To solve for the number of children at the concert with twice as many adults present in a total of 900 attendees, we let the number of children be x, set up the equation x + 2x = 900, and solve for x to find that there were 300 children.
Explanation:The question pertains to solving a problem involving proportions in a total population. Assuming there are twice as many adults as children at the school concert, we can use a 'let' statement to express the number of children as 'x'. Thus, the number of adults would be '2x' because there are twice as many adults as children. Since the total number of attendees is 900, we can set up the equation: x + 2x = 900.
To find the number of children, we combine like terms to get 3x = 900, and then divide both sides by 3 to find x. Thus, x = 900 / 3, which means x = 300. So, there were 300 children at the concert.
Step-by-Step Solution:Let the number of children be 'x' (let statement).Write the number of adults as '2x' because there are twice as many adults as children.Set up the equation for the total attendees: x + 2x = 900.Combine like terms: 3x = 900.Divide both sides by 3 to solve for x: x = 300.Conclude that there were 300 children at the concert.Inverse function y = x2 − 18x.
The question is about finding the inverse of the quadratic function y = x^2 - 18x. To find the inverse, swap x and y then solve for y, considering the function's restricted domain to ensure it's a function. Understanding transformations like scaling, reflecting, and translating is also crucial for interpreting and graphing functions.
Explanation:The student is asking about how to find the inverse function of a given quadratic function y = x2
- 18x. To find the inverse, we need to swap the x and y variables and solve for y. The steps involve setting x = y2 - 18y and then applying the quadratic formula or completing the square to solve for y. It is important to note that not all functions have inverses that are also functions without restricting the domain, especially quadratics, which are not one-to-one. However, if we consider only the increasing or decreasing intervals separately, we can find a suitable inverse restricted to that part of the domain.
The critical points like x and y intercepts can help us to verify if we have found the correct inverse function. Additionally, understanding the effects of various transformations on the function can be useful in graphing and interpreting the inverse.
Regarding transformations of functions, the operations may include scaling, reflecting, and translating the graph. For instance, the function f(x) = 2x - 2 features a y-intercept at (0, 2) and would be transformed as follows for different operations:
f(2x) which shrinks the graph horizontally by a factor of half.f(-2x) which reflects the graph across the y-axis.f(-2(x+1)) which results in a horizontal shift to the left by one unit by adding 1 to the independent variable x.Which of the following equations correctly expresses the relation between vectors A⃗ ,
B⃗ , and C⃗ shown in the figure?
A) A⃗ +B⃗ +C⃗ =0
B) A⃗ =B⃗ +C⃗
C) B⃗ =A⃗ +C⃗
D) C⃗ =A⃗ +B⃗
The Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 9 authors in all. Would you be surprised if none of the names f these authors were among the 10 most common? (Assume that authors' names are independent and follow the same probability distribution as the names of all residents.)
The probability suggests a 28.7% chance that none of the 9 authors have names among the 10 most common.
In a probability context, the likelihood of encountering one of the 10 most common names among the authors of your textbooks can be estimated based on the fact that these names account for 9.6% of all U.S. residents. However, the probability distribution of authors' names may not precisely mirror that of the general population, as authorship is influenced by factors beyond name popularity.
Given that there are 9 authors, each with an independent chance of having a name among the top 10, the probability that none of them have a common name is [tex]0.904^{9}[/tex], assuming an even distribution. This is because
0.904 represents the proportion of names that are not in the top 10.
Calculating this probability results in approximately 0.287, or 28.7%. So, there is about a 28.7% chance that none of the authors have a name among the 10 most common.
In a brief summary, it wouldn't be overly surprising if none of the authors' names matched the 10 most common names given the probability, but it's not an unexpected outcome. Probability alone doesn't guarantee specific outcomes in small samples.
use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating the f at the subinterval midpoints.
f(x)=x^4 on [0,2]
A function is a relationship between inputs where each input is related to exactly one output.
The average value of the function f(x) on [0, 2] is 3.03515625.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = [tex]x^{4}[/tex] on [0, 2]
Partitioning the interval into four subintervals of equal length.
= 2-0 / 4 = 2/4 = 1/2 = 0.5
This means the four subintervals are:
[0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].
Midpoints of each partitioned interval.
[0, 0.5] = 0.25
[0.5, 1] = 0.75
[1, 1.5] = 1.25
[1.5, 2] = 1.75
Now,
f(0.25) = [tex]0.25^{4}[/tex]
f(0.75) = [tex]0.75^{4}[/tex]
f(1.25) = [tex]1.25^{4}[/tex]
f(1.75) = [tex]1.75^{4}[/tex]
Now,
The average value of f(x) = [tex]x^{4}[/tex] on [0, 2].
= 1/2 [ ([tex]0.25^{4}[/tex] + [tex]0.75^{4}[/tex] + [tex]1.25^{4}[/tex] + [tex]1.75^{4}[/tex])/(2 - 0)]
= 0.5 [ ([tex]0.25^{4}[/tex] + [tex]0.75^{4}[/tex] + [tex]1.25^{4}[/tex] + [tex]1.75^{4}[/tex])/2 ]
= 3.03515625
Thus,
The average value of the function f(x) on [0, 2] is 3.03515625.
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Sales on credit are immediately counted as cash receipts?
The correct answer to this open question is the following.
Sales on credit are not immediately counted as cash receipts.
When a good is sold and people pay for it with cash, that is counted as cash receipts. Other methods don't. If the product is sold on credit, the store is not receiving any cash at all. It is receiving a promise of pay that has to be payable by the credit institution or the bank.
simplify the expression 3x^2(x^2-4x-2)+(5x^3+7x^2+2x+11)
Select one of the factors of x3y2 + 8xy2 - 5x2 - 40.
Can someone help me figure this out?
answer choices
(xy2 + 5)
(x2 + 4)
(xy2 - 5)
(x2 - 8)
Answer:
[tex](xy^2-5)\text{ is one factor of above polynomial}[/tex]
Step-by-step explanation:
Given the polynomial
[tex]x^3y^2+8xy^2-5x^2-40[/tex]
we have to select the option which is one of the factor of above polynomial.
[tex]x^3y^2+8xy^2-5x^2-40[/tex]
[tex]xy^2(x^2+8)-5(x^2+8)[/tex]
[tex](xy^2-5)(x^2+8)[/tex]
[tex]\text{Hence, }(xy^2-5)\text{ is one factor of above polynomial}[/tex]
∴ Option 3 is correct
Nathan cut 3 pieces of rope. Each was between 1.1 m and 1.2 m. Write down how long each piece might be.
The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is (4 points)
-1
39
35
71
A function assigns the values. The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To find the point at which the function has the maximum value we need to differentiate the function. Therefore, the function can be written as,
[tex]f(x) = 2x^3 - 18x^2 + 48x - 1 \\\\\dfrac{d}{dx}f(x) = \dfrac{d}{dx}(2x^3 - 18x^2 + 48x - 1)\\\\f' = 6x^2-36x+48[/tex]
Equate the function with zero to know at what value of x the function returns a maximum value.
6x² - 36x + 48 = 0
x² - 6x + 8 = 0
x² -2x -4x +8 = 0
(x-2)(x-4)=0
Since we want to the value in the interval of 0 to 3, therefore, 2 is the value at which the function will have its maximum value.
f(2) = 2(2)³ - 18(2)² + 48(2) - 1
f(2) = 39
Hence, The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
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To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], locate the critical points and evaluate the function at the critical points and endpoints. The maximum value is 71.
Explanation:To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], we need to locate the critical points and the endpoints of the interval. First, find the derivative of the function: f'(x) = 6x^2 - 36x + 48. Set the derivative equal to zero and solve for x to find the critical points. Then evaluate the function at the critical points and the endpoints to find the maximum value.
The critical points are x = 1 and x = 4. Evaluating the function at these points: f(1) = -7 and f(4) = 71. Evaluating the function at the endpoints of the interval: f(0) = -1 and f(3) = 35. The largest value is 71, so the maximum value of f(x) on the interval [0, 3] is 71.
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A motorist traveled 311 miles on 12 gallons of gas. To the nearest tenth, how many miles can the motorist travel on one gallon of gas?
A) 0.03 miles
B) 23.8 miles
C) 24.6 miles
D) 25.9 miles
how do i find what x equals for 7x-5=-5
Why isn't there work when carrying something horizontally at a constant speed?
use benchmarks to estimate 2.81+3.73
The length of a rectangle is 3 inches more than the width. the perimeter is 42 inches. find the length and width.
The minute hand of a clock is 9.5cm long. how far will the tip of the hand travel in one day
Which of the following are equal to the expression below?
square root of 40/2
A. square root of 10
B. 20
C. square root of 20
D. square root of 40/4
Which of the following points lie in the solution set to the following system of inequalities?
y > −3x + 3
y > x + 2
(2, −5)
(−2, 5)
(2, 5)
(−2, −5)
Answer:
Hi!
The correct answer is (2,5).
Step-by-step explanation:
To find which ordered pair is in the solution set of the system of inequalities:
y > −3x + 3 y > x + 2you have to replace the values into the system and both results have to be true.
For ordered pair (2,5) where x=2, and y=5.
y > −3x + 3 5 > -3(2) + 3 // replace the values5 > -6 + 35 > -3 is TRUE.AND
y > x + 2 5 > 2 + 25 > 4 is TRUE.Correct answer: (2,5)
what is the sum of the square roots of 16i?
The sum of the square roots of 16i is zero, as the positive and negative square roots cancel each other out when summed up.
Explanation:The sum of the square roots of 16i is found by first determining the square roots of the given complex number. The complex number 16i can be expressed in terms of its polar form, which then allows us to apply De Moivre's Theorem in order to find the square roots.
First, 16i is purely imaginary, with a magnitude of 16 and an argument that is π/2 or -3π/2 radians. By taking the square root of its magnitude and halving the argument, we find the two square roots, which are in fact ±4√i. Therefore, if we consider both the positive and negative square roots, the sum of the square roots of 16i would be 4√i + (-4√i), which simplifies to 0.
The sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
Explanation:To find the sum of the square roots of 16i, we first need to find the square root of 16i. To do this, we can write 16i in polar form.
16i = 16(cos (π/2) + isin(π/2))
Then, we can find the square root of 16i by taking the square root of the magnitude and halving the argument.
√16i = √16(cos (π/4) + isin(π/4))
√16i = √16 * cos (π/8) + √16 * isin(π/8)
√16i = 4(cos (π/8) + isin(π/8))
Therefore, the sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
Given the conditional statement "If it is January, then it is winter in the United States," which is true?
A) The Converse Of The Conditional
B) The Inverse Of The Conditional
C)The Contropositive Of The Conditional
D) Not Here ...?
Given the conditional statement, 'If it is January, then it is winter in the United States.' The convese and inverse aren't always true, but the contrapositive is, therefore, the correct answer is C) The Contrapositive of the Conditional.
Explanation:The given statement is 'If it is January, then it is winter in the United States.' In logic, this statement is termed as a conditional statement. Let's analyze the options provided:
The Converse of the Conditional: This would reverse the statement to 'If it is winter in the United States, then it is January.' This is not always true since winter lasts for three months: December, January, and February.The Inverse of the Conditional: This would negate both the original statement's hypothesis and conclusion, resulting in 'If it is not January, then it is not winter in the United States,' which is also not always true.The Contrapositive of the Conditional: This reverses and negates the statement, turning it into 'If it is not winter in the US, then it is not January.' This statement is true. If it's not winter (meaning it's spring, summer, or fall), it cannot be January.Learn more about Conditional Logic here:https://brainly.com/question/2114683
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convert to an improper fraction, type your answer with the negative in the numerator.
-8 3/4
The mixed number -8 3/4 can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, resulting in -29/4.
Explanation:The mixed number given is -8 3/4. An improper fraction is one where the numerator (top number) is greater than the denominator (bottom number). To convert a mixed number to an improper fraction, we should multiply the whole number by the denominator of the fraction and then add the numerator. Here, this would look like (-8*4)+3 = -32 + 3 = -29. The denominator stays the same. So, -8 3/4 is equal to -29/4 in improper fraction form.
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You roll two dice, what is the probability of rolling two even numbers?
Your class is learning how to tie knots.each student needs a peace of rope thatis 3/8 yards. how much do we need for 16 stdents
TRUE or FALSE. 6 1/3 percent is equal in fraction to 4/75
Which answer describes the type of sequence?
200, 40, 8, 1.6, ...
geometric
neither arithmetic nor geometric
arithmetic
Answer:
it is geometric
Step-by-step explanation
We have been given with the series
200,40,8,1.6
Arithmetic sequence is the sequence in which difference between consecutive terms is same that is common difference d
d=a_2-a_1
d=40-200=-160 herea_2=40,a_1=200
d=8-40=-32 herea_2=8,a_1=40
We can see the difference is not same
Hence, the given sequence is not arithmetic sequence.
Geometric sequence is the sequence in which ratio of consecutive terms is same that is common ratio r
r=\frac{a_2}{a_1}
r=\frac{40}{200}=\frac{1}{5} herea_2=40,a_1=200
r=\frac{8}{40}=\frac{1}{5} herea_2=8,a_1=40
r=\frac{1.6}{8}=\frac{1}{5} herea_2=1.6,a_1=8
We can see the ratio is same.
Hence, given sequence is geometric
Therefore, Option 1 is correct given sequence is geometric.
Answer:
The correct answer is A. geometric
Step-by-step explanation:
Find all solutions in the interval [0, 2π).
7 tan^3x - 21 tan x = 0
A) pi/3, 2pi/3, 4pi/3, 5pi/3
B) 0, pi/5, π, 6pi/5
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
D) 0, pi/3, π, 4pi/3
Robert buys 4 pounds of cauliflower at $0.85 a pound. He also buys 4 pounds of brussels sprouts. If he spends $6.40 on the vegetables, how much did the brussels sprouts cost per pound? A. $0.80 B. $0.75 C. $0.85 D. $0.76
A student faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random: a. two students and two faculty members and b. one faculty member and three students. ...?
To solve the question, calculate the total possible ways to form a committee and the ways for each specific case. The probability can be determined by dividing the specific event by the total outcomes. This involves the mathematical principles of combinatorics and probability.
Explanation:
The question is dealing with the concept of combinatorics and probability. In such cases, we look at the total possible outcomes and the outcomes of our specific event of interest.
For the first case, we need to select 2 students and 2 faculty members from respective pools of 20 and 5. The total ways to form a committee are combinations of 4 from 25 (20 students + 5 faculty). So, we have:
Total outcomes = C(25,4)
The event of interest (2 students and 2 faculty) can be calculated as the product of combinations of selecting 2 from each pool:
Specific event outcomes = C(20,2)*C(5,2)
To get the probability, we divide the outcomes of our event of interest by the total outcomes.
The second scenario works similarly. You want one faculty and three students:
Specific event outcomes = C(20,3)*C(5,1)
You'd again divide this result by the total possible outcomes (determined the same as the first scenario) to obtain the desired probability.
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The probability of forming a committee with two students and two faculty members is 15%, while the probability of forming a committee with one faculty member and three students is 45%.
Explanation:a. Two students and two faculty members:
To find the probability of selecting two students and two faculty members, we need to calculate the number of ways this combination can occur and then divide it by the total number of possible combinations.
The number of ways to select two students from 20 is C(20, 2) = 190.
The number of ways to select two faculty members from 5 is C(5, 2) = 10.
The total number of ways to form a committee of 4 from 25 volunteers is C(25, 4) = 12,650.
So the probability is (190 * 10) / 12,650 = 1900 / 12,650 = 0.15, or 15%
b. One faculty member and three students:
Similarly, the number of ways to select one faculty member from 5 is C(5, 1) = 5, and the number of ways to select three students from 20 is C(20, 3) = 1,140.
The total number of ways to form a committee of 4 from 25 volunteers is still C(25, 4) = 12,650.
So the probability is (5 * 1,140) / 12,650 = 5,700 / 12,650 = 0.45, or 45%
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Factor the polynomial. 54c 3d 4 + 9c 4d 2 A. 9c 3d 2(d 2 + 6c) B. 9c 3d 2(6d 2 + c) C. 9c 4d 2(d 2 + 6) D. 9c 4d 2(6d 2 + 1)
Alexander has 418 song on his mp3 player. he divides the songs into 11 equal groups. about how many songs are in each group
What form of a quadratic function would be graphed if the vertex at the same point as the y-intercept?