The measure of this angle in degrees is 20.52 degrees.
Step by step explanation:Given data is,1/360th of the circumference of the circle is 0.59 cm long Arc length, s = 103.25 cm We need to find the measure of the angle in degrees. Since we know that, the angle subtended by an arc at the center of the circle is 2θ, where θ is the angle subtended by the arc at any point on the circumference of the circle.And the circumference of the circle is 360θ.
Hence, we can find the length of the circumference of the circle. Circumference of the circle = 360 × 0.59Circumference of the circle = 212.4 cmNow, we can find the radius of the circle.r = s/2πr = 103.25/(2 × π) = 16.441 cmDiameter of the circle = 2 × rDiameter of the circle = 32.882 cmThe circumference of the circle = πdCircumference of the circle = π × 32.882Circumference of the circle = 103.26 cm Now, we can find the angle of the circle. Angle of the circle = 360θ103.26 = 360θθ = 103.26/360θ = 0.286 degrees So, the measure of this angle in degrees is 20.52 degrees.
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Given the following Year 12 balance sheet data for a footwear company:
Balance Sheet Data
Cash on Hand 2,000
Total Current Assets 78,000
Total Assets 315,000
Overdraft Loan Payable 4,000
1- Year Bank Loan Payable 8,000
Current Portion of Long-Term Loans 13,000
Total Current Liabilities 48,000
Long - Term Bank Loans Outstanding 105,000
Shareholder Equity Year11 Balance Year 12 Change Common Stock 10,000 0 10,000
Additional Capital 100,000 0 100,000
Retained Earning 30,000 22,000 52,000
Total Shareholder Equity 140,000 +22,000 162,000
Based on the above figures and the formula for calculating the debt-assets ratio, the company's debt-assets ratio (where debt is defined to include both short-term and long-term debt) is
a) 0.375
b) 0.413.
c) 0.40.
d) 0.318.
e) 0.333.
Based on the above figures and the formula for calculating the debt-assets ratio, the company's debt-assets ratio (where debt is defined to include both short-term and long-term debt) is 0.413 or 41.3%.
The given balance sheet data,
Balance Sheet Data
Cash on Hand 2,000
Total Current Assets 78,000
Total Assets 315,000
Overdraft Loan Payable 4,000
1- Year Bank Loan Payable 8,000
Current Portion of Long-Term Loans 13,000
Total Current Liabilities 48,000
Long-Term Bank Loans Outstanding 105,000
Shareholder Equity Year11 Balance Year 12 Change Common Stock 10,000 0 10,000
Additional Capital 100,000 0 100,000
Retained Earning 30,000 22,000 52,000
Total Shareholder Equity 140,000 +22,000 162,000
The debt-assets ratio is calculated by dividing the total debt (current liabilities + long-term loans) by the total assets.
In this case, the total debt is 48,000 + 105,000 = 153,000
and the total assets are 315,000.
Thus, the debt-assets ratio is 153,000/315,000 = 0.413.
Also, the debt-assets ratio is 0.413 * 100 = 41.3%
The correct answer is b) 0.413.
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HELP
Given the information in the diagram of circle P below, find:
Based on the information in the diagram of circle P, the magnitude of the missing angle are as follows;
m∠BPC = 80 degrees.
m∠ADC = 205 degrees.
What is the central angle property?In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.
Based on the information provided about circle P, the central angle of circle P is represented by m∠BPC and the measure of arc BC is equals to 80 degrees. Therefore, the magnitude of angle BPC is given by:
m∠BPC = 80 degrees.
Since m∠A is an inscribed angle, its magnitude can be calculated as follows;
m∠A = 1/2(m∠BPC)
m∠A = 1/2(80)
m∠A = 40 degrees.
For the magnitude of m∠ADC, we have:
m∠ADC = 360 - (80 + 75)
m∠ADC = 360 - 155
m∠ADC = 205 degrees.
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What is the domain of the square root function graphed below?
The inequality that represents x is x ≥ 0/
A square root function is defined ?The basic square rοοt οperatiοn. (οften knοwn as the "square rοοt functiοn") is a mapping that applies tο the set οf nοnnegative real numbers. The square rοοt functiοn, in geοmetric terms, cοnverts a square's area tο its side length.
The οrder οf pοsitive numbers is preserved by the square functiοn: greater numbers have larger squares. The square, then, is a mοnοtοnic functiοn οn the range [0, +]. With negative numbers, absοlute values are mοre significant than squares, making it a mοnοtοnically decreasing functiοn οn [(, 0]].
Here, The domain of the graph is domain : [0, +∞)
With this, we can clearly state that 0 < x < +∞
Thus, The inequality that represents x is x ≥ 0
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Tonia sells seashells to tourists throughout the year. During the summer
months her sales are very high and she makes a considerable profit. As the
seasons change it gets colder less people come to the beach and the less
foot traffic she has causes her to earn less. This cycle repeats every year.
Tonia's situation can be modeled through a(n)
function.
Tonia's situation can be modeled through a seasonal function, specifically a periodic function. This is because her sales and profits vary over time in a predictable pattern that repeats each year.
What is a seasonal function?A seasonal function is a type of mathematical function that models a repeating pattern or a cyclical behavior that occurs over a fixed interval of time. Seasonal functions are used to analyze and forecast patterns in time series data that have a clear seasonality or periodicity
One common type of periodic function is a sine or cosine function. These functions oscillate back and forth between two extreme values in a smooth, periodic way. In Tonia's case, her sales and profits might be modeled as a sine or cosine function that oscillates between high values during the summer months and lower values during the winter months.
Other types of periodic functions include sawtooth functions and square wave functions, which have a more abrupt change between their high and low values.
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One characteristic of all exponential functions is that they change by
One characteristic of all exponential functions is that they change by a constant factor at each step, which means that they exhibit exponential growth or decay.
The constant factor by which an exponential function changes is called the base, which is usually denoted by the symbol "b". If b is greater than 1, the function exhibits exponential growth, and if b is between 0 and 1, the function exhibits exponential decay.
For example, the function f(x) = 2^x is an exponential function with a base of 2. At each step, the function increases by a factor of 2. For instance, f(0) = 1, f(1) = 2, f(2) = 4, f(3) = 8, and so on.
On the other hand, the function g(x) = (1/2)^x is an exponential function with a base of 1/2. At each step, the function decreases by a factor of 1/2. For instance, g(0) = 1, g(1) = 1/2, g(2) = 1/4, g(3) = 1/8, and so on.
Therefore, exponential functions exhibit a characteristic change by a constant factor at each step, which leads to either exponential growth or decay.
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Kierran spends approximately 3 hours per day playing video games and approximately 20 minutes per day doing chores. If Kierran's mother tells him to play video games when he completes his chores, then she is employing the ______________ whereas if she restricts video game play and only allows him to play video games if he does his chores then she is employing the ___________________.
When she restricts video game play and only allows him to play games if he completes his tasks, she is using the punishment technique.
what is unitary method ?A mathematical strategy known as the unitary method involves identifying a single unit value and utilizing it to determine additional values based on how they relate to it. The inverse proportionality method and the method of proportionality are other names for it. When dealing with complex problems that include numerous units or quantities, the unitary technique is frequently employed to solve difficulties requiring ratios and proportions. Several industries, including banking, science, engineering, and mathematics, can use it.
given
When Kieran's mother instructs him to play video games after finishing his work, she is using the reinforcement approach.
Drive reduction theory, the Premack Principle
According to the Premack Principle, low probability conduct can be reinforced by using high probability behavior.
According to the hypothesis of drive reduction, animals will take actions to
When she restricts video game play and only allows him to play games if he completes his tasks, she is using the punishment technique.
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suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage. how many indicator variables would you need? group of answer choices 4
Suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage, then the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0.
What is a variable indicator?Indicator variable An indicator variable is a binary variable that indicates whether or not a specific condition or category is present. Indicator variables are typically used in statistical models to represent categorical data or conditions, and they are also known as dummy variables or binary variables.
Example suppose you want to conduct a statistical analysis to determine the impact of location and size on the price of a house. There are four possible locations: northeast, northwest, southeast, and southwest. We can use four indicator variables (one for each location) to represent this information.
For instance, if a house is in the northeast, the northeast indicator variable would be set to 1, while the other indicator variables would be set to 0. Similarly, if the house is in the northwest, the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0. We would use similar logic for the other two locations.
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Brittany needed new tires for her truck. She went to the auto shop and bought 4 tires on sale for $85.95 each. The salesman told her that she saved a total of $96.16. If Brittany saved the same amount on each tire, what was the original price of each tire?
The best solution gets brainlist
Answer:
$109.99
Step-by-step explanation:
The original price of each tire is [tex]\[/tex][tex]109.99[/tex]
Solution:Take the amount saved and divide by 4 to find the amount saved on each tire
[tex]96.16\div4 =24.04[/tex]
Add that to the sale price of each tire to find the original price
[tex]85.95+24.04 =109.99[/tex]
Therefore, The original price is $109.99.
James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Answer:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
Step-by-step explanation:
Initially, James had 18 litres of water, and he poured three-quarters of it from tank 1 into tank 2. This means that the volume of water left in tank 1 is:
18 - (3/4) * 18 = 4.5 litres
The volume of water in tank 2 is:
(3/4) * 18 = 13.5 litres
Next, he poured half of the water in tank 2 (which is now 13.5 litres) into tank 3. The volume of water left in tank 2 is:
(1/2) * 13.5 = 6.75 litres
The volume of water in tank 3 is:
13.5 * (1/2) = 6.75 litres
Finally, he poured one-third of the water in tank 3 (which is now 6.75 litres) into tank 1. The volume of water in tank 1 after this is:
4.5 + (1/3) * 6.75 = 6 litres
The volume of water in tank 3 after this is:
6.75 * (2/3) = 4.5 litres
So the final volume of water in each tank is:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
If AC = 57, find the measure of AB.
Segment Addition Postulate - Meaning, Formula & Examples
Answer:
AB = 27
Step-by-step explanation:
AC = AB + BC
[tex]{ \rm{57 = 3x + (4x - 6)}} \\ \\ { \rm{57 = 7x - 6}} \\ \\ { \rm{7x = 57 + 6}} \\ \\ { \rm{7x = 63}} \\ \\ { \rm{x = 9}}[/tex]
Therefore;
[tex]{ \rm{AB = 3x = 3 \times 9}} \\ { \boxed{ \rm{AB = 27}}}[/tex]
Our class is planning to paint a rectangular mural with an area of 60 square feet, it has to be at least 4 feet high but no more than 6 feet the length and width have to be hold numbers list of possible width for the
The possible widths for the rectangular mural are between 10 and 15 feet. We can also list the number of possible widths within this range, which is six. They are 10 feet, 11 feet, 12 feet, 13 feet, 14 feet, and 15 feet.
To determine the possible widths for the rectangular mural with an area of 60 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the area is given as 60 square feet and the length should be between 4 and 6 feet, we can set up inequality as follows:
4w ≤ 60 ≤ 6w
where w is the width of the mural in feet. Solving this inequality for w, we get:
10 ≤ w ≤ 15
It is important to consider the dimensions carefully to ensure that the mural meets the requirements and fits in the desired space. By having multiple possible widths, the class can select the most suitable one based on the available resources and space.
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Complete question:
Our class is planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list a number of possible widths for our class. Planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list the number of possible widths for it.
which of the following is an incorrect statement? if a density curve is skewed to the right, the mean will be larger than the median. in a symmetric density curve, the mean is equal to the median. the mean of a skewed distribution is pulled toward the long tail. the median is the balance point in a density curve.
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
what is mean ?The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.
given
None of the claims are untrue.
The mean will be greater than the median if a density curve is tilted to the right.
The mean and median are equal in a density curve that is symmetric.
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
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a:b=1:6
a:c=3:1
How many times is b bigger than c?
Answer:
18 times bigger
Step-by-step explanation:
3x≥12.
resultats ???
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x >= 4
Step-by-step explanation:
3x >= 12
x >= 4
this is nothing but → x ≈ (∞ , 4]
Hope it helps you ~In square $ABCD$ with sides of length 4 cm, $N$ is the midpoint of side $BC$ and $M$ is the midpoint of side $CD$. What is the area of triangle $AMN$,
Consequently, the area of triangle $AMN$ is equal to $A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4$ cm2.
The area of triangle $AMN$ in square $ABCD$ can be calculated using the formula for area of a triangle, $A = \frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the height of the triangle.
Since side $BC$ has a length of 4 cm, we can determine that $N$ is located 2 cm away from point $B$ and 2 cm away from point $C$.
Similarly, we can conclude that $M$ is located 2 cm away from point $C$ and 2 cm away from point $D$.
Therefore, the base of triangle $AMN$ is equal to 4 cm, and the height of triangle $AMN$ is equal to 2 cm.
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A single person earns a gross biweekly salary of $840 and claims 5 exemptions. How will federal taxes affect his net pay?
Option (a) it is the same as the gross pay. is true statement about a person who is claiming 5 exemptions and biweekly salary of $ 840.
What separates a gross pay from a net salary?Yοur incοme is referred tο be yοur grοss pay if it is unaffected by taxes and οther withhοldings.
When referring tο yοur yearly grοss incοme, the phrase "annual pay" is frequently used. Net pay is the amοunt that remains after deductiοns like sοcial security and incοme tax have been made.
the persοn want mοre exemptiοns, it means that persοn thinks that, his οr her salary is less than οthers when cοmpared with οther emplοyee having mοre expenditure, and he οr she dοes nοt want tο pay tax οr will pay minimum amοunt οf tax tο the Gοvernment.
Sο, tο dο this he want exemptiοns.
As,persοn earns a grοss biweekly salary οf $840 and claims 5 exemptiοns.
→it means he οr she want tο reduce his tοtal tax tο minimum amοunt.
→it means he οr she dοes nοt have enοugh mοney in his οr her pοcket thrοughοut the year.
→ there will be nο tax deductiοn οn persοn net pay.And if he fοund caught cheating , he will have tο pay Penality.
Sο, οptiοn (a) it is the same as the grοss pay. is true statement abοut a persοn whο is claiming 5 exemptiοns and biweekly salary οf $ 840.
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What is the total cost of order number four if the customer received 10% off and paid a 15% gratuity and 4.5% sales tax?
The cost of order number four would be $12.60.
What does US sales tax mean?
Sales taxes are levied on the purchase or leasing of products and services inside the United States. There is no federal general sales tax, and sales tax regulation is handled at the state level. Think about this sales tax illustration.
You want to know how much your purchase will cost after taxes before you check out at The Clothes Boutique. Your cart contains goods with a combined price of $100 after totaling up all the charges. You would calculate 9.5% of $100 since the sales tax in that county is 9.5%. (100 x 0.095).
The cost of order number four would be $12.60.
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Mr. Seda has a bag with 500 marbles. The marbles are either
green or yellow. He has 20 students in his class take turns
selecting 10 marbles from the bag without looking. Each student
records the number of green marbles and then returns the
marbles to the bag.
What is a reasonable estimate for the number of green marbles
in the bag?
TRY
IT
M Math Toolkit double number lines, grid paper
Samples
5
Nu
A reasonable estimate for the number of green marbles in the bag would be around 250, since the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green.
To estimate the number of green marbles in the bag, we can use the fact that the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green. This means that, with 20 students selecting 10 marbles each, we can expect to have at least 100 green marbles. We can then multiply this number by two to get a reasonable estimate of 200 green marbles. Since this is a slightly conservative estimate, we can round up to 250 green marbles for our reasonable estimate.
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Elise saved $184. She bought a scarf, a necklace, and a notebook. After the purchases, she still had $89. 50. The scarf cost three-fifths the cost of the necklace and the notebook cost one-sixth as much as the scarf. How much did the notebook cost?
The cost of the notebook is $4.50
Let's call the cost of the necklace "N" and the cost of the scarf "S". We know that Elise spent a total of $184 on the scarf, necklace, and notebook, so we can write:
S + N + NB = 184
We also know that after making her purchases, Elise had $89.50 left, so we can write:
89.5 = 184 - (S + N + NB)
Simplifying this equation, we get:
S + N + NB = 94.5
We're also given that the scarf cost three-fifths the cost of the necklace, so we can write
S = (3/5)N
Finally, we're told that the notebook cost one-sixth as much as the scarf, so we can write:
NB = (1/6)S
Now we can the substitution method here
(3/5)N + N + (1/6)(3/5)N = 184 - 89.5
Simplifying the right-hand side
(3/5)N + N + (1/6)(3/5)N = 94.5
Combining like terms on the left-hand side
(21/10)N = 94.5
Multiplying both sides by 10/21
N = 45
So the necklace cost $45. We can use this to find the cost of the scarf
S = (3/5)N = (3/5)($45) = $27
And we can use the cost of the scarf to find the cost of the notebook
NB = (1/6)S = (1/6)($27) = $4.50
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Ixl dilations-find the scale factor and center dilation
The scale factor is 2 and center dilation is reduced.
The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.
To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.
If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.
The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.
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What is the volume of a hemisphere with a diameter of 5.5cm, rounded to the nearest tenth of a cubic centimeter.
if the hemisphere has a diameter of 5.5, then its radius is half that or 2.75.
[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{2\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2.75 \end{cases}\implies V=\cfrac{2\pi (2.75)^3}{3}\implies V\approx 44~cm^3[/tex]
Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m
Answer:
the cross is the blue color
Find five consecutive integers if the sum of the first three is 7 more that the sum of the last two
the consecutive integers are 11, 12, 13, 14, 15 using the given condition.
What is an integer?The group of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic processes, including addition, subtraction, multiplication, and division. It's a good idea to have a backup plan in case something goes wrong. "Z" stands for a number.
Let the consecutive integers be n, n+1, n+2,n+3,n+4.
n+n+1+n+2=7+n+3+n+4
3n+3=14+2n
n=11
therefore the integers are 11, 12, 13, 14, 15.
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Translate the shape A seven squares right and five squares down
The points that form the corners of the shape have the following coordinates: (-1,-6), (0,-4), and (4,-6).
The graph is attached below
To plot these coordinates on a graph, first draw the x and y axes. Label the x-axis with integers from negative 6 to positive 6 and label the y-axis with integers from negative 7 to positive 3. Next, locate the point (-1, -6) on the graph by counting 1 unit to the left of the origin (0) on the x-axis and 6 units down on the y-axis. Place a dot at that location. Repeat the process for the point (0, -4) by plotting a dot at the point where the y-axis intersects the x-axis (0) and 4 units down on the y-axis. Finally, locate the point (4, -6) by counting 4 units to the right of the origin on the x-axis and 6 units down on the y-axis, and place a dot there.
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The missing graph in the question is in the image attached below
28) The waiting time for the first claim from a good driver and the waiting time for the first claim from a bad driver are independent and follow exponential distributions with mean 6 years and 3 years, respectively. What is the probability that the first claim from a good driver will be filed within 3 years and the first claim from a bad driver will be filed within 2 years? 18 18 18
Previous question
The probability that both events occur simultaneously is 0.1913.
We can model the waiting time for the first claim from a good driver and the waiting time for the first claim from a bad driver as independent exponential distributions with mean 6 years and 3 years, respectively.
Let X be the waiting time for the first claim from a good driver and Y be the waiting time for the first claim from a bad driver.
Then, P(X ≤ 3) = 1 - e^(-3/6) = 0.3935 and P(Y ≤ 2) = 1 - e^(-2/3) = 0.4866.
Since X and Y are independent, the probability that the first claim from a good driver will be filed within 3 years and the first claim from a bad driver will be filed within 2 years is
(X ≤ 3) * P(Y ≤ 2) = 0.3935 * 0.4866 = 0.1913(rounded to four decimal places).
(rounded to four decimal places).
Therefore, the probability that both events occur simultaneously is 0.1913.
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27. Let W be a subspace, and let S be a spanning set for W. Find a basis for W, and calculate dim(W) for each set S. a) S = COCIOC) 3 0 2 -2 b) S= -2 1 2 2 2
Answer:best thing for you is drink milk
Step-by-step explanation:
David is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, he can work no more than 16 total hours and must earn no less than $160. Also, he must work at most 13 hours landscaping. If
� x represents the number of hours landscaping and �y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer: One possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
Step-by-step explanation:
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
lua
Copy code
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20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
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13 12.3
The vertices of the feasible region are (0, 16), (12.3, 3.7), and (13, 0).
To determine one possible solution, we can evaluate the objective function (total earnings) at each vertex:
(0, 16): 13(0) + 8(16) = $128
(12.3, 3.7): 13(12.3) + 8(3.7) ≈ $167.1
(13, 0): 13(13) + 8(0) = $169
Therefore, one possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
Consider the second order differential equation with initial conditions u" +2u' - 5u = 5 sin(3t), u(1) = 3, u'(1) = 4.5. Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the "velocity function" ul. Do not use u(t) or v(t) to represent these functions. Expressions like sin(t) that represent other functions are OK. u= V Now write the first order system using matrices: u C ] [: + The initial value of the vector valued solution for this system is: u(1) = v(1)
The equivalent set of first-order equations in matrix form is [tex]w' = Cw + [0,[/tex] [tex]5sin(3t)^{T}[/tex] and the initial value of the vector-valued solution is w(1) = [tex][3,4.5]^{T}[/tex].
The given second-order differential equation as a set of first-order equations, we can define a new variable v(t) to represent the derivative of u(t), i.e., v(t) = u'(t). Then, we can rewrite the second-order differential equation as two first-order differential equations:
[tex]u' = v[/tex]
[tex]v' = 5sin(3t) + 5u - 2v[/tex]
where u' and v' represent the derivatives of u and v with respect to t, respectively.
To write this first-order system in matrix form, we can define the vector-valued function w(t) = [u(t), v(t)]^T and write the system as:
[tex]w' = [v, 5sin(3t) + 5u - 2v]^T[/tex]
where the superscript T denotes the transpose of a vector or matrix.
Using this notation, the initial value of the solution vector is given by w(1) =[tex][u(1), v(1)]^T = [3, 4.5]^T.[/tex]
In matrix form, the first-order system can be written as:
[tex][ u' ] [ v ]\\[ ] = [ ]\\[ v' ] [ 5sin(3t) + 5u - 2v ][/tex]
or
[tex]w' =\\[ u' ]\\[ v' ]\\[ v ]\\[ 5sin(3t) + 5u - 2v ][/tex]
where
w =
[tex][ u ]\\[ v ][/tex]
and the coefficient matrix C is given by:
[tex]C =\\[ 0 1 ]\\[ 5 -2 ][/tex]
A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).
Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.
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based on historical data, it takes students an average of 48 minutes with a standard deviation of 15 minutes to complete the unit 5 test. what is the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test?
Using central limit theorem, the probability that the class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is 0.00017332
What is the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test?We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean completion time for the class. According to CLT, the distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is given as 48 minutes, the population standard deviation is given as 15 minutes, and the sample size is 20. Therefore, the mean of the sample mean completion time is also 48 minutes, and the standard deviation of the sample mean completion time is 15/√20 ≈ 3.3541 minutes.
To find the probability that the class mean completion time is greater than 60 minutes, we can standardize the distribution of the sample mean completion time using the z-score formula:
z = (x - μ) / (σ / √n)
where x is the value we want to find the probability for (in this case, x = 60), μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (60 - 48) / (15 / √20) = 3.5777
Using a standard normal distribution table (or calculator), we can find the probability that a z-score is greater than 3.5777.
P = 0.00017332
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Elmer is on a Ferris wheel which has a diameter of 180 ft and whose center is 120 ft off the ground. Find all of the angles θ such that 0≤θ≤3π and such that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Leave your answers in exact form
The angles θ at which Elmer's carriage is at a height of 165 ft are θ = π/6, 13π/6 and 25π/6
The center of the Ferris wheel is represented by the point at the top of the triangle, and Elmer's carriage is represented by the lower point on the right-hand side of the triangle. We are given that the diameter of the Ferris wheel is 180 ft and that its center is 120 ft off the ground. This means that the radius of the Ferris wheel is 90 ft (half of the diameter), and that the distance from the center of the Ferris wheel to Elmer's carriage is also 90 ft.
We are also given that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Using trigonometry function , we can find the sine of θ as follows:
sin(θ) = (165 - 120) / 90
= 45 / 90
= 1/2
Therefore, we have:
θ = sin^(-1)(1/2)
= π/6
Since we are looking for all angles θ such that 0≤θ≤3π, we need to add multiples of 2π to our answer. The multiples of 2π that satisfy this inequality are 0, 2π, and 4π. Therefore, the solutions to the problem are:
θ = π/6, 13π/6, 25π/6
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