Answer:
The graph that shows the solution to the system of linear inequalities is the one that has a line with a slope of -2 and y-intercept of 1/2, and another line with a slope of 1 and y-intercept of 1/2. The region of the plane that lies between the two lines and satisfies both inequalities is the solution set.
In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is What is the probability that it takes three rolls until the player rolls doubles?
(a) (1/5)^3
(b) (5/6)^3
(c) (1/5) (5/6)^3
(d) (1/6) (5/6)^2
(e) (5/6) (1/6)^2
The probability of not rolling doubles on one roll of two fair six-sided dice is 5/6.
Hence, the probability of rolling doubles is 1/6. The probability of not rolling doubles in three rolls is (5/6)^3. So, the probability of rolling doubles on the third roll is 1 - (5/6)^3. This is the same as (1/6) (5/6)^2. So the correct answer is (d) (1/6) (5/6)^2.
The probability of rolling a specific number on one fair six-sided die is 1/6.
In this problem, we are looking for the probability of rolling doubles (i.e. getting the same number on both dice) in three rolls.
The probability of not rolling doubles in one roll is 5/6 (since there are five outcomes that are not doubles, out of a total of 6 possible outcomes).
The probability of not rolling doubles in three rolls is (5/6)^3, which represents the chance of not rolling doubles in three independent rolls, each with a 5/6 probability of not rolling doubles.
To find the probability of rolling doubles in three rolls, we subtract the probability of not rolling doubles in three rolls from 1:
P(rolling doubles in three rolls) = 1 - (5/6)^3 = (1/6) (5/6)^2
So, the correct answer is (d) (1/6) (5/6)^2.
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Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is given by E(t)=2600−50t.
Part 1) Terry started at an elevation of 2,600 ft.
Part 2) The elevation is decreasing by 50 feet per second.
we have
E(t) = 2600 -50t
where
E(t) is Terry's elevation in feet
t is the time in seconds
Part 1) For t=0
substitute the value,
E(0) = 2600 -50(0)
E(0) = 2600
therefore
The equation says us that Terry started at an elevation of 2,600 ft
Part 2) we have
E(t)=2600−50t
This is the equation of the line in slope-intercept form.
The slope m is equal to, m = -50 ft/sec
The slope is negative because is decreasing
therefore
The elevation is decreasing by 50 feet per second.
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Use the general slicing method to find the volume of the following solid. The solid with a semicircular base of radius 11 whose cross sections perpendicular to the base and parallel to the diameter are squares
The volume of the solid is 1789.33
For a circle of radius 11, we have the following equation:
x²+y²=11²
x²+y²=121
Now, making it explicit for x:
[tex]x=\sqrt{121-y^2}[/tex]
Then, if we consider that for a height y, the length x is double, we have that the length of each cross-section is given by:
[tex]s=\sqrt[2]{81-y^2}[/tex]
With this, we can propose the following integral to obtain the volume that they are asking us:
[tex]\int\limits^1_0 {s^2} \ \, dy \\\int\limits^1_0 ({\sqrt[2]{121-y^2})^2 } \, dy\\\\\int\limits^1_0 {4*(121-y^2)} \, dy\\\\4*(121y-\frac{y^3}{3} )[/tex]
Finally, calculating, we have that the volume is V=1789.33
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Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. Which statement best describes the meaning of one of the bars in the histogram? O 110 snacks have between 100 and 120 mg of sugar O 110 snacks have 7 mg of sugar. O 7 snacks have about 110 mg of sugar. O The largest number of snacks have 12 mg of sugar
The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.
A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.
In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.
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Please help! Image below…
Answer:
In order in which the boxes appear in the sentences
[tex]\textsf{y-intercept \;\;\boxed{28000}}\\\\\textsf{this represents dollar value for a car that is $\boxed{0}$ years old}\\\\\textsf{Slope of the regression line is $\boxed{-4900}$}[/tex]
Step-by-step explanation:
3. What is a Cartesian plane?
A. A graph used in mathematics to only compare linear planes.
B. A graph used in mathematics to calculate positive and negative multiplication tables.
C. A graph used in mathematics to create 3-dimensional shapes.
D. A graph used in mathematics to plot points.
The Cartesian, or rectangular, coordinate system is composed of an x-axis that runs horizontally and a y-axis that goes vertically.
What is meant by Cartesian plane?The rectangular coordinate system of the Cartesian plane, which bears Rene Descartes' (1596–1650) name, assigns each point in the plane a pair of integers.
An x-axis that runs horizontally and a y-axis that runs vertically make up the Cartesian, or rectangular, coordinate system. The origin is the place where the two axes meet. Any point can be characterized by its distance from the origin along the x-axis and along the y-axis, and this distance is represented by the symbol (x, y).
A two-dimensional coordinate plane produced by the intersection of the x- and y-axes is known as the cartesian plane in mathematics. At the location known as the origin, the x- and y-axes cross perpendicularly.
Therefore, the correct answer is option D. A graph used in mathematics to plot points.
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In the two units of company, the employees in unit one are 650 and monthly salary is N2750, the employees in unit two are 700 and monthly salary is N2500 then the combined arithmetic mean is
Answer:
2620
Step-by-step explanation:
Using long division to rewrite each rational function f(x)=2x/x+4
The other way of representing the given function is f(x) = 2 - 8/(x+4).
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, rational function f(x)=2x/x+4
Using Long division:
x + 4) 2x ( 2
2x + 8
-------------------------
-8
The remainder is -8.
Since the Degree of the remainder is less than the degree of the divisor then we are done.
Now using,
Dividend = divisor* quotient + remainder
=> 2x = 2 * (x+4) -8
Thus, f(x) = 2 - 8/(x+4)
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SAVINGS If $10,000 is deposited into a savings account that pays 1.8% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years?
Round to Nearest Dollar
The amount of money that is compounded monthly for 30 years will be $17,153.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
If $10,000 is deposited into a savings account that pays 1.8% annual interest.
Then the rate is given as,
r = 1.8% / 1200
r = 0.0015
Then the number of years is given as,
n = 30 x 12
n = 360
Then the amount of money that is compounded monthly for 30 years is given as,
A = $10,000 × (1 + 0.0015)³⁶⁰
A = $10,000 × (1.0015)³⁶⁰
A = $10,000 × 1.715
A = $17,153
The amount of money that is compounded monthly for 30 years will be $17,153.
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please help with this problem
The batting average and percentage hits for the players will be Albert Pujois= 0.356 and 35.6%, Stan Musial=0.376 and 37.6% and Rogers Honsby=0.402 and 40.2%.
What is average?
In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4. Thus, the meaning of average is to find the mean value of a group of numbers.
Average = Sum of Values/Number of Values
Also
Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:
Average = (x1+x2+x3+…+xn)/n
Now,
The batting averages and percentage of hits/bats for the players will be
Albert Pujois=187/524=0.356 and 35.6%
Stan Musial=230/611=0.376 and 37.6%
Rogers Honsby=203/504=0.402 and 40.2%
So I will put these in the order 1.Rogers Honsby 2.Stan Musial 3.Albert Pujois.
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Please help me with this question.
A sales presentation aims to attract and compel the audience to whom the presentation is made.
How do you create a sales presentation?Creating a sales presentation involves several steps:
Define the goal and audience of the presentation: Before creating the presentation, it is important to understand the goal of the presentation, and the target audience it is meant for. This will help you tailor the content of the presentation to the specific needs and interests of the audience.
Research the product or service: Understand the product or service you are selling inside and out. This will help you answer any questions that may come up during the presentation and show that you are an expert on the subject.
Create an outline: Once you have a clear understanding of your audience and the product or service, create an outline for the presentation. This will help you organize your thoughts and stay on track during the presentation.
Create compelling content: Use persuasive language and storytelling to create content that is engaging and easy to understand. Use statistics, testimonials, and visual aids to support your points.
Design the visual aids: Use charts, graphs, images, and other visual aids to supplement the text of your presentation. Make sure that the visual aids are clear and easy to understand, and that they support the points you are making.
Rehearsal: Practice the presentation several times before delivering it. This will help you build confidence and ensure that the presentation flows smoothly.
Delivery: During the presentation, engage with the audience and be responsive to their questions and feedback. Make sure that you are well-prepared and that you stay on track.
Follow-up: After the presentation, make sure to follow up with the audience and address any remaining questions or concerns they may have.
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Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... integral_1^infinity ln(x + 5)/x + 5 dx = O converges O diverges
The infinite series, [tex]ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx\\ [/tex] is diverges as the integral diverges.
We know that the Integral test : Suppose that f(x) is a continuous, positive and decreasing function on the interval [ k,∞) and that f(n)= a, then
If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is convergent then the series, [tex] \sum_{n = 1}^{ \infty } a_{n}[/tex]
If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is divergent so is [tex]\sum_{n = 1}^{ \infty } a_{n}[/tex].
We have an integral equals to an infinite series [tex] \frac{ln(6)}{6} + \frac{ln(7)}{7} + \frac{ln(8)}{8} + \frac{ln(9)}{9} + \frac{ln(10)}{10} + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx \\ [/tex]
[tex]\int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx = {\lim_{k-> \infty } \\}\int_{1}^{k} \frac{ln(x + 5)}{ (x + 5 )}dx [/tex]
[tex]= {\lim_{k-> \infty } \\}[ \frac{ {(ln(x+5))}^{2} }{2} ]_{1}^{k}\\ [/tex]
[tex] = \infty [/tex]
This implies that the integral diverges, so by integral test the series also diverges.
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Please help me with this question.
Answer:
a) 4
b) 2
Step-by-step explanation:
I use this sentence to remember quadrants:
All Students Take Coffe
- All trigs are positive in 1 Quadrant
- Sin and (cosine) is positive in 2 quadrant
-Tan and (Cotan) are positive in 3 quadrant
- Cos and (Sec) are positive in 4 quadrant
all other trigs other than those are negative.
a) cos is positive in 1 and 4 quadrant. Csc is reciprocal of Sin and is negative in 3 and 4 quadrant. 4th quadrant satisfies both conditions.
b) csc is reciprocal of Sin and is positive in 1 and 2 quadrants. Sec is reciprocal of Cos and is negative in 2 and 3 quadrant. 2nd quadrant fulfills both conditions.
For the following exercises, determine whether the relation represents a function. {(a, b),(b, c),(c, c)}
The relation {(a, b), (b, c), (c, c)} does not represent a function because for the input value "c", there are two possible output values, "c" and "c". In a function, for each input value, there can only be one output value.
The vertical line test may be used to assess whether or not a relation is a function by looking at its graph.
If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.
To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.
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1. You have a system of K equations in two variables, k >= 2. Explain the geometric significance of there being no solution.
If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.
What is a geometric significance?A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.
The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.
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System A
-2x-y+4=0
2x+y=4
System B
3x-y=6
3x+y=6
O The system has no solution.
The system has a unique solution:
(x, y) = (D
O The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
O The system has a unique solution:
(x, y) = D
The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
The correct statement regarding the equation is that A. the equation has no solution.
How to explain the equation?It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, the equation will be illustrated thus:
-2x - y + 4 = 0 .... i
2x + y = 4 ... ii
From equation i
-2x - y = -4
2x + y = 4
Add both equation will give 0.
The equation has no solution.
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there are n given points (numbered from 0 to n-1) on a plane maximum number of points inside the circle
Circle Detection Algorithm is a highly efficient and effective solution to finding the most number of points that lie on any one circle in a 2D real plane.
The algorithm to solve this problem is known as the "Circle Detection Algorithm." This algorithm starts by considering three points randomly selected from the given N points.
Next, the algorithm checks the number of points that lie on this circle. If this number is greater than the current maximum, then this circle becomes the new candidate for the circle that contains the most number of points.
To ensure that the algorithm is efficient, it is important to choose the points randomly, as this reduces the chances of getting stuck in a local maximum.
The mathematical formula to calculate the center and radius of the circle that passes through three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:
x = ( (y₂ - y₁)(y₃² - y₁² + x₃² - x₁²) - (y₃ - y₁)(y₂² - y₁² + x₂² - x₁²) ) / (2 * (x₃ - x₁)(y₂ -y₁) - 2 * (x₂ - x₁)(y₃ - y₁) )
y = ( (x₂ - x₁)(x₃² - x₁² + y₃² - y₁²) - (x₃ - x₁)(x₂² - x₁² + y₂² - y₁²) ) / (2 * (y₃ - y₁)(x₂ -x₁) - 2 * (y₂ - y₁)(x₃ - x₁) )
r = √(x₁ - x)² + (y₁ - y)²
Once the center and radius have been calculated, the algorithm can easily check the number of points that lie on the circle by calculating the distance of each point from the center and checking if it is equal to the radius.
Complete Question:
Given N points on the 2D real plane, what is the most efficient algorithm to find the most number of points that lie on any one circle?
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A coin flips 200 times. Heads 96 Tails 104
A proposed income tax charges 10% on a person's income up to $25,000 and then 20% on income above that. If a person has income of $60,000, what will their income tax be under the proposal?
Answer:
Step-by-step explanation:
The given parameters are:
10% on the first $25,000 of income
20% on income above $25,000
The above means that;
T(x) = x * 10%, when x <= 25000
T(x) = x* 20%, when x > 25000
Evaluate the products
T(x) = 0.1x, when x <= 25000
T(x) = 0.2x, when x > 25000
In this case, x = 60000
60000 > 25000
So, we have:
T(60000) = 0.2 * 60000
Evaluate
T(60000) = 12000
Hence. if a person has income of $60,000, their income tax be under the proposal would be $12000
Answer:The problem says that income up to $25,000 will be taxed at 10%. This is the first tier (or bracket). People who make more than $25,000, will pay 10% of their initial $25,000, and the higher rate of 20% on any income above $25,000. This is the second tier.
Let's calculate the amount of tax in this particular case. For a person making $60,000, they'll pay 10% of the first $25,000, and then 20% of the additional $35,000. We have,
Total Income Tax=Tax from Tier 1+Tax from Tier 2=10100⋅$25,000+20100⋅($60,000−$25,000)=$2,500+$7,000=$9,500.
Under the proposal, this person will pay $9,500 in taxes.
my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. when callie brooke raids the candy bowl, what is the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil? give your answer as a percent (including the percent sign) rounded to the nearest 0.01%.
If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.
How to find the probability?Total color = 5 gold + 7 blue + 10 pink
Total color = 22
Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil
Probability (pink) = 10/22
Probability (pink) = 0.45
Therefore the probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.
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Find an equation of the sphere with center (4, −12, 8) and radius 10.Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.)intersection with xy-plane intersection with xz-plane intersection with yz-plane
The equation of the sphere with center coordinates (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .
And different plane equations are :
Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²
Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²
Intersection with zx plane :( x - 4 )² + ( z - 8 )² = -44
Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :
( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²
⇒ x² -8x + y² + 24y + z² -16z + 224 = 100
⇒x² -8x + y² + 24y + z² -16z + 124 =0
Intersection with xy-plane
z = 0
( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²
⇒( x - 4 )² + ( y + 12 )² = 6²
Circle with center ( 4,-12) and radius 6.
Intersection with yz-plane
x = 0
( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²
⇒( y + 12 )² + ( z - 8 )² = (√84)²
Circle with center ( -12, 8) and radius √84.
Intersection with zx-plane
y = 0
( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²
⇒( x - 4 )² + ( z - 8 )² = -44
Not possible as radius cannot be negative.
Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:
xy-plane : ( x - 4 )² + ( y + 12 )² = 6²
yz plane :( y + 12 )² + ( z - 8 )² = (√84)²
zx plane :( x - 4 )² + ( z - 8 )² = -44
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the model shows that there are 9 picecs that are ft long i ready
Answer:
The model shows that there are 9 pieces that are each ft long.. The model shows that there are 9 pieces that are - 1.
A triangle is formed by the building's height
and shadow. Another triangle is formed by
the flagpole's height and shadow. Using the
following diagram, find the height of the
building.
Answer: 400 ft
Step-by-step explanation:
Since the triangles are Congruent Triangles (similar)
x/40 = 50/5
Cross multiply
5x = 2000
divide both sides by 5
5x/5 = 2000/5
x = 400 ft
5. An equilateral triangle is shown below.
Determine the AREA of the triangle.
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
[tex]altitude=\sqrt{8^2-4^2} =4\sqrt{2^2-1^2} =4\sqrt{3} \\area~of~triangle=\frac{1}{2} \times base \times altitude\\=\frac{1}{2} \times 8 \times 4\sqrt{3} \\=16\sqrt{3} \\\approx 27.7 ~in^2[/tex]
Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0
The point of intersection of the lines given is (1,4,2) and the plane determined is -3y +2z+8 = 0.
Let us first define the lines as -
L1 = x=3t+1, y=4t+4, z = 6t + 2
L2 = X=s+2 y=2s+6, z = 3s - 1
We have to find the intersection so -
= 3t+1 = s+2 ⇒ 3t - s - 1 = 0
= 4t+4 = 4t+4 ⇒ 4t - 2s - 2 = 0
= 6t + 2 = 3s - 1 ⇒ 6t - 3s + 3 = 0
Now, if we input the values of t and s as given in the question i.e., t = 0 and s = -1, we get -
= x = 1
= y = 4
= z = 2
These are the points of intersections of the given lines.
Now, the direction vector of L1 = (3,4,6) and L2 = (1,2,3)
So, the normal vector to the plane can be calculated using the determinant method.
[tex]\left[\begin{array}{ccc}i&j&k\\3&4&6\\1&2&3\end{array}\right][/tex]
On solving this, we get = -3j + 2k
The equation of the plane is -
= 0(x-1) - 3(y-4) + 2(z-2) = 0
= -3y +2z+8 = 0
The complete question that you might be looking for is given below -
Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0<t< 0 X=s+2 y=2s+6 2 = 3s - 1 , C < 5 < 0
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Como se calcula un ángulo de referencia?
The method to calculate the reference angle is discussed below.
What is reference angle?Reference Angle is the acute angle between the terminal side and the
x - axis.
Given is reference angle.
You determine a reference angle by looking at the terminal side of the angle you're working with and its relation with the positive or negative x-axis (depending on which quadrant the terminal side is in).
Therefore, the method to calculate the reference angle is discussed above.
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{Question in english -
How is a reference angle calculated?}
please help me will give u extra points :)
•
The compound inequality for the graph shown above include the following:
x < -2.
x > 5.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Since the point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.
Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.
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Double-Declining-Balance Depreciation
A building acquired at the beginning of the year at a cost of $107,600 has an estimated residual value of
$4,300 and an estimated useful life of 4 years. Determine the following.
rate
(a) The double-declining-balance
(b) The double-declining-balance depreciation for the first year
%
C
A method of accounting known as the double declining balance (DDB) maintenance method entails depreciating some assets at a rate that is twice that of straight-line depreciation. As a result, depreciation increases during the initial year of possession and decreases thereafter.
When is double dropping balance permissible?When to apply the twofold decreasing balance technique of depreciation When you buy assets that depreciate more rapidly in the first few years, the optimal scenario for using double reducing balance depreciation is that situation. The asset that lost value the most in the first few years of ownership is a car.
a) Straight-Line Depreciation Percent = 100% / 4 years = 25% / year
Depreciation Rate = 2 x 25% = 50% / year
b) Depreciation for a Period = 50% x Book Value at Beginning of the Period
Depreciation for Period 1 = 50% x $107,600 = $53,800
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A semi trailer is being packed with boxes that are 1 1/2 feet on each edge,
the cargo space of the trailer is 28 ft long, 8 1/2 ft wide, and 9 1/6 ft hight.
what is the maximum number of boxes that will fit in the trailer?
HELP PLSSSSSS!!
Answer:614
Step-by-step explanation:
The maximum number of boxes that can fit in the trailer can be calculated by dividing the volume of the trailer by the volume of each box.
First, we need to convert the dimensions of the boxes and the trailer to the same unit, such as cubic feet. The volume of each box is given by:
V_box = (1 1/2 ft)^3 = (1.5 ft)^3 = 3.375 ft^3
Next, we calculate the volume of the trailer:
V_trailer = 28 ft * 8 1/2 ft * 9 1/6 ft = 2070 ft^3
Finally, we divide the volume of the trailer by the volume of each box to find the maximum number of boxes:
N_boxes = V_trailer / V_box = 2070 ft^3 / 3.375 ft^3 = 614.07 boxes
Since we can only fit whole boxes in the trailer, the maximum number of boxes that will fit is 614.
Modeling with Composite Functions
A boutique prices merchandise by adding 80% to its cost. It later decreases by 25% the price of items that don't sell quickly.
a. Write a function f(x) to represent the price after the 80% markup.
b. Write a function g(x) to represent the price after the 25% markdown.
c. Use a composition function to find the price of an item after both price adjustments that originally the boutique $150.
d. Does the order in which the adjustments are applied make a difference? Explain.
a. f(x) = 1.8x.
b. f(x) = 1.35x.
c. f(150) = 1.35×150 ⇒ f(150) = 202.5.
d. The order in which the adjustments are applied doesn't make any difference.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.
Let, 'x' be the price of the merchandise.
So, After adding 80% to its cost it becomes [(100 + 80)/100]×x = 1.8x.
Later it decreases by 25% the price of items that don't sell quickly.
So, It has a value of (75/100)×1.8x = 1.35x.
a. A function f(x) to represent the price after the 80% markup is.
f(x) = 1.8x.
b. A function g(x) to represent the price after the 25% markdown is,
f(x) = 1.35x.
c. A composition function to find the price of an item after both price adjustments that originally the boutique $150 is,
f(150) = 1.35×150.
f(150) = 202.5.
d. Let, The price of the item be $100, after 80% makeup it would be
$180 and after 25% markdown it would be $135.
Again 25% markdown on $100 is $85 and an 80% markup is
75×1.8 = $135 hence no difference.
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