Answer:
2
Step-by-step explanation:
2 because 6 multipled by 1/3 is 2 and 2 multipled 3 is 6
2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of . One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.
(a) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
(b) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Yes, your answers are correct.
The volume of a cone is given by V = 1/3πr²h. Since the diameter of the first cone is 4, the radius is 2; therefore the volume is
V = 1/3π(2²)(8) = 32π/3
We divide the volume of the sink, 2000π/3, by the volume of the cone:
2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.
The diameter of the second conical cup is 8, so the radius is 4. The volume then is:
V = 1/3π(4²)(8) = 128π/3
Dividing the volume of the sink, 2000π/3, by 128π/3:
2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16
The requried,
(a) Carissa scoop out 63 cups.
(b) Carissa scoop out 16 cups
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The problem requires us to find out how many cups of water Carissa needs to scoop out of the sink to empty it, given the volume of the sink and the dimensions of the two cups. We can solve this problem by using the formula for the volume of a cone:
V = (1/3) * π * r² * h
First, simplify the volume formula for a cone to make it easier to manipulate:
V = 1/3πr²h
Next, plug in the given values for the first cone:
V = 1/3π(2²)(8) = 32π/3
Then, divide the volume of the sink by the volume of the first cone:
2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.
Now, calculate the volume of the second cone using the same formula:
V = 1/3π(4²)(8) = 128π/3
Finally, divide the volume of the sink by the volume of the second cone:
2000π/3 ÷ 128π/3 = (2000π/3) * (3/128π) = 2000/128 = 15.625 ≈ 16.
Divide the volume of the sink by the volume of the first cone to get the number of first cones that can fit into the sink:
2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ7
Use the geometric series 5^Ž (8)*-* to answer each question.
n=1
What are the terms in the series?
1 + 8 + ___+ ____+ ____
Answer:
First one is:
1 + 8 + 64 + 512 + 4096
Second one is:
73
Answer:
First one is:
1 + 8 + 64 + 512 + 4096
Second one is:
73
Step-by-step explanation:
Pedro throws a ball upward at a rate of 20 meters per
second from an initial height of 2 meters. The height
of the ball above the ground can be approximated by
h = -512 + 20t + 2, where t represents the amount of time,
in seconds, since the ball has been released.
What is the maximum height that the ball reaches?
Answer:
The maximum height that the ball reaches is of 3.96 meters.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
The height after t seconds is given by:
[tex]h(t) = -51t^2 + 20t + 2[/tex]
Which is a quadratic equation with [tex]a = -51, b = 20, c = 2[/tex]
What is the maximum height that the ball reaches?
This is [tex]h_v[/tex].
[tex]\Delta = b^2-4ac = 20^2 - 4(-51)(2) = 808[/tex]
[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{808}{4(-51)} = 3.96[/tex]
The maximum height that the ball reaches is of 3.96 meters.
I need help with this fast
Answer:
Evaluate for x=0.02,y=0.1,z=0.3
(3)(0.02)−(2(0.12)+0.33)
(3)(0.02)−(2(0.12)+0.33)
=0.013
Step-by-step explanation:
Kevin has 6 pounds of ham to make 12 sandwiches. He puts the same amount of ham on each sandwich. Which statement about Kevin’s sandwiches is true?
1.Each sandwich has one half pound of ham.
2. Each sandwich has 1 pound of ham.
3. Each sandwich has 2 pounds of ham.
4. Kevin has one half pound of ham left over.
statement 1 b/c 6/12 = 1/2
What quantity could go into the blank to make the equation a true statement? 5a + a + ___ = 10a
Answer:
[tex]4a[/tex]
Step-by-step explanation:
Just like addition.
Plz help me..........
Answer: 7 cubic meters
Step-by-step explanation:
you add
4x ^ 2 + 300 = 1, 596 help solve for the x please show work I will mark brainliest
Answer:
x=18 OR x=-18
Step-by-step explanation:
[tex]4x^2=1296\\x^2=324\\x=+-sqrt(234)\\x=18 OR x=-18[/tex]
Auditions are being held for the annual school musical.
There are 18 roles available in the show. If 75 students
try out, what percentage of the students will get a role in
the musical?
Pls help 20 points !
Answer:
the answer is 168 is the answer
what is the sum of 23 * 3/4?
Answer:
17 1/4
Step-by-step explanation:
69/4 = 17 1/4 or 17.25
Answer:
17 1/4
Step-by-step explanation:
23/1 *3/4
23*3 1*4 = 69/4 simplify 17 1/4
Question 2 of 10
Is AXYZ= AABC? If so, name the postulate that applies.
c
À X
Given:
ZYB
XY AB
YZ EBC
A
B
A. Congruent - SSS
B. Congruent - SAS
C. Might not be congruent
D. Congruent - ASA
The triangles XYZ and ABC are congruent by SAS postulate.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given two triangles XYZ and ABC.
If the two triangles are congruent, their corresponding sides and angles must be equal.
Given,
∠Y = ∠B
XY ≅ AB
YZ ≅ BC
SAS congruence theorem states that if two sides and an included angle of a triangle is equal to corresponding two sides and an included angle of the other triangle, then they are congruent.
So, ΔXYZ ≅ ΔABC by SAS postulate.
Hence the two triangles are congruent by SAS postulate.
Learn more about Congruence of Triangles here :
https://brainly.com/question/20521780
#SPJ7
Tulungan niyo po Ako sa module po sa Math
Step-by-step explanation:
1a)you are asked to find the number of girls and boys who received prizes
1b)The given facts are that out of 60 pupils, 40 being boys, 20 being girls, joined a Math Quiz competition. 20%of boys and 15 of girls received prizes.
1c)40 boys +20 girls=60 pupils.
1d) Find the number of girls and boys that re ceived prizes
20% of 40 boys
20/100 ×40= 8 boys won prizes
15% of 20 girls
15/100×20=3 girls won prizes
1d) 8 boys+3 girls=11 pupils won prizes
What is the least common multiple of 5 and 8?
Thank you in advance
Answer:
<z = 37
Step-by-step explanation:
<x = 90
<y = 53
<z = ?
<x + <y + <z = 180
90 + 53 + <z = 180
143 + <z = 180
<z = 180 - 143
<z = 37
Answer:
37
Step-by-step explanation:
180-90-53= 37
Can someone help me find the area?
Answer:
56
Step-by-step explanation:
4 x 5 = 20
20/2 = 10
4 x 5 = 20
20/2 = 10
6 x 6 = 36
20 + 36 = 56
______________________
Give Me Brainllest
Answer:
56
Step-by-step explanation:
Pleasee help ASAP! I appreciate anything, will give brainliest and try to help solve your questions if necessary.
Answer:
it 3
Step-by-step explanation:
okay this makes 0 sense... Show how you can solve the equation 3x=9 by multiplying each side by the reciprocal of 3... need to be the full steps pls
Answer:
x=3
Step-by-step explanation:
3x=9
Divide both sides by 3 and you get 1x=3 or basically x=3.
So the answer would be x=3.
2. The truth will prevail. (Justify your answers, no justification, no credit). (12 points each) a) In any given sample, the median is never larger than the mean, unless the distribution is symmetric. True or False. b) The sign of the correlation coefficient provides us with information regarding how good a line fits the data points we are studying. True or False. c) The range is always larger than the inter-quartile range. True or False
Answer:
False ;
False ;
False
Step-by-step explanation:
In a perfectly symmetric distribution, the mean and Median values are the same. But for skewed distributon, the median is greater than the mean (negatively skewed or left skewed data). Hence, the assertion is false.
The sign of the correlation Coefficient does not give information about how good a line fits. The sign attached to the correlation Coefficient gives information about the slope and hence, the type of relationship between the variables.
Positive (+) sign = positive relationship between variables ; negative (-) sign = negative relationship between variables.
C.)
The value of the range is not always higher Than the value of the interquartile range. The IQR might have the same value as the value of the range.
For instance :
Given the data :
1, 1, 1, 2, 2, 3, 4, 4, 4
Range = maximum - minimum
Range = 4 - 1 = 3
Interquartile range (IQR) :
IQR = Q3 - Q1
Q3 = 3/4(n+1)th term
Q3 = 3/4(10) = 7.5th term
Q3 = (7th + 8th) / 2 = (4+4)/2 = 4
Q1 = 1/4(10) = 2.5th term
Q1 = (2nd + 3rd) / 2
Q1 = (1 + 1) /2 = 1
Q3 - Q1 = 4 - 1 = 3
giving brainliest!! easy*
Answer:
4521.6
Step-by-step explanation:
pi*r^2*h = pi*144*10 = 1440 pi which is roughly 4521.6
Answer:
979.68
Step-by-step explanation:
Solve the system: 10x-9y=8 21y+15x=0.5
PLEASE HELP NEED ASAP
Answer:
x = 1/2
y = -1/3
Step-by-step explanation:
10x - 9y = 8 (Multiply by 3)
15x + 21y = 0.5 (Multiply by -2)
30x - 27y = 24
-30x - 42y = -1
-69y = 23
y = -1/3
10x - 9y = 8
10x - 9(-1/3) = 8
10x + 3 = 8
10x = 5
x = 1/2
What is the median of the numbers 312, 336, 488, 384, 368, 336, 416, 624
Answer:
376
Step-by-step explanation:
312,336,336,368,384,416,488,624
the middle numbers are 368 and 384
the median is the middle of the middle numbers
to find this number we add up 368 and 384 and divide the answer by 2
368+384=752
752/2=376
Answer:
376
Step-by-step explanation:
1. To find the median you have to first arrange the numbers in numerical order.
2. Count how many numbers you have.
3. Divide by 2. Go to the number in that position and average it with the number in the next highest position to get the median.
So considering you have 8 numbers if you divide 8 ÷ 2 = 4
the 4th number arranged is 368. Now to average 368 and 384. 368+384=752
752 ÷ 2 = 376
Answer Please this would be a huge help. (About Math BTW)
Answer:
The measure of the angle( F is 150 °)
Step-by-step explanation:
[tex]210 + f = 360 \\f = 360 - 210 \\ f = 150 \: \: degree[/tex]
I hope that is useful for you :)
How many different triangles can be made with the angle measures 30°, 60°, and 90°? A none B one © exactly two D more than two
help help please i did not understand
Answer:
The tree grows 3,14 centimeters per year
Answer: First you have to look at the years and see how much it increase each year. We start by seeing that in 1 year it is 3.14. In two years it will be 6.28. So, the answer each year the tree gets older it is 3.14 that you have to add. Hope it helps.
Step-by-step explanation:
ZABD and ZDBC are supplementary angles.
What is the measure of x?
X = [?]
7D
110%
А AT
X
B
>C
Angles are not drawn to scale.
Enter
Answer:
jngijmgjim
Step-by-step explanation:
gvnjv jg
Answer:
x=70°
Step-by-step explanation:
x+110=180 linear pair
x=180-110=70
You notice that the client's bedroom is also proportional to a larger office that you have already completed. The diagram below shows the bedroom (left) and completed office (right). Use this diagram for Questions 3-6.
It cost $120 to buy the materials for crown molding in the completed office. (Crown molding is the decorative border where the walls meet the ceiling. It will go all the way around all four walls.) Using the same materials, how much will it cost to buy all of the crown molding for the bedroom? Round up to the nearest whole dollar.
Answer:
D. 75
Step-by-step explanation:
The cost to buy all of the crown molding for the bedroom would be $75.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that bedroom and office in the diagrams below are similar rectangles and the walls on the left sides in the diagram are proportional, and the walls on the top sides in the diagram are proportional.
Since it will cost $120 to buy the materials for crown molding in the completed office. Thus Crown molding is the decorative border where , the walls meet the ceiling. It will go all the way around all four walls.
Hence, cost to buy all of the crown molding for the bedroom = $75.
More can be learned about proportions at;
brainly.com/question/24372153
#SPJ3
Work it out fast its a timed test
Answer:
$1400
Step-by-step explanation:
Answer:
$1,400.00
Step-by-step explanation:
You have to multiply $8.75 by the 20 hours to get $175, then you multiply that by 8 weeks to get $1,400
WILL MARK BRAINLIEST!!! PLEASE ANSWER!!! WRONG ANSWERS JUST FOR POINTS WILL BE REPORTED!!!!!!!!!!!!!!
Answer:
where's the question???
Step-by-step explanation:
Step-by-step explanation:
Volume of cylinder=πr²h
Mort bought his house in 2004 for $279,000. it was recently appraised at $186,000. What is the approximate percent of decrease in value
Answer:
33.3%
Step-by-step explanation:
(279,000 - 186,000) / 279,000 = 0.33333333333
0.33333333333*100= 33.3333333333
Formula used:
[tex]V_{2} -V_{1}[/tex] / [tex]V_{2}[/tex] × 100
V2= 279,000
V1= 186,000
The approximate percentage of the decrease in value of the house is 33.33%.
Purchase price of the house = $279,000
Appraisal cost of the house = $186,000
What is a percentage?The percentage is the value per hundred.
The percent of the decrease in value = (279000-186000)/279000 *100
The percent of the decrease in value =(93000/279000) *100
The percent of the decrease in value =33.33%
Hence, the approximate percentage of the decrease in value of the house is 33.33%.
To get more about percentages visit:
https://brainly.com/question/24304697
