Answer:
a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))
We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.
P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)
b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)
We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.
Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)
Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.
given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). output each floating-point value with two digits after the decimal point, which can be achieved as follows: print(f'{your value1:.2f} {your value2:.2f} {your value3:.2f} {your value4:.2f}')
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
Given three floating-point numbers x, y, and z, the output would be x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). The formula for each output is as follows:
x to the power of z: x^z
x to the power of (y to the power of z): x^(y^z)
The absolute value of (x minus y): |x-y|
The square root of (x to the power of z): √(x^z)
For example, if x = 2.00, y = 4.00, and z = 3.00, then the output would be: 8.00 4096.00 2.00 4.00
The calculation for each output is as follows:
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
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subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after 6 months, the numbers of respiratory tract infections each group had were compared.
Comparison of two randomly assigned groups is given by :
a. Given study is classified in experimental based.
b. Treatment group is represented by herb.
c. The independent variable is given by Placebo
d. The dependent variable represented by the Infection on respiratory tract .
e. Goal of the study is the comparison of two groups herb and the placebo.
Number of randomly assigned group = 2
One group is herb.
Second group is placebo.
a. Two different types of groups given so the study is experimental based.
b. Treatment group is represented by the group one herb.
c. Independent variable is represented by the group two placebo it does not dependent on herb treatment.
d. Dependent variable is represented by the infection on respiratory tract.
e. Goal of the study is given by the comparison of number of respiratory tract infection in each group.
Therefore, the answer of the following question based on the randomly assigned two groups is given by :
a. Study is experimental based.
b. Herb treatment.
c. Placebo represents the independent variable.
d. Infection represents the dependent variable.
e. Goal of the study is doing the comparison of two groups.
The above question is incomplete, the complete question is :
Subjects were randomly assigned to two groups. One group was given an herb and the other group a placebo. After 6 months the numbers of respiratory tract infections each group had were compared
a) Classify this study (circle the answer): experimental OR observational
b) Identify the treatment group:
c) Identify the independent variable_
d) Identify the dependent variable
e) What is the goal of this study?
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Suppose you have 6 homework assignments to complete one night.
In how many different orders can you complete all of the assignments
There are a total of 6 homework assignments that need to be completed one night. The number of ways to arrange n items in a specific order is n! (n factorial).
How many different orders can you complete all of the assignments?Therefore, for 6 homework assignments, the number of different orders in which they can be completed is 6! = 720.
This means that there are 720 different ways in which you can complete these 6 assignments on one night. Each permutation represents a unique order in which the assignments can be completed, such as starting with assignment 1, then 2, then 3, and so on, or starting with assignment 4, then 5, then 6, and then 1, and so on.
It is worth noting that this formula is only applicable when the order of the assignments matters. If the order of the assignments does not matter, then we would use the formula for combinations, which is n! / (r!(n-r)!).
Multiplying all of these options together results in 6 x 5 x 4 x 3 x 2 x 1 = 720 possible ways to complete the assignments in a different order. This is known as the permutation formula, which states that the number of ways to arrange n items in a specific order is n! (n factorial).
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A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. What are the appropriate hypotheses for this test?
H0: p = 0.28 versus Ha: p < 0.28, where p = the proportion of all high school students who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p > 0.28, where p = the proportion of all high school students who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p < 0.28, where p = the proportion of high school students in the sample who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p > 0.28, where p = the proportion of high school students in the sample who work a part-time job during the school year.
It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The student tests the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met. The standardized test statistic is z = –0.80 and the P-value is 0.2119. What conclusion should the student make using the α = 0.10 significance level?
Because the test statistic is less than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the test statistic is less than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
The student is investigating whether the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
To test this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student will use the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met, as the sample size is large enough (n = 100) and the sample is randomly selected. The standardized test statistic can be calculated as z = (P - p)/(σ/√n) = (0.46 - 0.50)/(√(0.50*0.50/100)) = -0.80. The P-value can be calculated as P(z ≤ -0.80) = 0.2119. Since the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
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review the select balance sheet and income statement for apple, inc. (found in the 10-k). for the account assigned to you (see below on assignments), identify assertions that you think are relevant for the assigned accounts.
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Account Assigned: Trade and other receivables
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Existence assertion means that the receivables must exist and they must be recorded in the books of Apple Inc. Rights and obligations assertion means that the receivables must be legally enforceable, and Apple Inc. must have the right to receive the payment from its customers. Completeness assertion means that all the receivables must be recorded in the books of Apple Inc. Valuation assertion means that the receivables must be recorded in Apple Inc.’s financial statements at the correct amount. Valuation can be measured by calculating the amount of receivables as a percentage of total revenue. For example, if the total revenue is $100 million and the total receivables are $20 million, then the receivables are 20% of total revenue.
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piece of material measures 38 inches Courtney cuts the piece of material into two pieces one piece measures 19 inches write an addition equation that could be used to find the length of the other piece of material
An addition equation that could be used to find the length of the other piece of material is,
38 = 19 + x.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
A piece of material measures 38 inches.
Courtney cuts the piece of material into two pieces.
One piece measures 19 inches.
Let x be the length of other pieces.
An addition equation that could be used to find the length of the other piece of material is,
38 = 19 + x
Therefore, 19 + x = 38 is an addition equation.
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Is y = 1 over 4 x 0.5 a power function? Explain your reasoning.
The function y = 1 over 4 x 0.5 is not a power function
What is a function?A function can be described as a rule, equation or expression that tends to explain the relationship between two variables.
These variables are;
The independent variableThe dependent variableThe types of functions are;
Into – functionPolynomial functionLinear FunctionIdentical FunctionQuadratic FunctionPower functionA power function is a function single that has a term that is product of a real number, a coefficient, and a variable raised to an exponent.
Hence, y = 1/4 × 0.5 is not a power function.
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What is the slope of the given line?
Answer:
2
- ------
3
Step-by-step explanation:
The equation of slope is m = (y2-y1)/(x2-x1)
You can find it by finding two random points on the line. I'll use (3, -2) and (-3, 2)
Note: The line is going downwards, so the answer should be negative.
So plugging those two points into the equation...
(2-(-2))/(-3-3)
Simplifying this we get (2+2)/(-3-3)
(4)/(-6)
If we divide both sides by 2, we get our final simplified answer of. 2/-3, also known as -2/3
if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is
we have distance from focus to its vertex =p, then distance between focus to directrix = p + p=2p
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.
Since the distance between the vertex and the focus is the same as the distance between vertex to directrix,
So, we have distance from focus to its vertex =p
then distance between focus to directrix = p + p=2p
The complete question is:-
if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is equal to?
(a) p (b) 2p (c) p+1 (d) p/2.
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factor $(x^2 y^2-z^2)^2-4x^2y^2$ as the product of four polynomials of degree $1$, each of which has a positive coefficient of $x$.
The four polynomials are all of degree 1 and each has a positive coefficient of x.
Polynomials:
A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
The factorization of the following expression is $(x2 y2 z2)4x2y2. $ is equal to (x2 y2 z2 2xy) (x2 y2 z2 + 2xy).
It is possible to factor the first factor further into $(x2 y2 z2 2-2xy) = (xy-z)(x2y+xyz+z2)$.
The second factor can be factored into the equation $(x2 y2 z2 + 2xy) = (xy+z)(x2 y-xyz+z2)
$
As a result, the original expression can be factored as $(x2 + y2 + z2).
2-4x2y = (xy-z)(xy+z)(xy+z)(xy-z)(xy+z)(xy-z)(xy-z)(xy-z)(xyz+z)$
Each of the four polynomials has a positive coefficient of x and is of degree 1.
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dont ignore please :( i need help
Answer:5
Step-by-step explanation:
HELP MATH THIGNY PLSSS
Answer:
Step-by-step explanation:
Your slope would be -1/4 because it is rise over run meaning your y-axis over your x-axis. I am not sure exactly what your question is needing but I hope that helps in some way.
what is the y intercept
x y
34 -52
51 -65
68 -78
Answer:
y- intercept = - 26
Step-by-step explanation:
to find the y- intercept, obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (34, - 52) and (x₂, y₂ ) = (68, - 78) ← 2 ordered pairs from the table
m = [tex]\frac{-78-(-52)}{68-34}[/tex] = [tex]\frac{-78+52}{34}[/tex] = [tex]\frac{-26}{34}[/tex] = - [tex]\frac{13}{17}[/tex] , then
y = - [tex]\frac{13}{17}[/tex] x + c
to find c substitute any of the ordered pairs into the equation and solve for c
using (51, - 65 ) , then
- 65 = - [tex]\frac{13}{17}[/tex] (51) + c = - 39 + c ( add 39 to both sides )
- 26 = c
then y- intercept = - 26
Which graph shows the new image of the rectangle after a translation of two units up?
The graph that shows the new image after a translation of two units up is:
The fourth graph.
(which is the third graph if we consider that the first is the original image).
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For this problem, we have a translation two units up, meaning that the x-coordinates of the figure remain constant, while two is added to each of the y-coordinates.
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What is the average speed of the car during the first two hours of the trip? (2 p
O0 miles/hour
20 miles/hour
O40 miles/hour
80 miles/hour
Answer:
20
Step-by-step explanation:
first hour 40mph
second hr 0
so average = 20
$40$ is $120\%$ of what number?
The questions are in the image
The sampling method used was random sampling.
What was the sampling method used?This sample may not be representative of the entire class as it does not consider the individual characteristics of the students and only takes into account the row that they are seated on.
Additionally, there is a potential for bias as the sample size is quite small and may not accurately reflect the overall population. Therefore, it would be beneficial to use a larger sample size or use a stratified random sampling method to ensure a representative sample.
The sampling method used was random sampling.
This sample is likely to be representative, as it was chosen randomly and evenly from the seating chart. However, there could be potential issues if the student's Exam 1 scores are not evenly distributed among the rows.
For example, if all the higher scores are concentrated in one row, then the sample may not be representative of the entire class. To ensure an accurate estimation of the average Exam 1 score for the entire class, it may be better to use stratified sampling, where each row is given equal weight and students are selected from each row with the same probability.
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Find the answer for "X"
Answer:
(x, y) = (2, 5)
Step-by-step explanation:
You want to solve the system of equations ...
y = 2x +1x = 12 -2ySolutionSubstituting for y, we have ...
x = 12 -2(2x +1)
x = 12 -4x -2 . . . . . eliminate parentheses
5x = 10 . . . . . . add 4x
x = 2 . . . . . . divide by 5
Then the value of y is ...
y = 2(2) +1 = 5
The solution is ...
x = 2y = 5<95141404393>
three girls shared a piece of land. One got x/3y of the land. Another got x/6y of the land. What fraction of the land will the third girl get.
The third girl will recieve a land area equals to the fraction (2y-x)/2y.
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
The fractions are x/3y, x/6y and z(say)
so sum of all the fraction must be 1 so
x/3y + x/6y + z = 1
⇒z = (2y-x)/2y
The third girl recieve a land area equals to (2y-x)/2y.
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write v as a linear combination of u1, u2, and u3, if possible. (enter your answer in terms of u1, u2, and u3. if not possible, enter impossible.
The v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
To find the linear combination of u1, u2, and u3 that equals v, we can use the method of solving a system of linear equations.
The equation for v in terms of u1, u2, and u3 is:
v = a1u1 + a2u2 + a3u3
where a1, a2, and a3 are the coefficients of the linear combination.
Plugging in the given values for v, u1, u2, and u3:
(-1,7,2) = a1(3,2,8) + a2(1,-3,-1) + a3(-2,1,-3)
We can solve this system of equations by equating the corresponding entries of the two vectors:
-1 = 3a1 + a2 - 2a3
7 = 2a1 - 3a2 + a3
2 = 8a1 - a2 - 3a3
We can then use any method to solve the system of equations, such as substitution, elimination or Cramer's rule.
By solving the system of equations we get:
a1 = -(1/9), a2 = (5/3), a3 = -(4/3)
Therefore, v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
It is possible to write v as a linear combination of u1, u2, and u3.
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Tracey makes her muffin recipe with 2 1/2 cups flour, 1 1/4 sugar, and 1 3/4 cups oatmeal. How many more cups of flour and oatmeal does Tracey use than sugar? Explain.
Tracey used 1 1/4 cups more flour and 1/2 cup more oatmeal than sugar.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Tracey makes her muffin recipe with 2 1/2 cups flour, 1 1/4 sugar, and 1 3/4 cups oatmeal.
The number of cups of flour Tracey used than sugar is,
= 2 1/2 - 1 1/4.
= 5/2 - 5/4.
= (10 - 5)/4.
= 5/4.
= 1 1/4 cups of more flour.
The number of cups of oatmeal Tracey used than sugar is,
= 1 3/4 - 1 1/4.
= 7/4 - 5/4.
= 2/4.
= 1/2 cup more oatmeal.
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A student's course grade is based on one midem that counts as 10% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 15% of his final grade. His midterm score is 68, his project score is 95, his homework score is 93, and his final exam score 62. What his overall final score? What letter grade did he eam (A, C, D, or F) Assume that mean of 50 or above is an A, a mean least 80 but less than 90 is a B, and so on.
The overall final score of the student is 86.35 and he got B grade in the exam.
What is Percentage?
Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole.
Let the final score to be 'f'
According to the question :
midterm score = 10% 68 = 6.8
class project score = 25% 95 = 23.75
homework assignment = 50% 93 =46.5
final exam = 15% 62 = 9.3
So, the Overall final score = midterm score + class project score + homework assignment + final exam
= 6.8 + 23.75 + 46.5 + 9.3
= 86.35.
Hence, he got grade 'B' .
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Jasmine has a bucket of $600 to spend on home renovations. She will spend $175 on a new sink and the remainder on countertops. The countertops cost 35 per square foot. What is the maximum number of square feet Jasmine can purchase ?
Answer: 12 square feet
600 - 175 = 425
425 / 35 per square foot = 12.14
The maximum number of square feet Jasmine can purchase is 12, because you can not purchase 0.14 of a square foot.
2. fill in the exclusive and inclusive ranges for the following items. be sure to show your work below. high score low score inclusive range exclusive range 7 6 89 45 34 17 15 2 1 1
The inclusive range includes all numbers from 2 to 89, while the exclusive range includes all numbers from 3 to 88, excluding the two endpoints.
Inclusive Range: Low Score (2) = Low Score (7) + 1 = 7 + 1 = 8
High Score (89) = High Score (45) + 44 = 45 + 44 = 89
Exclusive Range: Low Score (3) = Low Score (7) + 1 = 7 + 1 = 8
High Score (88) = High Score (45) + 44 = 45 + 44 = 89
The inclusive range includes all values within a given set of numbers, including the endpoints. In this case, the low score is 7 and the high score is 45. Adding 1 to the low score gives us a low score of 8, and adding 44 to the high score gives us a high score of 89. This gives us an inclusive range of 8 to 89.
The exclusive range excludes the endpoints, so we add 1 to the low score and subtract 1 from the high score. This gives us a low score of 8 and a high score of 88, giving us an exclusive range of 8 to 88. This means that the range excludes the values of 7 and 89 from the set.
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−3/5×8/6= helpplease
Answer:
-4/5 OR -0.8
Step-by-step explanation:
This problem is very simple but it can be broken down
First we do -3 times 8 and get -24
Then we do 5 times 6 and get 30
We put the first answer over the second which equals
-24/30
This can then be simplified further if we divide both sides by 6
-4/5 as a fraction
-0.8 as a decimal
-80% as a percent
Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+19y=0. separate your answers by commas.
For all values of k for which the function y=sin(kt) satisfies the differential equation y''+19y=0.
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable.
The given differential equation is
y'' + 19 y= 0
The following function satisfy the differential equation
y = sin(kt)
Differentiating twice with respect to t,
y'' = - k^2 sin(kt)
Putting the value in differential equation given above, we get
- k^2 sin(kt) + 19 sin(kt) = 0
k^2 = 19 ⇒ k = +/- sqrt(19).
points to know
(sin(at))'=acos(at)
and (cos(at))'=-asin(at)
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The terms power and exponent are used interchangeably
True or False?
True, the terms power and exponent have the same meaning.
Please help me with this!!
Answer:
0.084
Step-by-step explanation:
Decimal form:[tex]\sf Thousandth = \dfrac{1}{1000}\\\\\\[/tex]
[tex]\sf Eighty \ four \ thousandth = 84 * \dfrac{1}{1000}=\dfrac{84}{1000}\\[/tex]
= 0.084
The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by overbar(C)(x), is found by dividing C(x) by x. Find (x→9000) is under (lim)overbar(C)(x).
The average cost per tape is 10.
What is average cost?The average cost is the ratio of the total of cost of all the products to the total number of products. We can calculate the average cost by dividing the total cost by the total output quantity.
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. lim x →9000 C (x)
C (x) = 9000 + 9x
x
= 9000 + 9
x
Lim n→ 9000 C (x) = 9000 +9
9000
= 1 + 9
= 10
So, the average cost per tape is 10
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Let us choose some number t and consider a point A(2t+3,24t+1).Prove that all such points make a line.What is the slope and the y intercept of this line?
The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.
How to analyze and interpret parametric functions
Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:
y = f(x)
The rectangular form of the function is a line if and only if the resulting expression is of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableFirst, write the components of the parametric functions:
x = 2 · t + 3
y = 24 · t + 1
Second, clear variable t in each parametric expression:
t = (x - 3) / 2
t = (y - 1) / 24
Third, eliminate parameter t by transitive property:
(x - 3) / 2 = (y - 1) / 24
Fourth, obtain the equation of the line:
24 · (x - 3) = 2 · (y - 1)
24 · x - 72 = 2 · y - 2
24 · x - 70 = 2 · y
y = 12 · x - 35
Fifth, determine the slope and intercept of the equation of the line:
m = 12, b = - 35
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