(A) The global optimal solution is x = -π/2 and the local optimal solutions are x = (2n + 1)π/2
(B) The global optimal solution is x = (2n + 1)π/2
(C) the global optimal solution is x = (2n + 1)π/2
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
For the first problem:
(a) f(x) = sin x and X = [0, 3π]
The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.
The feasible set X = [0, 3π] contains all the local and global minima of f(x) = sin x, so the global optimal solution is x = -π/2 and the local optimal solutions are x = (2n + 1)π/2, where n is an integer.
For the second problem:
(b) f(x) = sin x and X = [1, 4π]
The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.
The feasible set X = [1, 4π] only contains some of the local minima of f(x) = sin x, so the global optimal solution is x = (2n + 1)π/2 where (2n + 1)π/2 is in the feasible set X and sin x is at its minimum.
For the third problem:
(c) f(x) = sin x and X = [-π/4, (11/4)π]
The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.
The feasible set X = [-π/4, (11/4)π] only contains some of the local minima of f(x) = sin x, so the global optimal solution is x = (2n + 1)π/2 where (2n + 1)π/2 is in the feasible set X and sin x is at its minimum.
For the fourth problem:
(d) f(x) = max(0, a,2-1) and X = (-00,00); and X = 10, (2/3) ; 0, If x = 0;
The objective function f(x) = max(0, a,2-1) has a global minimum at x = 0, where the function is 0. The function also has a local minimum at x = (2/3) where the function is (2/3)^2-1.
The feasible set X = (-00,00); and X = 10, (2/3) ; 0, If x = 0; only contains some of the local minima of f(x) = max(0, a,2-1), so the global optimal solution is x = (2/3) if (2/3) is in the feasible set X and the function is at its minimum, or x = 0 if 0 is in the feasible set X and the function is at its minimum.
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Can someone tell me how i find this problem?
Answer:
9.80
Step-by-step explanation:
x²=14²-10² = 196-100 = 96
x=√96 = √(16*6 ) = 4*√6 =4*2.45=9.80
I need help with this problem
Using Trigonometric identities, On the interval 0 2, we wish to locate all solutions to the equation 2sin() = 3. The sole answer is = 1.05.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
what is the solutions of 2sin(θ)=−√3 on the interval 0≤θ 2π?Determining the answer to the following equation is therefore important: 2sin(θ) = √3
To begin, split both sides by two to obtain:
sin(θ) = (√3)/2
Now consider the behavior of the inverse sine function:
Asin(x) = sin(x) and Asin(x) = x
We can therefore apply this to both sides to obtain:
Asin(sin(s)) = Asin(sin(s))/3)
θ = Asin((√3)/2) = 1.05
The single solution in the interval is: because we know that the sine function's period is 2 and that there is only one solution on the range between 0 and 2:
θ = 1.05
sin(3θ) = √3/2
θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3
We obtain = /9, 2/9 if k = 0.
We obtain = 7/9 and 8/9 if k = 1.
We obtain = 13/9 and 14/9 if k = 2.
Other values of k produce values of beyond the range [0, 2].
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As shown above, a classic deck of cards is made up of 52 cards. Suppose ne card is selected at random and
calculate the following probabilities.
Round solutions to three decimal places, if necessary.
The probability that a 8 of Diamonds is selected is
The probability that a Heart or Spade is selected is
The probability that a number smaller than 7 (counting the ace as a 1) is selected is
Step-by-step explanation:
a probability is always the ratio of
desired cases / totally possible cases
in our case, where we pull one card out of 52, the totally possible cases are, of course, 52.
now, we need to find the number of desired cases.
8 of diamonds is pulled.
well, that is one specific card. no other card matches this criteria. so, the probability is
1/52 = 0.019230769... ≈ 0.019
heart or spade is selected.
we have 13 cards of heart.
we have 13 cards of spades.
there is no overlap, so, together they are 26.
the probably is then
26/52 = 1/2 = 0.5
number smaller than 7 is pulled.
"smaller than 7" means 1..6.
that means 6 cards of each of the 4 suits = 24 cards.
the probability is then
24/52 = 6/13 = 0.461538462... ≈ 0.462
out of 200 bolts, 5 are defective. determine the probability that a randomly selected sample (without replacement) of size 10 will have no defective bolts. compare the results for hypergeometric distribution and its binomial approximation
The Hypergeometric distribution is 0.7717, and the binomial distribution is 0.7763. The probability from the binomial approximation is greater than the probability from hypergeometric distribution.
What is Hypergeometric distribution?In statistics, a hypergeometric distribution is a distribution function in which members of two groups are chosen from without being replaced. The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution. As a result, it is frequently used in random sampling to ensure statistical quality.
Given that,
The number of defective bolts are 5 out of 200.
Thus, the probability of 0 defective bolts is given as:
1. Hypergeometric distribution:
P (X= 0) = 5C 0 (195C 10) / (200C 10)
= 0.7717
2. Binomial approximation:
B(n, m/ N)
P (X= 0) = 10C 0 (0.025)^0 (1-0.025)^10
= 0.7763
Thus, probability from the binomial approximation is greater than the probability from hypergeometric distribution.
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using separation of variable method solve dy/dx=(1-x)(1-y)
Answer:
[tex]y=1-Ae^{\frac{1}{2}x^2-x}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{\text{d}y}{\text{d}x}=(1-x)(1-y)[/tex]
Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:
[tex]\implies \dfrac{1}{(1-y)}\;\text{d}y=(1-x)\;\text{d}x[/tex]
Integrate both sides of the equation separately:
[tex]\implies \displaystyle \int \dfrac{1}{(1-y)}\;\text{d}y= \int (1-x)\;\text{d}x[/tex]
[tex]\implies -\ln |1-y|+C=x-\dfrac{1}{2}x^2+D[/tex]
[tex]\implies \ln |1-y|-C=\dfrac{1}{2}x^2-x-D[/tex]
Write the two constants as one (a = -D + C):
[tex]\implies \ln |1-y|=\dfrac{1}{2}x^2-x+a[/tex]
Take exponents of both sides:
[tex]\implies e^{\ln |1-y|}=e^{\frac{1}{2}x^2-x++a}[/tex]
[tex]\textsf{As }\; e^{\ln y}=y:[/tex]
[tex]\implies 1-y=e^{\frac{1}{2}x^2-x+a}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies 1-y=e^{\frac{1}{2}x^2-x}e^{a}[/tex]
As [tex]e^{a}[/tex] is just a constant, replace it with A:
[tex]\implies 1-y=Ae^{\frac{1}{2}x^2-x}[/tex]
Rearrange to make y the subject:
[tex]\implies y=1-Ae^{\frac{1}{2}x^2-x}[/tex]
What are the benefits and limitations of quadratic models in real-world applications such as bridge design?
The benefits and limitations of quadratic models in real-world applications such as bridge design are listed below.
What are the benefits and limitations of quadratic models in real-world applications such as bridge design?Quadratic models are often used in real-world applications, such as bridge design, because of their ability to describe complex relationships between variables.
Some benefits of using quadratic models in these applications include:
1. Flexibility: Quadratic models are more flexible than linear models and can better capture non-linear relationships between variables.
2. Accuracy: Quadratic models can provide a more accurate representation of the data compared to linear models, especially when the data exhibits a curved trend.
3. Prediction: Quadratic models can be used to make predictions about the future based on past data. For example, they can be used to predict the load-bearing capacity of a bridge over time.
However, there are also some limitations of using quadratic models in real-world applications such as bridge design:
1. Overfitting: Quadratic models have the potential to overfit the data, leading to poor generalization to new data. This can result in an overly complex model that does not accurately represent the underlying relationships in the data.
2. Computational complexity: Quadratic models can be computationally more complex than linear models and require more advanced optimization techniques to solve.
3. Interpretation: Quadratic models can be difficult to interpret, making it challenging to understand the underlying relationships between variables.
4. Unpredictable behavior: Quadratic models can exhibit unpredictable behavior for certain input values, which may not be suitable for certain applications such as bridge design where the model must be reliable and predictable.
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two cards are chosen at random from a deck of 52 what is the probability that they have the same value? Answe choice a1/17. b.3/17 c.5/17 d.7/17
The probability will be 1/17 i.e. A.
What exactly is probability?
Probability expresses the likelihood of an event. This mathematical branch of study is concerned with the occurrence of a random event. The value ranges from zero to one. Probability is used in mathematics to anticipate the possibility that events will occur.
Probability refers to the possibility of something happening. This fundamental idea in probability theory is also used by the probability distribution. Before determining the chance of a certain event occurring, we must first determine the total number of possibilities.
The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.
Now,
Total cards =52
No. of ways to select 2 cards=52C₂
=52*51*50!/50!*2!=51*26
Now to select two cards with same values we have no. of ways =13*6
so probability that two cards are chosen at random from a deck of 52 and they have the same value=13*6/26*51=3/51=1/17
Hence,
The probability will be 1/17.
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Graph the equation −3x+5y=7 by plotting points using the line tool.
A graph of the linear equation -3x + 5y = 7 in slope-intercept form is shown in the image attached below.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate respectively.
Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph:
-3x + 5y = 7
5y = 3x + 7
y = 3x/5 + 7/5
Lastly, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
In conclusion, the slope of this linear equation is equal to 3/5 and it does not represent a proportional relationship.
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The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in
second, how far will fall in 3 seconds? How long will it take an object to fall 400 feet?
Answer:
144 feet
5 seconds
Step-by-step explanation:
A directly proportional distance between s and t can be written as
s ∝ t²
or in equation form
s(t) = k · t²
k = constant of proportionality
Given s = 16 feet for t = 1 second we get
16 = k (1)²
or
k = 16
and the equation is s(t) = 16t²
In 3 seconds the object will fall
s(3) = 16 (3)²
= 16 x 9
= 144
s(3) = 144
To find time taken to fall 400 feet, substitute for s s(t) = 400
400 = 16t²
16t² = 400
t² = 400/16 = 25
t = ± √25 = ± 5 seconds
Since time is non-negatiive,
t = 5 seconds
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
c) Find the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less.
The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of x = 53.68 cm
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 53.68 - 49.9 ) / 3.74
z = 1.0107
Now ,the p value from the z table is
P ( x < 53.68 ) = 0.84392
And , the probability is P ( x < 53.68 ) = 84.392 %
Hence , the probability is 84.392 %
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O
x (x² - x - 6) = 0
Answer:
The equation has 3 solutions x(1) = -2 x(2) = 0 x(3) = 3
Step-by-step explanation:
1.When the product of the factor equals 0, atleast one of the factors is 0
x=0
x^2 - x - 6 = 0
2.solve the equation for x
x = 0
x = -2
x = 3
hope this helped :D
Show that if f is a function from S to T, where S and T are finite sets with |S| > |T|, then there are elements s1 and s2 in S such that f(s1) = f(s2), or in other words, f is not one-to-one.
Hence proved f is not one-to-one.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value.
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.
Suppose that f is a function from S to T, where |S| > |T|. This means that there are more elements in S than there are in T.
Since f maps elements of S to elements of T, we can think of f as pairing elements of S with elements of T. However, since |S| > |T|, there will be at least two elements of S that are paired with the same element of T, and these two elements are s1 and s2.
Therefore, f is not one-to-one, as f(s1) = f(s2), meaning that two different elements of S are mapped to the same element of T.
This shows that if f is a function from S to T, where |S| > |T|, then there must exist elements s1 and s2 in S such that f(s1) = f(s2), and hence f is not one-to-one.
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Fill The Blank !!Maya's math teacher said that each question answered correctly on a test would be worth 5 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test. The independent variable,x,represents the _____ ,and the dependent variable is the _____because the ______depends on the _____A function relating these variables isR(X)=___So R(14)= ____ , meaning 14 ________________________________
The independent variable, x, represents the number of questions Maya answered correctly, and the dependent variable is the score, because the score depends on the number of questions Maya answered correctly. A function relating these variables is R(x) = [5x].
So R(14) = [70], meaning 14 correct answers will give a score of 70.
What is a variable?
In mathematics, a variable is referred to as the alphanumeric symbol used to represent a number or numerical value. An unknown quantity is represented as a variable in algebraic equations.
The variables can be divided into two groups, including dependent variable and independent variable.
We are given that each question answered correctly on a test would be worth 5 points.
So, the dependent variable is the score as it depends on the number of questions Maya answered correctly.
The independent variable is the number of questions Maya answered correctly.
From this, we get the function as R(x) = [5x].
Substituting 14 in place of x, we get
R(14) = [70]
This means that 14 correct answers will give a score of 70.
Hence, the independent variable, x, represents the number of questions Maya answered correctly, and the dependent variable is the score, because the score depends on the number of questions Maya answered correctly.
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Surface area of 15 yd
Surface area is, [tex]225\pi (yd^{2})[/tex] or [tex]706.86(yd^{2})[/tex] .
Step-by-step explanation:1. Identify the shape of the surface area of which we need to calcuiate the area.As we may see in the image, the surface area has the shape of a circle.
2. Recall the area formula for circles.Formula: [tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
3. Identify the given data.As we can see in the image, the radius of this circle is 15 yd (yards).
4. Use the data and calculate with the formula.[tex]A=\pi (15yd)^{2}\\ \\A=225\pi (yd^{2}) =706.86(yd^{2})[/tex]
5. Conclude.Surface area is, [tex]225\pi (yd^{2})[/tex] or [tex]706.86(yd^{2})[/tex] (706.86 square yards).
Write an equation that is perpendicular to
y
=
−
6
x
+
3
y=−6x+3 and goes through the point
(
12
,
10
)
(12,10).
The equation of the required perpendicular line is 6y = x - 48
With an example, define perpendicular line?
Lines at right angles to one another are referred to as perpendicular lines (90 degrees). A parallel line is shown as "||," which stands for the symbol. Perpendicular lines are denoted with the symbol "". Illustration of parallel lines The opposite sides of a rectangle.
equation = y =−6x+3
m₁ = -6
Let's consider the slope of the line perpendicular to the given line as m₂
m₁ * m₂ = -1
-6 * m₂ = -1
m₂ = 1/6
The equation of the line perpendicular to the given line and passing through the point (12,10)
y - y₁ = m (x - x₁ )
y - 10 = 1/6( x - 12 )
6( y - 10 ) = (x- 12 )
6y - 60 = x - 12
6y = x - 12 + 60
6y = x - 48
Thus, the equation of the required line is 6y = x - 48
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True or False?. Pie graphs are best with progression of amounts over time, whereas line graphs are better in showing parts of a whole or percentages.
Answer:
false
Step-by-step explanation:
Microeconomics
A firm producing leather shoes has a production function given below: = 2√ , in the short run, the firm's amount of capital equipment is fixed at = 100. The interest rate for K is $1 and the wage rate for L is$4. Based on this:
A. Calculate the firm’s short-run total cost curve and calculate the short-run average cost curve function
B. What is the firm’s short-run marginal cost function? Determine the Short-run Total cost (), short-run Average cost (), and short-run marginal cost () at twenty-five (25) and two hundred (200) levels of output.
C. Draw a graph for (, and )
D. Where does the curve intersect the curve? Explain why the curve always intersects the SAC curve at its lowest or minimum points
A. The firm's short-run total cost (TC) is given by TC = rK + wL, where r is the interest rate for capital and w is the wage rate for labor.
B. The short-run total cost at 25 units of output: TC = $100 + 4((25/2)^2) = $100 + 100 = $200
The short-run total cost at 200 units of output: TC = $100 + 4((200/2)^2) = $100 + 1600 = $1700
Please let's go ahead with the explanation to fully understand the solution,
How the solution was obtainedA. To calculate the firm's short-run total cost curve and average cost curve function, we need to know the amount of labor (L) the firm uses at each level of output (Q). We can use the production function to find the optimal combination of L and Q given the fixed amount of capital (K = 100).
The firm's short-run total cost (TC) is given by TC = rK + wL, where r is the interest rate for capital and w is the wage rate for labor.
The short-run average cost (SAC) can be calculated by dividing the short-run total cost by the level of output (Q): SAC = TC/Q
B. The short-run marginal cost (SMC) is the change in the total cost per unit change in the level of output. The SMC can be calculated as the derivative of the short-run total cost function with respect to Q.
At a level of output of 25, we have: TC = $100 + 4L, and Q = 2√L. So we can substitute L = (Q/2)^2 into the short-run total cost equation to find the short-run total cost at 25 units of output: TC = $100 + 4((25/2)^2) = $100 + 100 = $200
At a level of output of 200, we have: TC = $100 + 4L, and Q = 2√L. So we can substitute L = (Q/2)^2 into the short-run total cost equation to find the short-run total cost at 200 units of output: TC = $100 + 4((200/2)^2) = $100 + 1600 = $1700
The short-run average cost at 25 units of output is SAC = TC/Q = $200/25 = $8, and the short-run average cost at 200 units of output is SAC = TC/Q = $1700/200 = $8.5
The short-run marginal cost at 25 units of output is the derivative of the short-run total cost with respect to Q evaluated at 25 units of output. Since the short-run total cost is linear in Q, the short-run marginal cost is constant and equal to the wage rate, which is $4. The short-run marginal cost at 200 units of output is also constant and equal to $4.
C. A graph of the short-run total cost, short-run average cost, and short-run marginal cost functions can be plotted on the same graph, with Q on the x-axis and the corresponding cost on the y-axis.
D. The short-run average cost curve intersects the short-run marginal cost curve at the minimum point of the short-run average cost curve. This is because the short-run average cost is the derivative of the short-run total cost with respect to Q, and the short-run marginal cost is the derivative of the short-run total cost with respect to Q. At the minimum point of the short-run average cost curve, the first derivative (the short-run marginal cost) is equal to zero, and the second derivative (the short-run average cost) is negative.
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Solve the following system using the elimination method. Enter your answer as an ordered form (x,y) if there is one unique solution. Enter all is there are infinite solutions and enter none if there are none.
The elimination method involves adding or subtracting the two equations to cancel out one of the variables and obtain a single equation in one variable. We can then solve for that variable, and then use the original equations to find the other variable.
What does "system of equations" mean?
simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Here's the work for the given system of equations:
7x - 2y = 35
4x + 5y = -23
Multiplying the second equation by 2:
8x + 10y = -46
Adding the two equations to eliminate x:
15y = -11
Dividing both sides by 15 to solve for y:
y = -11/15
Using the first equation to find x:
7x - 2(-11/15) = 35
Expanding and solving for x:
7x + 22/15 = 35
Subtracting 22/15 from both sides:
7x = 35 - 22/15
Simplifying the right side:
7x = 35 - 22/15
7x = 77/15
Dividing both sides by 7 to solve for x:
x = 11/15
The solution to the system is (x,y) = (11/15, -11/15).
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A sine function has the following key features:
Period =12
Amplitude=4
Midline:y=1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the grapn closest to the first point.
Please show me on a graph how to do this.
Compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varied quantities and other variables.
Here, we have
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the middle line.
Period: 2π because the sine function repeats every 2π unit.
y-intercept: (0,0) because sin(0) = 0.
Now look at how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, because the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => C = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, this is the function searched
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line, and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
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i need help with test statistic and p value
The p=value of this sample is p = 0.076
What is meant by p-value?You should understand that the p value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true.
P values are used in hypothesis testing to help decide whether to reject the null hypothesis. The smaller the p value, the more likely you are to reject the null hypothesis.
This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 73.8
For the alternative hypothesis,
µ ≠ 73.8
Since the number of samples is small and no population standard deviation is given, the distribution is a student's true
Since n = 59,
Degrees of freedom, df = n - 1 = 59 - 1 = 58
t = (x - µ)/(s/√n)
Where
x = sample mean = 76.6
µ = population mean = 73.8
s = samples standard deviation = 8.6
t = (76.6 - 73.8)/(8.6/√58) = 2.8/1.13= 2.4779
We would determine the p-value using the t-test calculator. It becomes
p = 2.4779
Since alpha, 0.01 < than the p-value, 2.4779, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 73.8
Therefore, this p-value leads to a decision to accept the null hypothesis
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Mrs. Farley made 24 meat patties out of 72 ounces of hamburgers. How many ounces of hamburgers are in each meat patty?
Answer: Each meat patty would have 72 ounces of hamburger divided by 24 patties, which is equal to 3 ounces per patty.
Step-by-step explanation:
find a formula for the probability distribution of random variable X representing the outcome when a single die is rolled once
When a singular die is rolled once, the results are represented by the probability distribution P(X = x) = 1/6, 1,2,3,4,5,6 for random variable X.
What are examples and probability?Probability is the potential outcome of any random occurrence. This expression relates to estimating the chance that any certain event will take place. How likely are we to get a head, for example, if we flip the coin into the air? The solution to this question is based on the potential number of occurrences.
When one die is rolled, there are only six possible outcomes: 1, 2, 3, 4, and 5. Due to the equal likelihood of each scenario, its sp risk is 1/6. The following is true for the required posterior distribution of the random variable x:
P(X = x) = 1/6, 1,2,3,4,5,6
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Can someone help a brothra out
It would be A. y = -log x
I did it on desmos the graph website
Find the volume of the figure. Express answers in terms of pi, then round to the nearest whole number.
Answer: V=144π cm³
Step-by-step explanation:
A coin consists of brass and zinc and weighs 2.5 g if 1.75 g of brass are used to make the coin what percent of the coin is made of zinc
Answer:.
Step-by-step explanation:
.
find the vaule of the varibles if the answer is not an integer express it in simplest radical form
Therefore, in this sort of triangle with angles 30-60-90, the value of y is 10√3 and the value of x is 10.
what is variables ?In algebra, a logo (typically a letter) used to represent an undetermined numerical score in a calculation or algebraic expressions. Simply put, a variable is an amount that may have been changed and is not fixed. Categorical and numeric elements are the two main types of variables. Then, discrete and continuous subcategories are made for each category for the categorical and numerical elements, respectively. An overview of various types is given in this section. a metric that has a wide range of values. Someone that can change; a variable's sign; an element of a laboratory test that could vary.
given
As a result, this is a "special triangle." According to the 30-60-90 triangle, if the short leg is x, the hypotenuse will be 2x, and the long leg will be x√3.
Since we have the short leg, we can divide it by 2 to determine the hypotenuse, or y in this case:
20 /2 = 10
Next, divide the short leg by 3 to determine the long leg, or x in our case:
10 × √3 = 10√3
Therefore, in this sort of triangle with angles 30-60-90, the value of y is 10√3 and the value of x is 10.
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The midpoint of AB is at (-2,4). If A=(5,7), find B
B is: (?)
Using the midpoint formula, B is: (-9, 1).
How to Use the Midpoint Formula?The midpoint of a line segment is given by the average of the coordinates of the endpoints. So, the midpoint of AB is (-2,4), and A = (5, 7), we can find B by using the midpoint formula:
M(x, y) = [(x1 + x2)/2, (y1 + y2)/2]
Given:
A(5, 7) = (x1, y1)
B(?, ?) = (x2, y2)
M(x, y)
Plug in the values:
(-2, 4) = [(5 + x2)/2, (7 + y2)/2]
Solve for each coordinates of B:
-2 = (5 + x2)/2
-4 = 5 + x2
-4 - 5 = x2
x2 = -9
4 = (7 + y2)/2
8 = 7 + y2
8 - 7 = y2
y2 = 1
B is: (-9, 1)
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Help please!
Slope of one of the dotted lines:
Slope of the line of reflection:
The slope of one of the dotted lines is equal to 1.
The slope of the line of reflection is equal to -1.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, the slope of one of the dotted lines include the following;
Slope, m = (4 - 1)/(-1 - (-4))
Slope, m = 3/(-1 + 4)
Slope, m = 3/3.
Slope, m = 1.
For the line of reflection, the slope is given by:
Slope, m = (2 - 4)/(1 - (-1))
Slope, m = -2/(1 + 1)
Slope, m = -2/2.
Slope, m = -1.
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write an equation for a line perpendicular to y=3x+2 and passing through the point (-9,6)
y=
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 9, 6 ) into the partial equation
6 = - [tex]\frac{1}{3}[/tex] (- 9) + c = 3 + c ( subtract 3 from both sides )
3 = c
y = - [tex]\frac{1}{3}[/tex] x + 3 ← equation of perpendicular line
find the root of 4x²-12x+9=0 graphically taken values of x from -1 to + 4
Answer:
To find the roots of 4x² - 12x + 9 = 0 graphically, we need to plot the equation on a graph and find the x-intercepts, which are the roots.
Here are the steps to graph the equation:
Plot the x-axis and y-axis on the graph
Plot the points (x, 4x² - 12x + 9) for several values of x within the range of -1 to 4.
Connect the points to form a smooth curve.
Find the x-intercepts, where the curve intersects the x-axis. These points represent the roots of the equation.
After finding the x-intercepts, we can use the x-value of each intercept to substitute back into the original equation to find the corresponding y-value. This confirms that the x-intercepts are indeed the roots of the equation.
Note: The above steps can also be done using a graphing calculator or software.