As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.
What are a few selling price examples?The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.
Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:
y' = -12x + 190
By setting y' to zero and figuring out x, we obtain:
-12x + 190 = 0
x = 15.83
The critical value of x is therefore 15.83.
We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:
y'' = -12
The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.
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Find the mean, median, mode, and range of the data set after you perform the given operation on each data value.
9, 7, 12, 13, 9, 3; add 5
mean is average =9+7+12+13+9+3+5÷7=8.29
median is middle term =9
mode is frequented data=9
rang is the difference between maximum and minimum data=13_3=10
Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 37.85
Step-by-step explanation:
Substitute: 3.2x0.2+6.1^2
Calculate the product or quotient: 0.64+6.1^2
Calculate the power: 0.64+37.21
Calculate the sum or difference: 37.85
Answer: 37.85
pls mark brainliest
Which of the following statements is about CD and CE is true? A. CD is longer than CE B. CE is longer than CD C. CD and CE are the same length D. CE is 5 units long
From the given graph, CE is longer than CD.
What is the distance between two coordinates?The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Coordinates of E(8,6)
Coordinates of C(6,1)
Coordinates of D(3,-3)
x=8, y=6
x=6, y=1
x=3, y=-3
Distance CE=√{(8-6)² +(6-1)²} = √29
Distance CD=√{(6-3)² +(1+3)²}= √25=5
Therefore, CE is longer than CD.
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you decide to record the hair colors of people leaving a lecture at your school. what is the probability that the next person who leaves the lecture will have gray hair? express your answer as a simplified fraction or a decimal rounded to four decimal places. counting people blonde red brown black gray 50 40 39 33 43
The probability is a fraction of 43/205 which is approximately 0.2098.
What is the probability that the next person who leaves the lecture will have grey hair?To calculate the probability of the next person who leaves the lecture having gray hair, we need to know the total number of people who left the lecture, as well as the number of people who have gray hair.
From the given data, we can see that there were a total of 50+40+39+33+43 = 205 people who left the lecture. We also know that there were 43 people who had gray hair.
Therefore, the probability of the next person who leaves the lecture having gray hair is:
P(gray hair) = (number of people with gray hair) / (total number of people who left the lecture)
P(gray hair) = 43/205
P(gray hair) ≈ 0.2098
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Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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Please help physics due in 30 mins!!!!
The work done is 3750 Joules on the box.
What is the recipe for work completed?To quantitatively express this concept, the work W is equal to the force f times the distance d, or W = fd. If the force is applied at an angle to the displacement, the work is W = fd cos.t.
The equation W = F * d * cos(theta), where W is the work done, F is the force applied, d is the displacement of the item, and theta is the angle between the force and displacement vectors, can be used to solve this problem.
The force in this instance is 500 N, and the distance is provided as 15 m, and the 60 degree angle between the vectors of force and displacement.
So, by changing these numbers in the equation, we obtain:
W = 500 N x 15 m x cos (60 degrees)
We can simplify this to: Applying the trigonometric identity cos(60 degrees) = 1/2
W = (500 N) * (15 m) * (1/2)
W = 3750 J.
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Express the following in exponential notation: 16384
The exponential notation of 16384 is 2^14
16384 can be expressed in exponential notation as 2^14, where 2 is the base and 14 is the exponent.
In exponential notation, a number is expressed as a base raised to an exponent, where the base is the number being multiplied repeatedly and the exponent represents the number of times the base is multiplied.
In this case, 2 is being multiplied 14 times to arrive at the value of 16384. Exponential notation is a useful way to represent very large or very small numbers in a concise and standardized format, making it easier to work with and compare values across different scales. It is commonly used in scientific and mathematical contexts.
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Please help, due very soon !!
If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11
True. If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
When a two-digit number is reversed, it becomes a new number with the digits swapped, e.g., 12 becomes 21. The difference between the original number and the reversed number is obtained by subtracting one from the other. For example, the difference between 12 and 21 is 9. It can be observed that the difference between any two-digit number and its reverse is always a multiple of 9.
Now, let's consider the three-digit number ABC. When this number is reversed, it becomes CBA. The difference between the two is
(100C + 10B + A) - (100A + 10B + C) = 99(C - A),which is a multiple of 11.
Therefore, if a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
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Complete Question:
If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11. True/ False.
owen already has 3 plants in his backyard, and he can also grow 2 plants with every seed packet he uses. how many seed packets does owen need to have a total of 9 plants in his backyard? write and solve an equation to find the answer.
Answer:
3 seed packets
Step-by-step explanation:
So first, we know that for every 1 seed packet Owen uses, he can grow 2 plants. The ratio is 1:2 (1 = # of seed packets, 2 = # of plants). So now, we need to figure out how many seed packets he needs to have a total of 9 plants. Before we calculate anything, we need to subtract 3 from 9 because it is the total number of plants, and we get 6 plants. To calculate the amount of seed packets Owen needs, we need to get the ration (1:2) and multiply it by 3 on both sides because we need 6 plants. 2 × 3 = 6, and 1 × 3 = 3. The ratio is 3:6. So now we know that Owen needs 3 more seed packets in order to have a total of 9 plants in his backyard. :)
Please help me with my math!!
Answer:
The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.
Since a = -3 < 0, the parabola opens downwards and has a maximum point.
To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:
x = -3
y = -3(-3+3)^2 + 4 = 4
Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.
Hence, the answer is option C
Answer:
C) Maximum point; 4
Step-by-step explanation:
Given parabola:
[tex]y=-3(x+3)^2+4[/tex]
The given parabola is in vertex form:
[tex]\boxed{y = a(x - h)^2 + k}[/tex]
where:
(h, k) is the vertex of the parabola.a is the leading coefficient.By comparing the given equation with the vertex form, we can see that:
a = -3h = -3k = 4As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.
The vertex of the parabola is (h, k) = (-3, 4).
Therefore, the maximum value of y is 4, which occurs at x = -3.
Select all numbers that are solutions to the inequality w < 1
In the case of the inequality w < 1, we found that the set of solutions is (-∞, 1), which represents all real numbers less than 1.
The inequality w < 1 means that w is less than 1. To identify all the numbers that satisfy this inequality, we need to look for values of w that are less than 1.
We can continue this process and substitute different values of w in the inequality w < 1 to find more solutions. For instance, if we substitute w = -1, we get -1 < 1, which is also true.
Therefore, -1 is a solution to the inequality w < 1. However, if we substitute w = 2, we get 2 < 1, which is false. This means that 2 is not a solution to the inequality w < 1.
Therefore, the set of all numbers that are solutions to the inequality w < 1 is the set of all real numbers that are less than 1. We can represent this set using interval notation as (-∞, 1), where (-∞) represents all numbers less than negative infinity and 1 represents the upper bound of the interval.
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commuting times for employees of a local company have a mean of 63.6 minutes and astandard deviation of 2.5 minutes. what does chebyshev's theorem say about thepercentage of employees with commuting times between 58.6 minutes and 68.6 minutes?
According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.
Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
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You ate 4/12 of the pizza your family bought for dinner. Your brother ate 3/12 of the pizza. Which equation represents the fraction of pizza both you and your brother ate?
Answer:
7/12 pizzas have been eaten
Step-by-step explanation:
3 + 4= 7
7/12
7-12=5
5 pizzas left
Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 12. What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
A. -3
B. -1.5
C. 1.5
D. 3
could someone help me with 7 and 8 i don’t really understand this..
By answering the presented question, we may conclude that from the given graph we can say that zeros are = (-3,-1 ) and (--5,-9) ; y - intercept is, y = -2x/3 + 15 and vertex are = (-0-1)
What exactly are graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
from the given graph we can say that
zeros are = (-3,-1 ) and (--5,-9)
y - intercept is, y = -2x/3 + 15
vertex are = (-0-1)
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Solve for x to the nearest tenth.
2
X
4
10
Answer:
x ≈ 8.9
Step-by-step explanation:
using Pythagoras' identity.
the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
consider the right triangle on the left with hypotenuse h , then
h² = 2² + 4² = 4 + 16 = 20 ( take square root of both sides )
h = [tex]\sqrt{20}[/tex]
consider the right triangle on the right , then
x² + h² = 10²
x² + ( [tex]\sqrt{20}[/tex] )² = 10²
x² + 20 = 100 ( subtract 20 from both sides )
x² = 80 ( take square root of both sides )
x = [tex]\sqrt{80}[/tex] ≈ 8.9 ( to the nearest tenth )
The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5
None of the available options match the parabola's equation.
Which might be the parabola's equation?To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.
A parabola's vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the parabola's vertex.
[tex]y = a(x-5)^2 - 3[/tex]
These values are substituted into the equation to produce:
[tex]-15 = a(2-5)^2 - 3[/tex]
[tex]-15 = 9a - 3[/tex]
[tex]-12 = 9a[/tex]
[tex]a = -4/3[/tex]
[tex]y = (-4/3)(x-5)^2 - 3[/tex]
This equation is expanded and simplified to produce:
[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]
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expand and simplify 4(2x-1)+3(2x+5)
Answer:
Step-by-step explanation: 4(2x-1)+3(2x+5)
Expand the expression to eliminate the brackets
8x-4+6x+15.....Expansion
Now simplify by grouping like terms
8x+6x-4+15
8x+6x=14x
-4+15=11
Therefore simplification=14x+11
Here is the question please help
1) With regard to the statistical diagram given:
The total number of women in the group = 180130 women intend to vote for party A.2)
24 Adults chose EnglishYes, an equal number of Adults and children chose Math because the portion of the pie chart that represents the choice of Children and adults are both identical and equal to 1/4 or 25%.What is a statistical diagram?A statistical diagram is a visual representation of data using graphs or charts, typically used to summarize and communicate information about the distribution, relationship, or comparison of variables.
1)
a) To derive the total number of women in the group, we must remove 200 from 380.
That is:
Total women in the group = 380 - 200
= 180 Women.
b) To get women who intend to vote for party A.
We must first derive the total who intend to vote for Party A.
the total who intend to vote for Party A = 380 - 130
= 250
Women who intend to vote for party A = Total who want to vote for Party A - Men who want to vote for Party A.
Women who intend to vote for party A = 250 - 120
= 130
2)
a) Given that 48 adults were evaluated, the the portion of the pie chart that shows their choice of English reads 50%, it means that
Adults who Chose English = 48 * 50%
= 24
b) an equal number of Adults and children chose Math because the portion of the pie chart that represents the choice of Children and adults are both identical and equal to 1/4 or 25%.
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Can someone help me with this
Solving a system of equations we can see that he cost of a corn dog is $1.25 and the cost of the fries is $3.50
How to find the cost of each item?We can define two variables here:
x = cost of a corn dog.
y = cost of the fries.
With the information in the question we can write two equations, these two equations form a system of equations that we can solve, the system of equations is the one below:
2x + 3y = 13
4x + y = 8.50
We can isolate y in the second equation to get:
y = 8.50 - 4x
Replace it in the other one:
2x + 3*(8.5 - 4x) = 13
2x + 25.5 - 12x = 13
-10x = 13 - 25.5
x = -12.5/-10 = 1.25
Then:
y = 8.5 - 4*1.25 = 3.5
The cost of a corn dog is 1.25 dollars and the cost of the fries is 3.50 dollars.
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Translate Into a equation!
The sum of 7 times a number and 6 is 3
Step-by-step explanation:
x is the number.
the equation is
7x + 6 = 3
A shadow 9 feet long is cast by a plum tree that is 12 feet tall. What is the height of a nearby lemon tree that casts a shadow 6 feet long?
The height of the nearby lemon tree is 8 feet using the property of similar triangles.
What are similar triangles?Triangles that are similar to one another in shape but differ in size are called similar triangles. Their respective sides are proportional to one another, and their corresponding angles are equal. The ratio of the corresponding sides of two triangles that are comparable is constant across all pairs of corresponding sides. Problems involving unknown lengths or heights in comparable forms can be resolved using this attribute.
The given situation represent two proportional triangles.
We know that the ratio of lengths of similar triangles are equal thus,
height of plum tree / length of plum tree's shadow = height of lemon tree / length of lemon tree's shadow
Substituting the values we have:
12 / 9 = height of lemon tree / 6
Using cross multiplication:
height of lemon tree = 12 * 6 / 9 = 8 feet
Hence, the height of the nearby lemon tree is 8 feet using the property of similar triangles.
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What is the exact value of the trigonometric expression? State your answer in simplified radical form and include all work.
*Please reference included picture for problem. Thank you!
Answer:
The exact value of the given trigonometric expression is undefined.
Step-by-step explanation:
Given trigonometric expression:
[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]
To find the exact value of the given trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression
The exact value of cos(2π/3) is:
[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]
The exact value of tan(-7π/4) is:
[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]
Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:
[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]
Pizza burger taco shake
Answer:
Is there supposed to be a joke in this?
Answer:
bro what
Step-by-step explanation:
change the denominator of the fraction a+3/6-2a to 2(a^2-9)
The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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A love expert carried out a study to quantify the effect of love songs on emotion. To do so, he used 30 volunteers. He random
Publishers
assigned the 30 volunteers to listen to either a love song or classical music. Then he asked them to draw a heart on a piece of paper. He measured the size of the heart drawn from bottom to top, in inches, for each person. The results are displayed in the stem and leaf plots.
The analysis of the data to obtain the confidence interval of the difference in the means indicates;
99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct options are;
Name of Procedure
Two sample interval for [tex]\bar{x}[/tex]₁ - [tex]\bar{x}[/tex]₂Random
The volunteers are randomly selectedWe have a random sample of 15 subjects who listen to love songsWe have a random sample of 15 subjects who listen to classical music10%
The 10% condition is metNormal/Large Sample
The stemplot of the classical music sample data shows no strong skewness or outliersThe stemplot of the love song music sample data shows no strong skewness or outliers99% CI = (-0.302, 2.301)
Conclude;
We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
What is a confidence interval?A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.
The two-sample t-test can be used to construct the 99% confidence interval as follows;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
Where;
[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups
s₁, and s₂ = The sample standard deviations
n₁ and n₂ = The sample sizes
df = The degrees of freedom
t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2
The data indicates;
n₁ = n₂ = 15
[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63
[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13
Therefore, we get;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)
= 1 ± 2.763 × 0.469
= 1 ± 1.301
The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).
The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct statements, placed in the box are;
Name of Procedure;
Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
Random
The volunteers are randomly selected
The random condition is met
We have a random sample of 15 subjects who listen to a love song
We have a random sample of 15 subjects who listen to classical music
10%
The 10% condition is met
15 < 10% of all subjects like these who listen to love songs
15 < 10% of all subjects like these who listen to classical music
Normal/Large Sample
The Normal/Large condition is met
The stemplot of the classical music sample data shows no strong skewness or outliers
The stemplot of the love song music sample data shows no strong skewness or outliers
Therefore;
99% CI = (-0.301, 2.301)
Conclude;
We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
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Translate the sentence into an equation.
Seven more than the quotient of a number and 4 is equal 5to .
The following equation can be used to represent the sentence:
7 + (x/4) = 5 where x stands for a number.
What is a linear equation?A straight line on a graph is represented by a linear equation. It has a constant slope and y-intercept, one or more variables, typically expressed by x and y. Several different real-world situations can be represented by linear equations, such as estimating the cost of goods based on the quantity purchased or calculating a car's distance traveled based on speed and time. Finding the value of the variable that causes the equation to be true is the first step in solving a linear equation. In mathematics, science, engineering, and economics, linear equations are frequently employed.
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Lesson: 3.03
Buffy and Addy launch their rockets at the same time. The height of Buffy's rocket, in
meters, is given by the function f x=-4.9x²+25x. where x is the number of seconds
after the launch. The height of Addy's rocket, in meters, is given by the function
g x=-4.9x² +16x+15 where x is the number of seconds after the launch. Algebraically
find the moment when the rockets are at the same height, and then use that to
calculate the height. Round to the nearest hundredth.
Answer:
21.93 meters.
Step-by-step explanation:
To find when the rockets are at the same height, we need to set the two functions equal to each other and solve for x:
-4.9x² + 25x = -4.9x² + 16x + 15
Simplifying this equation, we get:
9x = 15
x = 15/9
x ≈ 1.67
Therefore, the rockets are at the same height after approximately 1.67 seconds.
To find the height at which the rockets are at the same height, we can plug this value of x into either of the two functions. Let's use Buffy's function:
f(1.67) = -4.9(1.67)² + 25(1.67)
f(1.67) ≈ 21.93
Therefore, the height at which the rockets are at the same height is approximately 21.93 meters. Rounded to the nearest hundredth, this is 21.93 meters.
PLS HELPPPP
A group of friends go to a basketball game. The function b(x) represents the amount of money spent, where x is the number of friends at the game. Does a possible solution of (4.5, $107.75) make sense for this function? Explain your answer.
• Yes. The input and output are both possible.
• No. The input is not possible.
• No. The output is not possible.
• No. Neither the input nor output is possible.
Part B: During what interval(s) of the domain is the baseball's height staying the same? (2 points)
Your answer
Part C: During what interval(s) of the domain is the baseball's height decreasing the fastest? Use complete sentences to support your answer.
• 6 -x ‹ 8; the slope is the steepest for this interval
• 8-x < 10; the slope is the steepest for this interval
• 6
• 6
Part A: During what interval(s) of the domain is the baseball's height increasing?
Answer:
This is not my own answer it is a copied one.
If h (x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h (x)) Then the pair given is (6.5, $92.25) Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)