Final answer:
The conditional probability formula for event B given event A is represented as P(B|A), which is calculated using P(A and B) / P(A). Using dice as an example, the events are described and demonstrated to be neither mutually exclusive nor independent due to overlapping outcomes and interdependence.
Explanation:
The conditional probability of event B given that event A has occurred is represented as P(B|A). To fill in the blanks in the provided formula, it would be P(B | A) = P(B ∩ A) / P(A). Using the provided scenarios, we need to calculate P(A), which is the probability that the sum of numbers on both cubes is less than 10, P(B), which is the probability that the sum of numbers on both cubes is a multiple of 3, and P(A and B), which is the probability that both events occur simultaneously. Finally, we use the formula P(A|B) = P(A and B) / P(B) to calculate the conditional probability.
For example, event A could be rolling a 3 or 4 first, followed by any even number, and event B could be rolling a sum at most 7 on two dice. These events are not mutually exclusive since they can both occur simultaneously, nor are they independent since the occurrence of one affects the likelihood of the other happening.
The completed conditional-probability formula is: P(B|A) = P(A ∩ B) / P(A)
To complete the conditional-probability formula for event B given that event A occurs first, we need to fill in the blanks with the appropriate terms:
P(B|A) = P(A ∩ B) / P(A)
Let's break down each term:
a0: Event A occurs
a1: Event B occurs
a2: Event A and B occur simultaneously (intersection of A and B)
a3: Event A occurs
a4: Event B occurs
Therefore, the completed conditional-probability formula is:
P(B|A) = P(A ∩ B) / P(A)
Mr Chan bought some pencils for a group of students. If he gives them 2 pencils each, he will have 10 pencils left. If he gives them 3 pencils each, he will have none left. How many students are in the group?
To find the number of students in the group, we can use algebra to solve two equations simultaneously.
Explanation:Let's solve this problem using algebra. Let's say there are x students in the group.
If Mr. Chan gives each student 2 pencils, he will have 10 pencils left. This can be expressed as the equation 2x + 10 = P, where P represents the total number of pencils Mr. Chan bought.
If Mr. Chan gives each student 3 pencils, he will have no pencils left. This can be expressed as the equation 3x = P.
Solving these two equations simultaneously, we can find the value of x, which represents the number of students in the group.
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What’s 180 divided by 12
The answer is 15. Take 180/12. 12 can only go into 18 1 time with a remainder of 6. bring down the 0 12 goes into 60 5 times for 60.
The solution to the given number division 180 divided by 12 is: 15
How to divide two numbers?When dividing two numbers, we know that the number that will be in the numerator part is called Dividend while the number that will be in the denominator part is called Divisor.
Thus:
180/12
180 is the dividend while 12 is the divisor
Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Factors of 12 are 1, 2, 3, 4, 6 and 12.
However, 12 is also a factor of 180 and the number that it is multiplied by to get 180 is 15. Thus:
180/12 = 15
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It can never equal to a what number ?
y = |x| means that if -∞ < x <∞ Then y will be between 0 < ∞
The answer is that y can never equal a negative number.
HELP!!!!PLEASE
MULTIPLE CHOICE!!!!
B. The equation has one solution.
Step 1. Subtract 2 from both sides
3 + x - 2 = -3x
Step 2. Simplify 3 + x - 2 to x + 1
x + 1 = -3x
Step 3. Subtract x from both sides
1 = -3x - x
Step 4. Simplify -3x - x to -4x
1 = -4x
Step 5. Divide both sides by -4
-1/4 = x
Step 6. Switch sides
x = -1/4
Can someone explain multiplicity of a zero?
Multiplicity refers to the exponents of the factors. For example:
x³(x + 1)(x + 2)²(x² + 1) = 0
x: has a multiplicity of 3 because its exponent is 3
x + 1: has a multiplicity of 1 because its exponent is 1: (x + 1)¹
x + 2: has a multiplicity of 2 because its exponent is 2
x² + 1: has a multiplicity of 1 because its exponent is 1: (x² + 1)¹
Hope this helped!
What is the standard form of the number shown in this calculator display?
3.82e+7
38.9e i think 60% sure
What is x > -3 as an interval notion?
(- 3, ∞ )
the parenthesis at both ends indicates x ≠ - 3 or ∞
if x ≥ - 3 then {- 3, ∞ )
the square bracket on the left indicates x can equal - 3
Final answer:
The inequality x > -3 in interval notation is (-3, ∞), which means that the solution set for x includes all values greater than -3, but does not include -3 itself.
Explanation:
When the inequality x > -3 is written in interval notation, it means that the solution set for x includes all values greater than -3, but does not include -3 itself. In interval notation, we use a round bracket to indicate that -3 is not included in the solution set. The interval notation for x > -3 is (-3, ∞). This notation represents a half-open interval, where -3 is excluded but all values greater than -3 are included. The symbol ∞ represents infinity, indicating that there is no upper bound for the values of x in this inequality.
Which transformation of a scalene triangle produces an image that is similar, but not congruent, to the original
A: A translation of 3 units to the right and 4 units down
B: A reflection in a line that makes a 30° angle with the horizontal
C: A dilation of magnitude 2 centered at the origin
D: A rotation of 90° about the origin
i believe the answer is B
Answer:
C: A dilation of magnitude 2 centered at the origin.
(for anyone in the future, this is correct!)
find the slope of the line
the slope is 3/-5!!!! if u go up 3 and to the LEFT 5 that means it is negative.
convert 7/11 into a decimal form. if your answer is a repeating decimal, round to two digits (hundreds).
7/11 in decimal form = .6363
Nicole did an aerobics class and yoga class for at total of 1 hour and 10 minutes. The yoga class was 30 minutes. The yoga class was 30 minutes longer than the aerobics class. How long was each class.
The aerobics class lasted 20 minutes and the yoga class lasted 50 minutes. This was determined by setting up an equation and solving for the duration of each class, given the total time and the information that the yoga class was 30 minutes longer.
Explanation:The student is trying to find out how long each class was—Nicole attended an aerobics class and a yoga class for a total of 1 hour and 10 minutes, with the yoga class lasting 30 minutes longer than the aerobics class. To find the answer, we can set up an equation. Let the duration of the aerobics class be x minutes. Therefore, the duration of the yoga class would be x + 30 minutes. According to the question, the total time spent in both classes is 70 minutes (1 hour and 10 minutes).
Now, we can write an equation that represents the total time:
x (aerobics class) + x + 30 (yoga class) = 70 minutes
Combining the x terms we get:
2x + 30 = 70
To find x, we subtract 30 from both sides of the equation:
2x = 40
Dividing both sides by 2 gives us:
x = 20
So the aerobics class lasted 20 minutes, and since the yoga class was 30 minutes longer, it lasted 50 minutes.
Solve -3 1/2 = 1/2x + 1/2x + x
- 3 1/2 = 2x
-7 /2 = 2 x
-7 /4 = x
-1 3/4 = x
calculate the average (arithmetic mean) of the list of numbers shown in the table. (rounded to the nearest tenth)
A. 46.3
B. 50.4
C. 50.5
D. 55.0
Hello!
AnswerThe mean of the numbers shown in the table is C. 50.5
__________________________________________________ExplanationTo calculate the mean, simply add up all the numbers and divide by the amount of numbers there are in the list.
18 + 55 + 101 + 96 + 55 + 18 + 22 + 23 + 22 + 57 + 88 = 555
There are 11 numbers in the table, so we divide by that.
555 / 11 = 50.45...
Finally, round to the nearest tenth: 50.5
the volume of a rectangular prism can be found by multiplying the length width and height of the prism which of the following following could be possible dimensions of a rectangular prism that has a volume of 75 ft
D
because 3*5=15 And 15*5=75
The graphs below show the number of honor roll students in each grade at Bridgeport Middle School. Which statement is true??
A. According to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll.
B. The scale on Graph 1 does not distort the differences in the number of students.
C. The two graphs use completely different data
D.both: “according to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll” and “the two graphs use completely different data”
Help algebra 2 questions.
For the first question, divide 200 by the seconds. You would get the answer 9.07. This answer is rounded to the nearest hundredth.
The second question, you would convert that to feet by using the units 1 meter = 3.28084.
If you converted it, the answer woudl be 29.75722 ft/second
Points S and T are midpoints of the sides of triangle FGH
what is GF ?
Answer:
Using triangle similarity theorems, GF is 16 cm (fourth option)
Step-by-step explanation:
If points S and T are midpoints of the sides of triangle FGH, the segment ST is parallel to the side GF and the triangles FGH and TSH are similars, and their corresponding sides must be proportionals, then:
GF/ST=FH/TH=GH/SH
TH=6 cm→FT=6 cm, because T is the midpoint of side FH, and:
FH=2 TH = 2 FT =2 (6 cm)→FH=12 cm
GS=4 cm→SH=4 cm, because S is the midpoint of side GH, and:
GH=2 GS = 2 SH =2 (4 cm)→GH=8 cm
ST= 8 cm
Replacing the known values in the proportion:
GF/ST=FH/TH=GH/SH
GF/(8 cm)=(12 cm)/(6 cm)=(8 cm)/(4 cm)
GF/(8 cm)=2=2
GF/(8 cm)=2
Solving for GF: Multiplying both sides of the equation by 8 cm:
(8 cm) [GF/(8 cm)]=(8 cm)(2)
GF=16 cm
If Points S and T are midpoints of the sides of triangle FGH, the measure of the length GF is 16cm. Option D is correct
To get the length of Gf, we will need to use the similarity theorem of a triangle as shown:
HT/TS = HF/Gf
From the diagram, we have the following:
HT = FT = 6cm
ST = 8cm
Substitute the given parameters into the formula to have:
6/8 = 6+6/GF
6/8 = 12/GF
6FG = 96
FG = 96/6
FG = 16cm
Hence the measure of the length GF is 16cm
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I’m picking a number between 1-10 if you get it right I WILL GIVE YOU 25 POINTS
help me please!!!!!
Nina earns $15 for each yard she mowes. she wants to buy a dress that coasts $109. how many yards will she need to mow to earn money for the dress? explain
she will need to mow 8 yards because 109 divided by 15 equals 7.2 but she cant just mow 7.2 yards so you round up to 8 yards
The selling price of an item is $520. After 6 months of not selling, it is marked down by 20%. After another another 6 months of not selling, it is further marked down by 30%. Find the sale price after both markdowns. Could you just tell me the steps and maybe give an example to this? Thank you.
To find the sale price after both markdowns, first apply a 20% markdown to the selling price and then apply a 30% markdown to the resulting price.
Explanation:To find the sale price after both markdowns, first apply the first markdown of 20%. To do this, multiply the selling price by 0.80 (1 - 0.20), since a 20% markdown is equivalent to selling at 80% of the original price. So, the price after the first markdown is $520 x 0.80 = $416.
Next, apply the second markdown of 30% to the price after the first markdown. Multiply $416 by 0.70 (1 - 0.30) to find the final sale price. $416 x 0.70 = $291.20.
Therefore, the sale price after both markdowns is $291.20.
Use the magic penny parable to determine how much money you would have after 8 days.
In the magic penny parable, choosing a penny that doubles in value every day leads to a significant amount of money. After 8 days, you would have 256 pennies.
Explanation:The magic penny parable is a story that demonstrates the power of compound interest. In the story, a person is given the choice between taking a million dollars or a penny that doubles in value every day for 30 days. By choosing the penny, they end up with over 5 million dollars at the end of 30 days.
To determine how much money you would have after 8 days, we can use the formula for compound interest:
Final amount = Initial amount * (1 + interest rate) ^ number of periods
In this case, the initial amount is 1 penny, the interest rate is 100% (as the penny doubles in value), and the number of periods is 8 days.
Using this formula, the calculation would be:
Final amount = 1 penny * (1 + 1)^8 = 1 penny * 2^8 = 1 penny * 256 = 256 pennies.
Therefore, after 8 days, you would have 256 pennies.
Brandon enters bike races he bikes 8 and 1/2 miles every 1/2 hour complete the table to find how far Brandon bikes for each time he interval else if he likes 8 and 1/2 Mile for 1/2 hour how many miles does he bike per 1 hour
We find he bikes 17 miles in a full hour.
Brandon bikes 8 and 1/2 miles in 1/2 hour. To find out how far he bikes in 1 hour, we need to double the distance, because one hour is twice as long as half an hour.
Miles per hour = Miles in half an hour * 2 = (8 + 1/2) miles * 2
Now, let's perform the multiplication:
8 * 2 = 16
1/2 * 2 = 1
Therefore, 16 + 1 = 17 miles per hour.
Brandon bikes 17 miles in 1 hour. This is the distance he would cover if he continues at the same pace for a full hour.
what is the m<PHJ
A. 100°
B. 120°
C. 140°
D. 160°
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
∠PML = 140°
∠KHP = 20°
We need to find the measure of ∠PHJ.
Let m ∠PHJ = x°
From the graph, we conclude that
∠PML = ∠PHJ + ∠KHP (Vertically opposite angle)
[tex]140^\circ=x+20^\circ\\\\140^\circ-20^\circ=x\\\\120^\circ=x[/tex]
Hence, Option 'B' is correct.
A fast food restaurant sold 35 burgers with cheese if the ratio sold with cheese compared to without cheese was 7:3 how many burgers did they sell total
Final answer:
To find the total number of burgers sold by the fast food restaurant, calculate the burgers sold without cheese using the ratio provided and then find the total by adding burgers with cheese and without cheese.
Explanation:
To find out how many burgers the fast food restaurant sold in total, we first need to determine the number of burgers sold without cheese. Since the ratio of burgers sold with cheese to without cheese is 7:3, we can calculate that for every 7 burgers sold with cheese, 3 were sold without cheese. Therefore, 35 burgers with cheese corresponds to 35 / 7 * 3 = 15 burgers without cheese. Hence, the total number of burgers sold is 35 (with cheese) + 15 (without cheese) = 50 burgers.
Ryan drives his car on a trip and goes 4,000Km , how many miles did he travel? (1 miles=1.609 km )
2,486.016 miles of distance Ryan drives his car on a trip.
Given that, Ryan drives his car on a trip and goes 4,000 km.
We need to find how many miles he travels.
How to convert kilometres to miles?1 kilometre is equal to 0.621371 miles (often shortened to .62) and 1 mile is equal to 1.609344 kilometres. Thus, to convert kilometres to miles, simply multiply the number of kilometres by 0.62137.
Now, divide the number of kilometres by 1.609
That is, 4000/1.609=2,486.016 miles
Therefore, 2,486.016 miles of distance Ryan drives his car on a trip.
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Heres the problems I need help with....asked this earlier to get answers that were apparently incorrect..this is about repeating decimals.
When changing a repeating decimal to a fraction, you look at the number(s) to the right of the decimal. If there is only 1 number (0.444444...) then the number that repeats is is going to be the numerator of your fraction, with the denominator being 9 (4/9). So...
1. -1 2/9 (-1 and 2/9)
2. -5/9
5. 5 8/9 (5 and 8/9)
If there are 2 or more numbers to the right of the decimal, you add 1 "9" to the denominator per repeating number (2 repeating numbers = 99, 3 repeating numbers = 999, etc...). An example to show this would be 0.87 repeating (0.87878787... = 87/99). Therefore...
3. 27/99
4. 50/99
I hope this helps!
Solving an equation like this
3x-4=18+5x
Deon split 3/4 lb of candy among four people. What is the unit rate in pounds per person? Write your answer in simplest form.
We can write this in expression form as follows:
[tex]\frac{3}{\frac{4}{4} }[/tex]
Notice that we get a 4/4 in the denominator in which case we multiply the two (because they are both denominators:
[tex]\frac{3}{\frac{4}4} } = \frac{3}{16}[/tex]
So, the unit rate is 3/16 lbs/person.
To find the unit rate in pounds per person, divide the total weight of the candy by the number of people. In this case, the unit rate is 3/16 lb per person.
Explanation:To find the unit rate in pounds per person, we divide the total weight of the candy (3/4 lb) by the number of people (4). This can be represented as 3/4 ÷ 4. To simplify the division, we can multiply the numerator and denominator by 4 to get rid of the fraction. This gives us 3/16 lb per person as the unit rate in pounds per person.
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whats the answer of the problem peter is 3 years older than his sister Anna. if times their combined age is 85 . determine Annas age
Answer:
Anna is 41 years old.
Step-by-step explanation:
Easiest way to do this is by building a equation,
Lest say Anna's age is [tex]x[/tex].
Then as Peter is 3 years older than Anna Peter's age should be [tex]x+3[/tex].
Then the combined ages of the two people is given as 85. So we can write an equation as,
[tex]x+(x+3)=85[/tex]
[tex]x+x+3=85[/tex]
[tex]2x+3=85[/tex]
[tex]2x+3-3=85-3[/tex] (deducting 3 from both sides of the equation)
[tex]2x=82[/tex]
[tex]x=41[/tex]
As we originally took Anna;s age as [tex]x[/tex]
We can say Anna is 41 years old.