The domain of function 1/x is (-∞, 0) U (0, ∞), which means all real numbers except 0.
What is a domain?In mathematics, the term "domain" refers to the set of possible input values for a function, equation, or expression. The domain represents the valid inputs that can be used to evaluate the function or expression and obtain a meaningful output.
For example, consider the function f(x) = x^2. The domain of this function is all real numbers because we can plug in any real number for x and obtain a valid output. However, if we consider the function g(x) = 1/x, the domain of this function is all real numbers except x = 0, because division by zero is undefined and we cannot evaluate the function at that point.
According to the given informationThe expression 1/x has a domain of all real numbers except x = 0. This is because division by zero is undefined, so the expression is not defined for x = 0. For all other values of x, we can evaluate 1/x and get a real number. Therefore, the domain of 1/x is (-∞, 0) U (0, ∞), which means all real numbers except 0.
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I don’t know the answer to the math problem
Answer:
54.1 cm
Step-by-step explanation:
1) Divide the circumference by pi (3.14…)
2) Your quotient (108.2… cm) is now the diameter of the circle. The diameter goes through the circle completely. The radius is half of the diameter, or it goes halfway through the circle. Hence, you would divide the previous answer by 2.
3) 108.2… cm divided by 2 should leave you with about 54.1… cm.
Exit
6-3: PRACTICE Part 2 Logarithms in Equations Algebra 2
Michael invests $1,000 in an account that earns a 4.75% annual percentage rate compounded continuously. Peter invests $1,200 in an account that earns a 4.25% annual
percentage rate compounded continuously. Which person's account will grow to $1,800 first?
Michael's account will grow to $1,800 after about year(s). Peter's account will grow to $1,800 after about year(s). So,
(Round to the nearest whole number as needed.)
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Answer: To solve this problem, we need to use the continuous compound interest formula:
A = Pe^(rt)
where A is the amount in the account, P is the initial principal, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time in years.
For Michael's account, we have:
A = 1000e^(0.0475t)
For Peter's account, we have:
A = 1200e^(0.0425t)
We want to find the time it takes for each account to reach $1,800. So we can set up the following equations:
1000e^(0.0475t) = 1800
1200e^(0.0425t) = 1800
We can solve each equation for t by taking the natural logarithm of both sides and isolating t:
ln(1000) + 0.0475t = ln(1800)
ln(1200) + 0.0425t = ln(1800)
Subtracting ln(1000) or ln(1200) from both sides, we get:
0.0475t = ln(1800) - ln(1000)
0.0425t = ln(1800) - ln(1200)
Dividing both sides by the interest rate and simplifying, we get:
t = (ln(1800) - ln(1000)) / 0.0475 ≈ 10.16 years for Michael's account
t = (ln(1800) - ln(1200)) / 0.0425 ≈ 10.62 years for Peter's account
Therefore, Michael's account will grow to $1,800 first, after about 10 years (rounded to the nearest whole number).
Step-by-step explanation:
Approximately how much of the area under a standard curve is within one standard deviation of the mean?
99%
95%
68%
80%
Answer:
Approximately 68% of the area under a standard normal distribution curve is within one standard deviation of the mean, also known as the 68-95-99.7 rule.
Specifically, the rule states that:
Approximately 68% of the area under the curve falls within one standard deviation of the mean.Approximately 95% of the area under the curve falls within two standard deviations of the mean.Approximately 99.7% of the area under the curve falls within three standard deviations of the mean.This means that if we have a normally distributed dataset with a mean of 0 and a standard deviation of 1, approximately 68% of the data points will fall within the range of -1 to +1 standard deviations from the mean.
Shannon and Leslie want to carpet is 16 1/2‘ x 16 1/2‘ square room. They cannot put carpet under the entertainment system that jets out. In square feet, what is the area of the space with no carpet?
The area of space with no carpet is 268.25 sq ft.
In order to calculate the area of square room we have to subtract the section that is not carpeted from the total area of the room.
The given dimensions of the room is 16 1/2‘ x 16 1/2‘ square room
therefore,
16.5 x 16.5 = 272.25 sq ft
now if we consider that the entertainment system is 2 feet in measurement then,
2 x 2 = 4 sq ft
hence, the space with no carpet is
271.25 - 4
= 268.25 sq feet
The area of space with no carpet is 268.25 sq ft.
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help would be absolutely appreciated
Thus, the given quadratic equation has two real roots x = 3 and x = -2.
Explain about the solution of quadratic function:A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.
The quadratic formula is employed to solve a quadratic to discover its roots, which can either be distinct or the same. A quadratic function must first be converted into a quadratic equation by being made equal to zero in order to be solved.Given equation:
x² - x - 6 = 0
Using the quadratic formula:
x = [-b ± √(b² - 4ac) ] / 2a
a = 1 , b = -1 and c = -6
x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1
x = [1 ± √(1 + 24) ] / 2
x = [1 ± 5 ] / 2
Now,
x = (1 + 5)/2 = 3
x = (1 - 5)/ 2 = -2
Thus, the given quadratic equation has two real roots x = 3 and x = -2.
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complete question:
Check whether the given equation has, one solution, two solution ,many solution or no real solution.
x² - x - 6 = 0
how many three-digit numbers less than 700 can be made using the digits 9, 7, 5, and 3 at most once? assume digits cannot be reused.
There are 24 three-digit numbers less than 700 that can be made using the digits 9, 7, 5, and 3 at most once. They are:
395, 379, 357, 593, 597, 537, 573, 935, 937, 957, 975, 375, 735, 753, 793, 359, 539, 579, 953, 973, 357, 537, 573
A drawer contains 3 red paper clips, 4 green paper clips, and 5 blue paper clips. One paper clip is taken from the drawer and is NOT replaced. Another paper clip is taken from the drawer. What is the probability that the first paper clip is red and the second paper clip is blue?
The probability of drawing a red paper clip first and a blue paper clip second is 15/132 or approximately 0.1136.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
The probability of drawing a red paper clip on the first try is 3/12, because there are 3 red paper clips out of 12 total paper clips in the drawer. Once a paper clip has been removed, there are 11 paper clips remaining, so the probability of drawing a blue paper clip on the second try is 5/11, because there are 5 blue paper clips remaining out of the 11 total remaining paper clips.
The probability of both of these events occurring is the product of their individual probabilities, so the probability of drawing a red paper clip first and a blue paper clip second is:
(3/12) * (5/11) = 15/132
Therefore, the probability of drawing a red paper clip first and a blue paper clip second is 15/132 or approximately 0.1136.
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the scatterplot below shows the relationship between the grams of fat and total calories in different food items. the equation for the least-squares regression line to this data set is y with hat on top equals 13.198 x plus 153.6. what is the predicted number of total calories for a food item that contains 25 grams of fat?
The predicted total number of calories for a food containing 25 grams of fat is approximately 483.55.
The equation for the least-squares regression line is:
z = 13.198x + 153.6
where ŷ= predicted value of y (total calories), x = value of the predictor variable (grams of fat), 13.198= slope of the line, and 153.6= y-intercept of the line.
To find the predicted total calories for a food with 25 grams of fat, simplify by substituting x = 25 into the equation.
z = 13.198x + 153.6
ŷ = 13.198(25) + 153.6
ŷ = 329.95 + 153.6
z = 483.55
Therefore, the predicted total number of calories for a food containing 25 grams of fat is approximately 483.55.
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a survey reports that 67% of college students prefer to drink more coffee during the exams week. if we randomly select 80 college students and ask each whether they drink more coffee during exams week. what is the probability that at most 60 say that they drink coffee during exam week?
From that 80 college students, the probability that at most 60 say that they drink coffee during exam week is 0.3085
This is a binomial distribution problem in which we want to know the probability it is that at least 60 students out of 80 choose to drink coffee during test week.
Here, we have:
n = 80 (number of trials)
p = 0.67 (probability of success in each trial)
q = 1 - p = 0.33 (probability of failure in each trial)
x ≤ 60 (number of successes we want to find the probability for)
This probability may be calculated using the binomial cumulative distribution function (CDF). The binomial CDF formula is as follows:
P(X ≤ k) = Σi=[tex]0^{K}[/tex] ([tex]_{n}C^{i} }[/tex]) * [tex]p^{i}[/tex] * ([tex](1-p)^{n-i}[/tex]
We can determine the chance of having 60 or fewer successes using this formula:
P(X ≤ 60) = Σi=[tex]0^{60}[/tex] ([tex]_{80} C^{i}[/tex]) * [tex]0.67^{i}[/tex] * [tex]0.33^{80-i}[/tex]
P(X ≤ 60) = 0.3085
As a result, the probability that at least 60 college students claim they consume coffee during test week is 0.3085, or around 31%. As a result, 0.3085 is the correct answer.
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A student is helping a family member build a storage bin for their garage. They would like for the bin to have a volume of 240 ft3 If they already have the length measured at 8 feet and the width at 6 feet, what is the height needed to reach the desired volume?
(A) 3 feet
(B) 3.5
(C) 4 feet
(D) 5 feet
Answer: The answer to your question is D! Brainliest?
Step-by-step explanation:
To find the height needed to reach a volume of 240 ft^3, we can use the formula:
Volume = length x width x height
Substituting the given values, we get:
240 = 8 x 6 x height
Simplifying:
240 = 48 x height
height = 240/48
height = 5
Therefore, the height needed to reach a volume of 240 ft^3 is 5 feet.
Answer: (D) 5 feet.
when utilizing a matlab built-in ode solver, in the function for one's states the variable for the state derivatives must be organized as a column vector. group of answer choices true false
It is true to say that when utilizing MATLAB's built-in ode solver, the function for one's states the variable for the state derivatives must be set as column vectors.
The Ordinary Differential Equation (ODE) solvers in MATLAB solve initial value problems with a varient state of properties. They consider state spaces as a column vector. For example, two solve a second degree ODE, It's two states in state space has to be arranges in a 1x2 column vector to pass it into a ODE solver.
Initial value problems with different attributes can be solved using theODE solvers in MATLAB.
Here the first ODE is of third order, so it will be converted to three equivalent first order ODEs. The second ODE is second order, so it will be converted to two equivalent first order ODEs.These solver can be used to solve the different type like the differential algebraic equations (DAEs), problems involving a mass matrix, and fully implicit problems. ODE45, is most frequently used ODE solver in MATLAB.It used to compare methods of orders four and five to determine an estimate error.
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The radius of a circle is 10 cm. Find its area in terms of π.
The area of a circle is given by the formula:
A = πr^2
where r is the radius of the circle.
Substituting the value of the radius as r = 10 cm, we get:
A = π(10)^2
A = 100π
Therefore, the area of the circle with radius 10 cm is 100π square centimeters.
~~~Harsha~~~
A random sample of size is selected from a population with. A. What is the expected value of (to 2 decimals)? B. What is the standard error of (to 2 decimals)? C. Show the sampling distribution of (to 2 decimals). D. What does the sampling distribution of show? Blank
A) The expected value of the sampling distribution is 0.40.
B) The standard error is 0.05.
C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.
D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.
A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.
B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.
C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.
D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.
The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.
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Complete Question:
A random sample of size 100 is selected from a population with p =0 .40.
A. What is the expected value (to 2 decimals)?
B. What is the standard error (to 2 decimals)?
C. Show the sampling distribution (to 2 decimals).
D. What does the sampling distribution of show?
PLSSSS HELP IF YOU TURLY KNOW THISSS
1. Multiply both sides by 2. 4 + 3x = 5 * 2
2. Simplify. 4 + 3x = 10
3. Subtract 4 from both sides to single out x. 3x = 10 - 4
4. Simplify. 3x = 6
5. Divide by 3. x = 6/3
6. Simplify. x = 2
Input 2 into the original equation to check this answer and you will get 5 = 5 which means that x = 2 is your final answer.
Answer: x = 2
Step-by-step explanation:
To solve for x, we will isolate the variable (x).
Given:
[tex]\displaystyle \frac{4+3x}{2}=5[/tex]
Multiply both sides of the equation by 2:
4 + 3x = 10
Subtract 4 from both sides of the equation:
3x = 6
Divide both sides of the equation by 3:
x = 2
At Jim's Hats, there are 6 baseball caps and 54 other hats. What percentage of the hats are baseball caps?
Answer: 10
Step-by-step explanation:
First you would add up to find the total amount of hats. The full amount is 60. The you would divide the 6 by 60. The answer is 0.1. That is ten percent.
Answer:
11%
Step-by-step explanation:
three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Each year the school randomly selects a sporting event for their family fun night. The superintendent also randomly selects a sporting event to attend. What is the probability that the superintendent will be at the family fun night sporting event?
The probability that the superintendent will be at the family fun night sporting event is 1/n, where n is the total number of sporting events held by the school each year.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Assuming that the superintendent is equally likely to attend any of the school's sporting events, the probability that they attend the family fun night sporting event is simply the ratio of the number of family fun night sporting events to the total number of sporting events.
If we assume that the school has n sporting events each year and that the family fun night sporting event is chosen randomly from these n events, then the probability that the superintendent attends the family fun night sporting event is 1/n.
Therefore, the probability that the superintendent will be at the family fun night sporting event is 1/n, where n is the total number of sporting events held by the school each year.
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Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.
Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.
Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.
So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.
However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).
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Complete Question:
Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
Which of these expressions are equivalent to p/3
Answer:
B) 3p/9
D)1/3p
Step-by-step explanation:
Quadrilateral JKLM has vertices J(3,5), K(7,8), L(13,5), and M(13,0). Which statements are true? Select all that apply.
~a.) Line Segment KL ║ Line Segment JM
~b.) Line Segment KL ≅ Line Segment JM
~c.) Line Segment JK ≅ Line Segment LM
~d.) Line Segment JK ║ Line Segment LM
~e.) Quadrilateral JKLM is a trapezoid.
~f.) Quadrilateral JKLM is an isosceles trapezoid.
The statements that are true are:
→ Line Segment KL ≅ Line Segment JM
→ Quadrilateral JKLM is a trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.
According to the given informationIn the quadrilateral JKLM
Using the distance formula, we can find the lengths of the line segments:
JK = √[(7-3)² + (8-5)²] = √58
KL = √[(13-7)² + (5-8)²] = √58
LM = √[(13-13)² + (0-5)²] = 5
JM = √[(13-3)² + (0-5)²] = √109
From this, we can analyze each statement:
a.) Line Segment KL ║ Line Segment JM
We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.
b.) Line Segment KL ≅ Line Segment JM
We found that the length of KL is equal to the length of JM. Therefore, statement b is true.
c.) Line Segment JK ≅ Line Segment LM
We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.
d.) Line Segment JK ║ Line Segment LM
We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.
e.) Quadrilateral JKLM is a trapezoid.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.
f.) Quadrilateral JKLM is an isosceles trapezoid.
An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.
Therefore, the statements that are true are b and e.
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Answer:
A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯
C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯
E) Quadrilateral JKLM is a trapezoid.
F) Quadrilateral JKLM is an isosceles trapezoid.
Step-by-step explanation:
These where the correct answer I got when taking the assignment with that question
Hw 22.2 -Permutations with repetition
There are 6 runners in s race .In how many ways can 3 runners finish in first ,second ,and third to win the gold ,sliver ,and bronze medals ?
Shopping While shopping for clothes, Tracy spent $34 less than 3 times what Jaclyn spent. Tracy spent $26. Write and solve an equation to find how much Jaclyn spent. Let x represent how much Jaclyn spent. The equation that can be used to determine how much Jaclyn has spent is
Which single basic motion will make these figures coincide?
The single basic motion that will make the figures coincide are
1) a linear motion.
2) Linear motion
3) Rotational motion
4) Translational motion
5) Rotational motion
6) translational motion
What are the basic motions in Physics?Here are some basic motions in physics:
Linear motion: This is the motion of an object in a straight line, such as a car moving down a highway or a ball being thrown straight up.
Circular motion: This is the motion of an object moving in a circle, such as a car driving around a roundabout or a satellite orbiting the Earth.
Projectile motion: This is the motion of an object that is thrown, launched, or dropped and then moves under the influence of gravity alone. Examples include a cannonball being fired or a basketball being shot.
Oscillatory motion: This is the motion of an object that repeats the same motion over and over again, such as a pendulum swinging back and forth or a guitar string vibrating.
Rotational motion: This is the motion of an object that rotates around a fixed axis, such as a spinning top or a bicycle wheel.
Translational motion: This is the motion of an object that moves from one place to another, such as a train moving from one station to the next.
Wave motion: This is the motion of a disturbance that travels through a medium, such as sound waves or ocean waves.
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PLEASE HELP!! 20 POINTS
Select the correct answer from each drop-down menu. Consider this equation. 1/x + 2/x+10 =1/3 Complete the statements to make them true. The least common denominator is . The equation will have valid solutions.
Answer: The least common denominator is 3x(x+10)
The equation will have 2 valid solutions
Step-by-step explanation: sorry if wrong
PLEASE HELPPPPP!!!!! Which statement correctly compares the shapes of the of the distributions!
Answer:
Could be B
Step-by-step explanation:
Southview HS is mirrored or symmetrical while the other is going up.
What is the answer to this problem?
The area of the shaded area is 3.27 ft²
How to the area of the shaded area?We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;
Area of shaded area = Area of sector - area of triangle
Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)
Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)
Area of shaded area = 3.27 ft²
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explain whether the mean or the median is amore appropriate measure of center for this data set?
The mean and median are both measures of center, but which one is more appropriate depends on the data set.
What is appropriate?Appropriate behavior is behavior that is socially acceptable and respectful of others. This includes treating others with kindness, politeness, and respect, refraining from using offensive language, and not engaging in hurtful or violent behavior. Appropriate behavior also means following established rules, laws, and cultural norms. Examples of appropriate behavior include being honest and trustworthy, showing respect for others and their property, and being courteous and polite.
The mean is the average of the data set and is affected by extreme values. The median is the middle value in the data set and is not affected by extreme values. If the data set has extreme values, the median is usually the more appropriate measure of center. If the data set does not have extreme values, the mean is usually the more appropriate measure of center.
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The box plot represents the midterm scores of the students in a class:
The percent of the students that had a score greater than or equal to 50 include the following: C. 75%.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:
Minimum (Min) = 30.First quartile (Q₁) = 50.Median (Med) = 60.Third quartile (Q₃) = 90.Maximum (Max) = 100.For the required percent, we have;
Q₁ = 50:
Percent = 100% - 25%
Percent = 75%
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The expression 0.9x represents the amount of pure copper sulfate in x liters of 90% copper sulfate solution.
a. Write an expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution.
b. A chemist added x liters of 90% copper sulfate solution to 3x liters of 25% copper sulfate solution. Use division to find the percentage of pure copper sulfate in the resulting solution.
The percentage of pure copper is
.
a) The expression for the amount of pure copper sulfate in 3x liters of 25% solution is 0.675x.
b) The percentage of pure copper sulfate in the resulting solution is 39.375%.
Percent compositionTo find the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution, we can first calculate the amount of copper sulfate in the solution and then multiply by the percentage of pure copper sulfate.Since the solution is 25% copper sulfate, we know that there are 0.25(3x) = 0.75x liters of copper sulfate in the solution.
The amount of pure copper sulfate in the solution is given by 0.9 times the amount of copper sulfate. Therefore, the expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution is:
0.9(0.75x) = 0.675x
To find the percentage of pure copper sulfate in the resulting solution, we need to calculate the total amount of pure copper sulfate in the solution and divide by the total volume of the solution.The amount of pure copper sulfate added from the 90% copper sulfate solution is 0.9x liters.
The amount of pure copper sulfate in the 25% copper sulfate solution is 0.675x liters.
The total amount of pure copper sulfate in the resulting solution is:
0.9x + 0.675x = 1.575x
The total volume of the resulting solution is:
x + 3x = 4x
To find the percentage of pure copper sulfate in the resulting solution, we divide the amount of pure copper sulfate by the total volume of the solution and multiply by 100:
(1.575x / 4x) * 100 = 39.375%
Therefore, the percentage of pure copper sulfate in the resulting solution is 39.375%.
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