We calculate that the probability of selecting an unripe cherry and an apple is roughly 6.22%.
To estimate the probability that you pick an apple that is ripe and a cherry that is not ripe, we can use a simulation. Here's one way to do it:
Start by creating a large number of simulations. For example, we could simulate 10,000 visits to the orchard.For each simulation, randomly select an apple and a cherry from the orchard. Use the given probabilities to determine whether each fruit is ripe or not. For example, we could use a random number generator to select a number between 0 and 1, and if the number is less than or equal to 0.92, we consider the apple to be ripe. Similarly, if the number is less than or equal to 0.86, we consider the cherry to be ripe.Check whether the apple is ripe and the cherry is not ripe. If both conditions are true, count this as a success. If not, count it as a failure. After simulating a large number of visits to the orchard, divide the number of successes by the total number of simulations to get an estimate of the probability. For example, let's say we simulate 10,000 visits to the orchard using the method described above. After counting the number of successes and failures, we find that there were 622 visits where we picked a ripe apple and a non-ripe cherry. The estimated probability of this happening is therefore:622 / 10,000 = 0.0622, or approximately 6.22%.
Therefore, based on this simulation, we estimate that the probability of picking a ripe apple and a cherry that is not ripe is approximately 6.22%. Note that the actual probability may be slightly different due to the random nature of the simulation.
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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test
The equatiοn οf the line οf best fit fοr this data-set is given as fοllοws:
y = 10x + 60.
Hοw tο οbtain the equatiοn fοr the line οf best fit?The slοpe-intercept definitiοn οf a linear functiοn is given as fοllοws:
y = mx + b.
In which the cοefficients are given as fοllοws:
m is the slοpe, representing the rate οf change οf the οutput οf the functiοn relative tο the input.
b is the y-intercept, representing the value assumed by the functiοn the input assumes a value οf zerο.
The functiοn gοes thrοugh pοint (0,60), hence the intercept b οf the line οf fit is given as fοllοws:
b = 60.
When x increases by 2, frοm 0 tο 2, y increases by 20, frοm 60 tο 80, hence the slοpe m is οbtained as fοllοws:
m = 20/2 = 10.
Hence the line οf fit is given as fοllοws:
y = 10x + 60.
Meaning that the third οptiοn is cοrrect.
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Complete question:
Data was cοllected οn the amοunt οf time that a randοm sample οf 8 students spent studying fοr a test and the grades they earned οn the test. A scatter plοt and line οf fit were created fοr the data.scatter plοt titled students' data, with pοints plοtted at 1 cοmma 75, 2 cοmma 70, 2 cοmma 80, 2 cοmma 90, 3 cοmma 80, 3 cοmma 100, 4 cοmma 95, and 4 cοmma 100, and a line οf fit drawn passing thrοugh the pοints 0 cοmma 60 and 2 cοmma 80
Determine the equatiοn οf the line οf fit.
y = 5x + 60
y = 5x + 80
y = 10x + 60
y = 10x + 80
Answer:
The equatiοn οf the line οf best fit fοr this data-set is given as fοllοws:
y = 10x + 60.
Step-by-step explanation:
I need this done for me please
The system of inequalities 3 and 4 have no solutions, while other solutions are computer below
Solving the system of inequalitiesThe given system of inequalities can be solved by graph
To solve a system of inequalities by graph, you will need to follow these steps:
Graph each inequality on the same coordinate plane.Identify the region that satisfies all of the inequalities. This region is the solution to the system of inequalities.If the region is bounded (i.e., has a finite area), then the solution is a set of points within the region. If the region is unbounded (i.e., has an infinite area), then the solution is a set of points that lie in a specific direction.The graphs are added as an attachment, and the some points in the system are as follows:
System 1: (0, 5)System 2: (5, -5)System 3 and 4: No solutionSystem 5, 6 and 7: (5,4)System 8: (0, 0)Read more about system of inequalities at
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Charlotte invested $730 in an account paying an interest rate of 3≥% compounded continuously. Khalil invested $730 in an account paying an interest rate of 33 % compounded daily. After 8 years, how much more money would Khalil have in his account than Charlotte, to the nearest dollar?
Answer:
Khalil would have $1,845 more than Charlotte, to the nearest dollar.
Step-by-step explanation:
In ∆DEF, m∠D=42°, m∠E=63°, and EF=24 in. What is DE to the nearest tenth of an inch? *Hint: Law of Sines
DE is approximately 30.3 inches to the nearest tenth of an inch.
Describe Law of Sines?The Law of Sines is a trigonometric formula used to find unknown sides and angles in any triangle, whether it is acute, obtuse, or right-angled. It relates the lengths of the sides of a triangle to the sine of the opposite angle.
The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the opposite angles.
We can use the Law of Sines to solve for DE.
The Law of Sines states that for any triangle ABC,
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths opposite the angles A, B, and C, respectively.
In this case, we know that:
m∠D = 42°
m∠E = 63°
EF = 24 in.
Let x be the length of DE.
Then, applying the Law of Sines to ∆DEF, we have:
x/sin(63°) = 24/sin(42°)
Solving for x, we get:
x = (24*sin(63°))/sin(42°) ≈ 30.3
Therefore, DE is approximately 30.3 inches to the nearest tenth of an inch.
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Every person in a group of 1000 people has a 1% chance of being infected by a virus. The process of being infected is independent from person to person. Using random variables, write expressions for the following probabilities and solve them with R.
(a) The probability that exactly 10 people are infected.
(b) That probability that at least 16 people are infected.
(c) The probability that between 12 and 14 people are infected.
(d) The probability that someone is infected.
Every person in a group of 1000 people has a 1% chance of being infected by a virus. The process of being infected is independent from person to person. Using random variables, write expressions for the following probabilities and solve them with R(a) The probability that exactly 10 people are infected
Solution:
a)Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X = 10) = dbinom {1000}{10} $ $(0.01)^{10}$ $(1-0.01)^{990}
Using R, the expression for the probability that exactly 10 people are infected is:
p1 <- dbinom(10, 1000, 0.01)Ans: p1
(b) That probability that at least 16 people are infected.
Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - $\sum\limits_{i=0}^{15}$ $ \dbinom {1000}{i} $ $(0.01)^i$ $(1-0.01)^{1000-i}$Using R, the expression for the probability that at least 16 people are infected is:
p2 <- 1-pbinom(15, 1000, 0.01)Ans: p2
c) The probability that between 12 and 14 people are infected
.Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01
. Then, P(12 ≤ X ≤ 14) = $\sum\limits_{i=12}^{14}$ $ \dbinom {1000}{i} $ $(0.01)^i$ $(1-0.01)^{1000-i}$Using R, the expression for the probability that between 12 and 14 people are infected is:
p3 <- sum(dbinom(12:14, 1000, 0.01))Ans: p3
d) The probability that someone is infected
.Let X be the number of people infected in a group of 1000 people.
Here, X follows a binomial distribution with n = 1000 and p = 0.01.
Then, P(X ≥ 1) = 1 - P(X = 0) = 1 - $ \dbinom {1000}{0} $ $(0.01)^0$ $(1-0.01)^{1000-0}$Using R, the expression for the probability that someone is infected is:
p4 <- 1-dbinom(0, 1000, 0.01)Ans: p4
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Rewrite r=1.5 sin theta in rectangular form
The polar curve r = 1.5sinθ in rectangular form is x² + y² - 1.5y = 0
How to write the polar curve in rectangular form?Since we have the polar curve r = 1.5sinθ and we want to convert it to rectangular form, we proceed as follows
We know that in rectangular form the polar curve is
x = rcosθ (1) and y = rsinθ (2)x² + y² = r² (3)So, multiplying r = 1.5sinθ by r, have that
r = 1.5sinθ
r × r = r × 1.5sinθ
r² = 1.5rsinθ
Substituting this into equation (3), we have that
x² + y² = r² (3)
x² + y² = 1.5rsinθ (4)
From equation (2), y = rsinθ
So, substituting this into equation (4), we have that
x² + y² = 1.5rsinθ
x² + y² = 1.5y
x² + y² - 1.5y = 0
So, the rectangular form is x² + y² - 1.5y = 0
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a patient is purchasing acetaminophen 500 mg tablets over-the-counter and asks the pharmacist how many they can take. what is the maximum number of tablets the pharmacist will tell them they should take of this product per day?
8 is the maximum number of tablets the pharmacist will tell them they should take of this product per day.
According to FDA guidelines, the maximum daily dosage of acetaminophen for healthy adults should not exceed 4,000 milligrams. This equates to a maximum of eight 500 mg tablets per day. It's essential to remember that the recommended dosage may differ based on individual factors such as age, weight, and medical conditions. Therefore, it's crucial to consult with a healthcare provider or licensed pharmacist before taking any medication. Always follow the recommended dosage and avoid exceeding the daily limit to prevent potential health risks associated with acetaminophen overdose.
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Jackson is making lemonade for a class party. He uses 3 tablespoons (tbsp. ) of lemonade mix for each 6 ounces of water. He wants to make 4 quarts of lemonade. How much lemonade mix does Jackson need?
A
2 tbsp. B
16 tbsp. C
32 tbsp. D
64 tbsp
As per the unitary method, Jackson needs 64 tablespoons of lemonade mix to make 4 quarts of lemonade. (option D).
First, we need to convert the 4 quarts of lemonade into ounces since we know the ratio in terms of ounces. One quart is equal to 32 ounces (8 oz per cup and 4 cups per quart). So, 4 quarts would be equal to 128 ounces (32 oz x 4).
Next, we need to determine how much lemonade mix is needed for every 6 ounces of water.
Therefore, the ratio of lemonade mix to water is 3 tablespoons/6 ounces.
Now that we have the ratio, we can use it to find out how much lemonade mix is needed for 128 ounces of water (4 quarts). We can set up a proportion using the ratio we just found:
3 tbsp / 6 oz = x tbsp / 128 oz
We want to solve for x, which represents the amount of lemonade mix needed for 128 ounces of water. To solve for x, we can cross-multiply and simplify:
3 tbsp x 128 oz = 6 oz x
384 tbsp oz = 6x
x = 64 tbsp
So the answer is D) 64 tbsp.
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It takes jerry 3 hours to clean all the tank in his section. It take hart x hours to clean all the tanks in his section. If they work together they can clean the tanks in 1 hour. What fraction does Jerry get done in 1 hour
The amount or fraction of work Jerry gets done in 1 hour is 1/3 when it takes him 3 hours to clean all the tank in his section and it take Hart x hours to clean all the tanks in his section.
We know that it takes jerry 3 hours to clean all the tank in his section and it take Hart x hours to clean all the tanks in his section,
when they work together, they can clean the tanks in 1 hour.
now let work be - 1
therefore,
work x Jerry = work x Hart
1×3 = 1×x
3 = 1x
3 = x
therefore in 1 hour work done by Jerry will be 1/3.
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Compounds angles identities
Answer:
Compound angle identities are trigonometric identities that relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles.
The main compound angle identities are:
1. sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
2. cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
3. tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))
where A and B are any two angles.
These identities can be used to simplify trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities.
For example, we can use the compound angle identity for sin(A + B) to find sin(π/4 + π/6):
sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)
sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)
sin(π/4 + π/6) = (√6 + √2) / 4
Compound angle identities are an important part of trigonometry and are used in various fields such as physics, engineering, and mathematics.
A cylinder has a height of 20 feet. Its volume is 7,598.8 cubic feet. What is the radius of the cylinder?
Answer:
The radius is approximately 11 feet. More exactly 10.997 when rounded to the nearest thousandth.
Step-by-step explanation:
A cylinder has a height of 20 feet.
h = 20
Its volume is 7,598.8 cubic feet.
V = 7598.8
The formula for the volume of a cylinder is:
V = pi•r^2•h
Fill in what is given.
7598.8 = pi•r^2•20
Now there is only one variable in the equation, r and we can solve for it.
Divide both sides by 20pi.
120.938658 = r^2
We will have to square root both sides to find r.
10.997 = r
So the radius is 10.997 feet (to the nearest thousandth) or round to 11 feet.
Help me find the slope of the line for each one it’s ok if you don’t know all of them
Answer:
1. 1/2
2. -4/1
3. 1/1
Step-by-step explanation:
Answer:
1 y=2/1+2
2 y=.25x+3
3 y=x-2
Step-by-step explanation:
Step-by-step
y=mx+b
1. 2
2. .25
3. 1
Ian went to dinner last night and remembers leaving a 6.50 tip. The tip was 20% of the cost of dinner. What was the cost of dinner before tip?
Answer:
$32.50
Step-by-step explanation:
20% * y = 6.5 =>
y =6.5 ÷ 20% =
6.5 ÷ (20 ÷ 100) =
(100 × 6.5) ÷ 20 =
650 ÷ 20 =
32.5
Percentage of 20% of what number = 6.5?
20% × ? = 6.5
20% of 32.5 = 6.5
Each prism has the same volume. Which has the least surface area? Explain or show your
reasoning.
This means that the cube will have less surface area than the rectangular prism.
What is surface area?Surface area is a measure of the total exposed area of an object, or the total area of its two-dimensional surface. It is a measurement of the total exposed area of a three-dimensional object and is used to calculate the amount of material needed to cover a given area. Surface area is commonly used in physics, chemistry, engineering, and mathematics.
The prism with the least surface area of the same volume is the cube. This is because a cube has equal length, width, and height, allowing for all of the sides to be equal in size. This means that the area of each side is the same and all six sides of the cube are congruent. This creates the least amount of surface area for a given volume, as compared to any other prism. To illustrate this, take a cube and a rectangular prism with the same volume. The cube will have 6 smaller sides, while the rectangular prism will have 5 larger sides and 1 smaller side. This means that the cube will have less surface area than the rectangular prism.
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Ally chooses a whole number
Write a number that Ally could have started with
Ally could have started with any whole number, including 0, 1, 2, 3, 4, etc. Whole numbers are numbers that don't contain any fractions, decimals, or negative numbers.
For example, 1/2 is not a whole number, but 2 is a whole number. When Ally chooses a whole number, she could choose any number that fits this criteria. For example, she could choose 0, 1, 4, 17, 100, or any other whole number.
Ally chooses a whole number. The whole numbers are integers that are greater than zero. It includes all the natural numbers (1, 2, 3, ...) and zero. Let's assume Ally selected a whole number as the question mentioned, we will have to determine the possible number options that Ally could have chosen.One whole number that Ally could have chosen could be 1. Since 1 is the first natural number, it is the smallest whole number. The other whole numbers are greater than 1. The next smallest whole number is 2, followed by 3, then 4, and so on.
There are an infinite number of whole numbers since they continue infinitely in both positive and negative directions. There is no limit to the largest or smallest whole number; therefore, Ally could have begun with any whole number.
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What is the volume of the composite figure?
A complex figure comprised of 2 rectangular prisms. Prism A has a length of 2 centimeters, a width of 5 centimeters, and a height of 6 centimeters. Prism B has a length of 8 centimeters, width of 3 centimeters, and height of 6 centimeters.
204 cm3
342 cm3
604 cm3
4,211 cm3
Answer:
its 204cm3
Step-by-step explanation:
2x5x6=60
8x3x6=144
144+60=204
hope this helps!
Find the perimeter of the triangle shown below.
:48
:96
:120
:160
12
20 H
16
Answer:
48
Step-by-step explanation:
[tex]perimeter = a + b + c \\ = 12 + 20 + 16 \\ = 48[/tex]
Find sin X pleaseeee
Answer:
sin(x) = 9/41
Step-by-step explanation:
is the given value a solution of the inequality t-7<10, t = 28
Answer:
28 is NOT a given solution to the equality
Step-by-step explanation:
For this inequality, we substitute 28 for t and see if the left side is less than the right side.
[tex]t - 7 < 10, t = 28\\(28) - 7 < 10\\21 < 10 \\False[/tex]
The statement is false, therefore the number provided is not a solution
PLEASE HELP
find the equation of the line
using exact numbers
Answer: y = -3x + 7
Step-by-step explanation:
slope = -3
y intercept = 7
suppose that 65% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. consider groups of 17 trucks and let x be the number of trucks in a group that have passed the inspection. what is the probability that at least 9 but fewer than 12 trucks pass the inspection?
There is a 55.75% probability that at least 9 but fewer than 12 trucks pass the inspection out of a group of 17 trucks undergoing a brake inspection at the inspection facility with a pass rate of 65%.
We can utilize the binomial distribution formula to resolve this issue. Out of a group of 17 trucks, let X represent the proportion of trucks that pass the inspection, and let p represent the probability of passing the test, which is 0.65. A binomial distribution with n = 17 and p = 0.65 is then followed by X.
Calculating the cumulative chance of receiving 9, 10, or 11 trucks passing the inspection can help us determine the likelihood that at least 9 but fewer than 12 trucks will pass the test. The binomial distribution formula can be used for this as follows:
P(X=9, X=10, X=11) = P(X=9, X=10, X=11)
Using the binomial distribution formula, we can get the probabilities for each of the following:
[tex]P(X=9) = (17 pick 9) (17 choose 9) * 0.65^9 * 0.35^8[/tex] = [tex]0.1837 \sP(X=10)[/tex] = [tex](17 select 10) (17 choose 10) P(X=11)[/tex] = [tex](17 select 11) * 0.65*10 * 0.35*7[/tex] = [tex]0.2197 * 0.65*11 * 0.35*6 = 0.1541[/tex]
In light of this, the likelihood that at least 9 but not all 12 vehicles pass the inspection is:
P(9 ≤ X < 12) = 0.1837 + 0.2197 + 0.1541 = 0.5575
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Suppose you were given the function F(x) = x4 - 2x³ + 3x² - 10x + 3 and
the factor (x - 2). What is the value of a?
The value of x =is 7.5.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
F(x)=x^4-2x^3+3x^2 - ax+3
F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3
F(2) = 16 - 16 + 12 - 2a +3
F(2) = 15 - 2a
15 - 2a = 0
15 = 2a
a = 7.5
Hence, The value of x =is 7.5.
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a 13 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
The top of the ladder is 12 feet above the ground, the bottom of the ladder will be moving away from the wall at a rate of 0.096 ft/s.
The question is: a 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
To answer this question, we can use the concept of right triangle geometry. We know that when the top of the ladder is 12 feet above the ground, the bottom of the ladder is 13 feet away from the wall.
We can use the Pythagorean Theorem to calculate the hypotenuse of this right triangle, which is the total length of the ladder. This will allow us to calculate the rate at which the bottom of the ladder is moving away from the wall.
The Pythagorean Theorem states that
a^2 + b^2 = c^2,
where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse.
In this case, a is 12 and b is 13.
Therefore,
122 + 132 = c^2, or c^2 = 169.
Therefore, c = 13.04 feet.
This is the total length of the ladder.
We now have the total length of the ladder, so we can calculate the rate at which the bottom is moving away from the wall.
Since we know the top is moving at a rate of 1.25 ft/s, and the total length of the ladder is 13.04 feet, the bottom must be moving at a rate of (1.25/13.04) = 0.096 ft/s.
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help i don’t know how to solve number 11, please
Answer: 21, 32. 6, 12.
Step-by-step explanation:
10 + 3d = 43. 3d = 33. d = 11.
3 x [tex]r^{3}[/tex] = 24. [tex]r^{3}[/tex] = 8. r = 2.
On social issues, _____ think people should be liberated from the ways of the past and able to decide for themselves about how to live
On social issues, progressives think people should be liberated from the ways of the past and able to decide for themselves about how to live.
Progressivism is a political and social philosophy that emphasizes individual liberty, equality of opportunity, and the role of government in protecting citizens from social and economic abuses.Progressives believe that people should be free to make their own choices about how to live their lives and that the government should not interfere with their decisions. They believe that individuals should have the right to make choices regarding their personal lives, including decisions about marriage, sexuality, and reproductive health.Progressives also advocate for the protection of the environment and the promotion of sustainable practices.
They believe that it is the government's responsibility to protect the natural world and to ensure that future generations have access to clean air, water, and food.In addition, progressives advocate for social justice and the elimination of discrimination on the basis of race, gender, sexuality, and religion. They believe that everyone should have equal access to education, healthcare, and other basic services, regardless of their background or socioeconomic status.Overall, progressives believe in the power of individuals to make positive changes in their own lives and in the world around them. They believe that by working together and advocating for social and economic justice, we can create a better future for ourselves and for future generations.
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Which expression is equivalent to the following complex fraction?
The expression that is equivalent to the following complex fraction is this: B. -2y + 5x/3x -2y.
What is an equivalent expression?An equivalent expression is one that produces the same result as the given one when simplified. To get the equivalent expression, we simply need to simplify the expression above and the one underneath.
After finding the lowest common multiples of the figures underneath and the ones above, the next thing to do will be to multiply by the numerators.
-2/x + 5/y = -2y + 5x
Also:
3/y - 2/x = 3x - 2y
So, option B is an equivalent expression of the complex fraction.
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Consider the following equivalent resonance structures for the carbonate anion. Charges have not been shown.
What is the average formal charge on each oxygen atom?
answerable question reference
A -0.33
B -0.67
C -1
D 0.33
E 0.67
This is an example of resonance where all three structures contribute to the description of the anion and none of them are more accurate than the others. The sum of the formal charges for each of the resonance structures is equal to the net charge of the anion.
The carbonate anion can be represented by three equivalent resonance structures. These structures differ in the placement of electrons and the distribution of formal charges on the individual atoms. Structure B has a formal charge of -0.67 on the oxygen atom and a formal charge of 0.33 on the carbon atom.
Structure D has a formal charge of 0.33 on the oxygen atom and a formal charge of -0.67 on the carbon atom. Structure E has a formal charge of 0.67 on the oxygen atom and a formal charge of -0.67 on the carbon atom.
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the current in a certain river is known to be 2 kph. at full throttle, a boat makes a 4 km trip in this river (2 km upstream and 2 km downstream)in a total of 11 minutes. at full throttle, what is the speed of the boat in still water?
The speed of the boat in still water is 5 km/h.
Let's denote the speed of the boat in still water as "v" (in km/h). Since the boat travels 2 km upstream and 2 km downstream, we know that the total distance traveled is 4 km.
Let's first calculate the time taken to travel 2 km upstream. We know that the current is flowing at 2 km/h, so the effective speed of the boat relative to the river is (v - 2) km/h (since it is going against the current). Therefore, the time taken to travel 2 km upstream is
time taken = distance / speed = 2 / (v - 2) hours
Similarly, the time taken to travel 2 km downstream is
time taken = distance / speed = 2 / (v + 2) hours
The total time taken for the round trip (2 km upstream and 2 km downstream) is given as 11 minutes, which is equivalent to (11/60) hours. Therefore, we can write
2 / (v - 2) + 2 / (v + 2) = 11/60
Multiplying both sides by (v - 2)(v + 2) gives
2(v + 2) + 2(v - 2) = (v - 2)(v + 2)(11/60)
Simplifying the right-hand side gives
(v - 2)(v + 2)(11/60) = (11/3)v^2 - 44/3
Substituting this expression into the previous equation and simplifying gives
22v = (11/3)v^2 - 44/3
Multiplying both sides by 3 gives
66v = 11v^2 - 44
Rearranging and solving for v using the quadratic formula gives
v = (11 ± √(11^2 + 4×44))/22
Taking the positive solution (since v must be positive) gives
v = 5 km/h
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Show how to change 9^8/7 into a radical expression
Answer:
Rewrite the expression using the negative exponent rule b−n=1bn b - n = 1 b n . 1y98 1 y 9 8.
Step-by-step explanation:
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
8
Step-by-step explanation:
4c ÷ 2 x 2 c=8
4 x 8 ÷ 2 x 2
4 x 8 ÷ 4
You can cancel the 4’s or multiply 4 x 8 then divide by 4, which is 8 :)
Given:-
[tex] \tt \: c = 8[/tex][tex] \: [/tex]
[tex] \tt{4c ÷ ( 2 \times 2 ) ---eqⁿ}[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 4c ÷ ( 2 \times 2 )[/tex][tex] \: [/tex]
now , put the given value of c = 8 in equation
[tex] \tt \: 4 ( 8 ) ÷ ( 2 \times 2 )[/tex][tex] \: [/tex]
[tex] \tt \: 32 ÷ 4[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \pink{ \: \: 8 \: \: }}}[/tex][tex] \: [/tex]
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hope it helps ⸙