According to the solution we have come to find that, As the metal lid was heated, it expanded so that it was not as tight. The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.
what is heat?
Heat is a form of energy that is transferred between objects or systems as a result of a temperature difference. It is the energy that flows from a body of higher temperature to a body of lower temperature until they reach a state of thermal equilibrium. Heat can be transferred through three different mechanisms: conduction, convection, and radiation.
Conduction involves the transfer of heat through direct contact between two objects that are at different temperatures. Convection involves the transfer of heat through the movement of fluids, such as air or water, due to differences in temperature. Radiation involves the transfer of heat through the emission and absorption of electromagnetic waves, such as infrared radiation.
The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.
When the metal lid was placed in hot water, the heat caused it to expand. This expansion allowed the lid to loosen from the glass jar, making it easier to turn. This is because metals generally expand when heated and contract when cooled. The expansion of the metal lid due to heat causes it to become slightly larger than before, thereby loosening its grip on the jar. As a result, the lid can be turned with less force, and it comes off easily.
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Which of the following is NOT equal to the "ratio of 3 to 4?
A. 3:4
B. 3÷4
C. 3x4
D. 3/4
Answer:
C. 3 x 4
There's not really a way to explain it. If you still have questions, I would recommend asking your teacher or someone you can trust.
Ryan and Kayley launch their rockets at the same time. The height of Ryan’s rocket, in
meters, is given by the function () = −3.4
2 − 64, where x is the number of seconds
after the launch. The height of Kayley’s rocket, in meters, is given by the function
() = −3.4
2 − 25 − 45 where x is the number of seconds after the launch.
Algebraically find the moment when the rockets are at the same height, and then use that
to calculate the height. Round to the nearest hundredth. Show all work.
At the moment when the rockets are at the same height, their height is approximately -223.34 meters. Note that this negative value indicates that they are both below the ground level.
How to find moment?
To find the moment when the rockets are at the same height, we need to set the two height functions equal to each other and solve for x:
-3.4x²- 64 = -3.4x² - 25x - 45
Simplifying and rearranging:
0 = 25x + 19
x = -19/25
So the rockets are at the same height after -19/25 seconds, or about 0.76 seconds.
To find the height at this moment, we can plug this value of x into either of the height functions. Let's use Ryan's function:
h(-19/25) = -3.4(-19/25)²- 64
= -3.4(361/625) - 64
= -223.34
So at the moment when the rockets are at the same height, their height is approximately -223.34 meters. Note that this negative value indicates that they are both below the ground level.
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please help i will rate braainliest and 100 points
Answer:
1 : I will give you the first one answer and trying later to answer all as possible!Step-by-step explanation:
First one are given in attachment!Completar la siguiente oración.
• El costo marginal es la derivada de la función........
.
A) Utilidad.
B Ingreso.
C) Costo.
D Demanda.
The marginal cost is the derivative of the cost function.
Option C is the correct answer.
What is marginal cost?Marginal cost is the additional cost incurred by a firm or producer when producing one more unit of a good or service.
It is the cost of producing an additional unit of output.
We have,
Marginal cost is a concept in economics that describes the additional cost of producing one additional unit of output.
It is calculated as the derivative of the total cost function with respect to the quantity produced.
In other words, if the total cost function is represented as C(q), where q is the quantity of output produced, then the marginal cost (MC) function is given by:
MC(q) = dC(q) / dq
The derivative represents the rate of change of the cost function with respect to the quantity produced, which gives the additional cost of producing one more unit of output.
For example, if a company produces 100 units of a product at a total cost of $1000, and then produces 101 units of the same product at a total cost of $1020, the marginal cost of producing the 101st unit is $20, which is the difference in cost between producing 100 units and producing 101 units.
Thus,
The marginal cost is the derivative of the cost function.
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The complete question.
Complete the following sentence.
The marginal cost is the derivative of the ________ function.
A) Utility.
B Income.
C) Cost.
D Demand.
Select the correct answer.
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently
two candidates. The results of the poll are shown in the two-way frequency table belo
Candidate A Candidate B
Total
Center City
152
198
350
Carsonville
205
266
471
Appleton
260
203
New Thomas
180
138
463
318
Total
797
805
1.602
a survey to gauge support for each of the
Based on the data shown, which of the following statements are true?
I. The two cities with the highest number of respondents both show more support for candidate A.
The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New
II. Thomas.
III. More residents of Center City responded to the poll than the number who responded from New Thomas
IV. Overall, more residents support candidate A than candidate B.
Options I and II contain claims regarding the two-way frequency table that are accurate.
How to interpret two-way frequency table?We are given the two-way frequency table that shows the newspapers recently conducted survey that gauges support for each of the two candidates.
Let us now analyze the options;
I) The two cities with the highest number of respondents are Carsonville and Appleton and from the table, they both show more support for candidate A and thus this option is true.
II) There are 266 supporters of candidate B in Carsonville. While there are 138 supporters of candidate B in New Thomas, we can see that 266 is not twice 138.This choice is untrue.
III) The number of residents that responded from Center city is 350 and we see that this is more than the number of residents that responded from New thomas which is 318 people.
The statement is true.
IV) This is untrue because candidate B has 805 supporters, which is greater than candidate A's 797 supporters. The assertion is thus untrue.
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If the volume of a rectangular prism is 23,504 m3 and it has a height of 16 m, what is the value of B, the area of the base?
Answer:
1,469 [tex]m^{2}[/tex]
Step-by-step explanation:
The volume of a rectangular prism is given by the following:
V = Bh, where B is the area of the base and h is the height.
In this problem, we are given that the volume is 23,504 [tex]m^{3}[/tex] and the height is 16 m.
23,504 [tex]m^{3}[/tex] = B × 16 [tex]m[/tex]
Dividing both sides by 16, we get:
B = 23,504 [tex]m^{3}[/tex] / 16 [tex]m[/tex] = 1,469 [tex]m^{2}[/tex]
Therefore, the value of B, the area of the base, is approximately 1,469 [tex]m^{2}[/tex].
Find the missing side lengths. Leaves your answers as radical in simplest form
Answer:
v = 2√2
u = 4
Step-by-step explanation:
Use trigonometry:
[tex] \tan(45°) = \frac{v}{2 \sqrt{2} } [/tex]
Cross-multiply to find v:
[tex]v = 2 \sqrt{2} \times \tan(45°) = 2 \sqrt{2} \times 1 = 2 \sqrt{2} [/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {v}^{2} + ( {2 \sqrt{2} )}^{2} [/tex]
[tex] {u}^{2} = ( {2 \sqrt{2}) }^{2} + ({2 \sqrt{2}) }^{2} = 4 \times 2 + 4 \times 2 = 8 + 8 = 16[/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{16} = 4[/tex]
Whats is the value of this expression [45-(6+3)]x 27
Answer:
972
Step-by-step explanation:
1. 6+3=9
2. 45-9=36
3. 27x36=972
I NEEDDD HELPPPPPPPP
Answer:
VX=33
Step-by-step explanation:
VW=2z-1
WX=z+3
XV=3z
VW=a
WX=b
XV=c
a+b+c=2z-1+z+3+3z
Perimeter=6z+2
P=68
68=6z+2
66=6z
z=11
VX=3x11
VX=33
1/3 (16a-8) expandesch expression
Answer: To expand the expression 1/3(16a-8), we can distribute the 1/3 to each term inside the parentheses:
1/3(16a-8) = 1/3(16a) - 1/3(8)
Simplifying each term:
1/3(16a) = (1/3)16a = (16/3)*a
1/3(8) = (1/3)*8 = 8/3
So the fully expanded expression is:
1/3(16a-8) = (16/3)*a - 8/3
Step-by-step explanation:
A ferris wheel can accommodate 60 people in 25 minutes. How many people
could ride the ferris wheel in 4 hours? What was that rate per hour?
The rate per hour for the ferris wheel is 144 people per hour.
What is rate per hour?Your pay for each hour of labour is expressed as an hourly rate. You might need to estimate your income for other applications or modify your personal budget after comparing the hourly and salaried pay rates.
The ferris wheel can accommodate 60 people in 25 minutes.
To find out how many people could ride the ferris wheel in 4 hours, we need to convert 4 hours to minutes, since the given rate is in minutes.
1 hour = 60 minutes
4 hours = 4 x 60 minutes = 240 minutes
So, in 4 hours, the ferris wheel could accommodate 240/25 = 9.6 (rounded to the nearest whole number) cycles of 60 people.
The total number of people that could ride the ferris wheel in 4 hours would be 9.6 x 60 = 576 people.
Now, to find the rate per hour, we divide the total number of people (576) by the number of hours (4):
Rate per hour = Total number of people / Number of hours
Rate per hour = 576 / 4 = 144 people/hour
Therefore, the rate per hour for the ferris wheel is 144 people per hour.
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angle bisector theorem
The value of the unknown term in the given triangle that satisfied the relation of angle bisector theorem is 9.
What about angle bisector theorem?
The angle bisector theorem is a fundamental theorem in geometry that relates the lengths of the sides of a triangle to the lengths of the segments formed by the intersection of an angle bisector with the opposite side.
Specifically, the angle bisector theorem states that the length of the segment of the side of a triangle that is opposite to the bisected angle is proportional to the lengths of the other two sides of the triangle. More precisely, if AD is the bisector of angle BAC in triangle ABC, then:
BD/DC = AB/AC
where BD and DC are the lengths of the segments of side BC that are adjacent to point A, and AB and AC are the lengths of the sides opposite to angles B and C, respectively.
This theorem is useful in many geometric constructions and proofs, and can be applied to various problems involving triangles and their properties.
According to the given information:
Using the concept of height and distance we have that,
[tex]tan(y) = \frac{4}{12} \\\\tan(2y) = \frac{2tany}{1-(tany)^{2} }[/tex]
In the given figure of triangle the value of tan(2y) = [tex]\frac{4+x}{12}[/tex]
So, when we correlate all of them we have that
[tex]\frac{2*\frac{4}{12} }{1-(\frac{4}{12}) ^{2} } = \frac{4+x}{12} \\\\x = 5[/tex]
So, the length of the unknown part is 9.
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If these solids were If these solids were candles that you could sell, and the cylinder shaped candie was $12.00. What would be the price of the cone shaped candle and the sphere shaped candle? (
The volume of wax is required to make 1 candle is 22.92 cu. in.
Explain about the shape of cone:A cone is a tri solid geometric object with an apex that is pointed at the top and a circular base. A cone has a vertex and one face.
The length of a line segment from a cone's apex to any point along the circumference of a cone's base is known as the slant height of the cone.An oblique cone is one that doesn't have its apex directly over the base's circle.Given data:
Candle's shape is cone.height h = 6 in.circumference c = 12 inchesLet the radius of the cone be 'r'.
circumference c = 2*π*r
c = 2*π*r
12 = 2*3.14*r
r = 6/3.14
r = 1.91
Volume of cone V = 1/3 * π * r² *h
Put the values:
V = 1/3 * 3.14 * 1.91² *6
V = 22.92 cu. in.
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Correct question:
A company makes candles in the shape of the cones. Their best selling candles has a height of 6 inches and the circumference of 12 inches What is the volume of wax is needed to make 1 candle.
can someone be kind enough to help me
Answer:
-9 < m - 12
Step-by-step explanation:
When you multiply or divide an inequality by a negative number, you flip the inequality sign.
Helping in the name of Jesus.
What is the vertical distance between (5, –12) to (5, 17)?
5 units
29 units
–29 units
–5 units
The vertical distance between two points is just the distance between the two y coordinates. Distance is positive.
|-12|+17 = 29 units
Answer: the answer is 29 trust me
Step-by-step explanation: don't have time for explanation sorry
((30/180)*2.80 + (40/180)*11.20
Answer:
0.47?
Step-by-step explanation:
Determine whether KM || JN. Explain or show work.
The segments KM and JN are parallel because the ratio LK : KJ = LM : MN are equivalent
Determining whether KM || JNfrom the question, we have the following parameters that can be used in our computation:
The triangle
To determining whether KM || JN, we make use of the following ratio
LK : KJ = LM : MN
Substitute the known values in the above equation, so, we have the following representation
8 : 5 = 12 : 7.5
Express as fraction
5/8 = 7.5/12
Simplify
So, we have
0.625 = 0.625
This means that KM || JN
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Pls someone help me.Allen prints a photograph with dimensions as shown. He purchases a 3-inch wide frame for the photo and frame.
The quadratic function representing the area of the photo and the frame is A(x) = 1.7x²+ 16.2x + 36
How to find area of Rectangle ?When calculating a rectangle's area, we multiply the length by the width of the rectangle.
Area of rectangle = length × breadth
To represent the photo and frame area, we need to add the photo area to the frame area. Since the frame is 3 inches wide on all sides, the photo dimensions are reduced by 6 inches in both length and width. Therefore the length of the photo with the frame is (x 6) inches and the width is (1.7 x 6) inches. Thus, the area of the photo and the frame can be represented by a quadratic function:
A(x) = (x 6) (1.7 x 6)
Expanding this expression, we get:
A(x) = 1.7x² + 16.2x + 36
So the quadratic function representing the area of the photo and the frame is A(x) = 1.7x²+ 16.2x + 36
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Suppose that Mars rotates on its axis once every hours. The equator lies on a circle with a diameter of miles.
(a) Find the angular speed of a point on its equator in radians per day ( hours).
(b) Find the linear speed of a point on the equator in miles per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
The answer of the given question based on the Angular speed is (a) the angular speed of a point on Mars' equator is π/2 radians per day. (b) the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.
What is Linear speed?Linear speed, also known as tangential speed, is the distance traveled by an object in a straight line per unit of time. It is the speed at which an object is moving along its path, tangent to the path at any given point. Linear speed is calculated by dividing the distance traveled by the time taken to travel that distance. The units of linear speed are typically expressed in meters per second (m/s), miles per hour (mph), or kilometers per hour (km/h), depending on the system of measurement used.
(a) The angular speed of a point on Mars' equator is the angle (in radians) that a point on the equator sweeps out as Mars rotates on its axis. Since Mars completes one rotation every 24 hours, the angular speed is:
angular speed =(2πradians)/ (24 hours)= π/12radians per hour
To find the angular speed in radians per day, we need to multiply by the number of hours in a day:
angular speed = (π/12 radians per hour) * (24 hours per day) = π/2 radians per day
Therefore, the angular speed of a point on Mars' equator is π/2 radians per day.
(b) The linear speed of a point on the equator is the distance traveled by a point on the equator in a certain amount of time. The distance traveled by a point on the equator in one rotation is equal to the circumference of the circle with a diameter of miles, which is:
C = πd = π(6794) ≈ 21343.98 miles
Since Mars rotates once every 24 hours, a point on the equator travels the circumference of the circle in 24 hours. Therefore, the linear speed of a point on the equator in miles per day is:
v = C/24 ≈ 889.33 miles/day
So the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.
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What is the x-intercept of the line illustrated in the graph below? (Enter your answer as a number. If necessary, round to the nearest tenth.)
The line passes through the horizontal axis 2.5 units to the left of the origin. It passes through the vertical axis 1 unit above the origin.
Using the point-slope form of the equation of a line. the x-intercept of the line is [tex]-2.5[/tex].
What is the intercept of the line?To find the x-intercept of the line, we need to find the point where the line intersects the x-axis. We know that the y-coordinate of this point is zero, because it is on the x-axis. Let's call the x-coordinate of this point "x".
We also know that the line passes through the point (-2.5,0), because it is 2.5 units to the left of the origin. Using the point-slope form of the equation of a line, we can write the equation of the line as:
[tex]y - 0 = m(x - (-2.5))[/tex]
where m is the slope of the line. To find the slope, we can use the fact that the line passes through the point [tex](0,1)[/tex] and [tex](-2.5,0)[/tex]:
[tex]m = (1 - 0) / (0 - (-2.5)) = 1 / 2.5 = 0.4[/tex]
Substituting this into the equation of the line, we get:
[tex]y = 0.4(x + 2.5)[/tex]
To find the x-intercept, we set y to zero and solve for x:
[tex]0 = 0.4(x + 2.5)[/tex]
[tex]-2.5 = x[/tex]
Therefore, the x-intercept of the line is [tex]-2.5.[/tex]
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expand (1+2)^4 using the Pascal Triangle
Answer:
81
Step-by-step explanation:
(1 + 2)⁴
1⁴ + 4(1³ × 2) + 6(1² × 2²) + 4(1 × 2³) + 2⁴
1 + 4(2) + 6(4) + 4(8) + 16
1 + 8 + 24 + 32 + 16
= 81
Suppose you just received a shipment of fourteen televisions. Two of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work.
The probability that both televisions work is ___
Answer: The probability that both televisions work is approximately 0.746, or 74.6%.
Step-by-step explanation:
To calculate the probability that both televisions work, we need to find the probability of selecting a working television, and then multiply that by the probability of selecting another working television from the remaining televisions.
Since 2 out of the 14 televisions are defective, that means there are 12 working televisions out of 14. So the probability of selecting a working television on the first draw is 12/14.
After the first television is selected, there will be 13 televisions left, with 11 working televisions. So the probability of selecting a second working television is 11/13.
Therefore, the probability that both televisions work is:
(12/14) x (11/13) = 0.746
So the probability that both televisions work is approximately 0.746, or 74.6%.
To calculate the probability that at least one of the two televisions does not work, we can use the complement rule. The complement of the event "both televisions work" is the event "at least one television does not work."
So, the probability that at least one television does not work is:
1 - 0.746 = 0.254
So the probability that at least one television does not work is approximately 0.254, or 25.4%.
Answer:
0.60, 0.40
Step-by-step explanation:
The probability that a television works is 11/14. The probability that a television is
defective is 3/14.
The probability that the first TV works and the second works is
[tex]\frac{11}{14}[/tex]×[tex]\frac{10}{13}[/tex]
(If the first selected TV works, the total number of televisions left is 13, and the
the number of working TV is 10).
Answer: 0.60.
The event that at least one of the two televisions does not work is the
opposite of the event ‘both TV work’. So the probability of at least one of the
two televisions does not work is
1- Pr (both works)= 1 − 11/14 ∙ 10/13 = 0.40.
Answer: 0.40.
oscar corporation produces and sells three products. unit data concerning each product is shown below. the company has 2000 hours of labor available to build inventory
Oscar Corporation can effectively allocate its 2000 labor hours to build Inventory for its three products, ensuring efficient production and maximizing profits
Based on the information provided, let's assume that the three products produced by Oscar Corporation are Product A, Product B, and Product C.
1. Determine the labor hours required for each product.
First, we need to know the labor hours required to produce one unit of each product. This information is essential in order to allocate the available labor hours effectively.
Calculate the labor efficiency for each product.
Divide the total number of units produced by the labor hours required for each product. This will help us determine the most efficient product in terms of labor utilization.
Allocate the available labor hours.
Using the labor efficiency data, allocate the 2000 available labor hours among the three products. Prioritize the most efficient product to maximize production.
Calculate the number of units produced for each product.
Multiply the allocated labor hours for each product by its respective labor efficiency to determine the number of units that can be produced.
Evaluate and adjust if necessary.
Review the results and adjust the allocation of labor hours if needed to meet the company's goals or demand for each product.
By following these steps, Oscar Corporation can effectively allocate its 2000 labor hours to build inventory for its three products, ensuring efficient production and maximizing profits.
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2 + 5 + 8 + 11 + 14
Use the arithmetic explicit formula to find n for the number 14 in the sequence. Use the formula.
Write the arithmetic sum formula.
Using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.
What is an arithmetic sequence?An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,...
The common difference of the sequence is d, and the number an is the first term.
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
So, we have the sequence:
2, 5, 8, 11, 14
Common difference = 5 - 2 = 3
Then, the formual is:
aₙ = a + (n - 1)d
Then, insert values:
aₙ = a + (n - 1)d
a₁₄ = 2 + (14 - 1)3
a₁₄ = 2 + (13)3
a₁₄ = 2 + 39
a₁₄ = 41
Therefore, using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.
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can somebody please do this with proof?
The length of the side AC is 4.00cm
How to determine the valueWe have different trigonometric identities and their ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Line CD = hypotenuse
Line Cy = Opposite = 4cm
Using the sine identity, we have;
sin 45 = 4/CD
cross multiply
CD = 4/0. 7071
Divide the values
CD = 5. 66cm
To determine the length of AC
sin 45 = AC/5.66
cross multiply the values
AC =sin 45 ×5.66
AC = 0. 7071 × 5. 66
multiply the values
AC = 4. 00cm
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Can someone please solve step by step. I'm having trouble understanding.
A multiple choice test consists of five questions, each of which has four choices. Each
question has exactly one correct answer. How many ways are there to fill out the answer sheet so that four answers are correct and one is incorrect?
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
What is possible way?It involves finding the most efficient and effective solution to a problem by exploring multiple options and assessing the pros and cons of each.
This can be found by calculating the number of possible ways to fill out the answer sheet.
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024..
To explain why this is happening, it is helpful to look at an example. Let's say the five questions are A, B, C, D, and E.
If a person wants to fill out the answer sheet so that four answers are correct and one is incorrect, they can either choose the correct answer for four of the questions, and then choose an incorrect answer for the fifth question, or they can choose the incorrect answer for four of the questions, and then choose the correct answer for the fifth question.
In terms of calculating the number of ways to fill out the answer sheet, this means that for each of the five questions, there are four possible ways to answer (four choices for each question). This means that there are 4
The answer to this question is 1024. This can be found by calculating the number of possible ways to fill out the answer sheet. Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
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1. What is the relationship between AD and AB?
2. What is the relationship between ACD and BDC?
3. What is the relationship between AC and CB? Explain.
4. True or False? Because BD is the angle bisector of ABC, AB = CB
1. The Similarity between AD and AB is that AD is half the length of AB.
2. The areas of triangles ACD and BDC are equal.
3. We can say that if AC is the longest side, then CB is the shortest side
4. False, The relationship between AD and AB is that AD is half the length of AB.
What do you mean by Triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
1) Since D is the midpoint of AB, we know that AD and DB have the same length. Therefore, we can say that:
AD = DB
Substituting AB for AD + DB, we can simplify to:
AB = AD + AD
or
AB = 2AD
So, the relationship between AD and AB is that AD is half the length of AB.
2) The areas of triangles ACD and BDC are equal, and we can write:
Area of ACD = (1/2) * AC * AD
Area of BDC = (1/2) * BC * DB
Since AD = DB, we can substitute and get:
Area of BDC = (1/2) * BC * AD
So, we can see that the areas of ACD and BDC are equal, and their bases AD and DB have the same length. Therefore, triangles ACD and BDC are equal in area and shape (they are congruent).
3) we can say that if AC is the longest side, then CB is the shortest side
4) False,
The relationship between AD and AB is that AD is half the length of AB.
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how do it prove this without approximately calculating the logarithm ?
Answer:
[tex]10 < {e}^{8} [/tex]
[tex] ln(10) < 8[/tex]
[tex] ln(10) - 8 < 0[/tex]
Since ln(10) > 0, it follows that ln(10) + 1 > 0, and so:
[tex]( ln(10) + 1)( ln(10) - 8) < 0[/tex]
[tex] {( ln(10)) }^{2} - 7 ln(10) - 8 < 0[/tex]
[tex]( { ln(10) })^{2} - 7 ln(10) + 1 < - 9[/tex]
[tex] {( ln(10)) }^{2} + 2 ln(10) + 1 < 9 ln(10) - 9[/tex]
[tex] {( ln(10) )}^{2} + 2 ln(10) + 1 < 9( ln(10) - 1)[/tex]
(ln(10) + 1)^2 < 9(ln(10 - 1)
ln(10) + 1 < 3√(ln(10) - 1)
(1 + ln(10))/3 < √(ln(10) - 1)
√(ln(10) - 1) > (1+ ln(10))/3
8 9/14 divided by 12
The value of 8 9/14 divided by 12 is
How to calculate the value of 8 9/14 divided by 12 ?The first step is to convert the mixed fraction to a proper fraction
8 9/14
= 121/14
The next step is to divide the proper fraction by 12
121/14 ÷ 12
= 121/14 × 1/12
= 121/168
= 0.720
Hence the value of 8 9/14 divided by 12 is 0.720
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I want to plant 45 rose plants, 81 lily plants and 63 chilli plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?
The greatest number of plants that can be put in one row is 315. We can have 45 rows of roses, 27 rows of lilies, or 21 rows of chili plants, each with 315 plants in a row.
How to find the the greatest number of plants I can put in one rowTo find the greatest number of plants that can be put in one row, we need to find the greatest common factor (GCF) of 45, 81, and 63.
First, we can find the prime factorization of each number:
45 = 3 x 3 x 5
81 = 3 x 3 x 3 x 3
63 = 3 x 3 x 7
Then, we can identify the common factors:
The factors of 45 are 3 and 5
The factors of 81 are 3 and 3
The factors of 63 are 3 and 3
The greatest common factor is the product of the common factors raised to their lowest power:
GCF = 3^2 x 5 x 7 = 315
Therefore, the greatest number of plants that can be put in one row is 315. We can have 45 rows of roses, 27 rows of lilies, or 21 rows of chili plants, each with 315 plants in a row.
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