Answer:
reflect over line b
counterclockwise rotation about P by 180 degrees
Step-by-step explanation:
reflecting over b will put it in the same place bc b goes down the middle of the rectangle
if you rotate it counterclockwise around p by 180 degrees it would flip it upside down but that doesn't really matter because the length on the top and bottom are equal
Answer:
I would check:
reflect over line b and check
counterclockwise rotation about P by 180 degrees
Step-by-step explanation:
First of all, b is a horizontal line going through the middle. If you reflect across it you will get the same rectangle just backwards but exactly the same position.
If you rotate 180, then you will get the exact same shape just upsides down.
Thanks and please give brainliest have a nice day :)
please answer this for me?
Answer:
n/a
Step-by-step explanation:
how does it feel
A BASKETBALL PLAYER MAKES A BASKET THROUGH A TEN FOOT HIGH BASKET FROM 20 FEET AWAY. IF THE SHOOTER RELEASES THE BALL FROM 8 FEET ABOVE THE GROUND AND THE BALL HAS A HORIZONTAL VELOCITY OF 10 FEET/SECOND. WHAT IS THE VERTICAL VELOCITY OF THE BASKET BALL?
Answer:
The vertical velocity of the ball when released = 10.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s
Step-by-step explanation:
The given parameters are;
The height of the basket = 10 feet
The horizontal location of the shooter from the basket = 20 feet
The height from which the shooter releases the ball = 8 feet
The horizontal velocity of the ball = 10 ft/s
Therefore, we have;
Time, t = Horizontal distance/(Horizontal velocity)
t = 20/10 = 2 seconds
The vertical velocity is given as follows;
s = u·t - 1/2·g·t²
Where;
u = The vertical velocity
s = The height above the initial height from which the ball is released
s = y - y₀
Where;
y = The final height of the ball in the calculation = The height of the basket = 10 foot
y₀ = The initial height from which the ball is released = 8 feet
∴ s = 10 - 8 = 2 feet
g = The acceleration due to gravity = 9.81 m/s²
Substituting gives;
2 = u × 2 - 1/2 × 9.81× 2²
u = (2 + 1/2 × 9.81× 2²)/2 = 10.81 m/s
The vertical velocity of the ball when released = 10.81 m/s.
The vertical velocity of the ball in the basket is given by the following relation;
v² = u² - 2·g·s
v² = 10.81² - 2×9.81×2 = 77.6161
v = √(77.6161) = 8.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s
A selection method is said to have utility when it 0 out of 1 points Which one of the following is the best example of a behavioral (or work sample) question? uestion 3 1 out of 1 points Artificial intelligence (AI) is sometimes used to analyze a candidate's psychological profile to whether it will fit Question 4 0 out of 1 points Laura applies for the position of ambulance medic. To give her a job simulation (behavioral interview) screening test, the interviewer
Question 4: Laura applies for the position of ambulance medic. To give her a job simulation (behavioral interview) screening test, the interviewer...
This question involves providing a job simulation or behavioral interview, which allows the interviewer to observe how the candidate performs in a simulated work situation. This type of question assesses the candidate's skills, abilities, and behavior in a real or simulated work scenario, providing a more accurate evaluation of their capabilities for the job.
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Given (x - 1)2 = 50, select the values of x.
X = -49
x = 51
x= 1+ 5V2
x = 1 - 5V2
Step-by-step explanation:
(x - 1)² = 50
Either x - 1 = +√50 or x - 1 = -√50.
Hence, x = +/-√50 + 1 = +/-(5√2) + 1.
Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in Group of answer choices predicting outcomes. producing data. graphing equations.
Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes.
Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes. This involves comparing the model's predictions with actual observed data or outcomes to assess its accuracy and reliability. By testing the model against real-world data, we can evaluate its validity and determine if it accurately represents the underlying reality or phenomenon being studied.
Producing data and graphing equations are related activities that can be part of the process of testing a model, but they are not the primary purpose of the model itself. Producing data involves collecting and generating empirical data that can be used to assess the model's predictions or outcomes. Graphing equations can be a way to visualize the relationships between variables in the model, but it is not the main purpose of the model itself. The primary purpose of constructing a model is to make predictions or generate hypotheses about how a system or phenomenon works, and testing these predictions against real-world outcomes is the key step in evaluating the model's value.
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a traffic cone, which has a height of 28 inches, a slant height of 29 inches, and the diameter of the base of 14 inches, needs to be painted orange. if the base is not painted, approximately how many square inches needs to be painted orange?
approximately 667.4 square inches of the traffic cone needs to be painted orange.
The traffic cone can be approximated as a frustum of a right circular cone, where the top of the frustum is the opening of the cone and the bottom of the frustum is the base of the cone. The area to be painted is the lateral surface area of the frustum, which can be calculated using the slant height and the generatix.
The generatrix is the distance between the tip of the cone and the edge of the frustum. We can use the Pythagorean theorem to find it:
generatrix = sqrt(slant height^2 - (diameter/2)^2)
generatrix = sqrt(29^2 - (14/2)^2)
generatrix = sqrt(783)
The lateral surface area of the frustum can be calculated using the generatrix and the slant height:
lateral surface area = pi * (generatrix + slant height) * (diameter/2)
lateral surface area = pi * (sqrt(783) + 29) * (14/2)
lateral surface area ≈ 667.4 square inches
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Suppose that the relation H is defined as follows.
H = {(4,4), (2, 0), (-9, 2), (8,-5)}
Give the domain and range of H.
Write your answers using set notation.
The domain and range of H is {4, 2 ,-9, 8} and {4, 0, 2, -5}.
Given:
H = {(4,4), (2, 0), (-9, 2), (8,-5)}
Domain = set of x values or inputs.
x values = {4, 2, -9, 8}
Domain = {4, 2 ,-9, 8}
Domain = -9 ≤ x ≤ 4
Range = set of y values or outputs.
y values = {4, 0, 2, -5}
Range = {4, 0, 2, -5}
Range = -5 ≤ x ≤ 4
Therefore he domain and range of H is {4, 2 ,-9, 8} and {4, 0, 2, -5}.
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A basket contains six apples and five peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit.
The first piece of fruit is an apple and the second piece is a peach. What’s the probability?
Answer:
6/11 * 5/10
3/11 or 0.27 repeating
Step-by-step explanation:
The test scores for the students in Mr. Miller’s math class are shown here.
52, 61, 69, 76, 82, 84, 85, 90, 94
What is the range of the test scores?
The range of the test scores in Mr. Miller's math class is 42.
What is the range?Mathematically, the range refers to the difference between the highest value and the lowest value in a data set.
The range is computed by subtraction of the lowest value from the highest value.
Mr. Miller can use the range to measure the spread or dispersion of the test scores.
Test Scores:
52, 61, 69, 76, 82, 84, 85, 90, 94
Highest score = 94
Lowest score = 52
Range = 42 (94 - 52)
Thus, we can conclude that for the math students in Mr. Miller's class, the range of their test scores is 42.
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Part b
what is the area of the target that earns at least 30 points on a throw?
select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion website. You are given the equation y(t)=2 sin 4 pi t + 5 cos 4pi t, which models the position of the weight, with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form, y(t) = A sin (wt+0).
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
How to find the canonical form of the equation for simple harmonic motion
Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.
The amplitude of the canonical function is determined by the Pythagorean theorem:
A' = √(2² + 5²)
A' = √ 29
The angular frequency C is the constant within the trigonometric functions from the non-canonical formula:
C = 4π
Then, we find the initial position of the weight in time: (t = 0)
y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)
y(0) = 5
And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)
5 = √ 29 · sin (4π · 0 + D)
5 / √ 29 = sin D
D ≈ 0.379π rad
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
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what is the expected number of wins for the month of november? (round your answer to two decimal places.)
the expected number of wins for the month of November is approximately 4.55.
To find the expected number of wins for the month of November, we first need to calculate the mean or expected value of the binomial distribution. We know that the probability of winning any given game is 0.3789, and there are 12 games in November.
Let X be the number of games won in November, then X follows a binomial distribution with parameters n = 12 and p = 0.3789.
The expected value of a binomial distribution is given by E(X) = np, where n is the number of trials and p is the probability of success in each trial. So, in this case, the expected number of wins for the month of November is:
E(X) = np = 12 x 0.3789 = 4.547
This means that, on average, we can expect the hockey team to win about 4 or 5 games in November, based on their historical win rate. However, it's important to note that this is just an average and there is always variability in the number of wins in any given month or season.
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Complete question is:
The probability that a certain hockey team will win any given game is 0.3789based on their 13 year win history of 391 wins out of 1032 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November.
What is the expected number of wins for the month of November? (Round your answer to two decimal places.)
A regular polygon first maps directly onto itself after rotating 10 degrees. How many sides does the polygon have?
Answer:
I think it is 8.
Step-by-step explanation:
But I might be wrong.
Answer:
36 sides
Step-by-step explanation:
360 degrees divided by the number of sides equals the rotation degrees. So in order to have your polygon map itself after rotating 10 degrees, it would have to have 36 sides. 360/36 = 10.
According to the direct instruction, what is the recommended amount of servings for milk or milk products per day?
a.5 cups
b.3 cups
c.1 cup
Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.
What are dairy products ?Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).
The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.
Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.
A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .
After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.
Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.
Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.
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Which of the following tools is used to capture data packets over time(continuously or overnight)?PuTTYTraffic AnalyzerWiresharkNetWitness Investigator
Wireshark is the tool used to capture data packets over time, either continuously or overnight.
Wireshark is a powerful network protocol analyzer that allows you to capture and examine data packets flowing through a network. It provides a comprehensive set of features for capturing, analyzing, and interpreting network traffic.
With Wireshark, you can capture packets from various network interfaces and save them to a capture file for later analysis. It supports capturing packets in real-time, allowing you to monitor network activity as it happens.
Wireshark offers detailed packet-level inspection, allowing you to examine packet headers, payloads, protocols, and other relevant information.
Furthermore, Wireshark supports numerous protocols and provides protocol-specific decoders to interpret and analyze different network protocols. It also offers advanced features like packet coloring, statistical analysis, packet comparison, and the ability to export captured data for further analysis or sharing with others.
Overall, Wireshark is widely used by network administrators, security professionals, and developers to diagnose network issues, troubleshoot problems, analyze network performance, and investigate security incidents by capturing and analyzing data packets over time.
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IGNORE THE NUMBERS IN THE TABLE PLEASE HELP ME GET THE RIGHT NUMBERS AND EQUATIONS !!!!
A school is constructing a rectangular play area against an exterior wall of the school building.
It uses 120 feet of fencing material to enclose three sides of the play area.
school building
(a) Complete the table by giving the length and area for each width. (The width is the side perpendicular to the building)
For a width of 5 feet, the length is 110 feet and the area is 550 square feet, and so on for each width.
Width (ft) Length (ft) Area (sq ft)
5
10
15
20
25
30
To complete the table, we need to find the length and area of the rectangular play area for each width, given that the total length of fencing material available is 120 feet.
Let the width of the play area be w, and let the length of the play area be l. Since the play area is against an exterior wall of the school building, we only need to fence the three remaining sides. Therefore, the total length of fencing material required is:
L = 2w + l
We know that L = 120 feet. Solving for l, we get:
l = 120 - 2w
The area of the rectangular play area is:
A = lw
Substituting l in terms of w, we get:
A = w(120 - 2w)
Simplifying, we get:
A = 120w - 2w^2
Now we can complete the table as follows:
Width (ft) Length (ft) Area (sq ft)
5 110 550
10 100 1000
15 90 1350
20 80 1600
25 70 1750
30 60 1800
Therefore, for a width of 5 feet, the length is 110 feet and the area is 550 square feet, and so on for each width.
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Consider a hypothesis test of difference of means for two independent populations x1 and x2.(a) What does the null hypothesis say about the relationship between the two population means?H0 says that the population means are different.H0 says that the population standard deviations are equal. H0 says that the population means are equal.H0 says that the population standard deviations are different.
H0 says that the population means are equal.
In the context of a hypothesis test for the difference of means between two independent populations (x1 and x2), the null hypothesis (H0) states the following about the relationship between the two population means:
H0 says that the population means are equal.
In other words, the null hypothesis assumes that there is no significant difference between the means of the two populations. The alternative hypothesis would then state that the population means are different. Remember that hypothesis testing is a process to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
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write this number in standard form.
(7 x 100) + (4 x 100 ) + (8 x 1,000)
help asap.
this is a 5th grader problem.
thank you.
worth 50 points!
Answer:
(7 x 100) + (4 x 100 ) + (8 x 1,000)
=700+400+8000
=1100+8000
=91009100 is the right answer.What is x divided by x?
Answer:
its 1
Step-by-step explanation:
the value of x and x is like having 1÷1 = 1
same with x : x÷x=1
since x is just a value
When x is divided by x , it's 1.
What is division?Division is the process of splitting a number or an amount into equal parts.
Here, given that,
x is divided by x
=x/x
=1.
Hence, When x is divided by x , it's 1.
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When temperature is measured in Celsius, a reading of 0 °C means that it is cold enough to freeze water.
Soren lives in Norway, and loves to ice skate on the pond near his house. When the temperature is below
0 °C, the pond is frozen and he can skate. But if the temperature rises above 0 °C, the melting ice makes
it too dangerous!
Answer:
32 degrees
Step-by-step explanation:
32 degrees is the below freezing point
Evaluate the algebraic expression:48/2h + 32/g = when f = 6, g = 8, h = 12 and j = 2.
Let's evaluate the following equation:
\(\text{ }\frac{48}{2h}\text{ + }\frac{32}{g}\)Given:
f = 6
g = 8
h = 12
j = 2
We get,
\(\text{ }\frac{48}{2h}\text{ + }\frac{32}{g}\)\(\text{ }\frac{48}{2(12)}\text{ + }\frac{32}{(8)}\)\(\text{ }\frac{48}{24}\text{ + }\frac{32}{8}\)\(\text{ }2\text{ + }4\)\(\text{ = 6}\)Therefore, the answer is letter C - 6.
Assume that demand for a commodity is represented by the equation
P = -2Q-2Q_d
Supply is represented by the equation
P = -5+3Q_1
where Q_d and Q_s are quantity demanded and quantity supplied, respectively, and Pis price
Instructions: Round your answer for price to 2 decimal places and enter your answer for quantity as a whole number Using the equilibrium condition Q_s = Q_d solve the equations to determine equilibrium price and equilibrium quantity
Equilibrium price = $[
Equilibrium quantity = units
The equilibrium price is $0 and the equilibrium quantity is 5 units.
To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.
Setting Q_d = Q_s, we can equate the equations for demand and supply:
-2Q - 2Q_d = -5 + 3Q_s
Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:
-2Q - 2Q_s = -5 + 3Q_s
Now, let's solve for Q_s:
-2Q - 2Q_s = -5 + 3Q_s
Combine like terms:
-2Q - 2Q_s = 3Q_s - 5
Add 2Q_s to both sides:
-2Q = 5Q_s - 5
Add 2Q to both sides:
5Q_s - 2Q = 5
Factor out Q_s:
Q_s(5 - 2) = 5
Q_s(3) = 5
Q_s = 5/3
Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:
P = -5 + 3Q_s
P = -5 + 3(5/3)
P = -5 + 5
P = 0
Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.
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20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The students weren't assigned the treatments (new menu item) at random.
In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.
The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.
In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly. If randomly assigned all the new menu items will have an equal probability of being chosen.
Therefore, option b is the correct option.
The complete question is -
Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?
a) There was no replication because students did not eat both menu items.
b) The treatments (new menu item) were not randomly assigned to the students.
c) An item that is currently on the menu should have been used as a control.
d) Students should not have been randomly selected.
e) There were no problems, and the study was a well-designed experiment.
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Samia created the following tables of values for a linear system. She concluded that there is no
solution to the system
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
How many solutions do a system of linear lines have?A system of equations, involving two linear lines has solutions as follows:
Unique Solution: When the lines intersect, the point of intersection is the solution.No Solution: When the lines are parallel, no solution exists.Infinite Solution: When the lines coincide, then all points on the line become solutions, giving an infinite number of solutions.How to solve the question?In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.
We are asked to comment on her conclusion.
To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.
Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.
Thus, the slope for:-
Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.
Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.
Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
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The 2017 balance sheet of Kerber's Tennis Shop, Inc., showed long-term debt of $5 million, and the 2018 balance sheet showed long-term debt of $5.2 million. The 2018 income statement showed an interest expense of $165,000. During 2018, the company had a cash flow to stockholders for the year was $70,000. Suppose you also know that the firm’s net capital spending for 2018 was $1,370,000, and that the firm reduced its net working capital investment by $69,000. What was the firm’s 2018 operating cash flow, or OCF?
Griffin's Goat Farm, Inc., has sales of $686,000, costs of $332,000, depreciation expense of $65,000, interest expense of $48,500, and a tax rate of 24 percent. What is the net income for this firm?
The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).
The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:
\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)
where EBIT is earnings before interest and taxes.
Calculate EBIT by subtracting interest expense from operating income:
EBIT = Operating Income - Interest Expense
We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.
EBIT = Interest Expense / (1 - Tax Rate)
= \(\$165,000 / (1 - 0)\)
= \(\$165,000\)
Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by \(\$69,000\).
Therefore:
\(\triangle Working Capital = \$69,000\)
Now, we can calculate OCF:
OCF = EBIT + Depreciation - Taxes + Δ Working Capital
=\(\$165,000 + 0 - 0 +\ $69,000\)
=\(\$234,000\)
Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .
To calculate the net income for Griffin's Goat Farm, we can use the following formula:
Net Income = EBIT - Interest Expense - Taxes
where EBIT is earnings before interest and taxes. We can calculate EBIT as:
EBIT = Sales - Costs - Depreciation
= \(\$686,000 - \$332,000 - \$65,000\)
=\(\$289,000\)
Next, we need to calculate taxes. We are given a tax rate of 24%, so:
Taxes = Tax Rate x (EBIT - Depreciation)
= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)
Now, we can calculate net income:
Net Income = EBIT - Interest Expense - Taxes
= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)
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Find ⊙ - notation in terms of n for the pseudocode below. Provide a short answer. for i=1 to n for j=1 to lgn for k=1 to i2 x=x+1
The overall time complexity of the pseudocode can be expressed as O(n * log(n) * \(n^2\)) or simply O(\(n^3\) log(n)).
The ⊙ notation is used to denote multiplication. In the given pseudocode, the line "for k=1 to i²" indicates a nested loop where the variable k iterates from 1 to the square of i. The expression "x=x+1" inside the nested loop suggests that the variable x is incremented by 1 in each iteration. Therefore, in terms of n, the ⊙ notation for the given pseudocode can be expressed as follows:
⊙(n) = n * log(n) * \(n^2\)
In this expression, n represents the upper limit of the first loop (from 1 to n), log(n) represents the upper limit of the second loop (from 1 to log(n)), and \(n^2\) represents the upper limit of the third loop (from 1 to i², where i ranges from 1 to n).
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the diameter of a circle is 16. by what number must the radius be decreased in order to decrease the area of the circle by $48\pi$?
To decrease the area of the circle by $48\pi$, we need to decrease the radius by a factor of $\sqrt{48\pi}$.
Since the original radius of the circle was 8, the radius must be decreased to
$\frac{8}{\sqrt{48\pi}} = \frac{8}{\sqrt{48}\sqrt{\pi}} = \frac{8}{\sqrt{48}} \approx \frac{8}{6.9282} \approx 1.1547$.Therefore, to decrease the area of the circle by $48\pi$, the radius must be decreased by a factor of about 1.1547.
This means that the radius must be decreased by a number that is about 1.1547 times smaller than the original radius of 8, or by about $8 \times (1 - 1.1547) = -0.6158$.
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1 A linear function is shown on the graph below.
8
6
4
2
-8
-6 -4
-2
2
6
-2
A
-6
-8
What is the slope of this function?
A. 5
B. 1
1
c. -4D.-4
Answer:
6
Step-by-step explanation:
a fence is to be built to enclose a rectangular area of 200 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.
Describe method to calculate dimensions of the enclosure that is most economical to construct?Let's assume that the rectangular area to be enclosed has dimensions length "L" and width "W", respectively.
We know that the area of the rectangle is 200 square feet:
L x W = 200
We also know that we need to enclose three sides of the rectangle with material that costs 6 dollars per foot, and one side with material that costs 14 dollars per foot.
The total cost, C, of the fencing can be expressed as:
C = 6(2L + W) + 14L
where 2L + W represents the length of the three sides that cost 6 dollars per foot, and L represents the length of the fourth side that costs 14 dollars per foot.
We can simplify this equation to:
C = 26L + 6W
using the equation L x W = 200.
Now we can use the method of calculus to find the minimum value of C. We take the derivative of C with respect to L, set it equal to zero, and solve for L.
dC/dL = 26 = 0
L = 0
This result means that the value of L that minimizes C is L = 0, which is obviously not a valid solution. This implies that the minimum value of C occurs at a critical point where dC/dL is undefined.
To find this critical point, we can use the equation L x W = 200 to eliminate one variable. Solving for W in terms of L, we get:
W = 200/L
Substituting this expression for W into the equation for C, we get:
C = 26L + 6(200/L)
Now we can take the derivative of C with respect to L and set it equal to zero:
dC/dL = 26 - 1200/L² = 0
Solving for L, we get:
L = √(46.15)
Substituting this value for L back into the equation for W, we get:
W = 200/√(46.15)
Therefore, the dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.
Learn more about critical point.
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A line with a slope of -7 passes through the points (4,5) and (5,g). What is the value of g?
Answer:
I think the answer would be -2 . hope it helps u .