Answer:
Step-by-step explanation:
A container has the shape of an open right circular cone, as shown in the figure above. The container has a radius of 4 feet at the top, and its height is 12 feet. If water flows into the container at a constant rate of 6 cubic feet per minute, how fast is the water level rising when the height of the water is 5 feet?
If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min
How to find the rate of change?When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.
We are given the dimensions of the tank as;
Radius; r = 4 feet
Height; h = 12 feet.
The water in the tank will also have a conical shape.
By similar triangles, we know that;
r/h = 4/12
r = h/3
Now the volume of the water is;
V = ¹/₃πr²h
Put h/3 for r in this volume equation to get;
V = ¹/₃π(h/3)²h
V = (1/27)πh³
Differentiating with respect to time gives;
dV/dt = (3/27)πh²(dh/dt)
We are given;
dV/dt = 6 cubic feet per minute
h = 5
Thus;
6 = (3/27)π(5²)(dh/dt)
dh/dt = 0.688 ft/min
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When firefighters are trying to put out a fire, the rate at
which they can spray water on the fire depends on the
water pressure. You can find the flow rate f in gallons
per minute using the equation, f = √120p, where p
is the nozzle pressure in pounds per square inch.
What pressure would be required to have a flow rate of
62 gal/min? show work
The pressure that would be required to have a flow rate of 62 gal/min is f=86.25
What is meant by nozzle pressure?The velocity of the stream is exactly proportional to nozzle pressure. In the given scenario, instead of a stream moving at 80 mph through the fire's super-heated gases, it moves at 60 mph.
The velocity increases as the pressure decreases in a convergent nozzle, but we know that pressure is inversely related to area.
The following formula can be used to compute the flow rate for a given nozzle. Q represents the flow rate. K = Nozzle K factor. P = Nozzle pressure differential. n = Is a constant that is determined by the type of spray pattern.
Given equation is,
f = √120p
Here p denotes the nozzle pressure in pounds per square inch
Also given that p=62 gal/min
f = √120p
Then,
f= √120(62)
f=√7440
f= 86.25
The pressure that would be required to have a flow rate of 62 gal/min is f=86.25
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HELP PLEASE NEED IT FAST
He has to climb UP 40 feet
Step-by-step explanation:
round 11,406 to the nearest:tens ,ten thousand , hundred
Answer:
Tens:11,410
Ten thousand :10,000
Hundred : 11,400
6. The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes. If the total value of the coins in the piggy bank is at least $4.35, find the smallest possible number of coins in the bank.
If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.
As per the question statement, The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, and the total value of the coins in this piggy bank is at least $4.35,
Then, we are required to determine the smallest possible number of individual coins in the bank.
To answer this question, first we will need to know the monetary values of nickels and dimes, that is,
(1 dime = 10 cents = $0.1), and (1 Nickel = 5 cents = $0.05).
Now let us assume that, there are "x" nickels and "y" dimes in that bank, Then as per the condition that, the number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, we can write an equation with the above assumed two variables, which is, [x = (2y - 1)]...(i)
And as per the other condition that, the total value of the coins in this piggy bank is at least $4.35, we can write another equation, which is,
[(0.1y + 0.05x) = 4.35]
Or, [100(0.1y + 0.05x) = (100 * 4.35)]
Or, [(10y + 5x) = 435]...(ii)
Now substituting eqn (i) in eqn (ii), we get,
[{10y + 5(2y - 1)} = 435]
Or, [(10y + 10y - 5) = 435]
Or, [(10y + 10y) = (435 + 5)]
Or, (20y = 440)
Or, [y = (440/20)]
Or, (y = 22)
Therefore, [x = {(2 * 22) - 1}]
Or, [x = (44 - 1)]
Or, [x = 43]
That is, If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.
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in a particular shop employees are given a 12.5% discount on any items they purchase.calculate the actual price an employee would pay for each of the following
1200
The actual price of an item is $1371.49.
Given that, the discount percentage is 12.5% and the selling price is $1200.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Let the actual price be x.
Now, x-12.5% of x =1200
⇒ x- 12.5/100 ×x=1200
⇒ x- 0.125x=1200
⇒ 0.875x=1200
⇒ x=1200/0.875
⇒ x=$1371.49
Therefore, the actual price of an item is $1371.49.
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Question 3(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
A wheat farmer plows 5 acres of land and collects 135 bushels of wheat. The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.
Is there a proportional relationship between the number of bushels of wheat collected and the number of acres plowed over the two days? Explain.
Yes, it is proportional because the farmer collected 7 bushels for every 1 acre plowed.
Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres plowed are not equivalent.
Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
A wheat farmer plows 5 acres of land and collects 135 bushels of wheat
The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.
Let us create a equation
Bushels/Acres
For first day:
Number of bushels of wheat=135
Number of acres of land=5
135/5=27
Next day:
Number of bushels of wheat=216
Number of acres of land=8
216/8=27
The proportional relation between 1st day and next day is same. It is proportional because the farmer collected 27 bushels for every 1 acre plowed.
Hence, Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=?
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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8. The price of a four-star dinner was $175 two decades ago. A report says that a dinner is 250% of what it was
20 years ago, how much would a four-star dinner cost today?
a.
Round the numeric answer to the nearest dollar.
I=
b. Use the answer in a meaningful sentence.
Answer:
Dinner should cost 250 today.
Step-by-step explanation:
Construct triangle ABC, in which AB = 6cm, angle BAC = 96° and angle ABC = 35°.
Measure the length of BC.
Give your answer to 1 d.p.
Answer:
BC = 7.9 cm
Step-by-step explanation:
To construct triangle ABC:
Draw a line 6 cm long. Label one endpoint A and the other endpoint B. Measure an angle of 96° from point A of AB in an anticlockwise direction. Draw a line.Measure an angle of 35° from point B of AB in a clockwise direction. Draw a line.The point of intersection of the two lines is point C of the triangle.Measure the length of BC. BC = 7.9 cm.
Sketch the graph of the exponential function. Label the y-intercept and at least two other points on the graph using both
positive and negative values of x.
f(x) = 5e^x
Answer:
Take a look at the attachment...
Hope this helps! :)
Evaluate y + (-32.577) for the following values of y.
value of y value of expression
-12.975 -45.552
-41.08
-74.003
-10.304
please help 3
what is(fog)(3)if f(x)=3x-1 and g(x)=4x2+9
The value of (fоg)(3) = 134.
What is composition of functions?
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Consider, the given functions
f(x) = 3x - 1, g(x) = 4x^2 + 9
First to find f(g(x)).
Let,
f(g(x)) = 3(4x^2 + 9) - 1
= 12x^2 + 27 - 1
f(g(x)) = 12x^2 + 26
Now, to find f(g(3)).
Plug x = 3 in the above equation,
f(g(3)) = 12(3)^2 + 26
= 12(9) + 26
f(g(3)) = 134
Hence, (fоg)(3) = 134.
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Give the following equation: f(x) =square root x-3+4 how will the graph move in comparison to the parent function.
Graph will shift from(0,0) to (3,4) after the shifting happens due to change in expressions of the parent function.
What is transformation of graph?Graph transformation is the process by which an parent graph, or graphed equation, is changed to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification in algebraic equations.
The deduced parent function is [tex]\sqrt{x}[/tex]
So, Domain= (0 , ∞)
Range= (0 , ∞)
Let us take (0,0) as the point and see the shifting of the point with respect to (0,0).
So when function is transformed to √x+3
Function shift from (0,0) to (3,0)
and when function is transformed to [tex]\sqrt{x+3} +4[/tex]
then point shifts to (3,4).
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It would be much appreciated if someone could aid me in solving question B for this problem. I have been unable to calculate the correct answer. Thank you so much in advance : )
A floating rate mortgage loan is made for $125,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower
and lender have negotiated a monthly payment of $1,000.
Required:
a. What will be the loan balance at the end of year 1?
b. If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year 2 and
year 5 if the payment remains at $1,000?
Complete this question by entering your answers in the tabs below.
Required A Required B
If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year
2 and year 5 if the payment remains at $1,000?
Note: Do not round intermediate calculations. Round your final answers to 2 decimal places.
Loan balance in year 2:
Interest accrued-Year 2:
Interest accrued - Years 2-Year 5:
The negative amortization at the end of year 1 is $2536.50
For the year 1 there will be still 12% rate of interest going on. There is a negative balance of $200 after payment of 1st month installment.
Thus negative amortization = FV(0.01x12 - 200)
Here 0.01 is the interest per month, 12 is the number of months in a year and -200 is the negative balance in first month
negative amortization = FV(0.01x12 - 200)
The negative amortization at the end of year 1 = $2536.50
The negative amortization at the end of year 5
The loan balance at the end of year 4 = FV(0.13x12x36x800 - 102536)
The loan balance at the end of year 4 = $16132.46
The negative amortization at the end of year 1 is $2536.50
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Find the approximate slope of the line that contains the points (5.1, -2.8) and (6.4,-1.2). State whether the line is increasing, decreasing, horizontal, or vertical.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is (fill in the blank)
B The slope is undefined
Is the line increasing, decreasing, horizontal, or vertical?
Horizontal
Increasing
Decreasing
Vertical
Answer:
slope = 16/13, increasing
Step-by-step explanation:
solve for the slope
-1.2-(-2.8)/(6.4-5.1)
= 16/13
it's positive meaning it's increasing
Find the additive inverse of A.
A = [tex]\left[\begin{array}{ccc}0&-2\\-3&-5&\\&&\end{array}\right\}[/tex]
The additive inverse of the matrix A is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]
How to determine the additive inverse of the matrix?From the question, the matrix is given as
[tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]
This matrix is given as matrix A
So, we have the following representation
A = [tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]
Next, we calculate the required matrix operation
The matrix operation is given as additive inverse of the matrix
This additive inverse of the matrix is calculated by negating each element present in the matrix
i.e. if an element in the matrix is a, the inverse would be -a
Using the above highlights as a guide, we have the following representations
Additive inverse = [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]
Hence, the additive inverse is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]
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4a) What is the unit rate of the equation? (Tell how you came up with this answer.)
Y=-4X
4b) What is the unit rate of the table? (Tell how you came up with this answer.)
X
2
3
4
5
6
4
6
8
10
12
I
4c) which proportional relationship has the greatest unit rate: the table or the equation? Tell how you arrived
at your answer, showing all work.
Answer:
Unit rate is 2
Step-by-step explanation:
Pick two columns of the ordered pairs. Lets use (2,4) and (3,6)
The x values are 2 and 3 and the y values are 4 and 6
Now you’re going to divide y by x so
4/2 = 2
6/3 = 2
(Always choose two ordered pairs so you know that your answer is right)
Unit rate of the table is 2.
Define unit rate.The units of concentration and rate are always going to be molars per second. We now understand that molar per second is equal to k times molar in units. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given,
Choose two columns from the paired ordered columns. Using (2, 4) and (3,6)
The x and y values are 2 and 3, respectively, and the
You will now divide y by x, so
4/2 = 2
6/3 = 2
Unit rate of the table is 2.
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A triangle has side lengths of (7m2) centimeters, (9m - 5) centimeters, and
(6n1) centimeters. Which expression represents the perimeter, in centimeters, of
the triangle?
5n - 7 + 16m
5m +5n+4
9m +5n
4
16m + 6n - 8
Submit Answer
The required expression 16m + 6n - 8 represents the perimeter of the triangle. which is the correct answer would be option (D).
A triangle has side lengths of (7m - 2) centimeters, (9m - 5) centimeters, and (6n - 1) centimeters.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
The perimeter of the triangle = (7m - 2) + (9m - 5) + (6n - 1)
Rearrange the terms likewise in the above equation,
The perimeter of the triangle = 7m + 9m + 6n - 2 - 5 - 1
Apply the arithmetic operation to get the required expression
The perimeter of the triangle = 16m + 6n - 8
Therefore, the required expression 16m + 6n - 8 represents the perimeter of the triangle.
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3. Solve for x: 2x+4=x-6.
a. x=-12
b. x = 10
C. X=-16
d. x=-10
Answer: D
Step-by-step explanation:
I dont gotta explain it, here you go bro :) its -10
Answer:
x=12
Step-by-step explanation:
2x+4=6x
x-6=6x
6x=6x
x=6+6
What word sentence represents this inequality?
A number is at least as large as 8.9
A number is no more than 8.9
A number is greater that 8.9
The word sentence which is used to represent the given inequality
p ≥ 8.9 is a number is at least as large as 8.9.
As given in the question,
Given inequality is equal to :
p ≥ 8.9
In the given inequality sign of greater than and equals to is used.
Explanation for the given word sentences:
A number is at least as large as 8.9.Meaning of at least is minimum this much.
At least as large means ( ≥) greater than or equal to
Option is correct.
A number is no more than 8.9.It represents the symbol (≤ )less than or equal to.
Incorrect option.
A number is greater than 8.9.It represents the symbol of > greater than only.
Incorrect option.
Therefore, the word sentence which is used to represent the given inequality p ≥ 8.9 is a number is at least as large as 8.9.
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what is the round figure of 2089.17
2089.17 rounded off to nearest tenths(1 decimal place) is 2089.2
2089.17 rounded off to the nearest one is 2089
When you "round to the nearest _____" regardless of what is in the blank the steps are nearly always the same:
Identify which place value you are rounding off a number. The smaller the place value, the more accurate the final result shall be.
Find the next smallest place value, the digit to the right of the place value you're rounding off to. For example, if you want to round to the nearest ten you would have to find the number at the one's place.
If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round off. Any digits after that number become zeros, or drop-offs if they're located after the decimal point. This is called rounding down a number or a sequence of numbers.
If the smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding off to by one place (+1). Any remaining digits before the decimal point become zeroes, and any digits that are after the decimal point are dropped. This is called rounding up of numbers.
For example, for rounding off a number 838.274, depending on which place value you'll round to, the final rounded-off answer will vary. Rounding off 838.274:
Rounding off the nearest hundred is 800
Rounding off the nearest ten is 840
Rounding off the nearest one is 838
Rounding off the nearest tenth is 838.3
Rounding off the nearest hundredth is 838.27
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Graphing and Solving Inequalities
m-1<-3. -4y <-20. 5+b>1. -18
Solutions for the given equalities:
m < - 2
y > 5
b > -4
What is inequality in mathematics?
An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
The given inequalities are
1) m - 1 < -3
Adding 3 on both sides, we get
m - 1 + 3 < -3 + 3
m + 2 < 0
Subtracting 2 from both the side, we get
m + 2 - 2 < 0 - 2
m < - 2
The graph of this inequality is shown below
2) -4y < -20
Dividing by -4, we get
y > 5
The graph of this inequality is shown below
3) 5 + b > 1
Subtracting 1 from both the side, we get
b + 4 > 0
b > -4
The graph of this inequality is shown below
4) y = -18
This is a point on a number line, and it can be shown as
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On a construction site, the amount of hours needed to do a job is
inversely proportional to the number of men working. If it takes 10 men
18 hours to repair a road, how long will it take 15 men to do the same
job if they work at the same rate?
It will take 12 hours for 15 men to do same job.
How to determine this?
When amount of hour ∝ 1/number of men
When H represent Hour
And M represent the number of men
k to represent the constant
H = k/M as it is inversely proportional
It takes 10 men 18 hours to repair a road
18 = k/10
k = 18 × 10
k = 180
How long will it take 15 men?
When k = 180
H = k/M
H = 180/15
H = 12 hours
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Tia has 28 yards of fabric. If each project needs 3 and one half yards of fabric, how
many projects can she complete?
1
Step-by-step explanation:
28-28=1 11111111111111111111111111
4×1+1×1/100+9×1/1000
What decimal represents each number
The decimal that represents the number 4×1+1×1/100+9×1/1000 is given as follows:
4.0119.
How to convert a fraction to a decimal number?A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:
Fraction = x/y.
The terms that represent x and y are listed as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.In this problem, we are given two fractions, and their decimal equivalents are given as follows:
1/100 = 0.01.1/1000 = 0.001.Hence the numeric value of the expression is given as follows:
4×1+1×1/100+9×1/1000 = 4 + 0.01 + 0.0019 = 4.0119.
Which is the decimal number represented by the fraction.
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There are three boxes on the table: The first box contains 2 quarters, the second box contains 2 nickels, and the last box contains 1 quarter and 1 nickel. You choose a box at random, then you pick a coin at random from the chosen box. If the coin you picked is a quarter, what's the chance that the other coin in the box is also a quarter?
The probability of choosing a box and picking two quarter coins in a row is 1/108
What is Probability?Probability is the branch concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1. 0 indicates impossibility of the event and 1 indicates certainty.
Probability= sample space / total possible outcome
therefore probability of choosing two quarters in a row = 1/6×1/6= 1/36
The probability of choosing the first box =1/3
Therefore the probability of choosing the first box and picking two quarters In a row is 1/36×1/3= 1/108.
Since box two contain no quarter and box three has only one quarter , the probability of choosing two quarters in a row is 0.
Therefore the probability of choosing a box at random and picking two quarters in a row is 1/108.
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Give an example of bounded sequence that are not conregent?
Answer The sequence {an = (−a)n}
Step-by-step explanation: The sequence {an = (−a)n} is bounded below by −1 and bounded above by 1, and so is bounded. This sequence does not converge, though; since |an − an+1| = 2 for all n, this sequence fails the Cauchy criterion, and hence diverges.
A theater is presenting a program on drinking and driving for students and their
parents or other responsible adults. The proceeds will be donated to a local alcohol
information center. Admission is $2.00 for adults and $1.00 for students. However,
this situation has two constraints: The theater can hold no more than 240 people
and for every two adults, there must be at least one student. How many adults and
students should attend to raise the maximum amount of money?
To raise the maximum amount of money,
attend.
adults and
students should
Using equations, to raise the maximum amount of money, 160 adults and 80 students should attend the theater program on drinking and driving.
What is an equation?An equation is a mathematical statement of the equality of two or more mathematical expressions, using the equation symbol (=).
In this situation, we form a system of equations, to show the maximum number of adults and students allowed for the program.
We also form an objective constraint of inequality to show the limit of the allowed number of people for the program.
Admission fee for adults = $2.00
Admission fee for students = $1.00
Equations:The total number allowed in the theater = 240 persons
The ratio of adults to students = 2:1
The sum of ratios is 3
The number of adults = 2x, where, the number of students = x.
2x + x = 240 ... Equation 1
3x ≤ 240 ... Equation 2
If 3x = 240
x = 80
Check:
3x ≤ 240
3(80) ≤ 240
240 = 240
Allowed Admission:Adults = 160 (2 x 80)
Students = 80 (1 x 80), which meet the second requirement or constraint.
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Which is the graph of g(x) = [x + 3]?
Answer:
Step-by-step explanation:
................ x2
