Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
Best Buy is currently selling the latest model of the iPad
Pro for $549.99. Since you are an employee there, you
receive a 5% discount. How much will the iPad Pro cost
you if you use your employee discount (before taxes).
Answer:
$522.49
Step-by-step explanation: 549.99*.05=27.50 (discount)
549.99-27.50=$522.49
Answer:
$522.49
Step-by-step explanation:
First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"
5% = 0.05
549.99 ⋅ 0.05 = 27.4995
That means the discount amount is $27.50
Subtract the discount amount from the original price
$549.99 - $27.50 = $522.49
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Help me please please please please
Answer:
1.
d. (-14) + (-8)
2.
a. (-14) + 8
Step-by-step explanation:
(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.
(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.
Answer:
1. D
2. A
Step-by-step explanation:
1. It asks you what expression has the same value as (-14)-8. All you need to do is find other equations that have the same value as that. So the equation is -14-8. IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5. If it's both negative: -(-5), it will be +5. If it is both positive: +(+5), it is going to be +5.
IMPORTANT!
- and + = -
- and - = +
+ and + = +
What we are looking for: -14-8
So choice A is (-14)+8 which is simplified to -14+8. So, this one isn't right.
Choice B: 14-(-8)= 14+8. So, it's incorrect.
Choice C: 14+(-8)= 14-8. Again, it's not -14-8 so it's not right.
Choice D: (-14)+(-8)= -14-8. This equation matches the one we are looking for! So it's correct!
2. Same thing as number 1. Let's simplify the equation it wants us to find first.
(-14)-(-8)= -14+8
So -14+8 is what we are looking for.
Choice A: (-14)+8= -14+8. It matches! So it is correct. Let's look at the other options anyway.
Choice B: 14-(-8)= 14+8. Nope. Not right.
Choice C: 14+(-8)= 14-8 because - always beats +. So, this one is also incorrect.
Choice D: (-14)+(-8)= -14-8. Oops, this is also wrong. So choice A is the right answer.
Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:
(When there is a number outside and inside a parentheses, multiply them.)
2(5)=10, CORRECT! 2+(5) is not 2 times 5. It's whatever is closest to the parentheses, in this case being the positive sign. So + and 5 is just 5!
IMPORTANT!
-2(-5)= - and - is positive, so positive (2 times 5). Positive 10.
-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.
+2(+5)= + and + is positive, so positive (2 times 5). Positive 10.
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies?
Answer:
(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.
coefficient of 8x+7y
Answer:
8
Step-by-step explanation:
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
8x→1
7y→1
The largest exponent is the degree of the polynomial.
1
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient of a polynomial is the coefficient of the leading term.
____________________________________________________________
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient in a polynomial is the coefficient of the leading term.
8
List the results.
Polynomial Degree: 1
Leading Term: 8x
Leading Coefficient: 8
Hope This Helps!!!
Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
Answer:
The answer is 216
Step-by-step explanation:
if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.
Which expression is equal to (1+6i)−(7+3i) ?
Answer:
- 6+3iStep-by-step explanation:
[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]
Question
Consider this expression.
4/2² - 6²
Type the correct answer in the box. Use numerals instead of words. For help, see this worked example e.
When a =
-5 and b = 3, the value of the expression is
Submit
Answer:
16
Step-by-step explanation:
4 * sqrt( a^2 - b^2)
Let a = -5 and b =3
4 * sqrt( (-5)^2 - 3^2)
Do the squaring first
4 * sqrt( 25 - 9)
Subtract inside the square root
4 * sqrt( 16)
Take the square root
4 * 4
Multiply 16
Answer:
[tex]\Large \boxed{16}[/tex]
Step-by-step explanation:
[tex]4\sqrt{a^2-b^2 }[/tex]
[tex]\sf Plug \ in \ the \ values \ for \ a \ and \ b.[/tex]
[tex]4\sqrt{-5^2-3^2 }[/tex]
[tex]4\sqrt{25-9 }[/tex]
[tex]4\sqrt{16}[/tex]
[tex]4 \times 4=16[/tex]
find m<SPT in degrees
Answer: 60°
Step-by-step explanation:
∠UQR = 180°
∠UQR = ∠UQ + ∠QR
180° = 115° + ∠QR
65° = ∠QR
∠QRT = 180°
∠QRT = ∠QR + ∠RS + ∠ST
180° = 65° + ∠RS + 55°
180° = 120° + ∠RS
60° = ∠RS
What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Find the value of the expression: −mb −m^2 for m=3.48 and b=96.52
Answer:
The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.
Step-by-step explanation:
Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:
[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]
[tex]f(3.48,96.52) = 323.779[/tex]
The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.
How to convert 2cm to feet?
Answer:
Divide by 30.48: It would be 0.0656168 feet.
Step-by-step explanation:
Answer:
0.0656
Step-by-step explanation:
2.54 cm = 1 in
12 in = 1 ft
2.54 * 12 = 30.48
2/30.48 = 0.0656167979
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
Question 2: Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
Answer:
?
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
Let "x" be the number of nickels, of dimes, and of quarters.
The value of the nickels is 5x cents.
The value of the dimes is 10x cents
The value of the quarters is 25x cents.
Equation:
Value of nickels + Value of dimes + Value of quarters =1320 cents
5x + 10x + 25x = 1320
Sove for "x". Then you will know the number of each coin.
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Answer:
$935.76
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Step 1
We find the Present value factor of sum
The formula =
(1 + i)^n
Where
i = maturity rate = 9% = 0.09
n = number of years = 10 years
Present Value = ( 1 + 0.09)^-10
= 0.4224
Step 2
We find the present value factor of annuity
The formula is given as:
1 - (1+i)^-n / i
i = maturity rate = 9% = 0.09
n = number of years = 10 years
= 1 - (1 + 0.09)^-10 /0.09
= 1 - 0.4224 /0.09
= 0.5775 /0.09
= 6.417
Step 3
The bond's current market price is calculated as:
= PV factor of Sum × Par Value + PV factor of annuity × coupon payment
Coupon payment is calculated as:
= Coupon interest × par value
= 8% × 1000
= 80
Hence,
= 0.4224 × 1,000 + 6.417 × 80
= 422.4 + 513.36
= 935.76
In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:
[tex]\$935.76[/tex]
We find the Present value factor of sum, by the formula of:
[tex](1 + i)^n[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]
We find the present value factor of annuity, by the formula as:
[tex]1 - (1+i)^{-n} / i[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]
The bond's current market price is calculated as:
[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]
Coupon payment is calculated as:
[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]
So continue the calcule;
[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]
See more about market place at brainly.com/question/24518027
What is the missing statement in step 10 of the proof?
Answer:
c/sin C = b/sin C
Step-by-step explanation:
Look at the statement in the previous step and the reason in this step.
c sin B = b sin C
Divide both sides by sin B sin C:
(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)
c/sin C = b/sin B
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.
(a) P(E ∪ F) =
(b) P(Ec) =
(c) P(Fc ) =
(d) P(Ec ∩ F) =
Answer:
(a) P(E∪F)= 0.8
(b) P(Ec)= 0.4
(c) P(Fc)= 0.7
(d) P(Ec∩F)= 0.8
Step-by-step explanation:
(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.
If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:
P(A∪B) = P(A) + P(B) - P(A∩B)
In this case:
P(E∪F)= P(E) + P(F) - P(E∩F)
Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1
P(E∪F)= 0.6 + 0.3 - 0.1
P(E∪F)= 0.8
(b) The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A. The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is P (Ac) = 1- P (A)
In this case: P(Ec)= 1 - P(E)
Then: P(Ec)= 1 - 0.6
P(Ec)= 0.4
(c) In this case: P(Fc)= 1 - P(F)
Then: P(Fc)= 1 - 0.3
P(Fc)= 0.7
(d) The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.
As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:
P(Ec intersection F) + P(E intersection F) = P(F)
P(Ec intersection F) + 0.1 = 0.3
P(Ec intersection F)= 0.2
Being:
P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)
you get:
P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)
So:
P(Ec∩F)= 0.4 + 0.3 - 0.2
P(Ec∩F)= 0.8
