Answer:
Step-by-step explanation:
e
cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
Please help physics due in 30 mins!!!!
The work done is 3750 Joules on the box.
What is the recipe for work completed?To quantitatively express this concept, the work W is equal to the force f times the distance d, or W = fd. If the force is applied at an angle to the displacement, the work is W = fd cos.t.
The equation W = F * d * cos(theta), where W is the work done, F is the force applied, d is the displacement of the item, and theta is the angle between the force and displacement vectors, can be used to solve this problem.
The force in this instance is 500 N, and the distance is provided as 15 m, and the 60 degree angle between the vectors of force and displacement.
So, by changing these numbers in the equation, we obtain:
W = 500 N x 15 m x cos (60 degrees)
We can simplify this to: Applying the trigonometric identity cos(60 degrees) = 1/2
W = (500 N) * (15 m) * (1/2)
W = 3750 J.
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2 numbers add together to make -4 but subtract to make 8 what are the 2 numbers
Answer:
x=2 and y= ‐6
Step-by-step explanation:
Let the two numbers be 'x' and 'y'
Here, it says two numbers add up to make -4
So,
x+y= ‐4 .....equation (i)
Also, its says two numbers subtract to make 8
So,
x‐y=8 .....equation (ii)
We have,
x+y= ‐4 .....equation (i)
x‐y=8 .....equation (ii)
Subtracting equation (i) from equation (ii)
x‐y=8
x+y=‐4
-----------
‐2y=12
y=12/‐2
y= ‐6
Now, replacing value of x in equation (i)
x+y= -4
4x+(‐6) = -4
4x‐6= ‐4
x= -4+6
x= 2
Therefore the unknown numbers are 2 and ‐6
need help with this question
The graph of the function h(x) can be obtained using a horizontal stretch by a factor of 4, a horizontal translation to the right by 2 units, and a vertical translation 3 units up of the graph of g(x).
The graph of the function g(x) is a translation of the function f(x) 3 units up and 6 units to the left.
The graph of the function f(x) moves 6 units above the origin.
What is a translation?In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented or modeled by the following mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.Based on the information provided about the functions, we have the following:
f(x) = (x - 6)²
g(x) = x² + 3
h(x) = 4(x - 2)² + 3
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can someone explain interval and set notation (algebra 2)
Interval notation is a way to represent an interval of real numbers on the number line. Set notation is a way to represent a set of elements.
What is interval and set notation?Interval notation is a way to represent an interval of real numbers on the number line.
The notation uses parentheses, brackets, and infinity symbols to indicate whether the endpoints of the interval are included or excluded from the set of numbers.
For example, [3, 8) represents the interval of real numbers from 3 (included) to 8 (excluded), while (-∞, 4) represents the interval of real numbers less than 4 (excluding 4), and extending to negative infinity.
Set notation is a way to represent a set of elements. It uses curly braces to enclose the elements of the set and can include various symbols to indicate properties of the set.
For example, {2, 3, 5, 7, 11} represents the set of prime numbers less than 12, while {x | x is an even number} represents the set of even numbers.
The vertical bar | is used to separate the variable (x in this case) from the condition that must be met for elements to be included in the set (x is an even number).
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=
Suppose that a new employee starts working at $7.32 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y = $7.32(1.04). Find
the amount of time after which he will be earning $10.00 per hour.
After what amount of time will the employee be earning $10.00 per hour?
years (Round to the nearest tenth of a year as needed.)
HELP PLEASE
Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can start by setting up the equation for the employee's hourly wage y after t years -
[tex]y = $7.32(1.04)^t[/tex]
We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -
[tex]10 = $7.32(1.04)^t[/tex]
Dividing both sides by $7.32, we get -
[tex]1.367 = 1.04^t[/tex]
Taking the natural logarithm of both sides, we get -
[tex]ln(1.367) = ln(1.04^t)[/tex]
Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -
ln(1.367) = t ln(1.04)
Dividing both sides by ln(1.04), we get -
t = ln(1.367)/ln(1.04) ≈ 9.64
Therefore, the employee will be earning $10.00 per hour after about 9.64 years.
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if the shaded cross sections of the solids have the same area, which of the following corresponds to the value of a: the side length of the base of the square prism?
Therefore, the value of 'a' when the shaded cross-sections of the solids have the same area is
:a = √(4A/π).
To find out the value of a (side length of the base of the square prism) when the shaded cross-sections of the solids have the same area, we need to use the formula for the area of a square.
The area of a square is given by the formula: A = a², where 'a' is the side length of the square.
Now, let's look at the two solids given in the question.
The first solid is a square prism with base 'a' and height 'a'.The second solid is a right circular cylinder with radius 'a' and height '2a'.The cross-section of the square prism is a square with side length 'a'.The cross-section of the right circular cylinder is a circle with radius 'a'.
Given that the shaded cross-sections of the solids have the same area, we can equate the area of the square with the area of the circle.
A = πr², where 'r' is the radius of the circle Substituting the values of 'r' and 'a', we get:A = πa²/4 = a²/4Multiplying both sides by 4, we get:4A = πa²
Now we can solve for 'a' by taking the square root of both sides a = √(4A/π).
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What is the quotient of 6. 208 × 10^9 and 9. 7 × 10^4 expressed in scientific notation?
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
Quotient:
The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.
Based on the given conditions, Formulate:
6.208× 10⁹ /9.7×10⁴
Simply using exponent rule with same base:
[tex]a^n. a^m = a^(n+m)[/tex]
= 6.208 × 1/9.7
Now,
the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³
Now solving, we get:
6.208/9.7 × 10¹³
Converting fraction into decimal, we get:
0.64× 10¹³
⇒ 6.4 × 10¹²
Therefore,
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
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16 ft
Find the area.
20 ft
12 ft
10 ft
15 ft A = [?] ft²
Round to the nearest
hundredth.
then the area would be: [tex]Area=\frac{(a+b)}{2*h}[/tex] = (16 ft + 10 ft)/2 x 15 ft = 150 ft²
What is area?Area is a mathematical term that refers to the measurement of the size or extent of a two-dimensional region or surface. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²). The area of a shape is determined by multiplying the length and width of the shape in the case of a rectangle or square, or by using more complex formulas for irregular shapes such as circles, triangles, or polygons. The concept of area is important in various fields such as mathematics, geometry, physics, engineering, and architecture, among others.
by the question.
. If we assume that these are the dimensions of a rectangle, then the area would be:
Area = length x width = 20 ft x 12 ft = 240 ft²
However, if we assume that the area is a trapezoid with a height of 15 ft, and the parallel sides of length 16 ft and 10 ft.
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A student has 30 minutes to complete an exam. There are 9 multiple choice questions worth 3 points each. There are also 3 short answer questions worth 5 points each. It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question. How many multiple choice questions and short answer questions should the student answer to maximize his score in the time remaining (Use x = multiple choice; y = short answer.)State the Objective Function (S for score) in the linear programming problem givenA. S = 5x + 3y B. S = 3x + 5y C. S = 2x + 6y D. S = 6y + 2x
The Objective Function in the linear programming problem given in the above-stated scenario is:
B. S = 3x + 5y
Linear programming is a statistical technique used to find a maximum or minimum value of an equation in order to find a solution to a problem. It is used to calculate how much to produce to maximize profits, how to allocate resources, and determine which investments to make.
Linear programming problems include an objective function, which is the equation to be maximized or minimized, and constraints that must be followed. Linear programming problems can be solved graphically or algebraically. In order to solve a linear programming problem, we first need to identify the objective function and constraints.
Objective Function in the linear programming problem:
The score of the student is to be maximized in the given time frame by answering the maximum number of questions of both types.
Therefore, the objective function is: S = 3x + 5y
Answer: B. S = 3x + 5y
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please help
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
According to the graph, the balloon ascends between seconds 0 and 2; it remains stable between seconds 2 and 3; drops rapidly between 3 and 4 seconds; it descends slowly between seconds 4 and 6. Additionally, the natural thing is that it does not ascend again because gravity will not allow it to ascend.
How to describe the movement of the pump?To describe the movement of the balloon we must analyze the relationship between the height of the bomb and time. Based on the above, we see that it ascends, holds, descends rapidly, and then slows its rate of descent as described below:
The balloon ascends between seconds 0 and 2.The balloon is stable between 2 and 3 seconds.The balloon descends rapidly between seconds 3 and 4.The balloon slowly descends between seconds 4 and 6.Learn more about balloon in: https://brainly.com/question/18884332
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A city's population was 84,000 at the beginning of 2020. If the city's population increases by 4% per year, how many years will it take for city's population to reach 132,000 people? a. The answer to this question is the solution to what equation? [Let a represent the number of years since the beginning of 2020.] Preview b. Solve the equation in part (a)
a. The answer to this question is the solution to the equation:
84000(1 + 0.04)^a = 132000
Where "a" represents the number of years since the beginning of 2020, and 0.04 is the decimal equivalent of 4%.
We use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, we assume that the population growth rate is compounded annually, so n = 1.
b. Solving the equation in part (a), we get:
(1 + 0.04)^a = 132000/84000
1.04^a = 1.5714
a = log(1.5714)/log(1.04)
a ≈ 9.9 years
Therefore, it will take approximately 9.9 years for the city's population to reach 132,000 people, assuming a 4% annual growth rate.
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ax + b = 0 is the standard form of linear equation in one variable, but why is 0 given as the answer to the equation? Shouldn’t it be a constant there, one which is not 0? Please answer
Answer:
Step-by-step explanation:
In the equation ax + b = 0, the value of x is not fixed and can vary based on the values of a and b. The purpose of this equation is to find the value of x that satisfies the equation, given the values of a and b.
For example, if a = 3 and b = -6, then the equation becomes 3x - 6 = 0. Solving for x, we get x = 2. Thus, 2 is the value of x that satisfies the equation.
The reason 0 is often used as an answer to this equation is because it represents a special case where b = 0. In this case, the equation becomes ax = 0, and the only solution is x = 0. However, in general, the value of x can be any real number that satisfies the equation.
If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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how does a form differ from shape? form is defined by its allegiance to mathematical construction. form has more than three sides. form has the third dimension of depth. shape has more volume than form. save
Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.
We have,
In the context of geometry and visual representation, the terms "form" and "shape" have distinct meanings and characteristics.
Form generally refers to a three-dimensional object that has depth, such as a solid object or a structure with volume.
It encompasses objects that have length, width, and height, and it extends beyond a two-dimensional representation.
Form can have irregular or complex shapes and is not limited to a specific number of sides.
Shape, on the other hand, refers to the two-dimensional outline or boundary of an object.
It is limited to the external appearance or silhouette of an object without considering its depth or volume.
Shapes are typically described by their attributes, such as the number of sides (e.g., triangle, square) or specific geometric properties (e.g., circle, rectangle).
Thus,
Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.
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555 centigrams = 55.5 ________
decigrams
grams
decagrams
hectograms
555 centigrams = 55.5 GRAMS
The metric system is based on multiples of 10, where each unit is 10 times larger or smaller than the previous one. In this system, "centi-" means one hundredth, so 1 centigram is one hundredth of a gram. Therefore, 555 centigrams is equal to 5.55 grams (since there are 100 centigrams in 1 gram).
On the other hand, "deci-" means one-tenth, so 1 decigram is one-tenth of a gram. Therefore, 555 centigrams is also equal to 55.5 decigrams (since there are 10 decigrams in 1 gram).
In summary, 555 centigrams is equal to:
55.5 decigrams
5.55 grams
555 centigrams is equal to = 55.5 decigrams
Solution:1 cg is equal to 10 dg, therefore 555 cg is equivalent to 55.5 dg.
1 Centigram = 1 x 10 = 10 Milligrams
555 Centigrams = 555 / 10 = 55.5 Decigrams
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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A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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The arrival time of an elevator in a 12 story dormitory is equally likely at any time range during the next 4.7 minutes. o. Calculate the expected arrival time. (Round your answer to 2 decimal place.) Expected arval time b. What is the probability that an elevator arrives in less than 1.8 minutes? (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) c. What is the probability that the wait for an elevator is more than 1.8 minutes? (Round intermediate c places and final answer to 3 decimal places.)
a. Calculate the expected arrival time:
Given: Time range for arrival of elevator during the next 4.7 minutes is equally likely. The expected value of a discrete random variable is calculated by multiplying each possible value by its probability and adding up the products. So, we can calculate the expected value of the elevator arrival time by integrating the value of the probability density function (which is a straight line in this case) over the given interval. The area under the curve of the probability density function over the entire interval of possible values is 1. The expected arrival time (E) of the elevator is given by: E = (1/4.7) ∫(0 to 4.7) tdt= (1/4.7) [t²/2] [from 0 to 4.7]= 2.3596 minutes or 2.36 minutes (rounded to 2 decimal places)Therefore, the expected arrival time is 2.36 minutes.
b. Probability that an elevator arrives in less than 1.8 minutes:
To calculate the probability of an event happening, we need to find the area under the probability density function (pdf) over the given interval (in this case, less than 1.8 minutes). The pdf is a straight line with a slope of 1/4.7, so the equation of the line is: f(t) = (1/4.7) t. The probability of the elevator arriving in less than 1.8 minutes is: P(T < 1.8) = ∫(0 to 1.8) f(t) dt= ∫(0 to 1.8) (1/4.7) t dt= (1/4.7) [t²/2] [from 0 to 1.8]= 0.56765 (rounded to 4 decimal places)Therefore, the probability that an elevator arrives in less than 1.8 minutes is 0.568 (rounded to 3 decimal places).
c. Probability that the wait for an elevator is more than 1.8 minutes: The probability that the wait for an elevator is more than 1.8 minutes is the complement of the probability that it arrives in less than 1.8 minutes. P(T > 1.8) = 1 - P(T < 1.8) = 1 - 0.56765= 0.43235 (rounded to 3 decimal places)Therefore, the probability that the wait for an elevator is more than 1.8 minutes is 0.432 (rounded to 3 decimal places).
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f(x) = x². What is g(x)?
-5
g(x) s
A. g(x) = -x²
B. g(x)=x²-3
C. g(x)=x²-3
D. g(x)=-3x²
f(x) = x²
Answer:
g(x)= x²-3
Step-by-step explanation:
C. g(x)=x²-3
Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea levelsm
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
OC. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
On the number line, move 3 units to the left. End at -9. The dolphin was 9 feet below sea level.
What is location?
Location refers to the specific position or coordinates of an object or point in space or time. It can refer to the physical location of an object or place on Earth, such as a building or city, or the position of an astronomical object in the universe.
In a mathematical context, location is often expressed as a set of coordinates or points in a coordinate system.
Location is an important concept in various fields, including geography, cartography, astronomy, and mathematics, and is often used to describe and locate objects, places, or events in a precise and accurate manner.
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A plan for a house is drawn on a 1:40 scale. If the length of the living room on the plan measures 4.5 inches, what is the actual length of the built living room? 45 feet 25 feet 15 feet 12 feet
Answer:
actual length = 15 feet
Step-by-step explanation:
using the conversion
12 inches = 1 foot
the actual length = 40 × scale length = 40 × 4.5 = 180 inches = 180 ÷ 12 = 15 feet
A road running north to south crosses a road going east to west at the point P. car A is driving north along the first road, and an airplane is flying east above the second road. At a particular time the car is 15 kilometers to the north of P and traveling at 55 km/hr, while the airplane is flying at speed 185 km/hr 10 kilometers east of P at an altitude of 2 km. How fast is the distance between the car and the airplane changing? 148.38 km/hr Draw a sketch that shows the roads intersecting at point P, Car A, and the airplane. Label the horizontal distance from P to the airplane x and the vertical distance from P to Car A as y, and let z represent the altitude of the plane. What equation relates the distance from Car A to the plane with x, y and z? Using implicit differentiation, solve for the appropriate derivative that answers the "how fast" question.
The distance between car A and the airplane is changing at a rate of 148.38 km/hr.
To better understand this answer, we can draw a sketch of the scenario and label the variables accordingly.
Let x represent the horizontal distance from P to the airplane, y the vertical distance from P to car A, and z the altitude of the airplane. The equation that relates the distance from car A to the plane can be written as:
[tex]d^2 = (x^2 + y^2 + z^2)[/tex]
We can use implicit differentiation to solve for the derivative of this equation with respect to time, which answers the “how fast” question. The derivative of the equation is:
x = 185t (horizontal distance from P to airplane)
y = 15 - 55t (vertical distance from P to car)
z = 2 (altitude of airplane)
Now we can substitute these expressions into our equation for the distance between the car and the airplane, and take the derivative with respect to time:
distance between car and airplane = sqrt((185t)^2 + (15 - 55t)^2 + 2^2)
d/dt(distance between car and airplane) = d/dt(sqrt((185t)^2 + (15 - 55t)^2 + 2^2))
= 1/2 * (185^2 * 2t + (15 - 55t)(-55)) / sqrt((185t)^2 + (15 - 55t)^2 + 2^2)
Evaluating this expression at t = 0 (the time when the car is at its closest point to the airplane), we get:
d/dt(distance between car and airplane) = 1/2 * (185^2 * 2(0) + (15 - 55(0))(-55)) / sqrt((185(0))^2 + (15 - 55(0))^2 + 2^2)
= 1/2 * (-825) / sqrt(15^2 + 2^2)
= -412.5 / sqrt (229)
The negative sign indicates that the distance between the car and the airplane is decreasing, as expected. Finally, we can take the absolute value of this expression to get the speed at which the distance is changing:
d/dt (distance between car and airplane)| = 412.5 / sqrt (229) ≈ 148.38 km/hr.
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. An Estate dealer sells houses and makes a commission of GHc3750 for the first house sold. He receives GHc500 increase in commission for each additional house sold. How many houses must she sell to reach a total commission of GHc6500?
Answer: Let's denote the number of additional houses sold after the first one as "x".
Since the commission for the first house sold is GHc3750, the commission for selling x additional houses is GHc500x.
Therefore, the total commission earned by selling x additional houses is:
GHc3750 + GHc500x
We want to find the value of x that makes the total commission equal to GHc6500. Setting up an equation and solving for x, we get:
GHc3750 + GHc500x = GHc6500
GHc500x = GHc2750
x = 5.5
Since we can't sell half of a house, we round up to the nearest whole number. Therefore, the estate dealer must sell a total of 6 houses (including the first one) to reach a total commission of GHc6500.
Step-by-step explanation:
Define the relation O on Z as follows: ᵾm, n € z, m O n <----> ⱻk € z |(m – n) = 2k +1 Which one of the following statements about the relation O is true? a. The relation is reflexive, symmetric, and transitive. b. The relation is not reflexive, not symmetric, and transitive. c. The relation is not reflexive, symmetric, and not transitive. d. The relation is reflexive, not symmetric, and transitive.
The relation O is not reflexive, symmetric, and not transitive is one of the following statements that is true about the relation O. which is option (C).
Given, [tex]\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1[/tex]
Let's verify for the following relations :
Reflexive relation:
[tex]\forall a\in Z, a O a \longrightarrow \exists k\in Z \mid (a-a)= 2k+1[/tex]
[tex]0\neq 2k+1[/tex] for all k [tex]\in[/tex] Z
Since 2k+1 can never be zero for any k [tex]\in[/tex] Z, hence we conclude that the relation O is not reflexive.
Symmetric relation:
Suppose a, b [tex]\in[/tex] Zsuch that a O b i.e. (a-b)=2k+1, where k[tex]\in[/tex] Z.
Now, we need to check whether b O a is true or not i.e. (b-a)=2j+1 for some j[tex]\in[/tex] Z
We have,
[tex](a-b) = 2k+1 \longrightarrow (b-a) = -2k-1 = 2(-k) - 1[/tex]
Let j=-k-1, then we have j[tex]\in[/tex] Z and 2j+1 = -2k-1
Hence, (b-a) = 2j+1, and we conclude that the relation O is symmetric.
Transitive relation:
Suppose a, b, c[tex]\in[/tex] Z such that a O b and b O c.
Now, we need to check whether a O c is true or not.
We have,
(a-b)=2k_1+1 and (b-c)=2k_2+1 for some k_1,k_2[tex]\in[/tex] Z
(a-b)+(b-c) = 2k_1+1 + 2k_2+1
a-c = 2k_1+2k_2+2
Let j=k_1+k_2+1, then we have j[tex]\in[/tex] Z and a-c=2j
Hence, (a-c) is even and we conclude that the relation O is not transitive.
Therefore, the relation O is not reflexive, symmetric, and not transitive. Hence, option (C) is the correct answer.
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Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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HELPPPPPPP PLEASEEEEEEEEEEEEEEE
y=mx+b
The required equation of straight line is y = 0.03x + 20.
What is an equation?
A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.
The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.
From the given graph we get 2 points.
i.e., (0, 20) and (2000, 80)
Slope of the line is
[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]
Then the equation will be
[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]
Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.
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At the local pet store, zebra fish cost $2.00 each and neon tetras cost $2.30 each. If Yumi bought 13 fish for a total cost of $27.50, not including tax, how many of each type of fish did she buy?
If Yumi bought 13 fish for total then yumi bought 8 zebra fish and 5 neon tetras.
What is substitution?Substitution is a mathematical operation that involves replacing a variable or expression in an equation, function, or formula with another variable, expression, or value.
According to question:Let's assume Yumi bought x zebra fish and y neon tetras.
x + y = 13 (equation 1)
2x + 2.3y = 27.5 (equation 2)
Using equation 1, we can solve for one variable in terms of the other:
x = 13 - y
Then, change x in equation 2 to the following expression:
2(13 - y) + 2.3y = 27.5
Simplifying and solving for y:
26 - 2y + 2.3y = 27.5
0.3y = 1.5
y = 5
So Yumi bought 5 neon tetras. To find how many zebra fish she bought, we can substitute y = 5 into equation 1:
x + 5 = 13
x = 8
Therefore, Yumi bought 8 zebra fish and 5 neon tetras.
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