The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
Given data,
A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.
The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;
r/h = 16/18
= 8/9
r = 8h/9
The volume of the cone is;
v = [tex]\frac{1}{3}\pi r^2h[/tex]
v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]
v = [tex]\frac{64}{243}\pi h^3[/tex]
Now, differentiating concerning x;
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex] [tex]\frac{64}{243}\pi h^3[/tex]
[tex]\frac{dv}{dt}[/tex]= 64π/243*[tex]\frac{d}{dt}[/tex] h³
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]
We have;
[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm
[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 55.19
[tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.
Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
To learn more about volume click here:
brainly.com/question/1578538
#SPJ4
assume that blood pressure readings are normally distributed with and a blood pressure reading of 145 or more may require medical attention. what percent of people have a blood pressure reading greater than 145?
0.08891% percent of people have a blood pressure reading greater than 145.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
145) = (145-120)/8 = 25/8.P(x > 145) = P(z > 27/8) = 0.0008891.. = 0.08891%Hence, 0.08891% percent of people have a blood pressure reading greater than 145.
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
Find the geometric mean between ab³ and a³b?
[tex]{ \green{ \sf{G = \sqrt{ ab}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ (ab³)(a³b)}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ a⁴b⁴}}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{G = \sqrt{ a².b²}}}}}}[/tex]
X
-3
-2
0
2
g(x)=x³+6x² + 12x+8
3
g(x)
-1
0
8
64
125
Determine the function's value when x=-1.
Og(-1)=-3
O g(-1)=0
O g(-1)=1
O g(-1)=27
The function g(-1) has its value to be (c) g(-1) = 1
How to evaluate the function at the input value?The definition of the function is given as
g(x)=x³+6x² + 12x+8
Rewrite the above function properly
So, we have the following representation
g(x) = x³ + 6x² + 12x + 8
To find the function g(-1), we set the value of x in the equation g(x) = x³ + 6x² + 12x + 8 to -1
This is represented by
Calculate g(x), when x = -1
Substitute -1 for x in the equation g(x) = x³ + 6x² + 12x + 8
So, we have the following equation
g(-1) = (-1)³ + 6(-1)² + 12(-1) + 8
Evaluate the exponents
This gives
g(-1) = -1 + 6(1) + 12(-1) + 8
Evaluate the products
This gives
g(-1) = -1 + 6 - 12 + 8
Evaluate the sum
g(-1) = 1
Hence, the value of the function is g(-1) = 1
Read more about functions at
brainly.com/question/10687170
#SPJ1
The temperature dropped to 24 degrees in 8 days. what was the average daily change in temperature? a) 3 degrees b) -8 degrees c) -3 degrees d) 16 degrees
The average daily change in temperature will be 3 degrees The temperature dropped to 24 degrees in 8 days
Since we know an average could be a single number taken as an agent of a list of numbers, as a rule, the whole of the numbers divided by how numerous numbers are within the list. We are said the temperature dropped to 24 degrees in the 8 days
So the average of it will be =24 /8 = 3, which means the temperature needed to drop for at least 3 degrees in order to get the sum of 28 in 8 days.
To know more about temperature refer to the link https://brainly.com/question/11464844?referrer=searchResults.
#SPJ4
Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of $117 but wants to buy more than 10 vegetables. The pumpkins are $5. 59 each. The squash are $3. 50 each. List THREE possible combinations of pumpkins and squash that latisha can purchase to represent the situation
(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.
Latisha's total wealth is $17.
More than 10 veggies are the number of vegetables that Latisha wants to purchase.
A pumpkin costs $5.50.
An autumn squash costs $3.50.
Let n pumpkins purchased equal x.
Purchased number of autumn squash = y
There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.
With x acting as the independent variable, we may identify many y's.
x ( Pumpkin) y(Autumn squash) (integral value)
8 20
6 24
10 17
Learn more about Combination here
https://brainly.com/question/28720645
#SPJ4
6 x 7/8
(six x seven eighth's) This is a review for last year but I forgot how to do it also can you show how you got it please?
Answer:
5 1/4 // 5.25
Step-by-step explanation:
convert 6 into a fraction:6/1 x 7/8multiply numerators by numerators, and denominators by denominators42/8 (6 x 7 = 42, 8 x 1 = 8)Simplify the fraction using the Lowest Common Multiples42/8 --> 21/4 convert the improper fraction into a mixed number:5 1/4OR
5.25Answer:
5 1/4
Step-by-step explanation:
You want the product of 6 and 7/8.
Product with a fractionYour written-out version of the question gives you a clue how to solve it:
six times seven eighths
The associative property of multiplication lets you rearrange this to ...
(six times seven) eighths = forty-two eighths
That is, the product is formed by multiplying the integer by the numerator, and expressing the whole thing over the denominator:
[tex]6\times\dfrac{7}{8}= \dfrac{6\times7}{8}=\dfrac{42}{8}\\\\=\dfrac{40+2}{8}=\dfrac{40}{8}+\dfrac{2}{8}=5+\dfrac{1}{4}\\\\=\boxed{5\dfrac{1}{4}}[/tex]
Improper fractionThe improper fraction is converted to a mixed number by looking at the quotient and remainder from the division: 42/8 = 5 r 2 = 5 2/8 = 5 1/4.
__
Alternate solution
Sometimes, it can be helpful to look at the problem another way.
6 × 7/8 = 6 × (1 -1/8) = 6 -6/8
= 6 -3/4 = 5 1/4
How do you solve #22?
1/7*5/3 um i need help plese i only have 1 secont
The product of the fractions 1/7*5/3 is 5/21.
The product of the fractions= product of the numerator/product of the denominator.
The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.
We multiply the 1 and 5, the numerators and 7 and 3 the denominators.
Therefore the product of the fractions is 5/21.
To learn more on fractions here:
https://brainly.com/question/10354322#
#SPJ1
Answer:
5/21
Step-by-step explanation:
Given problem,
→ (1/7) × (5/3)
Let's solve the problem,
→ (1/7) × (5/3)
→ (1 × 5)/(7 × 3)
→ 5/21
Thus, the answer is 5/21.
at a bowling alley, the cost of shoe rental is $2.25 and the cost per game is $4.25. if f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?
Answer:
The question is not complete so I am unsure what to solve for f(n)=$2.25x+4.25 or f(n)= $2.25x+4.25y
Step-by-step explanation:
Shoe rental $2.25
Per game $4.25
Depending on how many people are going to rent (x) and assuming they are only playing one game your equation would be
f(n)=$2.25x+4.25
However if the question does not state how many games are being played i would say
f(n)= $2.25x+4.25y
Question:
simplify 5√18
Answer template:
___ √ ___
The simplification of the number by solving square root 5√18 is 15√2.
What is meant by the term square root?A number's square root is a value that, if multiplied by itself, yields the original number. The other procedure to square an integer is to find its square root. Squares as well as square roots are hence related ideas.Providing that x is just the square root of y, the equation would be written as x=y or as x² = y. The radical symbol for the number's root is "√" in this instance. The square of the positive number is shown by multiplying it by itself. The original number is obtained by taking the square root of a square of such a positive number.For the given number
= 5√18
Find the factors of 18 by prime factorization.
18 = 2 ×3 ×3
Put in the number.
= 5√2 ×3 ×3
Taking 3 out of root.
= 5×3√2
Further solving.
= 15√2
Thus, the simplification of the number by solving square root 5√18 is 15√2.
To know more about the square root, here
https://brainly.com/question/428672
#SPJ13
Camilla borrows a book from the library for dd days. The library charges a late fee of 0. 10 dollars per day that the book is late. If Camilla returns the book more than 21 days after she borrowed it, the expression 0. 10(d-21) represents the total late fee Camilla owes
The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.
What is Algebra?
Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Camilla borrows a book from the library for d days.
The library charges a late fee 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it.
Then the expression will be 0.10d.
The total amount is given as
Total amount = 0.10 d
Total amount = 0.10 x 21
Total amount = $2.1
learn More about of Algebra here
https://brainly.com/question/11841980
#SPJ4
The temperature over the course of a day was being monitored. In the morning, the temperature was −3°F. In the middle of the day, the temperature rose to 12°F. After dark, the temperature dropped again to −6°F. What was the average temperature for the day?
A. −3°F
B. −1°F
C .1°F
D. 3°F
a marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce. how many kilometers did he run? (note: 1 mi
He ran 42.1 kilometers.
Define conversion.A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet. The act or process of transforming something into a different condition or form is known as conversion. to convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.
Given,
A marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce.
1 mile = 1.609
Converting miles into kilometer:
26.2 miles
= 26.2 × 1.609
= 42.1
He ran 42.1 kilometers.
To learn more about conversion, visit:
https://brainly.com/question/1822263
#SPJ4
Lines AB and CD are straight lines. Find x and y .
⇒ ∠AOC+∠AOE+∠EOD=180°(angles on a straight line are supplementary)
16°+90°+2y=180°
[tex]106+2y=180\\2y=180-106\\2y=74\\\frac{2y}{2} =\frac{74}{2} \\y=37[/tex]
∴y=37°
∠AOC+∠COF∠BOF=180°(angles on a straight line are supplementary)
16°+90°+4x=180
[tex]106+4x=180\\4x=180-106\\4x=74\\\frac{4x}{4} =\frac{74}{4} \\x=18.5[/tex]
∴x=18.5°
If p is portional to q and p =4.5 when q= 12 .
Find the relationship between p and q
P when q =16
Q when p= 2.4
The relationship between variables p and q is given by p = kq. Also, the value of the variable p when q = 16 is 6 and when p = 2.4, the variable q is 6.4.
How to determine the proportional relationship?Mathematically, a proportional relationship can be represented with the following mathematical expression:
p = kq
Where:
p and q are the variables.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = p/q
Constant of proportionality (k) = 4.5/12
Constant of proportionality (k) = 0.375.
When q = 16, the variable p is given by:
p = kq
p = 0.375 × 16
p = 6.
When p = 2.4, the variable q is given by:
q = p/k
q = 2.4/0.375
q = 6.4
Read more on proportionality here: brainly.com/question/12866878
#SPJ1
Find the equation of the straight line passing through the point (3, 5)
which is perpendicular to the line
y = 3x + 2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through (3, 5) perpendicular to the line y = 3x +2.
Perpendicular lineThe given equation is in slope-intercept form. This lets us identify its slope as 3.
y = mx + b . . . . . . line with slope m and y-intercept b
y = 3x +2 . . . . . . . line with slope 3 and y-intercept 2
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/3 . . . . slope of the perpendicular line
Point-slope formThe equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation for a line with slope -1/3 through point (3, 5) is ...
y -5 = -1/3(x -3)
Slope-intercept formSolving for y gives us ...
y = -1/3x +1 +5 . . . . . eliminate parentheses, add 5
y = -1/3x +6 . . . . . equation of the desired line
<95141404393>
(Constant of Proportionality MC)
The table shows a proportional relationship
X 1 2 3
y 14 28 42
Write an equation that represents the proportional relationship. Pls help
The equation that represents the proportional relationship is y = 14x.
We are given a table. The table contains the values for "x" and "y". The first row contains the data for the variable "x". The values of "x" are 1, 2, and 3. The second row contains the data for the variable "y". The corresponding values of "y" are 14, 28, and 42. We know that the table shows a proportional relationship between the values of "x" and "y". Let the constant of proportionality be represented by the variable "k".
y ∝ x
y = k*x
k = y/x
The value of k must be the same for each corresponding pair of values of "x" and "y".
k = 14/1 = 28/2 = 42/3 = 14
Hence, the equation is y = 14x.
To learn more about equations, visit :
https://brainly.com/question/10413253
#SPJ1
Answer:
y = 14x.
Step-by-step explanation:
please give me the right answer on this so I can turn it in to my math teacher
Answer: 16/18 and 10/16
Step-by-step explanation: The least common denominator would be 18 and 16 because you would multiply by 2.
Hoped This Helped!
question 4: a school group went to a carnival on a field trip. the function c(x) represents the amount of money spent in dollars, where x is the number of students. does a possible solution of (29.5, $212.50) make sense for this function? explain your answer.
Step-by-step explanation:
only limited sense.
first of all, directly it does not make any sense. we can only send integer number of students on a field trip. not half-persons.
therefore, 29.5 students for a single field trip calculation does not make sense.
but : we could want to use the same function to calculate or analyze the costs of multiple field trips by using things like mean values of students participating. there fractions as student numbers make sense.
can someone help its easy but im lazy plssss
The equation which represents the price of the ticket after the discount is y = 0.25x.
What is a linear equation?A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that the movie theatre is giving a discount of 75% the original cost of the ticket is x and discounted cost is represented by the variable y.
The equation for the cost of the ticket will be written as,
y = x - 0.75x
y = 0.25x
The graph of the linear equation is attached with the answer below.
To know more about a linear equation follow
https://brainly.com/question/4074386
#SPJ1
a(n) is a scatter chart with time on the horizontal axis and measurement scale on the vertical axis, displays the mean and control limits, and may mark two standard deviations from the mean. histogram control chart pareto chart gantt chart affinity diagram
A(n) Control Chart is a scatter chart with time on the horizontal axis, measurement scale on the vertical axis, displays mean and control limits, and may mark two standard deviations from the mean.
A control chart is one of the process improvement techniques or simply it is a graph to study how a process changes over time. In layman's terms the control chart shows if a process is under control or out of control. For calculating the average, there is always a central line in the control chart, an upper line and a lower line for upper control limit and lower control limit respectively.
The control charts are used to serve many purposes including monitoring a process for special variations and their causes and to remove them, estimating the process average and the variation, predicting the impacts of the process , etc.
learn more about control charts here :
https://brainly.com/question/28022940
#SPJ4
Base of an isosceles triangle can be right angles
We can actually deduce here that the statement, "base of an isosceles triangle can be right angles" is false.
What is an isosceles triangle?An isosceles triangle is actually known to be a triangle which has two sides equal and opposite angles of the sides also equal. In other words, an isosceles triangle must have at least two equal triangles.
Some of the properties of an isosceles triangle are:
It is a triangle whose two sides are congruent to each otherIt has a third side known as the base of the isosceles triangle.It has angles that are opposite to the equal sides which are congruent to each other.We see here that the base of an isosceles triangle cannot be a right angles. It is still to have one side as a right angle but not the two sides as right angles.
The complete question is:
True or false: Base angles of an isosceles triangle can be right angles.
Learn more about isosceles triangle on https://brainly.com/question/25812711
#SPJ1
1: 20% of 50 2: 50% of 80
Answer:
1. 10
Step-by-step explanation:
1. 20% of 50
[tex] \frac{20}{100} \: \: \: \times \: \: \: 50 \\[/tex]
=
[tex] \frac{1000}{100} [/tex]
= 10
Which term is a constant numerical value? I need so much help
Anna received a gift of $5,000 from her grandmother and decided to invest it. The expression 5000(1.0005)^12t represents the amount of money Anna is earning on her investment. Select all of the following that are equivalent expressions so that Anna can better understand how her money is invested.
a) 5000(1.0005^12)^t
b) 5025^12t
c) 5000(1+0.0005)^12t
d) 5000(1.0005^t)^12
e) (5000+2.5)^12t
f) 5000(1+0.06/12)^12t
The equivalent expression that represents the amount Anna can better understand how her money is invested is 5000(1+0.0005)^12t.
The correct answer option is option c.
What is the equivalent expression of Anna's investment?Based on the expression given, Anna's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^(nm)
Where,
FV = Future valueP = Present valueR = interest ratem = number of compoundingn = number of years5000(1.0005)^12t
Given options:
a) 5000(1.0005^12)^t
False
b) 5025^12t
False
c) 5000(1+0.0005)^12t
= 5,000(1.0005)^12t
True
d) 5000(1.0005^t)^12
False
e) (5000+2.5)^12t
False
f) 5000(1+0.06/12)^12t
= 5000(1 + 0.005)^12t
= 5000(1.005)^12t
False
In conclusion, the expression equivalent to Anna's investment is 5000(1+0.0005)^12t
Learn more on compound interest:
https://brainly.com/question/27212464
#SPJ1
a random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces. in this problem, what is the 0.7?
In this problem 0.7 is the standard deviation of the contents.
Define standard deviation.It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.
Given,
A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.
In this problem 0.7 is the standard deviation of the contents.
To learn more about standard deviation, visit:
https://brainly.com/question/16555520
#SPJ4
Please Help! What is the ratio of a:b?
a+3b/5 = a-2b/2
The ratio of a : b in the given expression is 16:3 .
In the question ,
it is given that
the algebraic expression is (a+3b)/5 = (a-2b)/2
we have to find the ratio of a:b ,
in order to find the ratio,
we cross multiplying ,
On cross multiplying , we get
2 * (a+3b) = 5 * (a-2b)
2a + 6b = 5a - 10b
5a - 2a = 10b + 6b
3a = 16b
dividing both sides by b ,
a/b = 16/3
a:b = 16:3
Therefore , The ratio of a : b in the given expression is 16:3 .
The given question is incomplete , the complete question is
What is the ratio of a:b in the expression (a+3b)/5 = (a-2b)/2 ?
Learn more about Ratio here
https://brainly.com/question/19617266
#SPJ1
what is 382 3/10 minus 191 87/100
Answer:
190 43/100
Step-by-step explanation:
First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D
divide 50x4-50x3+12x2+10x-2 by 5x-3
Dividing 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 with the long division method will result to a quotient of 10x³ - 4x² + 2 and a remainder of 1.
Long division methodThe method of long division involves the following steps:
Divide.Multiply.Subtract.Bring down the next number and Repeat the process to end at zero or arrive at a remainder.We sall divide the 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 by applying the long division method as follows;
50x⁴ divided by 5x equals 10x³
5x - 3 multiplied by 10x³ equals 50x⁴ - 30x³
subtract 50x⁴ - 30x³ from 50x⁴ - 50x³ + 12x² + 10x - 2 will result to -20x³ + 12x² + 10x - 2.
This process is repeated until we have a remainder of 1.
Therefore, by the long division method, we have quotient of 10x³ - 4x² + 2 and a remainder of 1.
Learn more about long division method here: https://brainly.com/question/25289437
#SPJ1
70 points need help asap
The angle ∠C is 130° by the alternative angles.
Given that,
In the figure we have a diagram.
We have to find the angle c.
The angles created on the opposing side of the transversal with regard to both straight lines when two straight lines are cut by it are referred to as alternative angles. Therefore, the angles that are on the opposing sides of the transversal and have distinct vertices are those.
We know that,
By alternative angles
∠M=∠C
So,
130°=∠C
Therefore, The angle ∠C is 130° by the alternative angles.
To learn more about angle visit: https://brainly.com/question/28451077
#SPJ1
