Answer:
Line 3
Step-by-step explanation:
we have
[tex]4(2x+3)=-20[/tex]
Verify each line
Line 1
[tex]4(2x+3)=-20[/tex] ----> the given equation
Line 1 is correct
Line 2
Distribute in the left side
[tex]8x+12=-20[/tex]
Line 2 is correct
Line 3
Subtract 12 both sides
[tex]8x=-20-12[/tex]
[tex]8x=-32[/tex]
The line 3 is not correct
Tessa made a mistake in Line 3 of the problem. The correct calculation should be -20 minus 12, which equals -32. The solution for x is -4.
Explanation:The subject of this problem is Mathematics, specifically algebra. Looking at the lines of the problem you provided, we can see that Tessa's mistake lies in Line 3 when she subtracts 12 from -20 and gets -8. The correct subtraction should be -20 minus 12 = -32.
So, Line 3 would correctly be 8x = -32 . To solve for x, we would then divide -32 by 8 to get x = -4.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ3
Use The four step process to find the slope of the tangent line to the graph of the given function at any point. ( simplify your answer is completely)
F(x)= 8x^2 +3x
I’ve been trying to do this problem for 20 minutes, please help
Answer:
The answer to your question is: 16x + 3
Step-by-step explanation:
Step 1 : f(x) = 8x² + 3x
f(x +h) = 8(x + h)² + 3( x + h)
f(x + h) = 8( x² + 2xh + h²) + 3( x + h)
f (x + h) = 8x² + 16xh + 8h² + 3x + 3h
Step 2 f(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)
= 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x
= 16xh + 8h² + 3 h
Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h
= 16x + 8h + 3
Step 4 lim f(x + h) - f(x)/ h = lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3
h ⇒0 h ⇒0 h ⇒0
Here, we are required to find the slope of the tangent line to the graph of the given function at any point.
The correct answer is 16x + 3.
The four step process to find the slope of the tangent line to the graph at any point is as follows;
First step (1):
First, there's a need to evaluate the value of F(x+h), the result of which is;f(x +h) = 8(x + h)² + 3( x + h) and yields;
f(x + h) = 8( x² + 2xh + h²) + 3( x + h)
and, f (x + h) = 8x² + 16xh + 8h² + 3x + 3h.
Second step(2):
Second step involves subtraction of F(x) from F(x+h), i.eF(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)
and, F(x+h) - f(x) = 16xh + 8h² + 3 h
Third step (3):
The third step involves dividing both sides of the equation by h, i.e{F(x+h) - f(x)} / h = (16xh)/h + (8h²)/h + (3 h)/h
This in turn yields;
{F(x+h) - f(x)} / h = 16x + 8h + 3.
Fourth step(4):
This step involves taking limits on both sides as h => 0., i.elim f(x + h) - f(x)/ h =
h=>0
lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3
h=>0. h=>0
Therefore, the slope of the tangent line to the graph of the given function at any point is;
16x + 3.
Read more:
https://brainly.com/question/10676072
Adams Co. uses the following standard to produce a single unit of its product: Variable overhead (2 hrs. @ $3/hr.) = $ 6 Actual data for the month show variable overhead costs of $150,000 based on 24,000 units of production.
The total variable overhead variance is ________.
a) 6,000F
b) 6,000U
c) 78,000U
d) 78000F
e) 0
A B and C are collinear, and B is between A and C. The ratio of AB to AC is 2:7. If A is at (0,-8) and B is (2,-4), what are the coordinates of point C?
Answer:
C = (7, 6)
Step-by-step explanation:
The problem statement tells us the relation between the points is ...
(B-A)/(C-A) = 2/7
7(B -A) = 2(C -A) . . . . . . multiply by 7(C-A)
7B -7A +2A = 2C . . . . . add 2A
C = (7B -5A)/2 . . . . . . . divide by 2
C = (7(2, -4) -5(0, -8))/2 = (14, 12)/2 . . . . . fill in the values of A and B
C = (7, 6)
When I worked at Southern it took me 8 minutes to get to work. Now, it takes me 26 minutes to get to work. What is the percent increase in the time it takes me to get to work?
Answer:
225%
Step-by-step explanation:
You can figure the percentage change from ...
percentage change = ((new value)/(old value) -1) × 100%
= (26/8 -1) × 100% = (3.25 -1) × 100% = 225%
Given triangle ABC with coordinates A(−6, 4), B(−6, 1), and C(−8, 0), and its image A′B′C′ with A′(−2, 0), B′(−5, 0), and C′(−6, −2), find the line of reflection.
The line of reflection is at y=?
Answer:
The line of reflection is at y = x+6.
Step-by-step explanation:
The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...
y = 1(x +4) +2
y = x + 6 . . . . . . . line of reflection
4. A rectangle has a width of 2 cm and a perimeter of 25 cm. Find the length and the area.
A ) ℓ = 12.5 cm and A = 21 cm2
B) ℓ = 10.5 cm and A = 25 cm2
C) ℓ = 10.5 cm and A = 21 cm2
D) ℓ = 12.5 cm and A = 25 cm2
Answer:
l = 10.5 cm and A = 21 cm2
Step-by-step explanation:
Area is w*l
Perimeter is 2(w+l)
Replacing the information known in the problem you can get the length with the perimeter
P = 2(w+l)
25 = 2(2+l)
12.5 = 2 + l
10.5 cm = l
with the length now you can find the area
A = w*l
A = 2*10.5
A = 21 cm2
Susan quits her administrative job, which pays $40,000 a year, to finish her four-year college degree. Her annual college expenses are $8,000 for tuition, $900 for books, and $2,500 for food. The opportunity cost of attending college for the year:
The opportunity cost of Susan attending college for a year is $51,400 ($11,400 of actual college expenses and $40,000 of foregone income from her previous job).
Explanation:The opportunity cost of attending college is determined not only by the actual expenditure but also by the income you forgo by not working. In Susan's case, her actual expenses include $8,000 for tuition, $900 for books, and $2,500 for food, which total to $11,400. However, since she quit her $40,000 a year job to attend college, that lost income is also part of her opportunity cost. So, we add the lost income to her college expenses to get the total opportunity cost. Therefore, the opportunity cost of Susan attending college for the year would be $51,400 ($40,000 + $11,400).
Learn more about Opportunity Cost here:https://brainly.com/question/13036997
#SPJ12
A new sidewalk will be 4 feet wide and 50 yards long. Eighty pounds of concrete mix covers 4 square feet and costs $3.65. How much will the concrete for the new sidewalk cost?
You earn $65,000 a year, are married, and claim your spouse, yourself, and two children. What amount is withheld weekly for federal income tax? A $111.00 b $115.00 c $125.00 d $120.00 e $110.00
Answer:
C
Step-by-step explanation:
Find the variance of this probability distribution. Round to two decimal places.
Answer:
Variance = 4.68
Step-by-step explanation:
The formula for the variance is:
[tex]\sigma^{2} =\frac{\Sigma(X- \mu)^{2}}{N} \\or \\ \sigma^{2} =\frac{\Sigma(X)^{2}}{N} -\mu^{2} \\[/tex]
Where:
[tex]X: Values \\\mu: Mean \\N: Number\ of\ values[/tex]
The mean can be calculated as each value multiplied by its probability
[tex]\mu = 0*0.4 + 1*0.3 + 2*0.1+3*0.15+ 4*0.05=1.15[/tex]
[tex]\frac{\Sigma (X)^{2}}{N} =\frac{(0^{2}+1^{2}+2^{2}+3^{2}+4^{2})}{5} =6[/tex]
Replacing the mean and the summatory of X:
[tex]\sigma^{2} = \frac{\Sigma(X)^{2}}{N} -\mu^{2} \\= 6 - 1.15^{2}\\= 4.6775[/tex]
Janelle plans to buy three boxes of popcorn for herself and 2 friends. If each box costs $1.95 how much change will she receive the when she pays with a ten dollar bill
If there is a 30% reserve requirement on a $1,000 deposit, how much must be set aside as a member bank reserve?
Answer:
$300
Step-by-step explanation:
30% of $1000 is ...
0.30 × $1000 = $300
Answer:
$300
Step-by-step explanation:
If there is a 30% reserve requirement on a $1,000 deposit, there must be $300 set aside as a member bank reserve.
30% of $1000 = $300
10 POINTS AND BRAINLIEST!!
A government agency can spend at most $125,000 on a training program. If the training program has a fixed cost of $45,000 plus a cost of $125 per employee, how many employees can be trained?
Answer:
Step-by-step explanation:
From the problem statement, we can setup the following equation:
[tex]125,000 = 45,000 + 125E[/tex]
where [tex]E[/tex] is the number of employees being trained.
Solving for [tex]E[/tex] will give us the answer:
[tex]125,000 = 45,000 + 125E[/tex]
[tex]80,000 = 125E[/tex]
[tex]E = 640[/tex]
[tex]\text{Hello there!}\\\\\text{The most that they can spend is \$125,000}\\\\\text{We know that the fixed cost of the program is \$45000}\\\\\text{They also need to pay \$125 for each employee}\\\\\text{We need to solve:}\\\\125000-45000=80000\\\\\text{Now divide 80,000 by 125 to see how many employees they can train}\\\\80000\div125=640\\\\\boxed{\text{They can train 640 employees}}[/tex]
The Spanish club began the year with $15.00 in its account. At the end of their candy sale fundraiser,the club had 654.75.How much money did the club make?
The money that club make $ 639.75.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The Spanish club began the year with $15.00 in its account.
At the end the club had = $654. 75
so, the Club earned
= 654. 75- 15
= 639.75
Hence, the money club make $ 639.75
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
Phil, Melissa, Noah, and olivia saw a tall tree that cast a shadow 34 feet long. They observed at the same time that a 5-foot-tall person cast a shadow that was 8.5 feet long. How tall is the tree?
Answer:
20 ft
Step-by-step explanation:
The tree's shadow is 34/8.5 = 4 times the length of the person's shadow, so the tree is 4 times a tall as the person:
4×5 ft = 20 ft . . . . . the height of the tree
_____
Shadow lengths are proportional to the height of the object casting the shadow.
Using the ratio given from the shadow of the 5-foot person, we set up a proportion and solve for the height of the tree, which is 20 feet.
Explanation:The question is asking about the height of a tree, which can be figured out through a method called similar triangles in geometry. In this case, Phil, Melissa, Noah, and Olivia observed a 5-foot tall person casting an 8.5-foot shadow and a tall tree casting a 34-foot shadow.
From this, we can set up a proportion to find out the height of the tree. This would look like 5/8.5 = x/34, where x is the height of the tree. Cross multiplying and solving for x gives us x = (5*34)/8.5, which equals to 20 feet. Therefore, the height of the tree is 20 feet.
Learn more about Proportions here:https://brainly.com/question/32430980
#SPJ11
Find the equation of the line in slope-intercept form that passes through the following points. Simplify your answer.
(−5,−8) and (−7,8)
Answer:
y=-8(x+6)
Step-by-step explanation:
The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,
First we are going to calculate m:
If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case we have A=(-5,-8) and B=(-7,8)
[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]
Replacing in the formula:
[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]
Then [tex]y=-8x+b[/tex].
We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:
Replacing the point (-5,-8):
[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]
Or replacing the point (-7,8):
[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]
The answer is the same with both points.
Then we have:
y=-8x-48
y=-8(x+6)
A farmer has 350 feet of fence available to enclose a 6125 square foot region in the shape of adjoining squares with sides of length x and y. The big square has sides of x and the small square has sides of length y. Find x and y
The values for x and y are as follows: ( x = 25 ) feet and ( y = 15 ) feet.
Explanation:To find the values of x and y, we can set up a system of equations based on the given information. Let( x ) be the side length of the large square and ( y ) be the side length of the small square. The perimeter of the entire fence is given by ( 4x + 4y = 350) feet, and the total area enclosed by the fence is( xy + xy = 2xy = 6125 ) square feet.
First, we solve the perimeter equation for x
4x + 4y = 350
[tex]\[ x + y = \frac{350}{4} \][/tex]
x + y = 87.5
Now, we have two equations:
x + y = 87.5
2xy = 6125
We can substitute the value of ( x + y ) from the first equation into the second equation:
2xy = 6125
2(87.5 - y)y = 6125
175y - 2y² = 6125
y² - 87.5y + 3062.5 = 0
Solving the quadratic equation, we find two possible values for y However, since the side length cannot be negative, we discard the smaller value, leaving us with y = 15 feet. Substituting this into the first equation, we find x = 25feet.
Therefore, the final answer is x = 25 feet and y = 15 feet.
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.
Answer:
Part a) 30+m
Part b) $36
Step-by-step explanation:
Part a) Identify an expression that represents the amount Susan spent on the fruits
The complete question in the attached figure
Let
m ------> the number of apples
n -----> the number of oranges
q ----> the amount Susan spent on the fruits
we know that
m+n=15 ----> (in total she needs 15 fruits)
n=15-m -----> equation A
q=3m+2n ----> equation B
Substitute equation A in equation B
q=3m+2(15-m)
q=3m+30-2m
q=30+m -----> expression that represents the amount Susan spent on the fruits
Part b) Identify the amount she spent if she bought 6 apples
we know that
If m=6 apples
substitute the value of m in the expression of Part a)
q=30+m -----> q=30+6=$36
Charles is making pumpkin latte his recipe makes five lattes and cars for 5 cups of milk for each cup of pumpkin Purée if child Charles is making 15 pumpkin lattes how many cups of milk will he need
Answer:
15 cups
Step-by-step explanation:
To make 15 lattes, Charles will triple his recipe, so use 3×5 = 15 cups of milk.
An opaque bag contains 5 green marbles, 3 blue marbles and 2 red marbles. If two marbles are drawn at random WITHOUT replacement, what is the probability of drawing a blue marble given the first marble was red?
Answer: [tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given : An opaque bag contains 5 green marbles, 3 blue marbles and 2 red marbles.
Total marbles = 5+3+2=10
Now, if it given that the a red marble is already drawn, then the total marbles left in the bag = 10-1=9
But the number of blue marbles remains the same.
Now, the probability of drawing a blue marble given the first marble was red :-
[tex]=\dfrac{\text{Number of blue marbles}}{\text{Total marbles left}}\\\\=\dfrac{3}{9}=\dfrac{1}{3}[/tex]
Hence, the required probability = [tex]\dfrac{1}{3}[/tex]
In woodshop class, you must cut several pieces of wood to within 3/16 inch of the teacher's specifications. Let (s-x) represent the difference between the specification s and the measured length x of a cut piece.
(a)Write an absolute value inequality that describes the values of x that are within the specifications.
(b) The length of one piece of wood is specified to be s=5 1/8 inches. Describe the acceptable lengths for this piece.
Answer:
(a) |s - x| ≤ 3/16
(b) 4 15/16 ≤ x ≤ 5 5/16
Step-by-step explanation:
(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:
|s - x| ≤ 3/16
__
(b) Put 5 1/8 for s in the above equation and solve.
|5 1/8 - x| ≤ 3/16
-3/16 ≤ 5 1/8 -x ≤ 3/16
3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x
5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8
Pieces may be between 4 15/16 and 5 5/16 inches in length.
An absolute value inequality can be used to represent the acceptable range of lengths for a piece of wood in a woodshop class. For a specified length of 5 1/8 inches, the acceptable lengths for the piece would be between 4 15/16 inches and 5 5/16 inches.
Explanation:Your task in woodshop class is to cut pieces of wood to within 3/16 inch of the teacher's specifications. The difference between the specification s and the measured length x of a cut piece is represented by (s-x).
(a) You can represent this situation with the absolute value inequality |s - x| ≤ 3/16, which shows that the difference between the specification and the measured length must be less than or equal to 3/16 inch.
(b) If the length of one piece is specified to be s = 5 1/8 inches, you can substitute that value into the inequality to find the acceptable range of lengths: |5 1/8 - x| ≤ 3/16. Solving the inequality gives you the range 5 - 3/16 inches ≤ x ≤ 5 + 3/16 inches, or between 4 15/16 inches and 5 5/16 inches.
Learn more about Absolute Value Inequality here:https://brainly.com/question/33786594
#SPJ2
If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack, a three, a club or a diamond. Round to the nearest hundredth. Please show your work! Thanks!
0.50
0.58
0.65
0.15
Answer:
0.65
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem we have
[tex]x=4+4+13+13=34[/tex]
because
total of three=4
total of jack=4
total of club=13
total of diamond=13
[tex]y=52\ cards[/tex]
substitute
[tex]P=\frac{34}{52}=0.65[/tex]
The table below shows an inequality and a number by which to divide both sides
Answer:
The answer to your question is: The last option is correct
Step-by-step explanation:
Just remember thta when we divide by a negative number, the inequality changes, then,
- 125 ≥ -135 divide by -5
25 ≤ 27
Answer:
25 < 27 not 25 ≤ 27
Step-by-step explanation:
-125 ≥ -135
on the number, you count through -125 before -135, so -125 is greater but not equal to -135.
-125/ -5 > -135/ -5
= 25 < 27
25 is less than 27. They are not equal.
If r is the remainder when the positive integer n is divided by 7, what is the value of r?
(1) When n is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.
Answer:
Step-by-step explanation:
Given that When n is divided by 21, the remainder is an odd number.
i.e. [tex]n=21m+k[/tex] where m is an integer and k a positive integer <21
When n is divided by 28, the remainder is 3
[tex]n=28c+3[/tex], where c is a positive integer
This can be written as
[tex]n=4(7c)+3\\n=7(4c)+3[/tex]
Since n is giving odd remainder when divided by 21,
we get r =3 as n is a multiple of 7 +3
Solve by Substitution
Show Steps
x = −5y + 4z + 1
x − 2y + 3z = 1
2x + 3y − z = 2
Answer:
(x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions
Step-by-step explanation:
Use the first equation to substitute for x in the remaining two equations.
(-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation
-7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1
y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z
__
2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation
-7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms
y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z
This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...
x = 1 -z
y = z
z is a "free variable"
Help please I am a bit confused on this.
Because there are 4 inside angles the sum of the four angles must equal 360 degrees.
Add the angles to equal 360:
4x + 3x + 2x + 3x = 360
Simplify:
12x = 360
Solve for x by dividing both sides by 12:
x = 360 /12
x = 30
Now you have x, solve for each angle:
ABC = 4x = 4 x 30 = 120 degrees.
BCD = 3x = 3 x 30 = 90 degrees.
CDA = 2x = 2x 30 = 60 degrees.
DAB = 3x = 3 x 30 = 90 degrees.
C. It's important to know that a four sides figure needs the inside angles when added together need to equal 360 degrees.
Good morning ☕️
____________________
Step-by-step explanation:
Look at the photo below for the answer.
:)
Ellinor made tables of values to solve a system of equations.First she found that the x-value of the solution was between 0 and 1, and then she found that it was between 0.5 and 1. Next,she made this table.
A.(0.5,-1.8)
B.(0.9,-2.1)
C.(0.7,-1.5)
D.(0.6,-1.4)
The best approximation of the solution is represented by the ordered pair, (0.7,-1.5), the correct option is C.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The system of equations are equations that have a common solution.
The equations are:
y = 2x-3
y = -5x +2
The ordered pair that is the best approximation of the solution is the point at which for a given value of x, the system of the equation has the same y value.
From the table, it can be seen that for x = 0.7, the y value for both the equation is similar, -1.5 and -1.6.
Therefore, (0.7, -1.5).
Your question seems incomplete, the complete question is attached with the answer.
To know more about Equation
https://brainly.com/question/10413253
#SPJ5
Bobby bought a bag of candy at the candy shop.His total came up to $0.68. He gave the cashier 9 coins. How many of each coin did Bobby give the cashier
Answer:
3 pennies2 nickels3 dimes1 quarterStep-by-step explanation:
You know that 3 pennies are involved, because $0.68 cannot be made without them.
Then 6 coins must make up 65¢. If 1 is a quarter, then the remaining 40¢ must be made using 5 coins. 4 dimes is too few, and 8 nickels is too many. However 3 dimes and 2 nickels is just right.
Bobby gave the cashier 1 quarter, 3 dimes, 2 nickels, 3 pennies.
Suppose A, B, and C are mutually independent events with probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3. Find the probability that exactly two of the events A, B, C occur.
By the law of total probability,
[tex]P(A\cap B)=P[(A\cap B)\cap C]+P[(A\cap B)\cap C'][/tex]
but the events A, B, and C are mutually independent, so
[tex]P(A\cap B)=P(A)P(B)[/tex]
and the above reduces to
[tex]P(A)P(B)=P(A)P(B)P(C)+P(A\cap B\cap C')\implies P(A\cap B\cap C')=P(A)P(B)(1-P(C))=P(A)P(B)P(C')[/tex]
which is to say A, B, and C's complement are also mutually independent, and so
[tex]P(A\cap B\cap C')=0.5\cdot0.8\cdot(1-0.3)=0.12[/tex]
By a similar analysis,
[tex]P(A\cap B'\cap C)=P(A)P(B')P(C)=0.03[/tex]
[tex]P(A'\cap B\cap C)=P(A')P(B)P(C)=0.12[/tex]
These events are mutually exclusive (i.e. if A and B occur and C does not, then there is no over lap with the event of A and C, but not B, occurring), so we add the probabilities together to get 0.27.
Final answer:
The probability that exactly two of the independent events A, B, and C occur is 0.43, calculated by adding the probabilities of each possible pair of events occurring while the third does not.
Explanation:
The student is seeking the probability that exactly two out of the three events A, B, and C occur given their individual probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3, and the fact that they are mutually independent events. To find this, we ned to consider the three scenarios where exactly two events occur: A and B, A and C, and B and C. The probability for each scenario is found by multiplying the probabilities of the two events occurring and then multiplying by the probability of the third event not occurring.
For example, the probability of A and B both occurring but not C is P(A) × P(B) × (1 - P(C)). To find the total probability that exactly two events occur, we sum up the probabilities of all three scenarios:
P(A and B but not C) = P(A) × P(B) × (1 - P(C))
P(A and C but not B) = P(A) × (1 - P(B)) × P(C)
P(B and C but not A) = (1 - P(A)) × P(B) × P(C)
We then calculate and sum these probabilities:
P(A and B but not C) = 0.5 × 0.8 × (1 - 0.3) = 0.5 × 0.8 × 0.7 = 0.28
P(A and C but not B) = 0.5 × (1 - 0.8) × 0.3 = 0.5 × 0.2 × 0.3 = 0.03
P(B and C but not A) = (1 - 0.5) × 0.8 × 0.3 = 0.5 × 0.8 × 0.3 = 0.12
Adding these probabilities together provides the final answer:
Σ P(exactly two events) = 0.28 + 0.03 + 0.12 = 0.43
Therefore, the probability that exactly two of the events A, B, and C occur is 0.43.
The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represented by the shaded region?
Answer:
The fraction of the area of ACIG represented by the shaped region is 7/18
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
In the square ABED find the length side of the square
we know that
AB=BE=ED=AD
The area of s square is
[tex]A=b^{2}[/tex]
where b is the length side of the square
we have
[tex]A=49\ units^2[/tex]
substitute
[tex]49=b^{2}[/tex]
[tex]b=7\ units[/tex]
therefore
[tex]AB=BE=ED=AD=7\ units[/tex]
step 2
Find the area of ACIG
The area of rectangle ACIG is equal to
[tex]A=(AC)(AG)[/tex]
substitute the given values
[tex]A=(9)(10)=90\ units^2[/tex]
step 3
Find the area of shaded rectangle DEHG
The area of rectangle DEHG is equal to
[tex]A=(DE)(DG)[/tex]
we have
[tex]DE=7\ units[/tex]
[tex]DG=AG-AD=9-7=2\ units[/tex]
substitute
[tex]A=(7)(2)=14\ units^2[/tex]
step 4
Find the area of shaded rectangle BCFE
The area of rectangle BCFE is equal to
[tex]A=(EF)(CF)[/tex]
we have
[tex]EF=AC-AB=10-7=3\ units[/tex]
[tex]CF=BE=7\ units[/tex]
substitute
[tex]A=(3)(7)=21\ units^2[/tex]
step 5
sum the shaded areas
[tex]14+21=35\ units^2[/tex]
step 6
Divide the area of of the shaded region by the area of ACIG
[tex]\frac{35}{90}[/tex]
Simplify
Divide by 5 both numerator and denominator
[tex]\frac{7}{18}[/tex]
therefore
The fraction of the area of ACIG represented by the shaped region is 7/18