(2 + √3)^2 - (2 - √3)^2 (expand the expressions)
4 + 4√3 + 3 - (4 - 4√3 + 3) (calculate)
4 + 4√3 + 3 - (7 - 4√3) (remove the parantheses)
4 + 4√3 + 3 - 7 + 4√3 (calculate and collect like terms)
0 + 8√3 (remove 0)
8√3
Write a sentence describing each of the following probabilities. (Note: A' = the complement of event A) P(A or A') = 1 P(A and A') = 0
Answer:
The following properties hold for all events A, B.
• P(∅) = 0.
• 0 ≤ P(A) ≤ 1.
• Complement: P(A) = 1 − P(A).
• Probability of a union: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
For three events A, B, C:
P(A∪B∪C) = P(A)+P(B)+P(C)−P(A∩B)−P(A∩C)−P(B∩C)+P(A∩B∩C).
If A and B are mutually exclusive, then P(A ∪ B) = P(A) + P(B).
• Conditional probability: P(A | B) = P(A ∩ B)
P(B)
.
• Multiplication rule: P(A ∩ B) = P(A | B)P(B) = P(B | A)P(A).
• The Partition Theorem: if B1, B2, . . . , Bm form a partition of Ω, then
P(A) = X
m
i=1
P(A ∩ Bi) = X
m
i=1
P(A | Bi)P(Bi) for any event A.
As a special case, B and B partition Ω, so:
P(A) = P(A ∩ B) + P(A ∩ B)
= P(A | B)P(B) + P(A | B)P(B) for any A, B.
• Bayes’ Theorem: P(B | A) = P(A | B)P(B)
P(A)
.
More generally, if B1, B2, . . . , Bm form a partition of Ω, then
P(Bj | A) = P(A | Bj )P(Bj)
Pm
i=1 P(A | Bi)P(Bi)
for any j.
• Chains of events: for any events A1, A2, . . . , An,
P(A1∩A2∩. . .∩An) = P(A1)P(A2 | A1)P(A3 | A2∩A1). . . P(An | An−1∩. . .∩A
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(9,9) and (1,-1)
Answer:
(5, 4)
Step-by-step explanation:
[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }[/tex]
(X₁, Y₁) is the coordinates of the 1st point and (X₂, Y₂) is the coordinates of the 2nd point.
Using the formula above,
[tex]midpoint \: of \: segment \\ = ( \frac{9 + 1}{2} , \frac{9 - 1}{2} ) \\ = ( \frac{10}{2} , \frac{8}{2} ) \\ = (5,4)[/tex]
a new neighborhood activity complex is being built in juctioncity. the perimeter of the rectangular playing field is 362 yards. the length of the field is 3 yards less than triple the width. what are the demensions of the playing field?
Answer:
width: 46 yardslength: 135 yardsStep-by-step explanation:
Let w represent the width of the playing field in yards. Then the length is 3w-3. The perimeter is given by ...
P = 2(L+W)
362 = 2((3w-3) +w)
181 = 4w -3
184 = 4w
46 = w
3(46)-3 = 135 . . . length
The playing field is 46 yards wide and 135 yards long.
The temperature is 3.5 degrees Fahrenheit at 7:00 am. During the next 4 hours, the
temperature decreases by-15.5 degrees. What is the temperature at 11:00 am?
A. -19 degrees F
B.19 degrees
C. 12 degrees F
D. -125 degrees F
Answer:
The answers is -19 degrees F
Hope it helps :3
multiply (x^3 − 3x^2 + 4) · (2x^3 + 3x^2 − 4x)
Answer:2x^6 - 3x^5 - 13x^4 + 20x^3 + 12x^2 - 16x
Step-by-step explanation:
Greetings from Brasil...
Let's apply the distributive property....
(X³ - 3X² + 4) (2X³ + 3X² - 4X)
2X⁶ + 3X⁵ - 4X⁴ - 6X⁵ - 9X⁴ + 12X³ + 8X³ + 12X² - 16X
2X⁶ - 3X⁵ - 13X⁴ + 20X³ + 12X² - 16Xwhat is the formula of LSD in a cuboid?
Answer: The volume of a cuboid is given by the formula V = LWH, and the surface area of a cuboid is given by the formula SA = 2lh + 2wh + 2lw where l = length, w = width, and h = height.
And i was just learning this a few days back lol
2. Use the distributive property to
write an equivalent expression.
5. (6 + 9) =
Answer:
3(2 + 3)
Step-by-step explanation:
both answers equal 15
Answer:
(9+6)
Step-by-step explanation:
Which number is lower?
A) 4.8
b) -9.9
Answer:
b) -9.9
Step-by-step explanation:
since its a negative its automatically smaller than any whole
hope this helps plz give brainliest
What is the GCF of 14, 4 and 42?
Answer:
GCF = 2 :)
Step-by-step explanation:
The greatest common factor is the biggest number that each number is divisible by.
There is no number greater than 2 that 14, 4 and 42 are all divisible by! :)
A model car has a scale of 3 inches to 2 feet. The length of the actual car is 14 feet. What is the length of the model car in inches?
Answer:
21 inches
Step-by-step explanation:
The model has a scale of 3:2
Simplify 3:2
1.5:1
14 * 1.5 = 21
The length of the model car is 21 inches
What is the solution set for -4x + 10 > 5x + 55?
Answer:
x = (- oo, -5)
Step-by-step explanation:
-4x + 10 > 5x + 55-4x - 5x > 55 - 10-9x > 45x < -5x = (- oo, -5)what is the slope of x-3y=12
Which rays form the 65 angle in this figure?
Answer:
BD and BC
Step-by-step explanation:
The angle is between this two lines
The rays BD and BC form the angle 65° in the figure.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
When two lines or rays intersect at a single point, an angle is created.
Here, the angle measure is 65°.
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
And it is created between two rays.
And those rays are BD and BC.
Therefore, the required rays are BD and BC.
To learn more about the angle measure;
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#SPJ5
x − 5 = 17 A) x = 22 B) x = 12 C) x = 3.4 D) x = -12
Answer:
A. X=22
Step-by-step explanation:
x - 5 = 17
x =17 + 5
x = 22
3. Find two possible lengths for CD if C, D, and E
are collinear, CE = 15.8 centimeters, and DE=
3.5 centimeters.
Given :
C, D, and E are col-linear, CE = 15.8 centimetres, and DE= 3.5 centimetres.
To Find :
Two possible lengths for CD.
Solution :
Their are two cases :
1)
When D is in between C and E .
. . .
C D E
Here, CD = CE - DE
CD = 15.8 - 3.5 cm
CD = 12.3 cm
2)
When E is in between D and C.
. . .
D E C
Here, CD = CE + DE
CD = 15.8 + 3.5 cm
CD = 19.3 cm
Hence, this is the required solution.
3. Find the equation of a line perpendicular to y=-9x+b and through point (-18,3)
Answer:
y = [tex]\frac{1}{9}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
y = - 9x + b ← is in slope- intercept form
with slope m = - 9
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-9}[/tex] = [tex]\frac{1}{9}[/tex] , thus
y = [tex]\frac{1}{9}[/tex] x + b ← is the partial equation
To find b substitute (- 18, 3) into the partial equation
3 = 2 + b ⇒ b = 3 - 2 = 1
y = [tex]\frac{1}{9}[/tex] x + 1 ← equation of perpendicular line
A pizza shop charges $7.00 for a cheese pizza and $1.50 per topping. The total charge for Megan’s pizza was $11.50. Write and solve an equation to determine how many toppings Megan ordered on her pizza.
Answer:
Step-by-step explanation:
The model below represents an equation. Which value of x makes the value true?
x=
geometry homework math
Answer:
12) 45°
13) 125°?
14) SQR, RQS, and QSR
I am not sure about my answers, but I hope that you will finish your homework!
2.5x + 6 = 3.25x + 3
Can someone write a real-world problem for this?
Answer:
2.5(x)+6=3.25(x)+3 4=x. Real world problem below
Step-by-step explanation:
Nico is organizing a party. Going skating, admission is 6 dollars, and each person pays 2.5 dollars for a pair of skates. If he has 3 other people in his group, the equation is 2.5(4)+6=24. He is also looking at going to a trampoline park. It is 3 dollars to get in, and 3.25 per person for an hour on the trampolines. This equation can be shown as 3.25(4)+3 which equals 24.
What is the base unit used to measure length and distance?...
Answer:
a meter (when using the metric system)
A computer’s BIOS is defined as the license that operates hardware. instructions within hardware. software within hardware. application software for hardware.
Answer:
instructions within hardware.
Step-by-step explanation:
I think it work
Answer:
answer is c
just took the quiz
Step-by-step explanation:
7.9, 6.8, 5.7, 4.6 what’s next
Answer: 3.5
Step-by-step explanation:
For this question, we are simply finding a pattern.
7.9-6.8=1.1
6.8-5.7=1.1
5.7-4.6=1.1
So we can see from above that the different between each adjacent numbers are 1.1.
Thus, the next number will be 4.6-1.1=3.52 = 1/2(7x - 4)
I need help finding the answer to this equation!!
Answer:
[tex]2 = \frac{1}{2} (7x - 4)[/tex]
________________________________
[tex]2 \times 2 = 7x - 4[/tex]
________________________________
[tex]4 + 4 = 7x[/tex]
________________________________
[tex]8 = 7x[/tex]
________________________________
[tex]x = \frac{8}{7}[/tex]
________________________________
[tex]x = 1 \frac{1}{7}[/tex]
________________________________
hope it helped you:)
simplify 1/3(15x-9)-1/5(25x+5)
Answer:
-4
Step-by-step explanation:
1/3(15x-9)-1/5(25x+5)
5x-3-5x-1
Combine like terms
5x and -5x cancel out
-3-1= -4
What is 6.729 x 10^6 in standard form?
4.052×106=4052000
Explanation:
The number is written in scientific notation, where we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of 10.
In general notation power of 10 is not used and we multiply the number in single digit by the power of 10 to get it in simple standard decimal notation.
Multiplying by a positive power of 10 means moving decimal to right and in case power is negative (this is when the number is less than 1) it meanss moving decimal to left. This is done by the power of 10.
Here we have
4.052×106= 4.0520000×100000= 4052000.
= 4052000
FInd the equation of a perpendicular line to y=-2 that passes through the points (4,-2)
Answer:
x = 4
Step-by-step explanation:
y=-2 is a horizontal line so x must be a vertical line through (4,-2)
Which benchmark fraction is 4/7 closest to? 1/4 3/4 1/2. 4/4. am actually 3 grade
Answer:
wow I am 6th grade and..... WHAT ARE THEY TEACHING YOU
Step-by-step explanation:
FAILURE OF THE SCHOOL SYSTEM
What is the answer to.. –2m = 8 − m
Answer:
-8
Step-by-step explanation:
Solve the equation:
-2m = 8 - m
-2m + m = 8
-m = 8
m = -8
If you would like to check the answer, plug the value of m back into the equation:
-2 (-8) = 8 - -8
16 = 16
Answer:
m = -8
Step-by-step explanation:
add m to both sides
-2m + m =8 - m + m
simplify
-m = 8
divide sides by -1
-m/-1 = 8/-1
simplify
m = -8
In the complex number 6-7i , what is the imaginary part
a is called the real part of the complex number and bi is called the imaginary part of the complex number. In the complex number 6 - 4i, for example, the real part is 6 and the imaginary part is -4i.
Point P is shown on the number line below. The distance between point Q and point P is 6 1/2 units. Which number could represent point Q?
A) -9 1/2
B) 1 1/2
C) 2 1/2
D) 10 1/2
Answer:
B is the correct answer for this question
Step-by-step explanation:
The number that could represent point Q is to be considered as the option c. 2 1/2.
Calculation of the number:Since
p = -4
q could be 6.5 units to the right or to the left of point p.
So, to the right it should be like
=p + q
= -4 + 6.5
= 2.5
Hence, The number that could represent point Q is to be considered as the option c. 2 1/2.
Learn more about number here: https://brainly.com/question/24338971