Note that the Economic Order Quantity is given as approximately 4,472.13 Units.
Economic Order Quantity, also known as Economic Purchasing Quantity, is the order quantity in inventory management that minimizes overall holding costs and ordering expenses. It is one of the most ancient traditional production scheduling models.
EOQ = √[(2 * AR* OC)/CC]
Were AR = Annual Requirement = 100,000 units
OC = Ordering Cost = Rs 20 per unit
CC = Carrying Cost = 10% of Per Unit Cost
Per Unit Cost = Rs. 2
Thus,
EOQ = √[(2 * 100,000* 20)/10% * 2]
EOQ = √[(4000000)/0.2]
EOQ = √20000000
EOQ = 4472.135955
EOQ [tex]\approx[/tex] 4,472.13 Units.
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Problem 10
1. The hexagon represents 1 whole.
Draw a pattern-block diagram that represents the equation 4.
Draw your diagram on paper, take a picture, and upload it using the image upload icon
If you do not have the ability to upload an image of your work, type "Diagram is on paper."
Porfavor lo necesito para el martes o si no voy a reprobar
According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)
How to graph the equation?According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.
In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.
Note: This question is incomplete. Here is the complete information:
Image attached
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A graphing calculator is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in, by 20 in. by cutting out equal squares of side x at eech corner and then folding up the sides (see the figure). 20 in. 12 in. (a) Find a function that models the volume V of the box. (b) Find the values of x for which the volume is greater than 230 in2. (Rgund your answers to three decimal places. Enter your answer using interval notation) (c) Find the largest volume that such a box can have. (Round your answer to three decimal places) in2
A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.
A function that models the volume V of the box can be found by subtracting four [tex]x2[/tex]from both the length and the width, and then multiplying the result to get the volume:
V = [tex](12 - 4x2)(20 - 4x2)[/tex]
To find the values of x for which the volume is greater than 230 in2, we can solve the equation
V = [tex](12 - 4x2)(20 - 4x2) = 230[/tex] for x.
This gives x values of ±2.636
Thus, the values of x for which the volume is greater than 230 in2 are x = [[tex]-2.636, 2.636[/tex]].
The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.
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Tuna can be bought in 12-oz cans for $1.10 each or in 10 oz cans that sell for $0.98 each. Which is a better buy? USE UNIT RATIOS TO ANSWER THIS PROBLEM.
Answer: Option 1
Step-by-step explanation:
I'd say the easiest way would be to find the prize per oz in both options
Option 1: $1.10/12oz = approx 0.092 (so around 9 pennies)
Option 2: $0.98/10oz = 0.098 (also 9 pennies but still slightly more than option 1)
You can check by choosing a random number of oz and multiplying them by the price to see which costs more
ex: 120 oz
option 1 : 10 x 1.10 = $11
option 2: 12 x 0.98 = $11.76
All of the following constructions start with a line segment except...
O constructing a 45° angle
O constructing a 30° angle
O constructing congruent angles
• constructing equilateral triangles
All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.
What is meant by line segment?The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.
An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.
A line segment serves as the foundation for the following angles and lines in geometry:
The process of creating a line perpendicular to a point on a line.
The creation of a 45-degree angle (45°).
The creation of a 30-degree (30-degree) angle.
Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.
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Please helppppp me with the question
Answer: 30 in
Step-by-step explanation:
To figure out perimeter, you have to add up all of the sides.
The sides of the triangle are 7, 10, and 13 in.
7+10+13=30
The answer is 30 inches.
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PLEASE HELP!!! VERY URGENT
A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following questions using complete sentences. 2 points for each correct answer and 2 points for each correct explanation.
i. What is the person's displacement from the starting point? How did you calculate this? Be sure to round to the nearest hundredth.
ii. From point B, in what direction would the person have to look in order to be looking back at point A (the starting point)? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
iii. A friend is standing at point A looking at point B. In what direction would that friend be looking? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
The answers are mentioned below.
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).
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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.
Therefore, the displacement can be calculated as the
√(500² + 300²)
= 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.
Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be
360 - 31.39
= 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.
However, the true bearing is measured from the north and therefore, the true bearing would be
90 + 59.04
= 149.04 degrees (rounded to the nearest hundredth).
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Problem #1
A motorist travelling at 90 km/h applied the brakes until the car stopped. If the stopping distance was 12 m, what was the acceleration? (-26 m/s2)
The acceleration was -26.04 m/s².
What are Equations of Motion?Equations of motion are a set of equations which describes the basic motion concepts like velocity, position, time and acceleration.
There are mainly three equations of motion.
v = u + at
s = ut + [tex]\frac{1}{2}[/tex] at²
v² = u² + 2as
v is the final velocity, u is the initial velocity, a is the acceleration, t is the time and s is the displacement.
Given,
Initial velocity of the motorist, u = 90 km/h = 90 × (5/18) m/s = 25 m/s
Final velocity of the motorist, v = 0 m/s (since the bike stopped)
Stopping distance, s = 12 m
Using the third equation of motion,
v² = u² + 2as
0² = 25² + (2a × 12)
24a = -625
a = -625 / 24 = -26.04 ≈ -26 m/s²
Hence the acceleration of the motorist was -26 m/s².
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13. Communicate and Justify A sequence starts with 16. The pattern is divide by 2. Another sequence starts with 1. The pattern is multiply by 2. Do the two sequences have the same number in the same position? Explain.
The two sequences have the same number (4) in the same position (third)
How to determine if the two sequences have the same number in the same position?From the question, we have the following parameters that can be used in our computation:
A sequence starts with 16. The pattern is divide by 2. Another sequence starts with 1. The pattern is multiply by 2Using the above as a guide, we have
Sequence 1: 16, 8, 4, 2, 1.....
Sequence 2: 1, 2, 4, 8, 16.....
The number 4 is in the same position for the two sequences
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Write an equation in slope intercept form for the line that passes through the two given points.(-3,4) (3,2)
Answer:
y = -1/3 x + 3
Step-by-step explanation:
To find the equation of the line that passes through the two points (-3,4) and (3,2) in slope-intercept form, we'll first find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two given points.
Plugging in the given points, we get:
m = (2 - 4) / (3 - (-3)) = -2 / 6 = -1/3
Next, we'll use the point-slope form of a line to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
We'll use the first given point, (-3,4), so we have:
y - 4 = -1/3 (x - (-3))
Expanding the right side of the equation, we get:
y - 4 = -1/3 x + 1
Finally, we'll rearrange the equation to get it in slope-intercept form, which is:
y = -1/3 x + b
where b is the y-intercept. To find b, we'll plug in one of the given points and solve for b:
y = -1/3 x + b
4 = -1/3 * (-3) + b
4 = 1 + b
b = 4 - 1
b = 3
So the equation of the line in slope-intercept form is:
y = -1/3 x + 3
Name
2-Step Word Problems
There were 24 polar bears and 38
penguins swimming in the ocean. 15
polar bears got out of the water.
How many polar bears and penguins
are left playing in the water?
polar bears and penguins
My brother made 46 snowballs and I
made 59 snowballs. My sister joined
us and made 25 more snowballs.
How many snowballs do we have
altogether?
i
My mother had a collection of 51
snow globes. She received 8 more
snow globes for her birthday. My
brother and I started fighting and
broke 12 snow globes. How many
snow globes does my mother have
left?
snowballs
snow globes
-
ate:
There were 83 adult penguins and
69 baby penguins playing on the hill.
55 mother penguins went home.
How many penguins are left playing
on the hill?
penguinsi
There are 47 polar bears and penguins in the water.
The number of snowballs made altogether is 130 snowballs.
The number of snow globes your mother has left is 47 snow globes.
The number of penguins left playing is 97 penguins.
How to solve word problems?Number of polar bears= 24
Number of penguins = 38
No. of polar bears that got out of the water= 15
Total polar bears and penguins in the water = (24 + 38) - 15
= 47
Number of snowballs made by your brother = 46
Number of snowballs made by you = 59
Number of snowballs made by your sister, brother and you = 25
Total snowballs made= 46 + 59 + 25
= 130 snowballs
Number of snow globes mother has = 51
Number of additional snow globes received = 8
Number of snow globes broken = 12
The number of snow globes your mother has left= (51 + 8) - 12
= 59 - 12
= 47 snow globes
Number of adult penguins(mother and father) = 83
Number of baby penguins = 69
Number of mother penguins that went home = 55
Number of penguins left playing = (83 + 69) - 55
= 97 penguins.
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Need help quick with this problem!!!!
The product of a, b, and c is 27/8.
What is an expression?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.
The given expression is
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]
To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:
Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]
Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]
Putting the simplified numerator and denominator together, we have:
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]
Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:
a * b * c = 3 * (-3/4) * (-3/2) = 27/8.
Hence, the product of a, b, and c is 27/8.
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Use the discriminant to describe the solutions as one real, two real, or two
imaginary solutions.
4. x2 − 15x + 12 = 0 5. 3x2 − 6x + 4 = 0
The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.
What is solution to the Equation?The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:
1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).
2) The equation has one repeating real solution if the discriminant equals zero (s).
Given:
x² − 15x + 12 = 0
Solving the Quadratic Equation
x² − 15x + 12 = 0
D = b² - 4ac
D = (-15)² - 4(1)(12)
D = 225 - 48
D = 177 >0
So, the Equation will have two Real solution.
b) 3x² − 6x + 4 = 0
Solving the Quadratic Equation
3x² − 6x + 4 = 0
D = b² - 4ac
D = (-6)² - 4(3)(4)
D = 36 - 48
D = -12 >0
So, the Equation will have Imaginary solution.
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NEED HELP!!!!!!!!!!!
Answer:
[tex]4x^{2} y^{3}[/tex]
Step-by-step explanation:
[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]
In the denominator, all the terms in the brackets or parenthesis will be squared:
= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]
Law of indices is applied:
[tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]
= [tex]4x^{4 - 2} y^{5 - 2}[/tex]
= [tex]4x^{2} y^{3}[/tex]
∴Option B
Solve the system by substitution.
y = 5x
y = 4x + 9
Answer:
x=9
Step-by-step explanation:
Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.
Justin jogged for four days in a row. On the second day, he jogged 75% of the distance he jogged the first day. On the third day, he jogged 1.5 miles, more than the distance he jogged the first day. If Justin jogged a total distance of 9.25 miles, how many miles did he jogged on the fourth day?
On solving the prοvided question, we can say that 4.75 miles were ran on day four.
What is equation?A mathematical equation is a formula that jοins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equatiοn in algebra.
Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences οn either side of a letter is described by a mathematical formula. Often, there is only οne variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.
On day one, Justin ran two miles.
He ran two miles on the second day, or 75% of it. Divide by 100 and multiply by 75 to get the percentage of two miles that is 75%.
On the secοnd day, I ran 1.5 miles, or 2 / 100, or 0.02 x 75. (I've run 3.5 miles so far)
He ran 1.5 miles further on the third day than the previous one:
1.5 + 1.5 = 3 (6.5 miles jogged sο far) (6.5 miles jogged so far)
The total number of miles run was 9.25, thus tο find the solution, we must subtract 6.5 from 9.25.
4.75 miles were ran οn day four, or 9.25 minus 6.5.
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Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount with an interest of 3% compounded quarterly Brooklyn
wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly Explain which method results in more money after 2 years Show all work
Answer:
To compare the amount of money that Patrick and Brooklyn would have after 2 years, we need to calculate the interest earned using each of their methods.
For Patrick, who deposited $300 with an interest rate of 3% compounded quarterly, the formula to calculate the amount after 2 years (8 quarters) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (3%)
n = number of times compounded per year (4)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.03/4)^(4 * 2)
A = $300(1.0075)^8
A = $300 * 1.06173
A = $318.52
For Brooklyn, who deposited $300 with an interest rate of 5% compounded monthly, the formula to calculate the amount after 2 years (24 months) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (5%)
n = number of times compounded per year (12)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.05/12)^(12 * 2)
A = $300(1.00417)^24
A = $300 * 1.09722
A = $328.17
Therefore, after 2 years, Brooklyn would have $328.17, which is more money than Patrick's $318.52.
Which of the symbols correctly relates the two numbers below? Check all that
apply.
A. =
B. >
C. Z
☐ D. <
E. >
OF. s
364? 225
The symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
The solution has been obtained by using concept of relational symbols.
What are relational symbols?
Relational symbols are used in mathematics to represent mathematical relations, which combine with one or more other mathematical objects to construct complete mathematical statements. These are the relational symbols for equality and comparison in arithmetic and common mathematics.
We are given 2 numbers as 364 and 225.
It is clearly visible that both the numbers are not same so, the symbol '≠' depicts the relationship between the two numbers.
Also, we know that the number 364 is greater than 225. So the another symbol depicting relation between the numbers is '>'.
Hence, the symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
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Question: Which of the symbols correctly relates the two numbers below? Check all that apply.
364? 225
A. =
B. >
C. ≥
D. <
E. ≤
F. ≠
how to solve equation below
Answer: (a) -6x²y
Step-by-step explanation:
[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:
[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75. What equation can you write to solve for x
The solution is, the value is, x = 49.6.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
or, 3x = 149
or, x = 49.6
Hence, The solution is, the value is, x = 49.6.
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F(x)=|x| is transformed to g(x)=|x|+4 what transformation happens from f(x) to g(x)
Step-by-step explanation:
The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.
So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units
What is the equation of the midline for the function given? f(x) = 9sin3x + -5.
After answering the provided question, we can say that the function's midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5
What exactly is an equation?A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2. midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5
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A container of gas at 29 psi is compressed to
one seventh its original volume. What is the
new pressure of the gas?
Answer in units of psi
Step-by-step explanation:
Since the original volume is 29 and they are looking for 1/7th of that, we can multiply these two numbers
[tex](29)( \frac{1}{7} ) = 4 \frac{1}{7} psi[/tex]
what are some three statements Symons why any of the objects does not belong with the others.
Here are three statements explaining why each of the objects doesn't belong with the others:
The StatementsSphere:
A sphere is a three-dimensional object with a curved surface, while the other objects listed have flat or angled surfaces.A sphere has an equal diameter at every point, making it a true round object, while the other objects have varying shapes and angles.The volume of a sphere can be calculated using the formula 4/3 * π * r^3, which is different from the formulas used to calculate the volume of the other objects listed.Cylinder:
A cylinder has two flat circular bases, while the other objects listed do not have flat circular bases.A cylinder has a curved lateral surface, while the other objects listed have flat or angled lateral surfaces.The volume of a cylinder can be calculated using the formula π * r^2 * h, which is different from the formulas used to calculate the volume of the other objects listed.Pyramid:
A pyramid has a flat base and triangular sides that meet at a single point, while the other objects listed have different shaped bases and sides.A pyramid has no curved surfaces, while the other objects listed have curved surfaces.The volume of a pyramid can be calculated using the formula (B * h) / 3, where B is the area of the base and h is the height, which is different from the formulas used to calculate the volume of the other objects listed.Cube:
A cube has square faces and equal lengths on all sides, while the other objects listed do not have square faces and/or do not have equal lengths on all sides.A cube has right angles between all faces, while the other objects listed do not have right angles between all faces.The volume of a cube can be calculated using the formula s^3, where s is the length of a side, which is different from the formulas used to calculate the volume of the other objects listed.Read more about squares here:
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please and answers please just need help
Answer:
100π - 192 or 122.159....
Step-by-step explanation:
In order to find the diameter we much first split the rectangle diagonally and find the hypotenuse using Pythagorean theorem.
a^2 + b^2 = c^2
16^2 + 12^2 = c^2
400 = c^2
c = 20
If the diameter of the rectangle is 20, the radius is just half of that which is 10. Then you just need to a do a basic calculation for area of a circle and then subtract out the area of the rectangle.
Area of circle = πr^2 = π(10^2) = 100π (keeping it in exact value since π is infinite)
Area of rectangle = lw = (16)(12) = 192
Area of shaded area = 100π - 192 (exact) = 122.159 (estimate)
The sum of two numbers is 160. One number is 40 more than the other. Find the numbers.
The larger number is
The smaller number is
Answer:
The larger number is 100
The smaller number is 60
Step-by-step explanation:
x + (40 + x) = 160
2x + 40 = 160
x + 20 = 80
x = 60
60 + (40 + 60) = 160
160 = 160
Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.
The option that is true for the central limit theorem is;
C: For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed
Let us look at all the given options to access which one clearly is correct about the central limit theorem;
a) This option is incorrect because the CLT theorem is based on ‘sample mean’ distribution.
b) This option is Incorrect because the theorem is true for any population distribution.
c) This option is correct because Irrespective of the population distribution, the sample means of repeated samples are normally distributed for larger n.
d) The “central limit theorem(CLT)” states that, the sample means of the repeated samples follows normal distribution for ‘large’ sample sizes. Thus, this option is incorrect.
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Find the power of 9↑1. Type your answer using digits.
Answer:
9^1 has a power of 1. it evaluates to 9
Step-by-step explanation:
Using logarithmic properties, what is the solution to log4(y - 9) + log43 = log481? Show all necessary steps.
Answer:
y = 36
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_4(y-9)+\log_43=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]
[tex]\implies 3(y-9)=81[/tex]
Divide both sides of the equation by 3:
[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]
[tex]\implies y-9=27[/tex]
Add 9 to both sides of the equation:
[tex]\implies y-9+9=27+9[/tex]
[tex]\implies y=36[/tex]
Therefore, the solution to the given logarithmic equation is y = 36.
Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
Help!!!!
I am very lost!
The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.
How to find the height of the plane?A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .
Therefore, the height of the plane can be found as follows:
The situation forms a right angle triangle.
Using trigonometric ratios,
tan 12 = opposite / adjacent
tan 12° = x / 4812
cross multiply
x = 4812 tan 12°
x = 4812 × 0.21255656167
Therefore,
x = 1022.82217476
x = 1023 metres.
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