A graduated cylinder has a mass of 80g when empty. When 20mL of water is added, the graduated cylinder has a mass of 100g. If a stone is added to the graduated cylinder, the water level rises to 45mL and the total mass is now 156g. What is the density of the stone?
Answers
The density of the stone which is added to cylinder is D = 2.24 gm/mL
What is Density?The density of a substance or liquid is given by the formula ,
Density ρ = Mass ( M ) / Volume ( V )
where ρ is the density, m is the mass, and V is the volume.
The mass of a material per unit of volume is its density. Density is most frequently represented by the symbol ρ
Given data ,
Let the density of the stone be represented as D
Now , The initial mass of the cylinder = 80 g
The amount of water added to the cylinder = 20 mL
So , mass of water + cylinder = 100 g
And , the mass of water added = 100 g - 80 g = 20 g
Now , the density of water = mass of water / volume of water
The density of water = 1 gm/mL
And , when the stone is added to the cylinder , the water level rises to 45mL
So , the volume of water displaced by the stone = 45mL - 20mL = 25mL
And , the final mass of cylinder = 156g
So , the mass of stone = 156 - 100 = 56 gm
Therefore , the density of the stone D = mass of stone / volume of stone
The density of stone D = 56 / 25
The density of stone D = 2.24 gm/mL
Hence , the density of stone is 2.24 gm/mL
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Related Questions
The volume of a certain gas increases by 25%. Complete the following statement.
The new pressure will be
of the original pressure.
120%
75%
80%
125%
Answers
Answer: D. 125%
Step-by-step explanation:
An INCREASE of 25% means the original volume (100%) + 25% = 125%
Answer:
\(\boxed{125\%}\)
Step-by-step explanation:
\(original \: pressure=100\%\)
\(increase=25\%\)
\(new \: pressure=100\%+25\%=125\%\)
The new pressure will be 125% of the original pressure.
gabriela makes quilts to sell at charities. she can make 9 quilts with 36 yards of material. how many yards of material would she require for 13 quilts ?
Answers
PLEASE HELP!! What is the surface area of the cone?
Answers
Hope this helped
Find two square numbers that total 45
Answers
x^2+^2=45
if ×=3 and y=6
then 9+36=45
Robert has available 400 yards of fencing and wishes to enclose a rectangular area. Express the areaAof the rectangle as a function of the widthwof the rectangle. For what value ofwis the arealargest? What is the maximum area?
Answers
Answer:
The answer is below
Step-by-step explanation:
a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.
the perimeter of a rectangle is given as:
Perimeter = 2(length + width) = 2(l + w)
Hence;
400 = 2(l + w)
200 = l + w
l = 200 - w
The area of a rectangle is given as:
Area = length × width
Area = (200 - w) × w
Area = 200w - w²
b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a
Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:
w = -b/2a = -200/2(-1) = -200/-2 = 100
A width of 100 yard has the largest area
c) l = 200 - w = 200 - 100 = 100 yards
Area = l × w = 100 × 100 = 10000 yd²
The maximum area is 10000 yd²
How do I properly graph an x<9 inequality on this number line?
Answers
To graph all the values less (but not equal) to nine (9) using the number line, we can use parentheses, which mean that the value is not equal to the number, or we can use an arrow with a circle above the number. We can see this as follows:
Or
In both cases, we can see that we are representing all the numbers less than 9 but not equal to 9. The arrow is pointed to the left (representing the numbers less than 9).
In interval notation, we can represent it as follows:
\((-\infty,9)\)
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20.
Answers
The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).
How to explain the relationshipIn the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.
To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).
If we subtract each value in column 1 from the corresponding value in column 2, we find that:
11 - 1 = 10
22 - 2 = 20
33 - 3 = 30
44 - 4 = 40
By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.
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Which method is the best method for solving the equation?
8x^2 - 13x + 3 = 0
Answers
Answer:
the best method is to use the quadratic formula ( Almighty formula)
Answer:
I didn't see any options provided prior to the question, however the best method that is used by those who study in mathematics for solving equations (^such as the one above^) would be the quadratic formula.
There are 8 girls and 5 boys on the math team. Which ratio correctly describes the relationship between boys and girls on
the math team?
There are 5 boys for every 5 girls.
There are 5 boys for every 13 girls.
For every 5 boys there are 8 girls.
For every 8 boys there are 5 girls.
Mark this and retum
Save and Exit
Next
Submit
Answers
Answer:
For every 5 boys there are 8 girls.
how much is an 18% tip on a 14$ lunch?
Answers
Answer needed immediately. pleaseeeee
A box contains 7 red, 8 white and 3 blue identical balls. If three balls are drawn at random from the box without replacement, calculate the probability that;
i) two are red and 1 is blue
ii) at least 2 are white
iii) 1 of each colour is drawn.
Answers
The probability that;
i). two are red and 1 is blue is 0.0257
ii). at least 2 are white is 0.1144
iii). 1 of each colour is drawn is 0.0343
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
Total possible outcome = 3 + 7 + 8 = 18
i). probability that two are red and 1 is blue = 7/18 × 6/17 × 3/16
probability that two are red and 1 is blue = 7/272
probability that two are red and 1 is blue = 0.0257
ii). probability that at least 2 are white = 8/18 × 7/17 × 7/16 + 8/18 × 7/17 × 3/16
probability that at least 2 are white = 70/612
probability that at least 2 are white = 0.1144
iii). probability that 1 of each colour is drawn = 7/18 × 8/17 × 3/16
probability that 1 of each colour is drawn = 7/204
probability that 1 of each colour is drawn = 0.0343
Therefore, the probability that; two are red and 1 is blue, at least 2 are white and 1 of each colour is drawn are approximately 0.0257, 0.1144 and 0.0343 respectively.
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6. How many 1/2 hour periods will make up 4 hours?
Answers
Answer:
8 1/2 hour periods will make up 4 hours.
Step-by-step explanation:
half an hour is 30 minutes, and there are 60 minutes in an hour. 4 hours=240 minutes. 240÷30=8.
hope this helps! best of luck <3
Explain how to use the unit-factor method to convert 120 pounds to kilograms.
Answers
Answer:
Step-by-step explanation:
lets remember that 1kg=2.2 lb
if
2.2 lbs................................1 kg
120lbs...................................? kg
120/2.2=54.54 kg
An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answers
Answer:
9
Step-by-step explanation:
The \(n\)term is \(2n+1\).
\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + \(n^2\) = 99
\(n^2\) + 2n - 99 = 0
Split the terms
\(n^2\) - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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A firm has the production function f(x,y) =x.5+y, where x is the amount of factor x it uses and y amount of factory. On a diagram we put x on the horizontal axis and y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that the slopes of all the isoquants that it meets have the same slope at the point where they meet this line. The straight line we drew was is the
Answers
The straight line that you drew on the graph is called an isocost line
What is the straight line you drew called?
The straight line that you drew on the graph is called an isocost line. An isocost line represents all the combinations of inputs that the firm can afford to purchase for a given cost.
The slope of an isocost line is equal to the ratio of the prices of the two inputs, and it represents the opportunity cost of using one input in terms of the other input.
If the slopes of all the isoquants that the isocost line intersects have the same slope at the point of intersection, it means that the firm is operating at a point of constant returns to scale.
This means that increasing both inputs by the same proportion results in a proportional increase in output.
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In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answers
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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divide and reduce to lowest terms Thank yall very much
Answers
Answer:
2\(\frac{23}{44}\)
Step-by-step explanation:
which statement best describes the difference between the formula for population and sample variance?
Answers
The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.
Difference between the formula for population and sample variance?The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.
The formula for population variance is given by:
σ² = (1/N) * ∑(X - μ)²,
where N is the total number of elements in the population, X is an individual value in the population, and μ is the mean of the population.
s²= (1/(n-1)) * ∑(X - m)²,
where n is the sample size and m is the mean of the sample.
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Chris needs to drive 24 miles to work. So far, he has driven 5.4 miles. How many more miles must he drive?
Answers
Answer:
18.6 miles
Step-by-step explanation:
Subtract Distance traveled from total distance
Total distance: 24 miles
Distance Traveled: 5.4 miles
24 - 5.4 = 18.6
Select the interval(s) where the function is increasing:
f(x) = x ^ 4 - 5x ^ 2 - 3
(- 9.3, - 3)
(- ∞,- 1.5)
(0, 1.5)
(-1.5, 0)
(1.5, ∞)
(-∞, ∞)
(-9.3, ∞)
Answers
(-1.5, 0) and (1.5, ∞)
Negative 1/3 in decimal form
Answers
Answer:
-0.3333334
Step-by-step explanation:
common sense
Answer:
-0.33
Step-by-step explanation:
A lending institution supplied the following data on loan approvals by four loan officers. Use α = .05 and test to determine whether the loan approval decision is associated with the loan officer reviewing the loan application.
Loan Approval Decision
Loan Officer Approved Rejected
Miller 24 16
McMahon 17 13
Lee 35 15
Sanchez 11 9
Answers
Answer:
As chi^2 < 7.815, and P > 0.05, we do not reject null hypothesis.
Thus, there is no significant evidence that the loan approval decision is not independent of the loan officer reviewing the loan application.
Step-by-step explanation:
Find the given attachment
Find the value of each variable in the following parallelogram - show work
Answers
Answer: x=14 y=10
Step-by-step explanation:
5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
Answers
5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown
b. The maximum height reached is about 147.5 feet
The time it takes the rock to reach the maximum height is about 2.47 seconds
What is a quadratic function?
A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.
The initial velocity of the rock = 79 ft/s
Height of the cliff above the beach from which the rock is thrown = 50 feet
The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50
Please find attached the graph of the height of the rock as a function of time, created with MS Excel.
Required; When the height of the rock will be 125 feet above the beach
When the height of the rock is 125 feet, we get;
h = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 0
-16·t² + 79·t - 75 = 0
The value of t obtained using an online tool are;
t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown
b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;
At the maximum point, x = -b/(2·a)
The function for the height; h = -16·t² + 79·t + 50, indicates that we get;
a = -16, b = 79, and c = 50
Therefore;
The time it takes the rock to reach the maximum height, t(max), is therefore;
t(max) = -79/(2 × (-16)) ≈ 2.47
It takes about 2.47 seconds for the rock to reach the maximum height
The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5
The maximum height reached by the rock is about 147.5 feet
Possible part of the question, obtained from a similar online question, includes;
a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.
Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.
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With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
Answers
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
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Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
Answers
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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to transform this function two units up on the y-axis, the equation will become: ______to transform this equation five units to the left along the x-axis, the equation will become: _____to transform this equation so that it opens down, the equation will become: _____to transform this equation two units down the y-axis AND five units to the right on the x-axis, the equation will become: _____
Answers
The first is
\(y=x^2+2\)The second is
\(y=(x-5)^2\)The third is
\(y=-x^2\)The fourth is
\(y=(x-5)^2-2\)The map shows an obstacle course at a school fair. The units are given in yards.
What is the total distance of
the obstacle course?
? yards
Start
(-40, -10)
Tire
Race
(-40, -30)
Finish
(10, 20)
Monkey
Bars
(40,20)
Rope
Climb
(40,-30)
Answers
The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Using this formula, we can calculate the distances between each pair of consecutive points as follows:
Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards
Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards
Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards
Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards
Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
Answers
9514 1404 393
Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
\(9^x-1=2\)
You can use logarithms, or your knowledge of powers of 3 to solve this.
\(9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}\)
Using logarithms, the solution looks like ...
\(x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}\)
What is the value of x?
Answers
Answer:
x = 9
Step-by-step explanation:
the answer is in the image attached
