The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5
What is the volume of a cylinder?A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved lateral surface. The volume of a cylinder is the amount of space contained within the cylinder. It can be calculated using the formula:
Volume of cylinder = πr^2h
Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively. Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:
Volume of Cleopatra's clock =[tex]\mathrm{ \pi r_c^2h_c}[/tex]
Volume of Ptolemy's clock = [tex]\mathrm{\pi r_p^2h_p}[/tex]
Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock. We are given that after 2 hours of draining, both clocks have the same water height. Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:
(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)
[tex]\pi r_c^2h_c / 4 = \pi r_p^2h_p / 5[/tex]
[tex]h_c / h_p = (r_p / r_c)^2 \times (5 / 4)[/tex]
We are not given the values of the radii, but we can see that the ratio of heights depends only on the ratio of the radii squared. Therefore, we don't need to know the actual sizes of the clocks, only the ratio of their radii. Let's call this ratio x:
[tex]x^2 = (h_c / h_p) \times(4 / 5)[/tex]
After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:
[tex]\pi r_c^2(h_c - 2h_c/4) = \pi r_p^2(h_p - 2h_p/5)[/tex]
[tex]\pi r_c^2h_c/2 =\pi r_p^2h_p/5*3[/tex]
[tex]r_c^2h_c/2 = r_p^2h_p/15[/tex]
Now, we can solve for the ratio of water heights after each clock has been draining for three hours:
Water height in Cleopatra's clock after 3 hours = [tex]\mathrm{h_c - (3/4)h_c = (1/4)h_c}[/tex]
Water height in Ptolemy's clock after 3 hours = [tex]\mathrm{ h_p - (3/5)h_p = (2/5)h_p}[/tex]
([tex]h_p[/tex] / (2/5)[tex]h_p[/tex] ) = ((1/4)[tex]h_c / h_c[/tex])
([tex]h_p[/tex] / (2/5)) = 1/4
[tex]h_p[/tex] = 2/5 * 1/4
[tex]h_p[/tex] = 1/10
Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:
[tex]h_p / h_c[/tex]= 1/10 / (1/4) = 2/5
And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:
[tex]h_c / (2/5)h_p[/tex] = (1/4) / (2/5)(1/10) = (1/4) / (1/20) = 5/4
Hence,
The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5
The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.
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Which number sentence is not true? 0<100, 0=0, -100<0, -100>0
1) Simplify the following
a) 3√2+5√2
b) √3 x √2
c) 3√5x2√7
d) 8√10-2√2 x √5
It takes an older computer twice as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 5 minutes to
send out the email. How long will it take the newer computer to send out the email on its own?
Do not do any rounding.
minutes
The time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.
What is a unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Let,
Time taken by new computer to send 1 email = x
Time taken by the old computer to send same mail = 2x
Using unitary method
In 1 minute
Work done by new computer = 1/x
Work done by old computer =1/2x
Given the time taken when both computers work together = 5 minutes
Work done in 1 minute by both = 1/5
So we can write,
1/x + 1/2x = 1/5
3/2x = 1/5
x = 7.5 minutes
Therefore the time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.
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Ms. Rod rolls a 6-sided die . If she rolls the die 57 times, how many times should she expect to roll a composite number?
By understanding what composite numbers are and how they relate to rolling a die, we can determine the expected number of times Ms. Rod will roll a composite number in 57 rolls.
A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is a number that can be factored into smaller positive integers.
To find the number of times Ms. Rod should expect to roll a composite number, we need to know how many numbers from 1 to 6 are composite. Only two numbers are prime in this range, namely 2 and 3. This means that the other four numbers (4, 5, and 6) are composite. Therefore, out of the 6 possible outcomes of rolling the die, 4 of them are composite numbers.
We can use this information to calculate the expected number of times Ms. Rod will roll a composite number. We know that she is rolling the die 57 times, and each roll has a probability of 4/6 (or 2/3) of resulting in a composite number. Therefore, we can use the formula for the expected value of a discrete random variable, which is:
Expected value = (number of trials) x (probability of success)
Plugging in the values, we get:
Expected value = 57 x 2/3
Expected value = 38
Therefore, we can expect Ms. Rod to roll a composite number about 38 times out of 57 rolls. However, it's important to note that this is just an expected value, and the actual number of times she rolls a composite number may vary.
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Shawna is playing a game that involves rolling a black numbered cube and a red numbered cube. The result of a red numbered cube represents a negative number, and the result of a black numbered cube represents a positive number. Shawna’s current score is 4. Then, Shawna rolls a red 5 and a black 3. Write and solve an equation to represent Shawna’s new score
Shawna's new score can be represented by the equation is New Score = Current Score + (Result of Black Cube) + (Result of Red Cube). So, Shawna's new score is 2.
In the game that Shawna is playing, rolling the black cube results in a positive number, while rolling the red cube results in a negative number. We are told that Shawna's current score is 4, which means that she has accumulated 4 points up to this point in the game.
Next, we are told that Shawna rolls a red 5 and a black 3. This means that the red cube resulted in a negative 5 and the black cube resulted in a positive 3.
To calculate Shawna's new score, we can add the results of these two rolls to her current score. However, we need to be careful to subtract the negative number, rather than adding it. This is because a negative number is actually a decrease in score.
Therefore, we can use the following equation to calculate Shawna's new score:
New Score = Current Score + (Result of Black Cube) + (Result of Red Cube)
Substituting in the values that we know, we get:
New Score = 4 + 3 + (-5)
Simplifying, we can combine the positive and negative numbers:
New Score = 4 - 2
Therefore, Shawna's new score is 2. This means that after rolling a red 5 and a black 3, her score has decreased by 2 points from her original score of 4.
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Macy spent 2hours working on homework she spent 1/4 of that time working on math
Time for working for history is 50 minutes.
First we need to multiply to make the fractions have equal denominators so we can add/subtract.
Science: 1/3 x 4/4=4/12
Math: 1/4 x 3/3=3/12
Now we can find the time she spent on history (I assume this is what you are looking for)
Total time-math time-science time=history time
12/12-4/12-3/12
=5/12
Macy spent 5/12 of her time working on history.
so totak fo 2 hours she spent 5/12 time to work on history
so 2 hours*5/`12 = 5/6 hours = 50 minutes
Q- Macy spent 2 hours working on homework she spent 1/4 of that time working on math he spent 1/3 of her time working on science find time for working for history.
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How can I find the population of the town? Many thanks
Find all remaining roots for 3x³- 7x² - 7x + 3 = 0; x = 3
The roots of the polynomial equation are x = −1, 1/3, and 3.
Finding Roots of a polynomial equationA polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
Finding the value(s) of 'x' that satisfy the polynomial equation p(x) = 0 is all that is required to solve the problem. A number "a" is a polynomial p(x) "zero" if and only when p(a) = 0.
Given that:
3x³- 7x² - 7x + 3 = 0
Factor the left side of the equation.
(x + 1) (3x − 1)(x − 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x + 1 = 0
3x − 1 = 0
x − 3 = 0
Set x + 1 equal to 0 and solve for x; x = - 1
Set 3 x − 1 equal to 0 and solve for x; x = 1/3
Set x − 3 equal to 0 and solve for x; x = 3
The final solution is all the values that make (x + 1)(3 x − 1)( x − 3) = 0 true is x = −1, 1/3, 3.
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COULD SOMEONE PLEASE HELP ME WITH #2!!
what is the surface area of a right cylinder with a radius of 6 units and a height of 14 units?
The surface area of a right cylinder with a radius of 6 units and a height of 14 units is equal to 753.6 square units.
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a right cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the surface area of a right cylinder formula, we have;
Surface area (SA) of cylinder = (2 × 3.14 × 6 × 14) + 2 × 3.14 × 6²
Surface area (SA) of cylinder = 527.52 + 226.08
Surface area (SA) of cylinder = 753.6 square units.
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25kg= blank lb i need help plese i have 2 min left
Answer: 25,000 grams
Step-by-step explanation:Really sorry if im wrong.
Is the product of (x − 3)2 a perfect square trinomial? Explain your reasoning
Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).
A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.
In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:
(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9
This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:
(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2
Therefore, the product of (x - 3)^2 is a perfect square trinomial.
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(-2, 2) and (4, -1) lie on a line, what is the equation of the line?
As (-2, 2) and (4, -1) lie on a line the equation of the line is: y = (-1/2)x + 1
We can use the slope-intercept form of a linear equation,
which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values, we get:
m = (-1 - 2) / (4 - (-2)) = -3/6 = -1/2
Now we have the slope (m = -1/2), and we can use either of the two given points to find the y-intercept (b).
Let's use the first point (-2, 2):
y = mx + b
2 = (-1/2)(-2) + b
2 = 1 + b
b = 1
So the equation of the line is:
y = (-1/2)x + 1
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the town's population has increased for 80,000 to 90,000 in the past 10 years. what was the present increase.
The percentage increase in the population of the town is 12%.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Increase in population = 90,000 - 80,000 = 10,000
Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%
Hence the percentage increase in the population of the town is 12%.
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c) In the following figure, AE = 8 cm, BE =3 cm and CE = 4 cm. Find the length of DE .
Answer:
DE = 6 cm
Step-by-step explanation:
The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:
CE × DE = AE × BE
4 × DE = 8 × 3
4 × DE = 24
DE = 6 cm
Hope this helps!
Question 3 Complete the following word problems by showing all your calculations: 3.1) Thato bought a bicycle for R 8 000 on a loan at Cycle lab. If the interest rate was 14% per annum for 3 years. a) What is the interest he will pay? b) What is the final amount he will pay for the bicycle? 3.2) The florist bought 200 roses for R900. If she sells the roses in a bouquet of five for R 35. a) What was the cost price per rose? b) What is the selling price per rose? c) What is the profit that she will make per rose? 3.3) The shopkeeper buys oranges and apples at a ratio of 4:3. How many apples will he buy, if he buys 96 oranges? (3) 3.4) Mr Dingaan started practicing the 1st of January to run a marathon of 140 km on the 1st of June. He practices every day for 3 hours and runs at a speed of 35km/hour. a) What is the distance that he runs in one day? b) What is the total distance he runs during the time that he practices, from January to June?
1a. The interest that Thato will pay equals to R3,840.
1b. The final amount he will pay for the bicycle will be R 11 840.
1a What is the interest he will pay?a) To calculate the interest that Thato will pay, you can use the following formula:
Interest = Principal * Rate * Time
Interest = R 8,000 * 0.14 * 3
Interest = R3 840
1b What is the final amount he will pay for the bicycle?Final amount = Principal + Interest
Final amount = R 8,000 + R 3,840
Final amount = R 11,840
2a What was the cost price per rose?Cost price per rose = Total cost of roses / Number of roses
Cost price per rose = R 900 / 200
Cost price per rose = R 4.50
2b. What is the selling price per rose?Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet
Selling price per rose = R 35 / 5
Selling price per rose = R 7.00
2c. What is the profit that she will make per rose?Profit per rose = Selling price per rose - Cost price per rose
Profit per rose = R 7.00 - R 4.50
Profit per rose = R 2.50
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A weeping willow that is
15
1515 feet in height grows to a maximum height of
35
3535 feet in
�
yy years at a constant rate of
24
2424 inches per year. Which of the following equations best describes this situation?
1
foot
=
12
inches
1foot=12inches
The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the initial height of the weeping willow be = 15 feet
Let the final height of the weeping willow be = 35 feet
The height in feet the weeping willow grows each year = 24 inches = 2 feet
Let the number of years be = y
On simplifying the equation , we get
35 = 15 + 2y
Subtracting 15 on both sides of the equation , we get
2y = 20
Divide by 2 on both sides of the equation , we get
y = 10 years
Hence , the equation is y = 10 years
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If cos A =0. 8945, find angle A to nearest tenth of a degree
The angle to the nearest tenth of a degree, we round the result to 50.7 degrees.
In trigonometry, cosine is a function that takes an angle as an input and produces a numeric value between -1 and 1 as an output. The cosine of an angle A is represented by cos A. In this problem, cos A is given to be 0.8945. To find the angle, we can use the inverse cosine function (or arccosine) which returns the angle in radians. To obtain the angle in degrees, we can multiply by 180/π (which is equal to 57.2958). The angle A is then equal to 50.6 degrees. To find the angle to the nearest tenth of a degree, we round the result to 50.7 degrees.
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Please Answer (Iready)
The expression for the given model will be 3÷2/5.
What exactly are expressions?
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.
Now,
as shown in figure the model is shaded uptil 3
and in 1 unit there are 5 total boxes which are divided in 2 parts
Therefore, it will be represented by 3÷2/5.
Hence,
The expression for the given model will be 3÷2/5.
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help me out please i
Answer: 2 *(3+4)= (2x3)+ (2x4)
Step-by-step explanation:
3 Hassan recorded the number of people in 60 passing cars.
Here are his results. Find:
a the missing frequency
b the modal number of people in a car
c the median
d the mean.
a) The missing frequency is 20
b) The modal number of people in a car is 1
c) The median is 3
d) The mean is 0.95
The sum of the frequencies must be 60.
The missing frequency by subtracting the sum of the other frequencies from 60
60 - (28 + 3 + 7 + 1 + 1) = 20
To find the median, we need to arrange the data in order from smallest to largest:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6
There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:
median = (3 + 3)/2 = 3
The mode is the value with the highest frequency, which is 1.
mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60
= (28 + 40 + 9 + 28 + 5 + 6) / 60
= 0.95
Therefore, the missing frequency, mode, median and mean has been found
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The given question is incomplete, the complete question is
Hassan recorded the number of people in 60 passing cars
people 1 2 3 4 5 6
frequency 28 ? 3 7 1 1
a)find the missing frequency
b)median
c)modal
d)mean
Please help, I’ll give brainliest!!!!!!!!!!!!
The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)
what is graph of a quadratic and linear equationA graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:
y = ax^2 + bx + c,
where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.
A graph of a linear equation is a straight line. A general form of a linear equation is given by:
y = mx + b,
where m is the slope of the line and b is the y-intercept.
In this problem, the ordered-pairs will be the point in which they intersect with each other.
Looking carefully at the graph, the ordered pair will be at points
A = (-2, 7)
B = (2, -1)
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through: (0,-5) and (-2,-3)
The equation of the linear function is y = x - 5
How to determin the equation of the linear functionFrom the question, we have the following parameters that can be used in our computation:
The ordered pairs (0,-5) and (-2,-3)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
This means that
y = mx - 5
Using the other point (-2, -3), we have
-2m - 5 = -3
Evaluate the like terms
-2m = 2
Divide by 2
m = 1
Substitute the known values in the above equation, so, we have the following representation
y = x - 5
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Complete question
Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.
y = ___?___
draw a coordinate plane and find points A(-2;0) B(1;4) C(-5;-1) D(5;0) E(0;0)
pls help me
20 points
Dawn spent $22. 5 on 9 gallons of gas.
What is the un-simplified rate of dollars-gallons, and gallons to dollars.
And what is the Simplified Unit Rate "per language" of dollars per gallon. And gallons per dollar?
Un-simplified rate of dollars-gallons = 22.5/9 $ and and gallons to dollars 9/22.5 $ . and simplified rate of dollars-gallons = 22.5/9 $ = 2.5 and and gallons to dollars 9/22.5 = 0.4 .
Here first we have to calculate the rate of gallons of gas as per gallons so for that we will find the rate of 1 gallons for that we will divide the 22.4$ to 9 gallons so ans is 22.5$/9 is the rate for 1 gallons
and 2nd we have to calculate the amount of gas as per $ like we have to calculate the the amount if we spend 1 $ so for that we will divide 9 gallons / 22.5$ = 9/22.5
And here in 1st part we are not calculate the ans in decimal as we have to calculate this on un-simplified ans .
and in 2nd part we calculate it .
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Leila had 1 3/4 of a bag of chips. Her brother gave her 1 1/2bags of chips. How many
does Leila have altogether?
how many pattern block trapezoids would create 2 hexagons
The right response is, "5 hexagons are made up of 15 pattern block trapezoids."
Geometric shapes known as pattern block trapezoids are frequently utilized in arithmetic instruction. On a flat surface, they are one of a number of forms that can be used to make tessellations, or repeating patterns. Different colored plastic or foam pattern block trapezoids are available in a variety of sizes, with each color denoting a distinct size and form. Pattern block trapezoids are frequently used to teach geometry principles like area, perimeter, and angles in addition to their application in making tessellations. They can also aid in the development of kids' spatial reasoning and problem-solving skills.
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move the lenghts to the lines in order from shortest to longest
shortest________ _________ __________ __________longest
1 kilometer 1 meter 1 millimeter 1 centimeter
[tex]20x+18=58[/tex]
you are skiing down a mountain with a vertical height of 900 feet. the distance from the top of the mountain to the base is 1800 feet. what is the angle of elevation from the base to the top of the mountain?
