a tank in the shape of an inverted right circular cone has height 6 meters and radius 3 meters. it is filled with 5 meters of hot chocolate. find the work required to empty the tank by pumping the hot chocolate over the top of the tank. the density of hot chocolate is
The work required to empty the tank is approximately equal to 267,656.6 joules.
The volume of the tank can be calculated as follows:
V = (1/3) * π * r² * h
Where r is the radius, h is the height, and π is pi. Plugging in the values:
V = (1/3) * π * 3² * 6
V = 54π
Next, we can find the mass of the hot chocolate in the tank:
m = V * ρ
Where ρ is the density of hot chocolate. Plugging in the values:
m = 54π * 1070
The work required to pump the hot chocolate out of the tank can be calculated using the formula:
W = mgh
Where m is the mass of the hot chocolate, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hot chocolate in the tank (5 meters). Plugging in the values:
W = m * 9.8 * 5
W = 54π * 1070 * 9.8 * 5
So, the work required to empty the tank is approximately equal to 267,656.6 joules.
Learn more about physics here: brainly.com/question/28600368
#SPJ4
Complete question:
A tank in the shape of an inverted right circular cone has height 6 meters and radius 3 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is 1070 kg.m³
The product of 2 decimals is 0. 36
What might the decimals be? Find as many answers as possible
Answer:
Step-by-step explanation:
we will find all the factors of 36 and then go for their decimals
.2 * 1.8 = .36
.3 * 1.2 = .36
.4 * .9 = .36
.6 * .6 = .36
A rectangle has a length of x and a width that is 8 units shorter than twice the length.
a. Draw a picture to represent the box.
b. Write a simplified polynomial to represent the area of the rectangle.
c. What would the area be if = 10 ?
Step-by-step explanation:
length = x
width = 2x-8
b.) to get the area you need to multiply the length and the width.
l×w= area
x(2x-8)
2x^2-8x
c.) 2x^2-8x = 10
subtract 10 both sides
2x^2-8x-10 = 0
2(x^2-4x-5) = 0
2(x-5)(x+1) = 0
x = 5
the area would be 10.
Lynn drives her car for work and drives an average of 1,100 miles each month. if her car gets 23 miles per gallon, how much fuel does she use each month?
Lynn used \(47.826\) gallons fuel in each month.
Average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Gallon is the unit for measuring liquids (fuel).
Mile is a unit of large distance.
Given,
Lynn drive her car for work an average of \(1100\) miles
Car get \(23\) miles per gallon.
It's mean car covers \(23\) miles distance in \(1\) gallon of fuel.
She used fuel in each month
\(=\frac{Total miles}{miles per gallon} \\=\frac{1100}{23}\\ =47.8260 gallon\)
Lynn used \(47.826\) gallons fuel in each month.
To know more about Lynn
https://brainly.com/question/12877834
#SPJ4
The graph shows point F located at (0, 3) and line d given by the equation y = -2.
Which point is equidistant from F and d?
(0,1)
(3,0)
(-3,5)
(-5,3)
Step-by-step explanation:
Since line d has a constant y-value of -2, any point equidistant from F and d must lie on a horizontal line passing through the point (0, 1) (which is the midpoint of the line segment connecting F to the y-axis).
Therefore, we can eliminate the points (-3, 5) and (-5, 3) since they do not lie on a horizontal line passing through (0, 1).
To determine which of the remaining two points, (0, 1) and (3, 0), is equidistant from F, we can calculate their distances from F:
Distance from (0, 1) to F: sqrt[(0-0)^2 + (1-3)^2] = sqrt[4] = 2
Distance from (3, 0) to F: sqrt[(3-0)^2 + (0-3)^2] = sqrt[18] = 3sqrt[2]
Since neither distance is equal, we can conclude that there is no point on the graph that is equidistant from F and d. Therefore, the answer is none of the given options.
find the volume 9m by 5m by 9m
Answer:
405m³
Step-by-step explanation:
I will assume these are the dimensions of a square or rectangle. To find the volume, we can use the formula [ v = b * h * l ].
v = 9 * 5 * 9
v = 45 * 9
v = 405m³
Best of Luck!
Step-by-step explanation:
volume=length×breadth×height
=9×5×9
405
Can you arrange 25 small squares to make a larger square? Can you arrange
35 small cubes to make a larger cube?
I need to answer this please
Question 3 of 10
Polygons AUHS, A'U' H'S', and A"U" H"S" are shown on the coordinate grid.
Y
-8
-6
A'
S" H" U'
-4
-2
S'
H'
U
4
S
6
2
A"
Which sequence of transformations map AUHS to A"U"H"S"?
A translation of (x,y) → (x-4, y-2) then rot:
The sequence of transformations you suggested does indeed map AUHS to A"U" H"S".
Transformation geometry is a branch of mathematics that deals with the study of geometric shapes and their transformations in space.
Apply the transformations to each vertex of polygon AUHS and see if the resulting vertices match the corresponding vertices of polygon A"U"H"S in order to evaluate whether the series of transformations you provided translates AUHS to A"U"H"S.
Let's begin by translating (x,y) (x-4, y-2). Each point is moved 2 units down and 4 units to the left by this transformation. Vertex A(-6,-6) would be changed to A"(-10,-8) in the following manner, for instance:
A'(-6,6) → A"(-10,4)
U'(-2,2) → U"(-6,0)
H'(4,2) → H"(0,0)
S'(-2,-6) → S"(-6,-8)
Let's now think about the rotation of the origin 90 degrees anticlockwise. Each point is rotated 90 degrees anticlockwise relative to the origin using this transformation. Vertex A"(-10,-8) would be rotated to A"(8,-10) in the following manner, for instance:
A"(-10,-8) → A'(8,-10)
U"(-6,0) → U'(0,-6)
H"(0,0) → H'(0,0)
S"(-6,-8) → S'(-8,6)
Therefore, the sequence of transformations you suggested does indeed map AUHS to A"U"H" S".
To know more about transformation follow
https://brainly.com/question/29754614
#SPJ1
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each linear equation to its slope and y-intercept. slope: 3/2 , y-intercept: 7/2 - x + 5 y = 4 slope: 5/2 , y-intercept: 7/2 5 y − x = 15 slope: 1/5 , y-intercept: 4/5 2 y − 3 x = 7 slope: 1/5 , y-intercept: 3 2 y = 5 x + 7 slope:- 5 , y-intercept:
The slope and intercept values for the equations given are :
slope = -1/5 ; intercept = 4/5slope = 1/5 ; intercept = 3Converting to slope-intercept formatThe slope intercept form of a linear equation is always written in the form:
y = bx + c1.)
x + 5y = 4
Make y the subject
5y = -x + 4
divide through by 5 to isolate y
y = -1/5x + 4/5
Hence, the slope = -1/5 and intercept = 4/5
2.)
5y - x = 15
make y the subject
5y = x + 15
divide through by 5 to isolate y
y = 1/5x + 3
Hence, the slope = 1/5 and intercept = 3
Learn more on slope-intercept: https://brainly.com/question/11533578
#SPJ1
Two friends, Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 37 shifts that she had a mean of 4.5 calls per shift. She knows that the population standard deviation for her shift is 1.1 calls. Jodi calculates from a random sample of 32 shifts that her mean was 5.3 calls per shift. She knows that the population standard deviation for her shift is 1.5 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.05 level of significance. Let Karen's shifts be Population 1 and let Jodi's shifts be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places
The Test value for difference between the mean numbers of calls for the two shifts at the 0.05 level of significance is 31.94
According to the question,
Karen's data:
Sample size : n₁ = 37
Sample mean = 4.5
Sample standard deviation : s₁ = 1.1
Jodi's data ,
Sample size : n₂ = 32
Sample mean = 5.3
Sample standard deviation : s₂ = 1.5
To calculate significance difference between two means we use t-test
t = difference of mean / √(pooled variance / n₁ + n₂)
Pooled Standard deviation = \(\sqrt(\frac{(n_1 - 1)s_1^{2} + (n_2 - 1)s_2^{2})}{n_1 + n_2 -2}\)
=> \(\sqrt(\frac{(37 - 1)1.21+ (32 - 1)2.25)}{37 + 32 -2}\)
=> \(\sqrt(\frac{(43.56+ 69.75)}{67}\)
=>\(\sqrt(\frac{(113.31)}{67}\)
=> √1.6911
t = 37 - 32 / (√1.6911/37+32)
=> 5 / √0.0245
=> 31.94 is test value
To know more about Test statistic here
https://brainly.com/question/14128303
#SPJ4
PROBABILITY AND STATISTICS:
The random size distribution table is:
X
-4
-2
0
1
3
5
p
0,2
0,1
0,25
0,2
0,2
0,05
a) Write down the function of distribution of this random size by regions. A drawing, formula and detailed calculation are required for each area.
b) Express the result obtained as F (x) =***
c) Calculate the value of F(3) -F(0).
d) In which area is the probability of entering F (3) -F (0)? (Answer as region X ≤ 9 or -9 ≤ X ≤ 9
etc., think carefully about which endpoint of the area is included and which is not.)
The value of F(3) -F(0). d) In which area is the probability of entering F (3) -F (0) is "0 ≤ X < 3".
a) The function of distribution by regions is:
For x < -4: F(x) = 0
For -4 ≤ x < -2: F(x) = 0.2
For -2 ≤ x < 0: F(x) = 0.2 + 0.1 = 0.3
For 0 ≤ x < 1: F(x) = 0.3 + 0.25 = 0.55
For 1 ≤ x < 3: F(x) = 0.55 + 0.2 = 0.75
For 3 ≤ x < 5: F(x) = 0.75 + 0.2 = 0.95
For x ≥ 5: F(x) = 1
b) Expressing the result obtained as F(x) =:
F(x) = {0, x < -4
0.2, -4 ≤ x < -2
0.3, -2 ≤ x < 0
0.55, 0 ≤ x < 1
0.75, 1 ≤ x < 3
0.95, 3 ≤ x < 5
1, x ≥ 5
c) F(3) - F(0) = 0.95 - 0.55 = 0.4
d) The probability of entering F(3) - F(0) is the probability of the random variable falling between 0 and 3. This can be expressed as:
P(0 ≤ X < 3) = F(3) - F(0) = 0.4
Therefore, the answer is "0 ≤ X < 3".
To learn more about distribution visit:
https://brainly.com/question/29062095
#SPJ11
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 19. Use the empirical rule to determine the following
The percentage of scores between 81 and 119 is given as follows:
68%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.81 and 119 are within one standard deviation of the mean, hence the percentage is of 68%.
Missing InformationThe problem asks for the percentage of scores between 81 and 119.
More can be learned about the Empirical Rule at brainly.com/question/10093236
#SPJ1
D=R(100-x)/100 for R
Write an equation to match the graph.
The equation which matches the absolute value function graph given as required is; y = -1 |x + 1| + 1.
What is the equation which matches the graph?As evident from the task content, the equation which matches the given graph is to be determined.
On this note, recall that the absolute value function takes the form;
f (x) = a |x - h| + k where the vertex is; (h, k).
Therefore, since the vertex is; (-1, 1); we have;
f (x) = a |x + 1| + 1
To find a; use point (0, 0)
0 = a |0 + 1| + 1
a = -1.
Ultimately, the equation which matches the graph is; y = -1 |x + 1| + 1.
Read more on absolute value equation;
https://brainly.com/question/24437140
#SPJ1
what is the answer of 12p + P
Answer:
13p
Step-by-step explanation:
because the P it have 1 hidden there
12p + 1p = 13p
PLEASE HELP I DONT UNDERSTAND
Answer:
x = 16
Step-by-step explanation:
16 and x have the same length.
the teacher workroom has a small room used for the meetings that it shaped like a square . if one wall measures 8 feet what is the area of the floor of that meeting room
The area of the teacher workroom is 64 feet squared
the basic geometry of a parallel plate capacitor does not affect its capacitance. TRUE/FALSE?
True. It's because the capacitance between two plates depends on the electric field between them, which is naturally geometry-dependent; if you have charges in different places, you get a different electric field.
A capacitor's capacitance is affected by the area of the plates, the distance between the plates, and the dielectric's ability to support electrostatic forces.
The capacitance of a parallel plate capacitor (depending on its geometry) is given by the formula C=Ad C = A d, where C is the capacitance value, A is the area of each plate, d is the distance between the plates, and is the permittivity of the material between the parallel capacitor's plates.
The curvature of the plates indicates whether the plates are spherical or cylindrical. As a result, the only factor that has no effect on the capacitance of the capacitor is the type of material used to make the plates.
To know more about Capacitance go through:-
https://brainly.com/question/27393410
#SPJ4
the u.s. bureau of labor statistics reports that 11.3% of u.s. workers belonged to unions in 2013. suppose a sample of 400 u.s. workers is collected in 2018 to determine whether union efforts to organize have increased union membership. if the sample results show that 58 of the workers belonged to unions, what is the p-value for your hypothesis test?
Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.
We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.
The null hypothesis is that the population proportion is equal to 11.3%:
H0: p = 0.113
The alternative hypothesis is that the population proportion is greater than 11.3%:
Ha: p > 0.113
The sample proportion is P = 58/400
= 0.145
The standard error of the sample proportion is:
SE = √(p*(1-p)/n)
= √(0.113*(1-0.113)/400)
= 0.0197
The test statistic is:
z = (P - p) / SE
= (0.145 - 0.113) / 0.0197
= 1.6244
The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:
p-value = P(Z > 1.6244)
= 0.0515 (using a standard normal distribution table)
To know more about hypothesis test,
https://brainly.com/question/30588452
#SPJ11
Find the exact value of cos J in simplest form.
√29
14
15
H
The cosine of angle J is given as follows:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:
Sine = length of opposite side/length of hypotenuse.Cosine = length of adjacent side/length of hypotenuse.Tangent = length of opposite side/length of adjacent side = sine/cosine.For the angle J in this problem, we have that:
4 is the adjacent side.\(\sqrt{98}\) is the hypotenuse.Hence the cosine of angle J is given as follows:
\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)
\(\cos{J} = \frac{4\sqrt{98}}{98}\)
\(\cos{J} = \frac{2\sqrt{98}}{49}\)
As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
A similar problem, also about trigonometric ratios, is given at brainly.com/question/24349828
#SPJ1
John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
(lol please help, I don't know how to format this-)
Based on the graph (see attachment), John's speed on each section of the walk are as follows:
At the first interval, John's speed is equal to 4 km/h.At the second interval, John's speed is equal to 0 km/h.At the third interval, John's speed is equal to 1.5 km/h.What is speed?Speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured as meter per seconds.
What is distance?Distance can be defined as the amount of ground covered (travelled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.
How to calculate the speed?Mathematically, speed can be calculated by using this formula;
Speed = distance/time
Based on the graph (see attachment), John's speed on each section of the walk can be calculated as follows.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the second interval, we have:
Speed = 6/0
Speed = 0 km/h.
For the third interval, we have:
Speed = 6/4
Speed = 1.5 km/h.
Read more on speed and distance here: https://brainly.com/question/17345820
#SPJ1
4/8 is closest to which benchmark fraction
Answer:
It is closest to 1/2
Step-by-step explanation:
First you need to see if the fraction can be simplified or not. Thankfully this can, and we get 1/2.
the perimeter of the polygon above is ___
7cm 7cm 2cm 2cm 5cm 4cm 4cm 6cm
The mean is ? = 137.0 and the standard deviation is ? = 5.3.
Find the probability that X is between 134.4 and 140.1.
0.4069
0.6242
0.8138
1.0311
The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.
To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:
z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906
z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.
To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:
P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.
As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.
To know more about probability, refer here:
https://brainly.com/question/12629667#
#SPJ11
Which of the following is the equivalent mathematical symbol of the expression, "A book of stamps at the post office has less than 10 stamps in it"? * b. s > 10 a. s < 10 d. s is greater than or equal to 10 c. s is less than or equal to 10
ANSWER
s < 10
EXPLANATION
With the 'less than' or 'greater than' symbol we can see that it's like an equal sign that has been shrinked on one end. In the smallest end we have to write the smallest expression or number and in the largest end we have to write the greatest expression or number.
For example: 5 < 10 is the same as 10 > 5, because the smallest number (5) is in the smallest end of the sign and the greatest number (10) is in the largest end of the sign in both expressions.
If 's' is the number of stamps, the expression says that there are 'less than' 10 stamps at the post office, so 's' has to be in the smallest end of the sign.
Can anyone help me with this please .
Answer:
Left: yes it is linear
Right: No it is not.
Step-by-step explanation:
Left Problem
The table on the left is linear. It's general form is
y = 6x + 7
x = 5
y = 5*6 + 7
y = 37
-------------------
x = 8
y = 6*8 + 7
y = 48 + 7
y = 55
------------------
y = 6*12 + 7
y = 72 + 7
y = 79
=============
Right Problem
The right problem looks like it is linear. It is not, I don't think. Do the same thing you did above.
y = 62x
x = 2
y = 2*62
y = 124
-----------------------
y = 62x
x = 6
y = 62 * 6
y = 372
---------------------
y = 62*x
x = 9
y = 62 * 9
y = 558
It should be 558 not 552
is 4/7 and 24/35 a ratios form a proportion
Answer:yes!
Step-by-step explanation:
What is the conversion of 3000 m to miles ?
The converted value of the units 3000 meters to the required miles is given by 1. 8641 miles ( round up to four decimal places ) .
Meters and Miles are related to each other as both are units which are used to measure the distance /length between any two or more endpoints.Standard form to Convert meters and miles is equal to :
1 meter = 0.000621371 miles
Now, the value of 3000 meters in miles we get by multiplying it by 0.000621371 we get,
3000 meters = ( 3000 ) × ( 0.000621371 ) miles
= ( 1.864113 ) miles
= ( 1.8641 ) miles ( round up to four decimals places )
Therefore, the value of 3000 meters to miles is equal to ( 1.8641 ) miles ( round up to four decimals places ) .
learn more about miles here
brainly.com/question/22616001
#SPJ4
an exponential relationship exists between the explanatory variable and the response variable in a set of data. the common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of
The value is closest to the predicted value of the response variable for x=4.8 is 1.26
The question requires you to substitute the value of x=4.8 in the least-squares regression line
The equation given is log (y)= 7.3 - 1.5x
Replacing x with real value, 4.8 you will have;
log(y) = 7.3 - 1.5(4.8)
log(y)= 7.3-7.2
log(y)=0.1
y=10^0.1
y=1.258
The dependent variables on the y-axis and the independent variables on the x-axis are shown as a linear connection by a regression line. By examining the data pattern the variables' effects have created, the correlation is established. In a regression graph, the regression line that is closest to the data points is shown.
For more information on regression line kindly visit
https://brainly.com/question/29214483
#SPJ4
Complete question is :
An exponential relationship exists between the explanatory variable and the response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(yˆ)=7.3−1.5xlog(y^)=7.3−1.5x. Which value is closest to the predicted value of the response variable for x=4.8x=4.8 ?