This statement is False as the probability of intersection of two events is always less than the probability of union.
This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.
The chance of two events A and B occurring together can be calculated using the following formula to see why:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.
When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.
P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:
P(A) + P(B) - P(A ∪ B) ≤ P(A ∪ B)This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.
For more such questions on probability of the intersection & union
https://brainly.com/question/21333099
#SPJ4
LMX is an equilateral triangle . The height, LW, of the triangle is 12in. What is the perimeter of LMX? 4 square root of 3. 8 square root of 2. 24 square root of 3. 36 square root of 2
The perimeter of the triangle is 36√2
How to determine the perimeter of the rectangleFrom the question, we have the following parameters that can be used in our computation:
height = 12
Also, we understand that the triangle is an equilateral triangle
This means that the other sides are
Sides = 12√2
The perimeter is then calculated as
Perumeter =3 * Sides
So, we have
Perimeter =3 * 12√2
Evaluate
Perimeter = 36√2
Hence, the perimeter is 36√2
Read more about perimeter at
https://brainly.com/question/17297081
#SPJ1
What is factors of 96?
Answer:
Step-by-step explanation:
The factors of 96 are the integers that divide evenly into 96. To find the factors of 96, you can divide 96 by integers starting from 1 and increasing until you reach 96.
The factors of 96 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
These are all the integers that divide evenly into 96.
Can someone please help me out with this?!?!
A school group went to a carnival on a field trip. The function c(x) represents the amount of money spent in dollars, where x is the number of students. Does a possible solution of (29.5, $212.50) make sense for this function? Explain your answer.
A: Yes. The input and output are both feasible.
B: No. Neither the input nor output is feasible.
C: No. The input is not feasible.
D: No. The output is not feasible.
Answer: A: Yes. The input and output are both feasible.
Step-by-step explanation:
To determine whether the solution (29.5, $212.50) makes sense for the function c(x), we need to evaluate whether the input and output are feasible and make sense in the context of the problem.
The input is given as 29.5, which represents the number of students. It is unclear from the information given whether a non-integer value for the number of students is feasible or not. However, if we assume that 29.5 students means 29 students and 1 child attending the carnival, then the input of 29.5 students is feasible.
The output is given as $212.50, which represents the amount of money spent at the carnival. It is reasonable to assume that a school group on a field trip would spend a certain amount of money at a carnival, and $212.50 is not an unreasonable amount to spend.
Therefore, based on the information given, we can conclude that the solution (29.5, $212.50) makes sense for the function c(x). So the answer is A: Yes. The input and output are both feasible.
Graph the following function on the axes provided.
f(x) =
2x+8
| −2x + 7
10
Click and drag to make a line. Click the line to delete it.
Click on an endpoint of a line to change it.
O
7
s
32 21
A
N
for
for
co
x < -1
x > 3
3
s
9
D
8
9 10
The graph of the system is added as an attachment
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x + 8 for x < -1
-2x + 7 for x > 3
The above system is a piece wise fucntion that include
Two linear equations
Next, we plot the graph
See attachment for the graph of the equation
Read more about equation at
https://brainly.com/question/18831322
#SPJ1
If a ¼ of a teaspoon is 1 ml, then how many millilitres are in 6 teaspoons?
Answer
4x6=24
24x1 ml=24ml
Answer:
the answer to your question is 24 milliliters!
Step-by-step explanation:
good luck!
7 times as much as the sum of 1 third and 4 fifths
The value of the expression is [tex]\frac{63}{20}[/tex].
What is an expression?An expression contains more than two variables or numbers with the mathematical operation.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]\frac{1}{4}[/tex] and [tex]\frac{4}{5}[/tex]
Now,
Simplify.
= 7 x [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{5}[/tex]
= 7 x [tex]\frac{5+4}{20}[/tex]
= 7 x [tex]\frac{9}{20}[/tex]
= [tex]\frac{63}{20}[/tex]
Thus,
[tex]\frac{63}{20}[/tex] is the expression.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ9
[tex]2(\sqrt[3]{64} +\sqrt{25} )[/tex]
The simplified form of the expression 2( ³√64 + √25 ) is 18.
What is the simplified form for the expression?Given the expression in the question;
2( ³√64 + √25 )
First, simplify each term.
2( ³√64 + √25 )
Rewrite 64 as 4³
2( ³√( 4³ ) + √25 )
Also, rewrite 25 as 5²
2( ³√( 4³ ) + √( 5² ) )
Now, pull the terms out of the radical, assuming positive real numbers.
Take the cube root of 4³
2( 4 + √( 5² ) )
Take the square root of 5²
2( 4 + 5 )
Add 4 and 5
2( 9 )
Multiply 2 and 9
18
Therefore, the simplified form is 18.
Learn about surds here: brainly.com/question/840021
#SPJ1
72f - 12g = 96 and 6f -2g =10 please gives steps and anwsers
Answer:
(f,g)=(1,-2)
Step-by-step explanation:
72f-12g=96, 6f-2g=10
72f-12g=96
f=5/3+1/3g
72(5/3+1/3g)-12g=96
g=-2
f=5/3+1/3x(-2)
f=1
(f,g)=(1,2)
How do i find the excluded/extraneous values of this rational equation?
The extraneous values of the rational function are given as follows:
x = 7 and x = -3.
How to obtain the extraneous values of the rational function?The extraneous values of a function are the values of x that are outside the function's domain.
In this problem, we have a rational function, hence the extraneous values are the values that make the denominators zero, as follows:
x² - 4x - 21 = 0 -> (x - 7)(x + 3) = 0 -> x = -7 and x = -3.x + 3 = 0 -> x = -3.More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
a car traveling at 10m/s starts to decelerate steadily. It comes to a complete stop in 10 seconds. What is the acceleration?
Answer: 1m/s
Step-by-step explanation: Accleration = Speed/Time
10/10 = 1
Find the area and the perimeter of the figure at right. Be sure to
organize your work so you can explain your method later.
24 m
20°
16 m
18 m
The perimeter of the figure is 68+24=92 cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
In the given figure there is a rectangle and right angle triangle.
The length of rectangle is 16 cm and width is 18 cm
Perimeter=2(length+Breadth)
=2(16+18)
=68 cm
Now let us find perimeter of triangle
Base of height is 6cm and base is 8
P=a+b+√a²+b²
=6+8+√6²+8²
=24
Hence, the perimeter of the figure is 68+24=92 cm.
To learn more on Rectangles click:
https://brainly.com/question/20693059
#SPJ9
Natalie flew home from vacation with a heavy bag. With the first airline she flew, Natalie had to pay $29 to check her bag, plus $4 for every pound that her bag was over the weight limit.
The next flight was with another airline that had the same weight limit. Natalie had to pay $6 per pound that her bag was over the weight limit, in addition to the checked bag fee of $23.
By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?
The airline fees was $41 each
The over the weight limit of the bag is 3 pounds
How large was each airline's fee?Number pounds of Natalie's bag = x
Airline 1:
29 + 4x
Airline 2:
23 + 6x
Equate airlines 1 and 2
29 + 4x = 23 + 6x
collect like terms
29 - 23 = 6x - 4x
6 = 2x
divide both sides by 2
x = 6/2
x = 3 pounds
Hence,
Airline 1:
29 + 4x
= 29 + 4(3)
= 29 + 12
= $41
Airline 2:
23 + 6x
= 23 + 6(3)
= 23 + 18
= $41
Read more on equation:
https://brainly.com/question/2972832
#SPJ1
Colleen won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Colleen a bucket of fish to divide evenly among 3 dolphins. Each dolphin gets 6 fish. Which equation can you use to find the number of fish f in the bucket before Colleen feeds the dolphins?
Since the fish was share evenly amongst the 3 dolphins, and each one got 6, the equation will be:
f = d x n
where
f represents the fish
d represents the dolphin
n represents the number of fish each got.
Step by step explanationLet's assume that the number of fish in the bucket before Colleen feeds the dolphins is "f". To find out how many fish there were in the bucket, you can use the following equation:
f = 3 * 6
where 3 is the number of dolphins and 6 is the number of fish each dolphin gets. Solving for "f", you get:
f = 3 * 6
f = 18
So there were 18 fish in the bucket before Colleen fed the dolphins.
Learn more on equations here https://brainly.com/question/22688504
#SPJ1
The function f(t) = 930(0.9965) represents the change in a quantity over t hours. What does the constant 0.9965 reveal about the rate of change of the quantity?
The constant 0.9965 is the rate of change per hour. Specifically, it represents the factor by which the quantity changes every hour. In this case, the factor is less than 1, indicating that the quantity is decreasing over time.
To see how this rate of change works, consider an example:
If the initial quantity is 930, after one hour the quantity will be:
f(1) = 930(0.9965) ≈ 926.20
That is, the quantity has decreased by a factor of 0.9965, or about 0.35%.
After two hours, the quantity will be:
f(2) = 930(0.9965)^2 ≈ 922.42
That is, the quantity has decreased by a factor of 0.9965 twice, or about 0.70%.
So the constant 0.9965 reveals the rate of change of the quantity, which is a decrease of about 0.35% per hour.
Find the value of x. Round to the
nearest tenth.
12
X=[?]
Answer:
9.8
Step-by-step explanation:
two angles are given, 35 and 90. subtract these from 180 to get 55, the corresponding angle of x. we can then use law of sin to solve.
sin90/12 = sin55/x
sin55 * 12 = 9.8 , 9.8 = sin90x , 9.8/sin90
=9.8
Hong made 162 for 9 hours of work. At the same rate, how much would he make for 13
hours of work?
Since Hong made 162 dollars for 9 hours of work, we can set up the proportion:
162 dollars / 9 hours = x dollars / 13 hours
where x is the amount of money Hong would make for 13 hours of work.
To solve for x, we can cross-multiply and simplify:
162 dollars × 13 hours = 9 hours × x dollars
2106 = 9x
x = 234
Therefore, at the same rate, Hong would make 234 dollars for 13 hours of work.
Need help???!!!! Please
Reason:
-2 * 2 = -4
-2 + 2 = 0
These values are found through trial and error. The order of -2 and 2 doesn't matter.
What is the equation of the line through (-2, 8) with slope 3 in point-slope form?
Answer:
[tex]y-8=3(x+2)[/tex]
Step-by-step explanation:
The equation of the line with slope [tex]m[/tex] passing through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
if 12,00 people voted in the election how many were from 50 to 64 years old
The required population of the city is approximately 44,44.44.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Let's use algebra to solve for the population of the city.
Let P be the population of the city. We know that 27% of the population is from 50 to 64 years old.
The number of people from 50 to 64 years old is 27% of the whole population, which can be expressed as,
0.27P
We can set up an equation to relate the number of people from 50 to 64 years old to the number of eligible voters,
0.27P = x
where x is the number of people from 50 to 64 years old who voted.
We can solve for P by multiplying both sides of the equation by the reciprocal of 0.27,
P = x / 0.27
Substituting x with 1200,
P = 12,00 / 0.27 = 4444.44
Therefore, the population of the city is approximately 44,44.44.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ1
Complete quesiton,
'if 12,00 people voted in the election how many were from 50 to 64 years which is 27% of the whole population, calculate the population of the city?
Bella and George each ordered a
personal pan pizza. Bella ate of 1
4th
Pizza and George ate
7
8th of his pizza. How much more did George eat
Answer: 5/8
Step-by-step explanation:
We can make the fractions easier to read by changing 1/4 to 2/8, simply by multiplying the fraction by 2/2.
2/8 : 7/8
now you can see how much more George ate.
7/8 - 2/8 = 5/8
George ate 5/8 more than Grace.
Robert is painting a house. He has 35 cans of paint. He has used 30 kinds of paint on the walls. Now he needs to paint the trim. If each section of the trim takes 1/2 can of paint, how many sections of trim can he paint? Show your answer as an inequality with symbols, in words, and with a number line. Make sure your solution makes sense for this situation.
Answer:
x ≤ 10Maximum number of trims that can be painted with 5 cans is 10See number line imageStep-by-step explanation:
There are 5 cans left over after painting the walls.
Let x represent the maximum number of trims that can be painted
Since each trim requires 1/2 a can, x trims will take x/2 cans
This cannot exceed 5 cans so we get the inequality:
x/2 ≤ 5
Multiplying by 2 both sides of inequality:
x ≤ 10
In words:
Maximum number of trims that can be painted with 5 cans is 10
Number line attached
Find the Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water.
The Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.
What is fundamental counting principle?The Basic Counting Principle is a technique used in mathematics, more especially in probability theory and combinatorics, to determine how many combinations of options, items, or outcomes are possible. The Rule of Multiplication, the Product Rule, the Multiplication Rule, and the Basic Counting Rule are some of its alternate names.
It has a connection to the Sum Rule, often known as the Rule of Sum, which is a fundamental counting method used to calculate probabilities.
According to the Basic Counting Principle, if a decision or event has a potential result or set of options, and a different decision or event has b possible outcomes or choices, then the sum of all the unique combinations of outcomes for the two is ab.
Using the fundamental counting principle, if an event occurs in m ways and another event occurs in n ways then the total occurrence is given as (m)(n).
Given that,
m = 3 for choosing between sizes.
n = 3 for distilled, filtered, or spring water.
Thus, the total number of occurrence is given as:
T = (3) (3) = 9
Hence, the Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.
Learn more about fundamental counting principle here:
https://brainly.com/question/28384306
#SPJ1
The dimensions of a cylindrical are shown in the diagram. Find the total surface area of the can in terms of pi
R=3
h=4.5
The total surface area of the cylinder is S = 45π units²
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the surface area of the cylinder be represented as S
Now , the equation will be
The height of the cylinder h = 4.5 units
The radius of the cylinder r = 3 units
So , Surface area of cylinder = 2πr ( r + h )
Substituting the values in the equation , we get
Surface area of cylinder S = 2π ( 3 ) ( 3 + 4.5 )
On simplifying the equation , we get
Surface area of cylinder S = 2π ( 3 ) ( 7.5 )
Surface area of cylinder S = 45π units²
Hence , the surface area of cylinder is 45π units²
To learn more about cylinder click :
https://brainly.com/question/16134180
#SPJ9
Ian went shopping for a new pair of pants because of a sale. The store was offering a
40% discount. If the price on the tag was $40, what would be the price after the
discount but before tax, to the nearest dollar and cent?
The price after the discount but before tax, to the nearest dollar and cent is $24.
How is discount calculated?Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. "Off",
Discount is equal to List Price – Selling Price.
Given that, the store was offering a 40% discount.
The discount on the price tag of $40 is:
Discount = 40 (40/100) = $16.
The new price after the discount but before tax is:
New price = 40 - 16
New price = $24.
Hence, the price after the discount but before tax, to the nearest dollar and cent is $24.
Learn more about percentage here:
https://brainly.com/question/14695543
#SPJ1
∠A=___° Round your answer to the nearest hundredth.
The measure of ∠A is 37.6°. Angle is a geometric figure that can be described as the amount of rotation.
What is angle?A figure produced by two rays, line segments, or lines that have a same endpoint is called an angle. It is measured in degrees, with a complete 360-degree angle. The Greek letter theta is commonly used to represent it. An angle can be acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), or reflex (more than 180 degrees).
∠A is an angle measure and is commonly represented by the symbol "∠A". calculate the measure of ∠A, an angle must be given in degrees. The answer is then rounded to the nearest hundredth. For example, if the angle measure of ∠A is 37.58°, then the answer would be 37.6°.
To know more about angle click-
brainly.com/question/460763
#SPJ1
A new phone sells for $250 and a used one sells for $75. How many of each are sold if the sales for the day totals $625?.
The number of new phone sold is 1 and the number of old phone sold is 5, if the sales for the day totals $625.
It is given that
A new phone sells for $250
and a used one sells for $75
Let number of new phone is sold = x
and number of old phone is sold = y
Here the total profit for the day is $625
So, 250x + 75y = 625
or 10x + 3y = 25
Now the value of x and y satisfy the above equation, if we take x = 2 and more than 2, it is clear that it not satisfy the above equation. So we made a conclusion here x must be equal to 1 here.
Now, if x = 1
10(1) + 3y = 25
3y = 15
y = 5
To know more about linear equation
https://brainly.com/question/2291167
#SPJ4
Challenge A family wants to rent a car to go on vacation Company A charges $75.50 and 16 per mile Company B charges $50.50 and 10g per mile. How much more does Company A charge for x miles than
Company B?
For xmiles, Company A charges dollars more than Company B
(Simplify your answer. Use integers or decimals for any numbers in the expression)
OSS
Help me solve this View an example Get more help.
Clear all
Question
7
Check answer
of 12
Back
Using a system of equations, Company A charges 25 + 0.06x more than Company B.
What is a system of equations?A system of equations involves two or more equations whose solutions are found concurrently or at the same time.
A system of equations is also known as simultaneous equations.
Company A Company B Difference
Fixed charge $75.50 $50.50 $25 ($75.50 - $50.50)
Variable charge per mile $0.16 $0.10 $0.06 ($0.16 - $0.10)
Let the number of miles covered = x
Equations:The total cost of Company A (Equation 1) = 75.50 + 0.16
The total cost of Company B (Equation 2) = 50.50 + 0.1
The difference in total cost for x miles = 25 + 0.06w
Thus, for each mile of travel that the family rents the car, Company A will charge more than Company B by exactly 25 + 0.06w.
Learn more about simultaneous equations at https://brainly.com/question/148035.
#SPJ1
Help please…………………………………..
The limit as x approaches -2 is equal to 0. The correct option is B.
How to calculate the limit?The limit of the function f(x) = x² - 4 / x + 2 as x approaches 2 is equal to 0. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:-
The limit of the function f(x) = x² - 4 / x + 2 as x approaches -2 is equal to 4. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:
f(-2) = (-2)² - 4 / -2 + 2 = 4 - 4 / 0 = 0
So, the limit as x approaches -2 is equal to 0.
Learn more about limit on:
https://brainly.com/question/29795586
#SPJ1
A bag contains 12 white balls and some red balls. The probability of drawing a red ball is 5/11. Find the number of red balls.
Answer:
Step-by-step explanation:
x=12wb+rb
probability of rb=5/11
12+11=23
5/23
rb=5/23
A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 5 centimeters. The vertical height between these bases is 2.7 centimeters. That vertical height intersects the bottom base, leaving 3 centimeters between it and the vertex to the left. The side on the right is the longest at 6.8 centimeters. There is a horizontal line connecting the vertex of the bottom base to the 6.8-centimeter side and that line is 3.4 centimeters.
Which of the following represents the total area of the figure?
24.52 cm2
31.49 cm2
42.07 cm2
49.04 cm2
The area of the shape is given as 24.52 cm2
How to solve for the areaWe have two triangles and 1 rectangle
we have to find the area of the triangles first and then solve for the area of the rectangle.
The area of a triangle = 1/2bh
for first triangle
area = 1/2 * 2.7 * 3
= 4.05
for second triangle
height = 6.8 - 2.7
= 4.1
area = 1/2 * 3.4 * 4.1
= 6.97
For the rectangle
area = l * w
= 2.7 * 5 = 13.5
The area = 13. 5 + 6.97 + 4.05
= 24.52 cm2
Read more on area of a triangle here:https://brainly.com/question/17335144
#SPJ1