Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.
The possible answers are 0.2, 1.7, 3.9 or 5.6. When googled the answer always comes up 3.9. I always get 1.6527 which rounds up to 1.7. How about you?
Answers
volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm
60-39.25 = 20.75 cu cm was in 1st cup
volume of cylinder = pi *r^2 *h
20.75 = 3.14 *2^2 *h
20.75 = 3.14*4*h
20.75 = 12.56*h
h = 20.75 /12.56 = 1.652 round to 1.7
Answer:
The height of glass 1 is 1.7 cm.
Step-by-step explanation:
We are given the following information in the question:
The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.
Volume of glass 2 = Volume of cone =
[tex]\displaystyle\frac{1}{3}\pi r^2h\\\\\text{Putting value of r and h}\\\\= \frac{1}{3}\times 3.14\times \frac{5}{2}\times \frac{5}{2}\times 6 = 39.25\text{ cubic cm}[/tex]
Volume of glass 1 =
[tex]\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}[/tex]
Volume of glass 1 = Volume of cylinder =
[tex]20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\ 20.75 = 3.14\times \displaystyle\frac{4}{2}\times \frac{4}{2}\times h\\\\h = \frac{20.75}{3.14\times 2\times 2} 1.656 \approx 1.7[/tex]
Thus, the height of glass 1 is 1.7 cm.
Related Questions
When creating a bar graph to represent data, the researcher used a scale that was too small. The outcome was a graph that appeared to show very little variation. This is a classic example of an error in which phase of inferential statistics? A.data gathering B.data organization C.data analysis D.probability-based inference
Answers
The error in using a scale that is too small on a bar graph falls under the data organization phase. This phase involves selecting a scale that accurately represents data without distorting trends or variations.
Explanation:When creating a bar graph to represent data, if the researcher uses a scale that is too small, resulting in a graph that shows very little variation, it is likely an error in the data organization phase. This is because choosing an appropriate scale is a key part of the process of organizing data for visualization. A scale that's too small can compress the data too much and fail to show important differences between data points, while a scale that's too large can exaggerate these differences. In a well-organized graph, the scale should be such that it both accurately represents all the data and makes it easy to identify trends and variations.
It is important to be skeptical of graphs and understand that data organization can have a significant impact on how the information is perceived. A graph is a single visual perspective, and therefore, it is crucial that the scale used does not distort the underlying relationship it is intended to represent. When organizing data in a graph, it's essential to select a scale that neither overshadows nor exaggerates the significant figures and trends of the data points.
Using a scale that is too small in a bar graph is an error in the data organization phase of inferential statistics.
Explanation:The error of using a scale that is too small and resulting in a bar graph that shows very little variation is a classic example of an error in data representation, which falls under the phase of in inferential statistics.
Which symbol makes the following statement true? 413,115 431,511
Answers
The first number is less than the second number
If the maximum of 63 years is accidentally recorded as 630 years, how will this affect the mean?
Answers
Solve The Following Question:
5/13t = -9
Answers
Then t =( -9*13) / 5
T=-23.4
5/13t=-9
to find t divide both sides by 5/13
t = -9 / 5/13=
-117 /5 =-23.4
t = -23.4
a ramp has a height of 3 foot and a base of 12 feet what is the angle of elevation
Answers
Let x = angle of elevation.
arctan(tan x) = arctan(3/12)
x = arctan(3/12)
x = 14.05°
identify the number in the hundreth(1/100)position 15.386
Answers
When you are dealing with decimal place value, you simply need to know that all of the numbers to the left are classified as, ones, tens, hundred, etc. The numbers to the right of the decimal start at tenths, hundredths, thousandths, etc.
I am attaching an image to show what I mean, I hope this helps.
Take care,
Diana
Help Yaya ASAP Please
Jessica and Marcus each earn the same amount of money every week mowing lawns. Jessica saves 50% of her money and Marcus saves 1/4 of his money.
Which statement is correct?
A. Marcus saves 4/5 as much money as Jessica.
B. Jessica saves 4/5 as much money as Marcus.
C. Marcus saves twice as much money as Jessica.
D. Jessica saves twice as much money as Marcus.
Answers
marcus saves 1/4.....1/4 = 25%
Therefore, jessica saves twice as much as marcus
A summer baseball league is creating teams of 25 players each from a group of 265 players. How many players will be left over after the teams of 25 players are created?
A. 10
B. 11
C. 15
D. 250
Answers
265 divided by 25= 10 with 15 remaining
So the answer is C
HELP PLSSSSS Triangle ABC is an equilateral triangle. The angle bisectors and the perpendicular bisectors meet at D in such a way that CD = 2DE.
The radius of the inscribed circle is____
units, and the radius of the circumscribed circle is___
units.
Answers
DE = 8.7/3 = 2.9
CD = 2DE = 5.8
For the inscribed circle, where center is point D. The radius is length DE.
This is because the circle will touch the 3 points where the bisectors intersect with sides of triangle.
radius = 2.9
For circumscribed circle, the center will also be point D. The radius is CD.
The circle will touch 3 points of triangle, A,B,C.
radius = 5.8
Answer: For clarification, the answer is 2.9 for the first one and the second is 5.8
Step-by-step explanation: They are correct for PLATO users I got them right.
write an expression that shows how to multiply 4 x 362 using place value and expanded form.
Answers
(4×300) + (4×60) + (4×2)
1200 + 240 + 8
1448
To multiply 4 x 362 using place value and expanded form, first expand 362 to (300 + 60 + 2). Then multiply 4 with each value, resulting in 1200, 240, and 8. The sum of these results gives the final answer, 1448.
Explanation:The multiplication expression of 4 x 362 using expanded form and place value can be represented as follows:
Firstly, write 362 in its expanded form. You can express it as (300 + 60 + 2).Then, multiply 4 by each number of the expanded form of 362. The operation would be: 4 x 300 = 1200, 4 x 60 = 240, and 4 x 2 = 8.Finally, add all the resulting numbers together to get the final answer. The operation would be 1200 + 240 + 8 = 1448.
So, 4 multiplied by 362 using place value and expanded form equals to 1448.
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A Chinese restaurant offers buffet takeout for $4.99 per pound. How much does your takeout meal cost?
Answers
Answer:
1.99
Step-by-step explanation:
What is the greatest possible product of a 2 digit number and a 1 digit number?
Answers
Highest 1-digit number = 9
Highest possible sum from 2, 2-digit numbers = 198
Highest possible sum from 2, 1-digit numbers = 18
Largest 2-digit integer: 99
9 * 99 = 891
If you need to cut 5 pieces of glass from a 14 feet length, how long should each piece be?
Answers
14 / 5 = 2.8 feet each
2.8 feet = 2 feet 9.6 inches
2 feet 9 3/5 inches
Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for 4 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?
Answers
Tip is added to that total.
240X.10 = $24
240+24 = $264
Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.
How much time passes until the second bus catches up with the first bus?
Answers
40t = 60(t-1)
distribute the right side
40t = 60t-60
subtract 60t from each side
-20t =-60
divide both sides by -20
t = -60 / -20 = 3
3 hours
Consider the expression 3 * 2 ^ 2 < 16 + 5 andalso 100 / 10 * 2 > 15 - 3. which operation is performed second
Answers
should be performed in the order PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)/
Therefore, obtain
3 * 2 ^ 2 < 16 + 5
3 * 4 < 16 + 5 Exponentiation first
12 < 16 + 5 Multiplication second
Similarly, obtain
100 / 10 * 2 > 15 - 3
100 / 20 > 15 - 3 Multip[lication first
5 > 15 - 3 Division second
Tommy can exchange 8 euros for 11 dollars.
At this rate, how many dollars can Tommy get with 12 euros?
Answers
Hope this helps and have a great day!
Tommy would be able to get $16.50.
The first step would be to find out the number of dollars you need to exchange for a single Euro.
If 8 Euros go for $11, one Euro would be:
= Amount of dollars / Amount of Euros
= 11 / 8
= $1.375 per Euro
For 12 Euros therefore, the number of dollars Tommy would get is:
= Amount of Euros x conversion factor
= 1.375 x 12
= $16.50
In conclusion, Tommy would get $16.50.
Find out more at https://brainly.com/question/7418508.
find the next three terms in the geometric sequence: 2, 4, 8, 16
Answers
its keeps multiplying each number by 2
A rancher has 50,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. what is the maximum area of each pasture?
Answers
Let the side of the rectangle parallel to the three internal fences be x and the other side of the rectangle be y, then the total length to be enclosed is given by 5x + 2y.
Given that the rancher has 50,000 linear feet of fencing available, then
[tex]5x + 2y = 50,000 \\ \\ 2y = 50,000 - 5x \\ \\ y = \frac{50,000}{2} - \frac{5}{2} x=25,000-2.5 x[/tex]
Thus, the dimensions of the rectangular field to be fences is x by (25,000 - 2.5x).
The area of a rectangle is given by length times width.
Thus, the area of the rectangular field is given by
[tex]Area=x(25,000 - 2.5x)=25,000x-2.5x^2[/tex]
For the area to be maximum, the derivative of the area with respect to x equals 0.
Thus,
[tex]\frac{d}{dx}(Area)=25,000-5x=0 \\ \\ \Rightarrow5x=25,000 \\ \\ \Rightarrow x= \frac{25,000}{5} =5,000[/tex]
Thus, the the maximum area to be enclosed is given by
[tex]Area=25,000(5,000)-2.5(5,000)^2 \\ \\ =125,000,000-2.5(25,000,000) \\ \\ =125,000,000-62,500,000 \\ \\ =62,500,000[/tex]
Therefore, the maximum area of each pasture is given by
[tex] \frac{62,500,000}{4} =15,625,000\ square\ feet[/tex]
Final answer:
To find the maximum area of each pasture, we can create a rectangular field and divide it into four equal pastures. By using the given linear footage of fencing, we can find the dimensions of the rectangular field and calculate the area for each pasture.
Explanation:
To find the maximum area of each pasture, we can start by creating a rectangular field using the given 50,000 linear feet of fencing. Let's consider the length of the rectangular field as 'x' and the width as 'y', with x being the longer side.
The perimeter of the rectangular field is given by 2x + y = 50,000. Since we want to divide the field into four equal pastures, we can divide the rectangular field into four equal widths, with each width being y/4.
Therefore, the area of each pasture is x * (y/4) = (x*y)/4.
To find the maximum area, we can substitute 2x + y = 50,000 into the formula for the area of each pasture. Solving for y in terms of x gives us y = 50,000 - 2x.
Substituting this value of y into the formula for the area, we get A = x * ((50,000 - 2x)/4).
To maximize the area, we can differentiate the area formula with respect to x and set it equal to zero. Solving this equation will give us the value of x that maximizes the area. Once we have that, we can substitute it back into the area formula to find the maximum area of each pasture.
A car travels down a highway at 25 m/s. An observer stands 100m from the highway.
a) How fast is the distance from the observer to the car increasing when the car passes in front of the observer?
(Use decimal notation.)
The rate is =
(b) How fast is the distance increasing 10s later?
(Use decimal notation. Give your answer to three decimal places.)
The rate is =
Answers
Part (a):
Before the car passes the observer, we have [tex] \frac{dh}{dt} \ \textless \ 0[/tex]; after it passes, we have [tex]\frac{dh}{dt} \ \textgreater \ 0[/tex].
So at the instant it passes we have [tex]\frac{dh}{dt} = 0[/tex], given that [tex]\frac{dh}{dt} = 0[/tex] varies continuously since the car travels at a constant velocity.
Therefore, the rate the distance from the observer to the car increasing when the car passes in front of the observer is 0m/s
Part (b):
By the Pythagorean Theorem, we have
[tex]h^2=x^2+100^2[/tex]
Thus,
[tex]2h\frac{dh}{dt}=2x\frac{dx}{dt} \\ \\ \Rightarrow\frac{dh}{dt}= \frac{x}{h} \frac{dx}{dt}[/tex]
where: [tex]\frac{dx}{dt}[/tex] is the velocity at which the car is travelling.
Since the car travels at 25 m/s, so after 10 seconds, the distance (in meters) along the road that the car has traveled, x, is given by
[tex]x=speed\times time=25\times10=250 \ meters.[/tex]
and
[tex]h^2=250^2+100^2=62,500+10,000=72,500 \\ \\ \Rightarrow h= \sqrt{72,500} =269.26 \ m[/tex]
Therefore,
[tex]\frac{dh}{dt}= \frac{x}{h} \frac{dx}{dt} \\ \\ = \frac{250}{269.26} (25) \\ \\ =0.9285(25) \\ \\ =23.212 \ m/s[/tex]
The rate at which the distance from the observer to the car is increasing is 25 m/s, both when the car passes in front of the observer and 10 seconds later.
Explanation:To find the rate at which the distance from the observer to the car is increasing, we need to use the concept of relative velocity. When the car passes in front of the observer, its velocity is perpendicular to the line connecting the observer and the car. Therefore, the rate at which the distance is increasing is equal to the speed of the car. In this case, the rate is 25 m/s.
To find how fast the distance is increasing 10 seconds later, we need to consider the fact that the car is still moving at a constant velocity of 25 m/s. Therefore, the rate at which the distance is increasing remains the same. So, the rate is still 25 m/s.
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3.24 repeating as a mixed number in simplest form
Answers
So if you make a fraction out of the numbers to the right of the decimal..how would it look
A repeating mixed number is a mixed fraction, which after converted to decimal; the numbers after the decimal point repeat without end.
3.23 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
Given that
[tex]Number = 3.24[/tex]
First, we represent as a fraction
[tex]Number = \frac{324}{100}[/tex]
To represent the number as a repeating mixed number, we simply subtract 1 from the numerator
[tex]Number = \frac{324}{100 - 1}[/tex]
[tex]Number = \frac{324}{99}[/tex]
Represent as a mixed number
[tex]Number = 3\frac{23}{99}[/tex]
Hence, 1.12 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
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Maggie is having the flooring replaced in her kitchen, living room, and master bedroom. The kitchen is getting slate tile. The tile cost $1.73 per-square-foot plus an installation fee per-square-foot. The area of the kitchen is 120 square feet, and the total cost for the flooring with installation comes to $740.40. The living room is getting hand-scraped hardwood flooring. The hardwood cost $4.98 per-square-foot plus an installation fee per-square-foot. The area of the living room is 200 square feet, and the total cost for the flooring with installation comes to $1,688.00. The master bedroom is getting berber carpet. The carpet cost $2.48 per-square-foot plus an installation fee per-square-foot. The area of the master bedroom is 180 square feet, and the total cost for the flooring with installation comes to $928.80. Place the flooring type in order from the least amount to the greatest amount of cost to install per-square-foot.
Answers
let i be the instalation fee, and i2 and i3 correspond to scenarios 2 and 3
(1.73)(120)+i=740.40
(4.98)(200)+i2=1,688.00
(2.48)(180)+i3=928.80
i=532.8
i2=692.00
i3=482.4
ok, so we have the total installation cost for each room. Now we divide that by square feet.
532.8/120=4.44
692.00/200=3.46
482.4/180=2.68
Ordering that from least to greatest, you get Berber carpet, hand-scraped hardwood, and slate tile, which has the greatest installation fee.
Brainliest answer?
Which colonial power's policy was based on assimilation of native peoples?
Answers
In Seattle, the tax on a property assessed at $570,000 is $12,540. If tax rates are proportional in this city, how much would the tax be on a property assessed at $460,000?
Answers
cross multiply
570,000x = 5768400000
x = 5768400000 / 570,000
x = 10,120 <=== tax on 460,000
Final answer:
To find the property tax on a $460,000 property, first, find the tax rate by dividing the known tax of $12,540 by the assessed value of $570,000 to get approximately 0.022. Then multiply $460,000 by this tax rate to get an estimated tax of $10,120.
Explanation:
To calculate the property tax on a property assessed at $460,000 in Seattle, given the tax rate is proportional, we can use the tax information from another property as a reference. In this case, we know a property assessed at $570,000 has a tax of $12,540. This allows us to find the tax rate by dividing the tax amount by the assessed value of the property.
Step 1: Determine the tax rate.
Tax Rate = Tax / Assessed Value
Tax Rate = $12,540 / $570,000
Tax Rate ≈ 0.022
Step 2: Calculate the tax for the property assessed at $460,000 using the tax rate.
Tax = Assessed Value × Tax Rate
Tax = $460,000 × 0.022
Tax ≈ $10,120
Thus, the property tax on a property assessed at $460,000 would be approximately $10,120, assuming the tax rates are indeed proportional.
Elsa is on the swim team. Each week she swims a total of 2000 meters. How many kilometers does she swim each week?
Answers
2,000 meters = 2 kilometers
hope thid helps :)
Simplify 3(4x + 6) - 9x.
-15x + 18
3x + 18
3x + 6
12x + 18 - 9x
Answers
Apply the Distributive Property:
3 (4x) + 3 * 6 - 9x
Multiply by 4 by 3 to get 12:
12x + 3 * 6 -9x
Multiply 3 by 6 to get 18:
12x + 18 - 9x
Subtract 9x from 12x to get 3x:
3x + 18
Your answer is the second option!
The expression 3(4x + 6) - 9x simplifies to 3x + 18 by distributing the 3 and then combining like terms.
To simplify the expression 3(4x + 6) - 9x, we need to follow the steps of distribution and then combine like terms.
First, distribute the 3 into the parentheses: 3 * 4x is 12x and 3 * 6 is 18, giving us 12x + 18.Next, subtract the 9x from 12x: 12x - 9x equals 3x.Combine the result with the 18, to end up with the simplified expression 3x + 18.Therefore, the simplified form of 3(4x + 6) - 9x is 3x + 18.
A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles.What is the probability that you choose a blue marble and then another blue marble, assuming you replace the first marble?
Answers
The probability of drawing a blue marble and then another blue marble from a bag, with replacement of the first marble, is calculated by multiplying the probability of the first event by the probability of the second event since the first event's outcome does not change the conditions for the second draw. In this case, the probability is 1/16.
The question involves calculating the probability of drawing two blue marbles consecutively from a bag, with replacement of the first marble before drawing the second one. To find this probability, we calculate the chance of drawing a blue marble twice, taking into account that the composition of the bag remains the same after the first draw due to replacement.
The total number of marbles is 5 red + 3 blue + 2 green + 2 yellow = 12 marbles. The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles, which is 3/12 or 1/4. Since the first marble is replaced, the probabilities remain the same for the second draw. Therefore, the probability of drawing a blue marble on the second draw is also 1/4.
To find the combined probability of both events happening in succession, we multiply the probabilities of each individual event: (1/4) * (1/4) = 1/16. Thus, the probability of drawing a blue marble and then another blue marble, with replacement, is 1/16.
Write a number between 1 and 50 that has at least 8 factors. B.) Write the factors.
Answers
24 has 8 factors with 1,2,3,4,6,8,12,and 24
~hope i help~
Answer:
24 has 8 factors with 1,2,3,4,6,8,12,and 24
Step-by-step explanation:
A meteor crater is 4100 feet in diameter. Approximate the distance around the crater. Use 3.14 for piπ
Answers
Circle area= 2* 3.14 * radius= 2 *3.14 * 1/2 * 4100ft= 12874ft
HOPE THIS HELPS!!!
Clara's suitcase weighs 58 1/4 pounds, but the airline's weight limit for suitcases is 50 pounds. How much weight does she need to remove from her suitcase?
Answers
Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.
To find out how much weight Clara needs to remove from her suitcase, we subtract the airline's weight limit from the weight of her suitcase.
First, let's convert 58 1/4 pounds to a proper fraction:
[tex]\[ 58 \frac{1}{4} = \frac{58 \times 4 + 1}{4} = \frac{232 + 1}{4} = \frac{233}{4} \][/tex]
Now, let's subtract the airline's weight limit from Clara's suitcase weight:
[tex]\[ \text{Excess weight} = \frac{233}{4} - 50 \][/tex]
To subtract fractions, we need a common denominator:
[tex]\[ \text{Excess weight} = \frac{233}{4} - \frac{200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{233 - 200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{33}{4} \][/tex]
Now, let's convert this back to a mixed number:
[tex]\[ \text{Excess weight} = 8 \frac{1}{4} \text{ pounds} \][/tex]
So, Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.