The probability of event A given the event B is 0.35 or 7/20.
Here, we have,
It is given that A and B are two events.
Given probabilities are as follows:
Probability of A and B is = P(A and B) = 0.14
Probability of B = P(B) = 0.4
We know that the conditional probability of event A given B is given by,
P(A | B)
= P(A and B)/P(B)
= 0.14/0.4
[Substituting the value which are given]
= 14/40
= 7/20
[Eliminating the similar values from numerator and denominator]
= 0.35
Hence the probability of event A given the event B is 0.35 or 7/20.
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complete question:
Probabilities for two events, event A and event B, are given.
P(A and B) = 0.14
P(B) = 0.4
What is the probability of event A given B?
Hint: Probability of A given B = P(A and B) divided by P(B)
*100 points*
Find P(red 7,black face card)
The probability of drawing a red 7 and black face card is P ( A ) = 1/221
Given data ,
Let the probability of drawing a red 7 and black face card be P ( A )
Now , the compound probability is given by\
The number of red 7 cards = ( red of diamonds 7 + red of hearts 7 )
Probability of drawing a red 7 = 2/52
Now , the card is not replaced , so the total number of remaining cards = 51
And , number of black face cards = 6
Probability of drawing a black face card = 6/51
So , P ( A ) = 2/52 ( 6/51 )
P ( A ) = 12 / 2652
On simplifying , we get
P ( A ) = 1/221
Hence , the probability is P ( A ) = 1/221
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Please no trolls! I need the right answer!
the cost of admission to a concert is $65 for 3 children and 5 adults, if x is the cost of 1 child and y is the cost of one adult, write a liner equation in slope-intercept form to represent this situation.
Answer: y = (-3/5)x + 13
This is the same as writing \(\text{y} = -\frac{3}{5}\text{x}+13\)
note: -3/5 = -0.6
==========================================================
Work Shown:
x = cost of 1 child
y = cost of 1 adult
3x = cost of 3 children
5y = cost of 5 adults
3x+5y = total cost of everyone mentioned so far
3x+5y = 65 dollars
------------
Let's solve for y to get it into slope intercept form (y = mx+b)
3x+5y = 65
5y = -3x+65
y = (-3x+65)/5
y = (-3x)/5 + 65/5
y = (-3/5)x + 13 is the final answer.
This is now in y = mx+b form
m = -3/5 = slopeb = 13 = y intercept------------
Optional Section:
If you wanted to graph this equation, then plug in x = 0 to find that y = 13.
One point on the line is (0,13) which is the y intercept. We can quickly determine this by looking at the last value of y = (-3/5)x+13.
Then starting at the y intercept location, move down 3 and to the right 5 to arrive at (5, 10) as another point on the line. This "down 3, right 5" motion is directly due to the slope -3/5
slope = -3/5 = rise/runrise = -3 = go down 3run = 5 = go to the right 5In summary, the two points (0,13) and (5,10) are on the straight line.
What is the first step in substitution process?
Solve one of the equations for one of the variables as the first step in substitution method.
In order to write one of the equations as x = or y =, we must first determine which variable in the two equations is the simplest to solve for. The other equation will then have either the x or the y replaced appropriately. The outcome will be a single-unknown equation that we can solve. Isolating a variable whose coefficient is 1 or -1 is useful.
Step 1: Solve one of the equations for one of the variables.
Step 2: Enter the expression as a replacement in the remaining equation. The outcome will be a single-variable linear equation that can be solved.
Step 3: Resolve the last equation.
Step 4: To find the value of the other variable, substitute the result into the other equation.
Step 5: The intersection of the two equations, which represents the coordinates of the ordered pair, is the system's solution.
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Solve n x 8 = 24
please help me and solve the equation.
Answer:
3
Step-by-step explanation:
Set it up as
8n = 24
n = 24/8
n = 3
Answer:
n=3
Step-by-step explanation:
24 divided by 8 is equal to n
go back and substitute the answer 3 x 8= 24
that is a fact if it is a fact then it is true and you have your answer.
If the equation y=-5x+12 is translated up five units, what would the new equation be?
Answer:
y=-5x+17
Step-by-step explanation:
Answer:
[see below]
Step-by-step explanation:
We would add '5' to the y-intercept (12) to make a translation up 5 units.
y = -5x + 12 + 5
y = -5x + 17
Hope this helps.
a random variable x follows a binomial distribution with mean 6 and variance 3.6. find the values of the parameters n and p
Values of parameters n and p for the binomial distribution with mean 6 and variance 3.6 are n=15 and p=0.4, respectively.
What is binomial?In probability theory and statistics, the binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent and identical trials, where each trial can result in only two possible outcomes, often labeled as "success" and "failure".
The distribution depends on two parameters: the probability of success (p) and the number of trials (n). The probability of getting exactly k successes in n trials can be calculated using the binomial probability mass function.
The binomial distribution has applications in various fields, including quality control, genetics, and finance, among others.
We know that for a binomial distribution, the mean and variance are given by:
Mean = np
Variance = np(1-p)
Substituting the given values, we have:
Mean = 6
Variance = 3.6
Thus, we can write two equations:
6 = np
3.6 = np(1-p)
We can solve for n and p by substituting the first equation into the second equation:
3.6 = (6/p) * (1-p) * p
3.6 = 6 - 6p
6p = 6 - 3.6
p = 0.4
Substituting this value of p into the first equation, we get:
6 = n * 0.4
n = 6 / 0.4
n = 15
Therefore, the values of the parameters n and p are n = 15 and p = 0.4, respectively.
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) your friendly ice-cream store sells 7 varieties of ice-cream. how many ways are there to choose 12 ice-creams if there are plenty of each variety, except that there are only 7 raspberry ice-creams left and you absolutely must buy at least 2 chocolate and 3 raspberry ice-creams?
There are 5,113,368 ways to choose 12 ice-creams from the friendly ice-cream store, given the conditions that we must buy at least 2 chocolate and 3 raspberry ice-creams.
To solve this problem, we can break it down into a few steps:
Step 1: Choose 2 chocolate ice-creams. There are 7 varieties of ice-cream, but we only need to worry about the chocolate ones for now. We must choose 2 chocolate ice-creams, and there are plenty of each variety, so this can be done in 1 way.
Step 2: Choose 3 raspberry ice-creams. We must choose 3 raspberry ice-creams, but we only have 7 left. This means we must choose all 7 raspberry ice-creams, and then choose 2 more ice-creams from the remaining 5 varieties. We can do this in $\binom{5+2}{2} = \binom{7}{2} = 21$ ways.
Step 3: Choose 7 more ice-creams. We have already chosen 2 chocolate and 3 raspberry ice-creams, which leaves us with 7 more to choose. We can choose these from any of the 7 varieties, and there are plenty of each variety, so this can be done in $7^{7}$ ways.
Step 4: Multiply the possibilities from each step. To get the total number of ways to choose 12 ice-creams satisfying the given conditions, we need to multiply the number of possibilities from each step. So the total number of ways is:
$1 \cdot 21 \cdot 7^{7} = \boxed{5,\!113,\!368}$
Therefore, there are 5,113,368 ways to choose 12 ice-creams from the friendly ice-cream store, given the conditions that we must buy at least 2 chocolate and 3 raspberry ice-creams.
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Katie has 8 black marbles, 12 clear marbles, and 14 blue marbles in a bag. If she picks one at random, what is the probability that she will pick a black marble? (Enter your answer as a fraction in its reduced form.) a 4/17 b 7/34 c 6/17 d 12/34
Answer:
a 4/17
Step-by-step explanation:
if you add them all up, you get 34. 8 out of 34 reduced is 4/17
Answer:
4/17
Step-by-step explanation:
8 black marbles, 12 clear marbles, and 14 blue marbles = 34 marbles
P( black) = number of black/ total
= 8/34
=4/17
HELP PLSSS THIS IS HARD SOMEONE
Answer:
the answer is (0,1)
hope this will help you ❤️
at a meeting ,everyone shakes hands exactly once with every other person . if there are 55 handshakes . then what Is the number of people attending
The shelf is made of 3 pieces of wood, each 0.3 meters wide. There is also 0.05 meter of space between the shelf and wall on each side. What is the width, in meters, of Joslyn's closet
Answer:
1.05
Step-by-step explanation:
To start, you need to know how long the shelving is, so you would multiply 0.3*3 since there are three pieces of wood. After you do that, you need to find out exactly how much space is from the shelving to the wall, so multiply 0.05*2 since there are two sides of the shelf. Add it all together for a total of 1.05
My calculator work will be posted below.
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The table shows the amount of snow, in cm, that fell each day for 30 days. Amount of snow (s cm) Frequency 0 s < 10 8 10 s < 20 10 20 s < 30 7 30 s < 40 2 40 s < 50 3 Work out an estimate for the mean amount of snow per day
The mean amount of snow per day is equal to 19 cm snow per day.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
For the total amount of snow based on the frequency, we have;
Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)
Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135
Total amount of snow (s cm), F(x) = 570
Now, we can calculate the mean amount of snow as follows;
Mean = 570/30
Mean = 19 cm snow per day.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
How many five-digit numbers have distinct digits which are decreasing from left to right? (for example, $96531$ is such a number. )
There are 252 five-digit numbers with distinct digits that are decreasing from left to right.
Counting and permutations:
Counting refers to the process of determining the number of possible outcomes in a given situation. Counting often involves the use of combinatorial techniques, such as combinations and permutations.
Permutations refer to the number of ways that a set of objects can be arranged in a particular order.
Here we have
Five -digit numbers have distinct digits which are decreasing from left to right
To form a five-digit number with distinct digits that are decreasing from left to right, we need to choose 5 digits from 0 to 9 such that no digit repeats and they are arranged in descending order.
The first digit can be any of the 9 non-zero digits (since the number cannot start with 0). The second digit can be any of the remaining 8 non-zero digits, and so on.
Hene, the total number of such five-digit numbers = ¹⁰C₅
= 10!/5!(10-5)! = 252
Therefore,
There are 252 five-digit numbers with distinct digits that are decreasing from left to right.
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All tubes of watercolor paint at an art supply store have the same price. An artist has a coupon for $0.80 off each tube of paint she buys. She buys 12 tubes of paint and pays a total of $70.20 after the coupon is applied. Write an equation to find r, the regular price of each tube of paint. No need to solve the equation.
Answer:
R=70.20-$0.80(12)
Step-by-step explanation:
What is the sum
No links please
Answer:
Step-by-step explanation:
he total amount resulting from the addition of two or more numbers, amounts, or items
Answer:
(2/5x+1/5x)+(5/8-1/4)
3/5x+(5/8-2/8)
3/5x+3/8
PLEASE HELP whoever answers all of them and first i’m giving brainliest.
Answer:
1. To solve a one-variable equation, it may be necessary to first multiply by using the Distributive Property
2. The next step is to combine like terms as needed.
3. Then solve for the variable by applying inverse operations.
4. If solving lead to a true equation, then the equation has infinitely many solutions.
5. if solving leads to an untrue equation, then the equation has no solution.
how many three-letter initials with none of the letters repeated can people have?
To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.
To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.
After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.
Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.
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A triangle has two sides of length 12 and 17. What is the largest possible whole-number length for the third side?
Answer:
20
Step-by-step explanation:
I don't understand the question but hope it helps
question a cup has the shape of a right circular cone. the height of the cup is 12 cm, and the radius of the opening is 3 cm. water is poured into the cup at a constant rate of 2cm3/sec what is the rate at which the water level is rising when the depth of the water in the cup is 5 cm? (the volume of a cone of height h and radius r is given by v
When the water in the cup is 5 cm deep, the rate at which the water level is rising is \(\mathrm{\frac{32\pi}{25}\;cm/s}\).
A cone is a shape that is made by utilizing a sequence of line segments or lines to join the points on a circular base to a single point, known as the apex or vertex. This shape's volume formula is \(V=\frac{1}{3}\pi r^2h\) where h is the cone's height and r is the cone's radius.
Given that h is 12 cm, r is 3 cm, and the rate is 2 cm³/s.
Using similar triangle rules,
\(\begin{aligned}\frac{h}{r}&=\frac{12}{3}\\\frac{h}{r}&=4\\r&=\frac{1}{4}h\end{aligned}\)
Then, the volume becomes,
\(\begin{aligned}V&=\frac{1}{3}\pi\left(\frac{1}{4}h\right)^2h\\&=\frac{\pi h^3}{48}\end{aligned}\)
The change in volume is written as,
\(\begin{aligned}\frac{dV}{dt}&=\frac{dV}{dh}\times\frac{dh}{dt}\\2&=\frac{dV}{dh}\times\frac{dh}{dt}\\2&=\frac{3\pi h^2}{48}\frac{dh}{dt} \end{aligned}\)
Substituting the height h = 5 cm and rate = 2 cm³/s, we get the rate as,
\(\begin{aligned}2&=\frac{3\pi(5)^2}{48}\frac{dh}{dt}\\2&=\frac{75\pi}{48}\frac{dh}{dt}\\\frac{96\pi}{75}&=\frac{dh}{dt}\\\frac{dh}{dt}&=\mathrm{\frac{32\pi}{25}\;cm/s}\end{aligned}\)
The required answer is \(\mathrm{\frac{32\pi}{25}\;cm/s}\)
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Paris is preparing for the 2024 Olympics. Their newly built single-depth olympic size swimming pool (50m by 25m by 2m) needs to be filled up. If the water bill is equivalent to $1 per 1000 gallons, roughly how many dollars will it cost to fill up the pool?
There will be 660.425 dollars cost to fill up the pool.
The newly built single-depth olympic size swimming pool (50m by 25m by 2m) needs to be filled up.
Here,
Length of swimming pool = 50m
Width of swimming pool = 25m
Depth of swimming pool = 2m
What is the volume of the cuboid?The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.
The volume of a cuboid is length × breadth× height
As it is 3D geometry
The volume will be L×W×H i.e. 50×25×2 = 2500 m³
Since one cubic meter is equal to 264.172052 gallons,
So 2500 m³ = 264.17 × 2500 = 660425 gallons
If the water bill is equivalent to $1 per 1000 gallons
So 660425/1000 = 660.425
Hence, there will be 660.425 dollars cost to fill up the pool.
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Which is the better value? Circle it. 3 sandwiches for 15.00 or 4 sandwiches for 21.00?
Answer:
I say 3 sandwiches for 15.
Step-by-step explanation:
to find the best price divided the numbers
15 divided by 3= 5
5 is the price per sandwich for this
21 divided by 4= 5.25
5.25 per sandwich
the 3 for 15 is a better deal. You save money.
Consider the following exponential probability density function. f(x) = 1/3 4 e^-x/3 for x > 0 a. Write the formula for P(x < x_0). b. Find P(x < 2). c. Find P(x > 3). d. Find P(x < 5). e. Find P(2 <.x <5).
The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.
The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:
F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx
a. Write the formula for P(x < x_0):
Using integration, we can solve this formula as follows:
F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]
= [-4e^(-x_0/3) + 4]/3
b. Find P(x < 2):
To find P(x < 2), we simply substitute x_0 = 2 in the above formula:
F(2) = [-4e^(-2/3) + 4]/3
≈ 0.4866
Therefore, the probability that x is less than 2 is approximately 0.4866.
c. Find P(x > 3):
To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:
P(x > 3) = 1 - P(x < 3) = 1 - F(3)
= 1 - [-4e^(-1) + 4]/3
≈ 0.3528
Therefore, the probability that x is greater than 3 is approximately 0.3528.
d. Find P(x < 5):
To find P(x < 5), we simply substitute x_0 = 5 in the above formula:
F(5) = [-4e^(-5/3) + 4]/3
≈ 0.6321
Therefore, the probability that x is less than 5 is approximately 0.6321.
e. Find P(2 < x < 5):
To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:
P(2 < x < 5) = P(x < 5) - P(x < 2)
= F(5) - F(2)
= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3
≈ 0.1455
Therefore, the probability that x is between 2 and 5 is approximately 0.1455.
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Which equation, solved for x, is equivalent to y-h=x-g/k
A.x=k(y-h)-g
B.x=ky -h+g
C.x=k(y-h) +9
D.x = ky-h-9
Answer:
a
Step-by-step explanation:
The equation equivalent to the given equation y-h=x-g/k is .x=k(y-h) +g. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is y-h=x-g/k. The equation will be solved as,
y-h = ( x-g ) / k
k( y-h ) = x - g
k( y-h ) + g = x
Therefore, the equation equivalent to the given equation y-h=x-g/k is .x=k(y-h) +g. The correct option is C.
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what is the difference between the domain and the range of a function?
Answer:
The domain is all the x values of a function while the range is all the y values of a function.
Answer:
Step-by-step explanation:
The domain of a function is the set of input (x-) values for which the function is defined. The range is the set of output (y-) values; often there are limitations.
For example, the sine function y = sin x is defined for all real x; for every input x, there is a corresponding output y. The sine function has a limited range in that the minimum value of the sine is -1 and the max is +1. There is no graph above y = -1 or below y = +1.
How many ways are there to construct a string of 3 digits from the decimal numbering system if the numbers cannot be repeated
There are total 720 ways according to the permutation by which construct a string of 3 digits from the decimal numbering system.
According to the statement
we have to tell that by how many ways we construct a string of 3 digits from the decimal numbering system.
So, For this purpose,
let a three digits from 0 to 9.
So, There are total digits are 10 and we have to construct three digits.
so, we use permutation here:
Permutation are one of the two different ways of grouping elements of a set into subsets. In a permutation, the elements of the subset are listed in a specific order.
So, here become P(10,3)
And according to formula it become
P(10,3) = 10! / 7!
P(10,3) = 10 * 9 * 8
P(10,3) = 720.
So, There are total 720 ways according to the permutation by which construct a string of 3 digits from the decimal numbering system.
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consider the following table. what is the probability of red? red blue total yes 15 21 36 no 38 13 51 total 53 34 87 g
The probability of red is 0.1724, given the following table.
The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.
The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.
The probability of Red can be calculated using the formula;
P(Red) = (Frequency of Red) / (Total Frequency)
Using the values provided in the table
,P(Red) = 15/87P(Red) = 0.1724
Hence, the probability of red is 0.1724.
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add my sc tregan_fought
Trina is trying to decide which lunch combination to order at a sandwich shop: 4, 5, 6, or
7. Each combination comes with the choice of an apple, an orange, or a pear. How many
possible outcomes are there for a lunch combination and a piece of fruit?
apple
orange
pear
apple
5
orange
pear
apple
orange
pear
apple
orange
pear
Type the answer in the box.
10
PLZ HELP ME WITH THIS!!!!!!
Which set of ordered pairs represents a function?
{(-1, 1), (9, -3), (9, -1), (-8, 2)}
{(-9, -5), (2, -1), (1, 5), (2, 0)}
{(6, 6), (4, 6), (-1, 1), (-4, 0)}
{(−5,−3),(−5,8),(4,2),(−7,−8)}
Answer:
{(6, 6), (4, 6), (-1, 1), (-4, 0)}
Step-by-step explanation:
The reason why this set of ordered pairs represent a function is because no domains have more than 1 unique ranges.
The price of a venti vanilla bean Frappuccino from Starbucks is $4.45, but you have only $3 with you. Your friend is working and gets you a discount of 20%. How much does the drink cost with the discount? Do you have enough to buy the drink? How much money are you short?
Answer: WIth the discount: $3.56, you do not have enough money, and are $0.56 short.
Step-by-step explanation:
Find 20% of 4.45
(4.45*0.2)= 0.89
Subtract the 20% from 4.45.
4.45-0.89=3.56
$3.56 is more than the $3 you have.
Subtract the $3 you have from the discounted price.
3.56-3.00=0.56
you are $0.56 short.