Answer:
Here
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the length, width, and height.
Volume = Length x Width x Height
Volume = 11 ft x 8 ft x 4 ft
Volume = 352 cubic feet
The surface area of a rectangular prism is found by adding up the areas of all six faces.
Surface area = 2lw + 2lh + 2wh
Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)
Surface area = 176 + 88 + 64
Surface area = 328 square feet
Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.
Which of the following equations will produce the graph shown below? A. x²/20 + y²/20 = 1 B. 20x² - 20y² = 400 C. 6x² + 6y² = 144 D. 5x² + 5y² = 80
An equation that will produce the graph shown above include the following: D. 5x² + 5y² = 80.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided above, we have the following parameters:
Radius, r = √16 = √80/5
Center, (h, k) = (0, 0).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = (√80/5)²
5x² + 5y² = 80.
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NO LINKS!!! URGENT HELP PLEASE!!
Express the statement as an inequality Part 5a^2
Answer:
a) x < 0 excluding zero.
b) y ≥ 0
Step-by-step explanation:
a)
"x is negative": This means that x is less than zero. Negative numbers are any numbers less than zero, so this statement implies that x is a negative number. For example, x could be -1, -2, -3, and so on.
so answer is x < 0 excluding zero.
"x > 0": This means that x is greater than zero. Positive numbers are any numbers greater than zero, so this statement implies that x is a positive number. For example, x could be 1, 2, 3, and so on."x ≤ 0": This means that x is less than or equal to zero. Non-positive numbers are any numbers less than or equal to zero, so this statement implies that x could be zero or any negative number. For example, x could be -1, -2, -3, or 0."x < 0": This means that x is strictly less than zero. This statement implies that x is a negative number, but it does not include zero. For example, x could be -1, -2, -3, and so on, but not 0."X < 20": This means that x is less than 20. Any number less than 20 satisfies this statement, so x could be any negative number, zero, or any positive number less than 20."x = 0": This means that x is exactly equal to zero. The value of x is not positive or negative, but zeroThe inequality that expresses the statement "x is less than 0" using the expression "5a^2" would be:
5a^2 > 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a". The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the two expressions, we get the inequality:
5a^2 > 0 and x < 0
b)
The statement "y is nonnegative" means that y is greater than or equal to zero. Therefore, the valid options for y are:
"y ≥ 0": This means that y is greater than or equal to zero. Any non-negative number satisfies this statement, so y could be 0, 1, 2, and so on."y > 0": This means that y is strictly greater than zero. Any positive number satisfies this statement, so y could be 1, 2, and so on, but not 0."y ≤ 0": This means that y is less than or equal to zero. The only value that satisfies this statement is y = 0."y < 0": This means that y is strictly less than zero. No non-negative number satisfies this statement, so there are no valid options for y in this case."y = 0": This means that y is exactly equal to zero. This statement is true because zero is nonnegative.Therefore, the valid option for y is y ≥ 0.
As the given statement "y is nonnegative" cannot be expressed as an inequality involving the expression "5a^2". The expression "5a^2" is a polynomial in the variable "a", and it is not related to the variable "y" in the statement.
The inequality that expresses the statements "x is less than 0" and "y is non-negative" using the expression "5a^2" would be:
5a^2 > 0 and y ≥ 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a".
The inequality "y ≥ 0" means that "y" is non-negative, or greater than or equal to zero.
The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the three expressions, we get the inequality:
5a^2 > 0 and y ≥ 0 and x < 0
I hope this helps!
Help please !!!!!!!!!!!!!!!!!!!!!
The constant of proportionality is 2/3
The length of the missing sides of triangle NRF are:
RF = 4.5
NR = 6
Similar Triangles : Calculating the constant of proportionalityFrom the question, we are to calculate the constant of proportionality in the similar triangles
Constant of proportionality =
Corresponding side length on triangle GTY / Corresponding side length on triangle NRF
Constant of proportionality = GY / NF
Constant of proportionality = 6 / 9
Constant of proportionality = 2/3
We are to find the length of the missing sides of triangle NRF
By the similarity theorem, we can write that
3 / RF = 6 / 9
3 / RF = 2/3
Cross multiply
2 × RF = 3 × 3
2 × RF = 9
RF = 9/2
RF = 4.5
4 / NR= 6 / 9
4 / NR= 2/3
Cross multiply
2 × NR = 4 × 3
2 × NR = 12
NR = 12/2
NR = 6
Hence,
The length of the missing sides are
RF = 4.5
NR = 6
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Please Help Quickly ASAP Hurry Geometry
Questions in the picture
The area of the figure, given the vertices on the coordinate plane, is 14 square units.
How to find the area ?The shoelace formula can be used to find the area. First, find the sum of the products :
= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)
= 2 + 6 + 8 + 16 - 2
= 26
Then the products of the y coordinate and the x coordinates :
= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 × -1 )
= - 2
We can then find the absolute value to be:
= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28
The area is then:
= 28 / 2
= 14 square units
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the area of a circle is 144m2 What is the diameter of the circle
Step-by-step explanation:
AREA = pi r^2
144 = pi r^2 shows r = 6.77 m ( or sqrt ( 144/pi) )
then diameter = 2 * r = 13.54 m (or 2 sqrt (144/pi) )
Answer:
7.64
Step-by-step explanation
This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D
The number of customers, y, queueing at the payment counter at a given time t, is given by equation:
y=t^3-14t^2+50t,where 0≤t≤8.5,
t is the number of hours after the shop opens at 9 am
Required:
1. Advise the management of the shop as to when they can deploy more cashiers and the number of customers queueing at that time. (6 Marks)
2. Determine the number of man-hours spent per day by shoppers queueing
Answer: 1. To find the time when the management should deploy more cashiers, we need to find the time when the number of customers queueing is the highest. We can find the maximum value of y by taking the derivative of the equation and setting it equal to zero:
dy/dt = 3t^2 - 28t + 50 = 0
Solving for t, we get:
t = (28 ± sqrt(28^2 - 4350)) / (2*3) = 4.67 or 9.33
Since the time has to be between 0 and 8.5 hours, the maximum occurs at t = 4.67 hours. Therefore, the management should deploy more cashiers around 1:40 pm (9:00 am + 4.67 hours). At this time, the number of customers queueing is:
y = 4.67^3 - 14(4.67)^2 + 50(4.67) = 51.64
So, there will be approximately 52 customers queueing at that time.
2. To find the number of man-hours spent per day by shoppers queueing, we need to integrate the equation for y over the range 0 ≤ t ≤ 8.5:
∫(0 to 8.5) y dt = ∫(0 to 8.5) (t^3 - 14t^2 + 50t) dt
Evaluating the integral, we get:
= [(1/4)t^4 - (14/3)t^3 + 25t^2] from 0 to 8.5
= (1/4)(8.5)^4 - (14/3)(8.5)^3 + 25(8.5)^2
= 1907.81
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 1908.
Step-by-step explanation:
To determine when the shop should deploy more cashiers, we need to find the maximum point of the function y(t), which corresponds to the peak of the queue. The maximum point of a cubic function is found at its turning point, which is where its derivative equals zero. Therefore, we can find the turning point by taking the derivative of y(t) and setting it equal to zero:
y'(t) = 3t^2 - 28t + 50
0 = 3t^2 - 28t + 50
Using the quadratic formula, we get t = 4.47 or t = 3.19.
However, we need to make sure that the maximum point lies within the given range of 0 ≤ t ≤ 8.5. Since 3.19 is within this range and 4.47 is not, the maximum point occurs at t = 3.19 hours after the shop opens.
What is the number of man-hours spent per day by shoppers queueing?To find the number of customers queueing at that time, we simply plug in t = 3.19 into the original equation:
y(3.19) = (3.19)^3 - 14(3.19)^2 + 50(3.19) ≈ 30.8
Therefore, the management of the shop should deploy more cashiers at 12:11 pm (9 am + 3.19 hours) when there are approximately 30.8 customers queueing.
To determine the number of man-hours spent per day by shoppers queueing, we need to find the total area under the curve of y(t) from t = 0 to t = 8.5. This area represents the total number of customers queueing during the day.
Using integration, we get:
∫(t^3 - 14t^2 + 50t)dt = (t^4/4) - (14t^3/3) + (25t^2) + C
where C is the constant of integration.
Evaluating this expression at t = 8.5 and t = 0, and subtracting the latter from the former, we get:
(8.5^4/4) - (14(8.5)^3/3) + (25(8.5)^2) - (0^4/4) + (14(0)^3/3) - (25(0)^2) ≈ 2233.1
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 2233.1. Note that this assumes that each customer spends exactly one hour in the queue, which may not be realistic, but provides a rough estimate of the total time spent.
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A mirror is placed 45 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.
36 ft
39.5 ft
56.25 ft
72 ft
If the hiker is 6 feet tall, then the height of the waterfall will be: 32.57 feet.
How to determine the height of the waterfallWe can solve this problem using similar triangles. Let us call the height of the waterfall "h". Then, the distance from the base of the waterfall to the mirror is also "h" (since the mirror reflects the top of the waterfall down to the hiker's eye).
Using similar triangles, we can set up the following proportion:
(h + 6 feet) / 45 feet = 6 feet / 7.5 feet
Cross-multiplying and simplifying, we get:
h + 6 feet = 270 feet / 7
h + 6 feet = 38.57 feet
h = 32.57 feet
So, the correct height given the variables is 32.57 feet.
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Answer:
36 ft
Step-by-step explanation:
We can use the concept of similar triangles to solve this problem. The ratio of the heights of the hiker and the waterfall is the same as the ratio of their distances to the mirror.
Given:
Distance from mirror to waterfall = 45 feet
Distance from mirror to hiker = 7.5 feet
Hiker's height = 6 feet
Let's set up a proportion:
(Hiker's height) / (Hiker's distance to mirror) = (Waterfall's height) / (Waterfall's distance to mirror)
Substitute the given values:
6 / 7.5 = (Waterfall's height) / 45
Now solve for the height of the waterfall:
Cross-multiply:
6 * 45 = 7.5 * (Waterfall's height)
270 = 7.5 * (Waterfall's height)
Divide by 7.5:
Waterfall's height = 270 / 7.5
Waterfall's height = 36 feet
So, the height of the waterfall is 36 feet.
Among the provided options, the correct answer is:
a) 36 ft
Nora has 3 poster boards. She plans to divide them into sixths. How many sixths can Nora make from the 3 poster boards?
i-Ready
Classify and Compare Quadrilaterals-Instruction - Level C
How are these rectangles alike? Choose true or false for each statement.
Both have 4 sides.
Both have 4 right angles.
Both have all sides the same
length.
True False
O
O O
X
According to Classification of Quadrilaterals,
i. Both rectangles have 4 sides - True
ii. Both rectangles have 4 right angle - True
iii. Both rectangles have all sides the same length - False
The classification of Quadrilaterals
Quadrilaterals are a type of geometric shape that have four sides. There are different types of quadrilaterals, and they can be classified based on the characteristics of their sides and angles. The main classifications of quadrilaterals are:
Trapezoid or Trapezium: a quadrilateral with only one pair of parallel sides.
Kite: a quadrilateral whose two adjacent pairs of sides are of equal length.
Parallelogram: a quadrilateral with opposite sides that are parallel to each other.
Rhombus: a quadrilateral with all sides equal in length.
Rectangle: a quadrilateral with opposite sides that are parallel and all four angles are right angles (90 degrees).
Square: a quadrilateral with all sides equal in length and all four angles are right angles (90 degrees).
These are the main classifications of quadrilaterals, and each type has its own specific properties and characteristics that distinguish it from the others.
According to the given information:
i. Both have 4 sides - True
A rectangle has four sides because it is defined as a quadrilateral with two pairs of parallel sides and four right angles. This means that opposite sides of a rectangle are parallel to each other and have the same length, while adjacent sides are perpendicular to each other and form right angles.
So, by definition, a rectangle must have four sides in order to meet these criteria and be classified as a rectangle.
ii. Both have 4 right angle - True
In a rectangle, by definition, opposite sides are parallel to each other and adjacent sides are perpendicular to each other. This means that each of the four corners of a rectangle must form a right angle, where two sides meet at a 90-degree angle.
iii. Both have all sides the same length - False
Not all rectangles have all sides the same length. While a square is a type of rectangle where all sides are equal, rectangles can have different lengths for their adjacent sides.
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please answer and explain how to get it.
The value of x is given as follows:
x = 21 cm.
How to obtain the value of x?The value of x is obtained applying the proportions in the context of the problem.
The ratio between the volumes is given as follows:
2430/90 = 27.
The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:
x/7 = cubic root of 27
x/7 = 3
x = 21.
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Use the following scenario. Five surf shops sell the same pair of flip-flops for the following set of prices: {$17.00, $15.50, $15.00, $18.00, $15.00}.
Select all the correct measures of center and variation for the data set.
a. Range = 4
b. IQR = 2.50
c. Median = 15.50
d. Third quartile = 17.50
e. Mean = 15.80
Answer: b, c, d,
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The measurements of the circumstances and radii of circles with different areas are recorded and analyzed. Which statement justifies why this information can be used to approximate the value of pi?
A. The area of a circle varies inversely as the radius.
B. The circumference of a circle varies inversely as the radius.
C. The circumference of a circle varies directly as the radius.
D. The area of a circle varies directly as the radius.
The correct answer is C. The circumference of a circle varies directly as the radius.
What is circumference?It is calculated by multiplying the diameter of a circle by pi, or by measuring the length of a curved line that encloses the shape.
The relationship between the circumference of a circle and its radius is a linear equation, where the circumference is equal to two times pi times the radius, or C = 2πr.
The circumference of a circle varies directly as the radius, meaning that if the radius of a circle is doubled, the circumference will also double.
This linear relationship can be used to approximate the value of pi, which is a constant ratio between the circumference and the diameter of any circle.
Therefore, the statement that justifies why the measurements of the circumference and radii of circles with different areas can be used to approximate the value of pi is that the circumference of a circle varies directly as the radius.
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The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.
In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was Xbar=282. We want to estimate the mean score in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation =40.
If we take many samples, the sample mean Xbar varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score in the population. What is the standard deviation of this sampling distribution?
Give your answer to four decimal places.
The standard deviation of the sampling distribution is approximately 0.3292.
What is central limit theorem?The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.
Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.
The standard deviation is given by the formula:
SD = σ/√(n)
Now, substituting the value of σ = 40, n = 147,400 we have:
SD = σ/√(n) = 40/√(147400) ≈ 0.3292
Hence, the standard deviation of the sampling distribution is approximately 0.3292.
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How many gallons of a 80% alcohol solution and a 20% alcohol solution must be mixed to get 9 gallons of 60% alcohol solution?
In linear equation, x = 6 gallons (of 80% alcohol)
y = 3 gallons (of 20% alcohol)
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Let
x = liters of 80% alcohol
y = liters of 20% alcohol
There are two unknowns, we need two equations
x + y = 9. (1)
0.80x + 0.20y = 0.60(x+y) (2)
From (1)
x + y = 9
y = 9-x
Substitute the value of y into (2) and solve for x:
0.80x + 0.20y = 0.60(x+y)
0.80x + 0.20(9-x) = 0.60(x+9-x)
0.80x + 1.8 - 0.20x = 0.60(9)
0.80x + 1.8 - 0.20x = 5.4
0.6x = 3.6
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 9
6 + y = 9
y = 3 gallons (of 60% alcohol)
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need help on this question from edmentum
The correct location of each of the expressions obtained the properties of exponents are;
2; (3²·4³·2⁻¹)/(3·4)², ((3·2)⁴·3⁻³)/(2³·3)
1; (3⁻³·2⁻³·6³)/((4⁰)²)
1/2; (2⁴·3⁵/(2·3)⁵)
What are exponential operations?Exponential operations are operations involving two numbers, which includes the base number and the exponent.
The exponential expressions can be simplified using laws of indices or the properties of exponents as follows;
(2⁴·3⁵)/((2·3)⁵) = (2⁴·3⁵)/(2⁵·3⁵) = (2⁴/2⁵) × (3⁵/3⁵)
(2⁴/2⁵) × (3⁵/3⁵) = (2⁴/2⁵) × 1 = 1/2
Therefore; (2⁴·3⁵)/((2·3)⁵) = 1/2
(3²·4³·2⁻¹)/((3·4)²) = (3²/3²)·(4³/4²)·(2⁻¹)
(3²/3²)·(4³/4²)·(2⁻¹) = 1 × 4 × (1/2) = 2
Therefore; (3²·4³·2⁻¹)/((3·4)²) = 2
((3·2)⁴·3⁻³)/(2³·3) = ((3⁴·2⁴)·3⁻³)/(2³·3)
((3⁴·2⁴)·3⁻³)/(2³·3) = (3⁴/3)·(2⁴/2³)·3⁻³ = (3³·3⁻³)·2 = 2
Therefore; ((3·2)⁴·3⁻³)/(2³·3) = 2
(3⁻³·2⁻³·6³)/((4⁰)²) = (3⁻³·2⁻³·6³)/1
(3⁻³·2⁻³·6³)/1 = (6³/3³)/2³
6³/3³ = 2³
Therefore; (6³/3³)/2³ = 2³/2³ = 1
(3⁻³·2⁻³·6³)/((4⁰)²) = 1
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How many total mangement are there in the organization if 40 have a technical degree and 100 have a non technical degree
The total number of employees in the organization will be 140.
Given that:
There are 40 employees who have a technical degree
There are 100 employees who have a non-technical degree
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The total number of employees are calculated as,
Total = Employees who have a technical and non-technical degree
Total = 40 + 100
Total = 140
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The rectangular coordinates of a point are (17,0). Find the polar coordinates.
The polar coordinates of the point (17,0) are (r,θ) = (17,0). This means that the point is located on the positive x-axis, at a distance of 17 units from the origin.
To find the polar coordinates of a point given in rectangular coordinates, we need to use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point.
In this case, the point is (17,0), so x = 17 and y = 0. Using the formulas above, we get:
r = √(17² + 0²) = 17θ = tan⁻¹(0/17) = 0
In polar coordinates, a point is represented by an ordered pair (r,θ), where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.
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(x- 4 8/11) + 1 9/11 = 7 3/11 what is x?
Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.
Explain about the mixed fractions:A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls in between two whole numbers.
Multiply the whole integer by the denominator, then add the numerator to create an incorrect fraction out of a mixed number. The response here becomes the new numerator, while the denominator stays the same.
Given expression:
(x- 4 8/11) + 1 9/11 = 7 3/11
Solving all the mixed fractions in proper fractions:
4 8/11 = (4*11 + 8) / 11 = (44 + 8) /11 = 52/11
1 9/11 = (1*11 + 9) /11 = (11 + 9)/ 11 = 20/11
7 3/11 = (7*11 + 3) /11 = (77 + 3)/11 = 80/ 11
Put the obtained results in expression:
(x- 52/11) + 20/11 = 80/11
x - 52/11 = 80/11 - 20/11
x - 52/11 = (80 - 20)/11
x - 52/11 = 60/11
x = 60/11 - 52/11
x = (60 - 52) / 11
x = 8/ 11
Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.
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Provide an example of a function that does not have an inverse function. Explain how you determined this.
Answer:
f(x) = x^2
Step-by-step explanation:
A function that does not have an inverse function is called a non-invertible or many-to-one function. An example of a non-invertible function is:
f(x) = x^2
To determine if a function is invertible, we need to check if it passes the horizontal line test. If a horizontal line intersects the graph of the function at more than one point, then the function is not invertible.
For the function f(x) = x^2, if we draw a horizontal line at any value of y, it will intersect the graph of the function at two points, one on the positive x-axis and the other on the negative x-axis.
Therefore, f(x) is not invertible, as it fails the horizontal line test.
In other words, there are multiple x-values that correspond to a single y-value. For example, both x = 2 and x = -2 have the same y-value of 4. As a result, there is no unique inverse function that could map a value of 4 back to a single x-value.
In conclusion, the function f(x) = x^2 is an example of a non-invertible function, as it fails the horizontal line test and does not have a unique inverse function.
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)
F(x, y, z) = [tex]xyz^3[/tex] i + [tex]x^2z^3[/tex] j + [tex]3x^2yz^2[/tex] k
Answer:its is conservative
Step-by-step explanation:
eading Tools
Two students began a proof of the law of sines.
C
A
Student I
sin(A)=
Sin(B) =
bsin(A) =h
asin(B) = h
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A)=
sin(B) ==
asin(A) = h
bsin(B) = h
B
asin(A)=bsin(B)
sin(A)=sin(B)
a
Which student correctly started the proof, and what should that student do next to complete the proof?
Answer: no answer
Step-by-step explanation:
Evaluate the surface integral ∫∫H4ydA where H is the helicoid (i.e., spiral ramp) given by the vector parametric equation
r⃗ (u,v)=⟨ucosv,usinv,v⟩, 0≤u≤1, 0≤v≤9π.
According to the given information, the value of the surface integral is 8/3.
What is surface area?The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
According to the given information:The surface integral of a vector field F over a surface S is given by:
∬S F ⋅ dS = ∬R (F ⋅ ru × rv) dA
where R is the parameter domain of the surface S, ru and rv are the partial derivatives of the position vector r(u,v) with respect to u and v, and dA = ||ru × rv|| dudv is the area element on the surface.
In this case, we want to evaluate the surface integral:
∫∫H 4y dA
where H is the helicoid given by the vector parametric equation:
r(u,v) = <u cos(v), u sin(v), v>, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.
The position vector r(u,v) has partial derivatives with respect to u and v given by:
ru = <cos(v), sin(v), 0>
rv = <-u sin(v), u cos(v), 1>
The area element is given by:
dA = ||ru × rv|| dudv = ||<cos(v), sin(v), u>| dudv = u dudv
Therefore, the surface integral can be written as:
[tex]$\int\int_H 4y dA = \int_0^{9\pi} \int_0^1 4(u\sin v)u dudv$\\$= \int_0^{9\pi} \sin v \int_0^1 4u^2 du dv$[/tex]
[tex]$= \int_0^{9\pi} \sin v \left(\frac{4}{3}\right) dv$\\$= \left[-\frac{4}{3} \cos v\right]_0^{9\pi}$[/tex]
= 8/3
Hence, According to the given information the value of the surface integral is 8/3.
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Who knows how to do thisssssss
I Got U Bro! Answer:(x+5)2+(y+3)2=16
:D
Question in attachment...................
Answer:
12.5ft tall.
Step-by-step explanation:
The volume of a rectangular box is V = L x W x H
We are given volume, length, and width, allowing us to solve for height.
3000 ft^3 = 96 ft x 2.5 ft x H ft
Divide both sides by 96 x 2.5 to isolate H
3000 / (96 x 2.5) = H
H = 12.5 ft.
Answer:
12.5 feetStep-by-step explanation:
It's given that One of the first electronic computer was in the shape of a huge box. It was 96 m long and 2.5 m wide.
Length of the box = 96 feet
Breadth of the box = 2.5 feet
Also The amount of space inside was approximately 3,000 cubic feet i.e volume of the box is 3000 ft³.
We know that volume of cuboid is calculated by,
Volume = l × b × h96 × 2.5 × h = 3000
240 × h = 3000
h = 3000/240
h = 12.5 feet
Therefore, Height of the computer is 12.5 feet
The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 5600 calories per day. However, they discover that they are missing 28,000 calories. Using the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 5,600 calories of food per day until he or she gets back to base camp.
Be sure to explain how you came up with your plan. Include all work necessary to support your answer.
Please answer as soon as possible due in an hour. Thank you.
The word problem shows that we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.
How to calculate the valueThe plan for the rest of the trip involves splitting the group into two parts: 3 members continuing to the South Pole with 2.5 days of food, and 2 members returning to base camp with 2.5 days of food.
28,000 calories / 5,600 calories per day = 5 days of food
So we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.
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Write the 10th term of each sequence. first term 7 and common difference 15
As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.
what is arithmetic progression ?An arithmetic progress (AP) in mathematics is a set of numbers where each term following the first is formed by adding a predetermined constant to the term before it. The mathematical progression's common difference is the name of this unchanging constant. For instance, the number progression 3, 7, 11, 15, 19,... has a common difference of 4 and is an arithmetic progression. The formula: yields the nth word of an arithmetic progression. a n = a 1 + (n - 1)d where n is the desired term's number, a n is the sequence's nth term, a 1 is its first term, d is its clear differentiation, and n is its number.
given
We can use the following formula to determine the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15:
a n = a 1 + (n - 1) * d
where a n represents the nth term in the series, a 1 represents the first term, d represents the common difference, and n is the desired term's number.
Inputting the values provided yields:
[tex]a 10 = 7 + (10 - 1) (10 - 1) * 15 \\a 10 = 7 + 9 * 15 \\a 10 = 7 + 135 \\a 10 = 142[/tex]
As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.
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A basketball with a 12 cm radius is placed into a 24 cm x 24 cm x 24 cm box. The
amount of space inside the box but outside the basketball is
cm³
(Use 3.14 for 7).
The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.
We have to find the volume of the box and volume of the basketball to determine the space outside it.
Box is in rectangular shape.
Volume of the box = 24 × 24 × 24
= 13824 cm³
Basketball is spherical in shape.
Volume of the sphere = 4/3 π r³
= 4/3 π (12)³
= 2304π
= 7234.56 cm³
Amount of space inside the box but outside the basketball is,
13824 cm³ - 7234.56 cm³ = 6589.44 cm³
Hence the required space is 6589.44 cm³.
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32 is what percent of 50?
Answer:
To find the percentage, you need to divide the first number by the second number and then multiply by 100. In this case:
32 ÷ 50 = 0.64
Multiplying by 100 gives:
0.64 × 100 = 64
Therefore, 32 is 64% of 50.
Step-by-step explanation:
Answer:
64%
Step-by-step explanation:
32/50 x 2 (you need to make it over 100)
= 64/100
= 64%
Hassim's Fireworks & Cycles had free cash flow of R129 550 this year, and expects this to grow by 3% each year for the foreseeable future. The company has a weighted average cost of capital of 8%. What is the value of the company today? 01R 119 186 O2 R 139 914 4. R1 271 945 R2 668 730
Answer:
To calculate the value of Hassim's Fireworks & Cycles today, we can use the formula for the present value of a growing perpetuity:
PV = FCF / (r - g)
where PV is the present value, FCF is the free cash flow, r is the weighted average cost of capital, and g is the growth rate.
Substituting the given values, we get:
PV = 129550 / (0.08 - 0.03)
PV = 2591000
Therefore, the value of Hassim's Fireworks & Cycles today is R2,591,000.
Physicians at a clinic gave what they thought were drugs to 820
patients. Although the doctors later learned that the drugs were really placebos,
52% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patient's condition improving is .48
Test the hypotheses that the proportion of patients improving is >
.48
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
what is null hypothesis ?The null hypothesis in statistics is a claim that presupposes there is no statistically significant distinction among the two or even more variables be compared. The antithesis of the alternative hypothesis, it is frequently denoted as H0 (Ha). While conducting statistical studies, the null is often evaluated to see if there is sufficient proof against it or not. The default assumption is typically the null hypothesis, and it serves as a benchmark for comparison of the statistical analysis's findings. A statistically significant distinction between the variables under comparison is said to exist if the statistical analysis yields sufficient data to refute a null hypothesis.
given
To test the hypothesis, we can utilise a z-test. This is the test statistic:
[tex]z = (x - E) / σ[/tex]
where x is the observed percentage of patients whose conditions are getting better. x = 820 * 0.52 = 426.4 is the result. Therefore:
z = (426.4 - 393.6) / 0.026 = 1245.98
P(Z > z) = 1 - P(Z z) is the p-value for this one-tailed test, where Z is a normal standard variable. By using a typical table or calculator, we discover:
P(Z > 1245.98) < 0.0001
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
We have enough data to draw the conclusion that the percentage of patients whose conditions are improving is more than 0.48.
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