along its height.
We want to know how many different pairs of parallel edges there are. Starting with the length, the number of unique pairs is:
₄C₂ = 6
The same is true for the width and height. So the total number of different pairs of parallel edges is:
3 × 6 = 18
5,731÷34 show ur work
Answer:
168.558
Step-by-step explanation:
168.58
34√5731.0
-34 ↓3
23 3
-204 ↓1
28 1
- 272 ↓0
19 0
-170 ↓0
20 0
-170 ↓0
30 0
-272 ↓0
28 0
and just goes on..
The vertex of this parabola is at (2,-4). When the y-value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
Answer:
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (2, - 4), thus
y = a(x - 2)² - 4
To find a substitute (- 3, - 3) into the equation
- 3 = a(- 3 - 2)² - 4
- 3 = 25a - 4 ( add 4 to both sides )
1 = 25a ( divide both sides by 25 ), hence
a = [tex]\frac{1}{25}[/tex]
y = [tex]\frac{1}{25}[/tex] (x - 2)² - 4 ← in vertex form
= [tex]\frac{1}{25}[/tex] (x² - 4x + 4) - 4 ← in expanded form
Hence the coefficient of the x² term is [tex]\frac{1}{25}[/tex]
Answer:-5
Step-by-step explanation:
A 3-digit numeral is formed by selecting digits at random from 2,4,6,7 without repetition. Find the probability that the number is formed greater than 600. P(greater than 600)
The probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].
What is probability?Probability is the chance that something will happen, or how likely it is that an event will occur.
What is the formula for the probability?The formula for the probability is
[tex]P(E) = \frac{number \ of \ favorable \ outcomes }{Total\ number\ of\ outcomes}[/tex]
Where,
P(E) is the probability of any event.
What is permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
What is the formula for the permutation?The formula for the permutation is given by
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the permutation
n is the total number of objects
r is the total number of objects to be selected
According to the given question.
We have total four numbers 2, 4, 6, 7.
So,
The total number of three digits can be formed using these four numbers = [tex]^{4} P_{3}[/tex] = [tex]\frac{4!}{(4-3)!} =\frac{4\times 3\times 2\times 1}{1}[/tex][tex]=24[/tex]
Now, for making three digits number which are greater than 600 by using 2, 4, 6, 7 without repetition is given by
Number of ways for filling hundred place is 2 (either 6 or 7).
Number of ways for filling tens place is 3 (if 6 is placed at hundred place then remaining numbers are 7, 2, 4 and if 7 is place at hundred place then remaining numbers are 6, 2, 4).
Number of ways for filling one place is 2(because only 2 number are left).
Therefore, the total numbers of three digits can be formed by using these numbers 2, 4, 6, and 7
[tex]= 2\times 3\times 2\\=12[/tex]
So,
the probability that the number is formed greater than 600
= [tex]\frac{total\ three\ digits\ numbers\ which\ are \ formed \ by\ using\ 1,\ 2, \ 3, \ and\ 4\ which\ are\ greater\ than\ 600 }{Total \ three\ digits\ numbers\ formed\ by \ using \ 1,\ 2,\ 3,\ and \ 4}[/tex]
[tex]= \frac{12}{24}[/tex]
[tex]= \frac{1}{2}[/tex]
Therefore, the probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].
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Answer:
1) 95
2) -12
3) 7
4) 1,700
5) 57
6) 3,070