The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
Since the tank is cylindrical in shape, its volume can be written as:
V = πr²d,
where V is its volume, r is the radius, and d is the depth.
The radius is constant, given r = 5ft.
Thus the volume can be shown as:
V = π(5)²d,
or, V = 25πd.
Differentiating this with respect to time, we get:
δV/δt = 25πδd/δt ... (i),
where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.
Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.
Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:
δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.
Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
The question written correctly is:
"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"
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Explain when the solution set of an inequality will be the empty set or the set of all real numbers. Show an example of each.
Answer:
There are two cases when the solution set of an inequality will be the empty set or the set of all real numbers.
The first case is when the inequality is always false no matter what value is chosen for the variable. For example, the inequality x > 5 has no solution because there is no value of x that is greater than 5. In this case, the solution set is the empty set.
The second case is when the inequality is always true no matter what value is chosen for the variable. For example, the inequality x > -∞ has infinitely many solutions because there is no value of x that is not greater than -∞. In this case, the solution set is the set of all real numbers.
Step-by-step explanation:
Select the correct answer.
What is the value of this expression when a = 2 and b = -3?
a³ - 6³
5
-208
Explanation:
If the complete expression is a³ – 6³
then a³ – 6³ with a being equal to 2 is
(2)³ – (6)³ =
(2 × 2 × 2) – (6 × 6 × 6)
=
(4 × 2) – (36 × 6)
=
(8) – (216)
=
-208
This is done with substitution, just do the arithmetic with 2 in the place of a.
Answer: 7
Step-by-step explanation:
Substitute the given values of a and b into the expression:
(a)3 - (b)3 = (2)3- (3)3
5 5
Then evaluate the expression using the order of operations:
8- (-27) = 35/5
5
= 7
Use the regression line for the data in the scatterplot to answer the question. on average, how many more goals will a player score for every additional hour of practice?
On average the more goals will a player scores for every additional hour of practice is 3/4.
Given a regression line for the data in the scatterplot which is shown in figure.
This question can be solved by finding the slope of the line.
Slope is the ratio of vertical change to horizontal change between two points on the line.
Here, we can find the slope by taking the two points which is on the line.
Let us take the two points be A(1.5,2) and B(6.5,6)
Now, we will find the slope using the formula, we get
m=(y₂-y₁)/(x₂-x₁) where (x₁,y₁)=(1.5,2) and (x₂,y₂)=(6.5,6)
Substitute the values in the formula, we get
m=(6-2)/(6.5-1.5)
m=4/5
The slope which we find is near to the slope 3/4.
Hence, the more goals will a player score for every additional hour of practice from the regression line is 3/4.
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If a researcher counting how many seconds each bystander helps a stranger Struggling to pick up a heavy box
Answer:
You didn't finish the whole question.
Step-by-step explanation:
We have to calculate mean of the data.
Mean is the sum of numbers divided by total numbers included.
Mean=∑X/n
where n is the number.
Mean =(10+15+10)/3
=35/3
=11.67
What do you understand by mean ?in mathematics, a quantity that has a value intermediate between those of the extreme members of some set. numerous types of manner exist, and the method of calculating an average depends upon the relationship known or assumed to control the alternative members.
The mean, or average, is calculated by adding up the scores and dividing the whole by the number of scores. consider the following number set: 3, 4, 6, 6, 8, 9, 11. The mean is calculated in the following way: 3 + 4 + 6 + 6 + 8 + 9 + 15 = 51
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A bake shop sells twenty different kinds of pastries. Twelve of them were chocolate. Zack randomly buys eight kinds of pastries. What is the chance that four of them will be chocolate
Answer:
Just look at the other answer
Step-by-step explanation:
5/7 - 3/2 in simplest form HELP ASAP
[tex] \frac{5}{7} \: - \: \frac{3}{2} [/tex]
First, we find the lowest common denominator which is "14", we put it in the common numerator.[tex] \frac{10 \: - \: 21}{14} [/tex]
We subtract the numbers.[tex] \boxed{ \bold{- \frac{11}{14} }}[/tex]
MissSpanish[tex]\boldsymbol{\sf{\dfrac{5}{7}-\dfrac{3}{2} }}[/tex]
The least common multiple of 7 and 2 is 14. Convert 5/7 and 3/2 to fractions with like denominators.
[tex]\boldsymbol{\sf{ \dfrac{5\times2}{7\times2}-\dfrac{3\times7}{2\times7} \ \ \to \ \ \ Simplify }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{10}{14}-\dfrac{21}{14} }}[/tex]
Since 10/14 and 21/14 have the same denominator, subtract their numerators to subtract them.
[tex]\boldsymbol{\sf{\dfrac{10-21}{14} \ \ \to \ \ \ Subtract}}[/tex]
Subtract 21 from 10 to get −11.
[tex]\red{\boxed{\boldsymbol{\sf{-\frac{11}{14} }}}} \ \ \to \ \ \boldsymbol{\sf{Answer}}[/tex]
{ Pisces04 }How do I do the distribution table and the proccess plss help
Answer + Step-by-step explanation:
p(X=3) = the probability that X is equal to 1 or 2 or 3 minus (the probability that X is equal to 2 plus the probability that X is equal to 1)
Because ,when X = 2 or X = 1 the largest number is not 3 so we have to subtract those values .
……………………………………………………………
the probability that X is equal to 1 or 2 or 3 is :
[tex](\frac{3}{6} )^4 = \frac{81}{1296}[/tex]
Then
[tex]p\left( X=3\right) =\frac{81}{1296} -(\frac{1}{1296} +\frac{15}{1296}) =\frac{65}{1296}\\\\p\left( X=4\right) =\frac{4^4}{1296} -(\frac{1}{1296} +\frac{15}{1296}+\frac{65}{1296}) =\frac{175}{1296}\\\\p\left( X=5\right) =\frac{5^4}{1296} -(\frac{1}{1296} +\frac{15}{1296}+\frac{65}{1296}+\frac{175}{1296}) =\frac{369}{1296}[/tex]
Verification:
1+15+65+175+369+671 = 1 296
x + 7 = -9 expressions
Answer:
x = -16Step-by-step explanation:
x + 7 = -9
Subtract 7 from both sides
x + 7 - 7 = -9 - 7
Simplify
x = -16
Answer:
x=-16
Step-by-step explanation:
x+7=-9
x=-9-7
x=-16
I need help
are they no solution or infinite solutions?
I'm getting ready for high school so I'm reviewing 8th grade math.
Answer:
1. No.
2. Yes, there is no solution here.
Step-by-step explanation:
The former:
[tex]8(5x - 3) = 6(-3x - 4); \\ 8 * 5x - 8 * 3 = 6 * (-3x) - 6 * 4; \\ 40x - 24 = -18x - 24; \\ 40x + 18x = -24 + 24; \\ 58x = 0; \\ x = 0.[/tex]
[tex]\{0\}[/tex] is our set of solutions.
The latter:
[tex]3x - 13 = 7(x + 2) - 4(x - 7); \\ 3x - 13 = 7x + 7 * 2 - 4x - 4 * (-7); \\ 3x - 13 = 7x + 14 - 4x + 28; \\ 7x - 4x - 3x = -13 - 14 - 28;\\ 0x = 55; \\ x \in \emptyset.[/tex]
In other words, there is not any solution from the set of real numbers that suits us.
Which type of rigid transformation is shown? Identifying the Type of Rigid Transformation
The transformation is translation
What is Translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
The figure is attached below:
As per the definition the figure shows that size hasn't changed.
Hence, the transformation is translation.
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Find a in degrees.
a
6
√11
5
? ]°
Round to the nearest hundredth.
Answer:
33.55°
Step-by-step explanation:
let alpha be X
sin x= √11/6
sin x= 0.5527
x= sin-1 0.5527
x= 33.55°
5. Verbal
Explain how to find a line perpendicular to a linear function that passes through a given point.
Answer:
The required line can be found by substituting the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.
Step-by-step explanation:
In the given question, it is given that a linear function passes through a given point.It is required to find a line perpendicular to the function.When two functions are perpendicular, the product of their slopes is equal to -1.Thus, substitute the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.The equation of a parallel line to a linear function that passes through a point can be explained using the examples below.
We have,
The parallel line to a linear function that passes through a point can be explained using the examples below.
Example:
Let's find a line parallel to the linear function y = 3x - 2 that passes through the point (2, 5).
Step 1: Given linear function and point
Linear function: y = 3x - 2
Point: (2, 5)
Step 2: Determine the slope of the given linear function
The slope (m) of the given function y = 3x - 2 is 3.
Step 3: Use the slope to find the equation of the parallel line
Since the parallel line has the same slope (3), its equation will be
y = 3x + b, where "b" is the y-intercept that we need to find.
Step 4: Substitute the coordinates of the given point into the equation of the parallel line
Using the coordinates (2, 5) of the given point, we can solve for "b":
5 = 3(2) + b
5 = 6 + b
b = 5 - 6
b = -1
So, the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5) is:
y = 3x - 1.
Thus,
The equation of a parallel line to a linear function that passes through a point can be explained using the examples above.
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What is the value of sin 0 given that (3-4) is a point on the terminal side of 0
Using trigonometric relations, we will see that:
sin(θ ) = -0.8
How to get the sine of the angle?
For any point (x, y), the angle between the positive x-axis and the ray that connects the origin with the point (x, y) is:
θ = Atan(y/x)
In this case, the point is (3, -4), then the angle is:
θ = Atan(-4/3) = -53.13°
Then the sine of theta is:
sin(θ = -53.13°) = -0.8
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Keira and Nathan are dragging a box across a floor, as shown in the diagram on the left. Kiera pulls at an angle of 30below the horizontal and with a force of 80 poundsNathan pulls at an angle of 50 degrees above the horizontal and with a force of 85 pounds. The diagram on the right shows the triangle that represents this situation . What is the magnitude of the resultant force acting on the box ?
Answer:
165.0
30 plus 50 plus the 85 equals 165
The magnitude of the resultant force acting on the box is 126.4 pounds.
Hence the correct answer is C.
Given that Kiera pulls at an angle of 30below the horizontal and with a force of 80 pounds Nathan pulls at an angle of 50 degrees above the horizontal and with a force of 85 pounds.
We need to determine the magnitude of the resultant force acting on the box.
To find the magnitude of the resultant force acting on the box, we can use the law of cosines.
The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle θ opposite to side c, the following equation holds:
c² = a² + b² - 2ab × cos(θ)
In this case, we have a triangle formed by the two forces exerted by Keira and Nathan, and we want to find the magnitude of the resultant force, which corresponds to side c.
Let's assign the following values:
a = 80 pounds (force exerted by Keira)
b = 85 pounds (force exerted by Nathan)
θ = 180° - 30° - 50° (angle opposite to the resultant force)
θ = 100°
Now we can plug these values into the law of cosines equation:
[tex]F = \sqrt{80^2 + 85^2 -2\times 80 \times 85\times \cos100}[/tex]
Solving we get,
F = 126.4
Hence the magnitude of the resultant force acting on the box is 126.4 pounds.
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Rice is sold at Ghc56.00 per bag of 50kg. A trader bought some bags of rice and paid GHc1,344.00.
How many bags of rice did the trader buy
if 1bag is 56.00
x bags= 1344.00
solution
[tex] \frac{1344.00}{56.00} = 24[/tex]
the trader bought 24 50kg bags of rice
PLEASE LIKE AND MARK AS BRAINIEST IF HELPFUL I HOPE SO
PLEASE HELP MEE.
measure of angle B = 27 degrees, measure of angle C = 82 degrees, b = 14. Find the length of c to the nearest
tenth.
=======================================================
Work Shown:
[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(27)}{14}=\frac{\sin(82)}{c}\\\\c\sin(27) = 14\sin(82)\\\\c=\frac{14\sin(82)}{\sin(27)}\\\\c\approx 30.5375398\\\\c\approx \boldsymbol{30.5}\\\\[/tex]
I used the law of sines. Make sure your calculator is in degree mode.
The confirmation diagram shown below was made with GeoGebra. It is a free geometry and algebra app that I use all the time.
During the snow storm your pipes burst you called preston the plumber who charges $50 for a serice call and $5 per hour. if your bill was for $120 total,how long did it take preston to repair your broken pipes
It takes Preston 14 hours to repair the broken pipes.
Given Information
Cost of service call charged by Preston, the plumber, S = $50
Preston charges $5/hour.
Preston's charge per hour, P = $5
The total bill, B = $120
We have to calculate the number of hours Preston take to repair the broken pipes.
Calculating the Number of Hours
Total service charge of Preston = Total bill - Service Call Charge
= B - S
∴ Number of hours Preston took to mend the broken pipe is given by,
H = (B - S)/P
H = $(120 - 50)/$5
H = 70/5
H = 14 hours
Therefore, Preston took 14 hours to repair the pipes.
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6. (04.05 MC)
Which Inequality matches the graph? (1 point)
-2x+3y>7
2x+3y <7
-3x+2y>7
3x-2y <7
Answer: is D
Step-by-step explanation:
Does this table represent a function? Why or why not?
X
2234
5
y
1
4
4
2
5
OA. No, because one x-value corresponds to two different y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
OC. No, because two of the y-values are the same.
D. Yes, because there are two x-values that are the same.
No, because one x-value corresponds to two different y-values.
How to determine the true statement about the table?The table of value is given as:
x 2 2 3 4 5
y 1 4 4 2 5
From the above table, we have:
When x = 2, y = 1 and 4
This means that 1 value of x points to multiple values of y
The above means that the table does not represent a function
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Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
Answer:
3 months
Step-by-step explanation:
Let x be the number of months CDs are added at Tom and Nita's respective rates of 1 and 5 CDs/month.
Tom's collection after x months is = 30 + 1x
Nita's collection after x months is = 18 + 5x
At some point they will have equal numbers of CD's, so set the equations equal to each other:
30 + 1x = 18 + 5x
4x = 12
x = 3 months
At 3 months both Tom and Nita will have the same number of CDs.
Tom: 30 + 1*3 = 33 CDs
Nita: 18 + 5*3 = 33 CDs
x = 3
Step-by-step explanation:We can create a system of equations to represent the situation we have been given.
Creating the Equations
In this system, we can create an equation to represent both people's collections.
First, we can create Nita's.
To create the equation we can start with the constant. We are told she starts with 18 CDs. So, this will be one of the terms.Next, we can multiply x by 5. We can do this because x represents the number of months that have passed and 5 is the number of CDs she adds per month. This means 5x will be another term.Finally, the constant and variable will add up to the total number of CDs, which is represented by y. So, the expression will be set equal to y.All of this creates the equation: 5x + 18 = y.
Next, we can do the same to find Tom's equation.
Tom starts out with 30 CDs. So this will be the constant term.Each month he adds 1 CD. This means that we can multiply 1 by x to make the term 1x.Finally, like with Nita's this expression will be set equal to y.This creates the second equation: 1x + 30 = y.
The system is:
5x + 18 = y
1x + 30 = y
Solving the System of Equations
One method to solve a system of equations is substitution. Substitution is when you substitute an expression for a variable. Since both expressions are set equal to y, we can substitute the expressions for y and set them equal to each other.
This creates the new equation: 5x + 18 = 1x + 30. Then, solve normally.
First, subtract 1x from both sides4x + 18 = 30
Next, subtract 18 from both sides.4x = 12
Finally, divide both sides by 4x = 3
This means after 3 months the number CDs will be equal.
Please Help Asap!!!!
please help ill give whoever has the best answer the brainliest answer
Answer:
It would be B the distance from the ground to the kite :)
Step-by-step explanation:
The graph shows this situation best out of the other 3 choices!
Have an amazing day!!
Please rate and mark brainliest!!
BRAINLIEST, URGENT
A ride at an amusement park repeatedly drops riders four times to the bottom of a tower and rises back up one-half the height that it drops each time it reaches the bottom. The ride initially drops riders from a distance of 50.0 meters above the bottom of the tower. What is the ride's maximum height above the bottom of the tower, in meters, between the second and third time it reaches the bottom of the tower?
Answer:
12.5 m
Step-by-step explanation:
1st drop 50 m
2nd drop 50/2 = 25 m
3rd drop 25/2 = 12.5 m
What is 78 to the square root closer to
Answer:
The square root of 78 is: 8.8317608663278468547640427269593.
This number is closer to the number 9.
Step-by-step explanation:
Use calculator to find square root. Then round it up.
Hope this helps!
If not, I am sorry.
What prism or other 3-dimensional shape would you use to model the tree trunk below? (Rectangular prism, triangular prism, square prism, or cylinder). If the height of the tree trunk is 13 ft and the radius is 1.5 ft, what is the volume in cubic feet? Round to the nearest tenth.
Answer:
A cylinder,
91.9 ft^3 to nearest tenth.
Step-by-step explanation:
That would be a cylinder,
Volume of the given tree trunk
= π r^2 h
= π * 1.5^2 * 13
= 91.89 ft^3.
If gasoline costs $ 3.77 per gallon when you pay with a credit card, but $0.08 per gallon less if you pay with cash, how much do you save by filling up a 8-gallon tank and paying for it with cash?
Answer:
$0.64
Step-by-step explanation:
Cost for 8 gallons of gas
Credit Card at $3.77/gal
Cash at $(3.77 - 0.08)/gal: $3.69/gal
(8 gal)*($3.77/gal) = $30.16
(8 gal)*($3.69/gal) = $29.52
Savings is $0.64
Simplify completely:
√320x2y³
simplify the radical by breaking the radicand up into a product of known factors,assuming positive real numbers.
Sorrry i cant write answer is that form but
the answer is 8 then square root of 5x rais to power 2 then write y raise to power3.
What is the range of f?
Answer: [tex][-3,7][/tex]
Step-by-step explanation:
The range of a function is the set of y-values
A company produces packets of soap powder labeled Giant Size 32 Ounces. The actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight
In order to be labeled overweight the weight of box should be of 34.15 ounces.
Given mean of 33 ounces, standard deviation=0.7 ounces. Production of packets of 32 ounces.
Because it is normally distributed samples are solved using the z score formula.
In this Z=X-meu/st
meu is sample mean and st is population standard deviation.
We have to find the z score and then p value from the z table.
meu =33 and st=0.7
Top 5% so X when Z has a p value of 1-0.05=0.95. So X when Z=1.645.
Z=(X-meu)/st
1.645=(X-33)/0.7
X-33=0.7*1.645
X-33=1.1515
X=1.1515+33
X=34.1515 ounces.
Hence to be labeled overweight the box must have 34.15 ounces weight.
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Fossils of Lystrosaurus, a dinosaur without the ability to swim or fly, can be found across Africa, India, and Antarctica.
What does this indicate?
A. That those continents were all connected during the time Lystrosaurus lived.
B. That they went extinct because they could not adapt.
C. That they later evolved either the ability to swim or the ability to fly.
D. Those continents were separated at the time Lystrosaurus lived.
Answer:
A
Step-by-step explanation:
Pangaea is the name for the land mass before the continents split. The continents would have been connected during that species life time.