A tank can be filled by an inlet pipe in 12 hours and emptied by a drain pipe in 16 hours. How long will it take to fill the tank if both pipes are left open?
It will take 48 hours, to fill the tank if both pipes are left open simultaneously.
We are given the following data -
The time taken to fill the tank by inlet pipe = 12 hrs
so, the rate of filling = 1/12
The time taken to empty the tank by drain pipe = 16 hrs
so, the rate of emptying = - 1/16
Therefore, the total work done by both pipes can be given by the following formula -
(1/rate of filling) + (1/rate of emptying) = (1/rate of net change)
1/12 + (-1/16) = (1/Rn)
Therefore, (1/Rn) = 1/12 - 1/16 = 1/48
To find how long it will take to fill the tank, we need to find the reciprocal of the rate of net change:
1/Rn = 1/(1/48)
Rn = 48
So it will take 48 hours, to fill the tank if both pipes are left open.
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The Lockheed Martin F-22
Military Raptor can travel
3,000 miles in 2 hours.
What is it's top speed?
Answer:
1,500
Step-by-step explanation:
It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!
Pleas answer these questions..
Refer to the image attached.
which of the following is equivalent to 0.00648?
Question Down Below: (Please i really need to complete this right now) Please anyone :(
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Let x = number of vegetarian meals
Let y = number of meats.
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
In this case, the daily budget is 600.
Subtract the equations
y = 275
Number of meats = 275
Number of vegetarian meals = 325 - 275 = 50
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if 750 amounts to 885 in three years at a simple interest, find the rate of interest?
PLEASE ANSWER THE QUESTION ITS URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The Rate of Interest is 6%.
Step-by-step explanation:
S.I= Amount - Principle
S.I=885-750=135.
Rate= S.I*100/(P*T)
Rate=(135*100)/(750*3)
Rate=6%
Simple Interest:Simple interest is a quick and easy method of calculating the interest charge on a loan.
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Determine the solutions of the equation. What solution makes sense for the situation?
The dimensions of the rectangle are 8 inches as width and 13 inches as length.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation is given as:
x² + 5x - 104.
x² + 13x - 8x - 104
x(x + 13) - 8 (x + 13).
x - 8 = 0
x = 0 + 8
Width = 8
Length = x + 5
= 8 + 5.
= 13
The width is 8 inches and length is 13 inches.
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Determine the solutions of the equation. What solution
makes sense for the situation?
A rectangle has a length that is 5 inches greater than its
width, and its area is 104 square inches. The equation (x
+5)x = 104 represents the situation, where x represents
the width of the rectangle.
(x + 5)x = 104
x2 + 5x - 104 = 0
What are the dimensions of the rectangle?
how do i find the square root of a circle
Answer: by putting some clothes on
Step-by-step explanation:
comon man put some clothes on man do it for the kids
Dylan drove from Liverpool to Sunderland at an average speed of 50 mph for 3 hours and 30 minutes. He then drove from Sunderland to Edinburgh at an average speed of 65 mph for 2 hours. Work out how many miles Dylan travelled in total.
Answer:
305 miles
Step-by-step explanation:
You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.
DistanceDistance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi
Dylan travelled a total of 305 miles.
Please help!!!
What are some of the important steps to consider when solving an exponential or logarithmic equation? How can identities and logs help you to solve these equations? How are identities and logarithms confusing? Cite examples that help illustrate your ideas, and show steps to solve such equations in your post. Ask clarifying questions about anything you find confusing
Solving exponential and logarithmic equations requires a strong understanding of the properties of exponents and logarithms, as well as the use of logarithmic identities and inverse operations. It is important to simplify expressions and isolate the variable using basic algebraic operations, logarithmic identities, and inverse functions.
When solving exponential or logarithmic equations, there are several important steps to consider:
Simplify the equation using basic algebraic operations, such as multiplication, division, addition, and subtraction.
Isolate the exponential or logarithmic expression on one side of the equation.
Use the properties of exponents or logarithms to simplify the expression, if possible.
Use logarithmic identities such as logarithmic rules and change-of-base formula to simplify the expression.
Solve for the variable by using inverse operations.
Check your answer by substituting it back into the original equation and verifying that both sides are equal.
Identities and logs can be helpful in solving exponential and logarithmic equations because they provide a set of rules that can be used to simplify expressions. For example, logarithmic identities such as log(a * b) = log(a) + log(b) and log(a/b) = log(a) - log(b) can be used to simplify expressions containing products and quotients.
However, identities and logarithms can also be confusing because they involve complex concepts and require a solid understanding of logarithmic properties. This can make solving exponential and logarithmic equations challenging for some students.
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I need help with substitution the two parts are 4x+5y=48 and 7x-3y=-10. i need to find x and y
The solution to the simultaneous equation is x = 38 and y = 8
How to determine the valueFrom the information given, we have the equations;
4x+5y=487x-3y=-10From equation (1), make 'x' the subject of formula;
4x = 48 - 5y
Divide both sides by 4
x = 48 - 5y/4
Substitute the value x in equation (2)
7(48 - 5y/4) - 3y = -10
expand the bracket
336 - 35y/4 - 3y = -10
Find the lowest common multiple
336 - 35y - 12y/4 = -10
336 - 47y/4 = -10
cross multiply
336 - 47y = -40
collect like terms
-47y = 376
y = 8
Substitute the value into equation 3
x = 48 - 5(8)/4
x = 48 - 10
x = 38
Hence, the values are 38 and 8
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A publishing industry report predicts that magazine subscriptions will drop by 8% each year,
If this prediction is correct, then how many subscribers will a magazine with 85,630
subscribers have in 8 years?
Suppose the prediction of an annual drop in magazine subscriptions of 8% is correct. In that case, the number of subscribers that a magazine with 85,630 subscribers will have in 8 years, using an exponential function, is 43,947.
What is an exponential function?The exponential function is an expression in the form of f(x) = bˣ, where the b constant is called the base and the x variable is called the exponent.
Exponential functions may describe exponential growth or exponential decay.
Exponential decay refers to a decrease or drop, where the decay rate is known.
The annual drop in magazine subscriptions = 8%
The number of current magazine subscribers = 85,630
The number of years for the prediction = 8 years
Decay factor = (1 - 8%) = 0.92
The number of magazine subscribers in 8 years = 85,630 x 0.92^8
= 85,630 x 0.5132189
= 43,947
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The value of x is 40% of y. What are possible values for x and y? *
Answer:
x = 40 and y = 100
Step-by-step explanation:
random number 100
40% of 100 = 0.40 * 100 = 40
What is the midpoint of the line segment with the endpoints J(–9, –4) and K(7, 8)? (–5, –1) (–2, 1) (–1, 2) (3, 5)
Answer:
(-1,2)
Step-by-step explanation:
Recall the midpoint formula:
[tex]\frac{x^1+x^2}{2}[/tex] to solve for the X coordinate and [tex]\frac{y^1+y^2}{2}[/tex] to solve for Y.
Replace the variables with their appropriate numbers.
[tex]X(\frac{-9+7}{2})[/tex] [tex]Y(\frac{-4+8}{2})[/tex]
[tex]X(\frac{-2}{2} )[/tex] [tex]Y(\frac{4}{2} )[/tex]
[tex]X(-1)[/tex] [tex]Y(2)[/tex]
Therefore, the answer is (-1,2)
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 5, reflected across the x-axis, and shifted by 6 units left.
A. G(x) = -5ln (x - 6)
B. G(x) = 5ln (x + 6)
C. G(x) = -5ln (x + 6)
D. G(x) = 5ln (x - 6)
The function after transformation is G(x) = -5 ln (x+6) is the correct answer.
The correct answer is an option (C)
Here, the function is f(x) = ln x
A function f(x) is stretched vertically by a factor of 5.
As we know for a vertical stretch, we need to multiply the whole function by the factor of stretching.
If the stretching factor is m, then after stretching the function becomes
⇒ m × f(x)
Here, stretching factor m = 5
So the transformed function would be,
G(x) = 5 f(x)
⇒ G(x) = 5 ln x
Now, function is reflected across the x-axis, so the function becomes
⇒ G(x) = -5 ln (x+6)
Then the function is shifted by 6 units left, so after translation the function becomes
⇒ G(x) = -5 ln (x+6)
Thus, we can conclude that the function f(x) = ln x after transformation would be G(x) = -5 ln (x+6) is the correct answer.
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Nasim went to the store to buy some coffee. The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount. With the coupon, how much would Nasim have to pay to buy 3 pounds of coffee? Also, write an expression for the cost to buy p pounds of coffee, assuming at least one pound is purchased.
Nasim have to pay for 3 pounds of coffee is $10.75.
The expression for p pounds of coffee is 4.75p - 3.5.
What is Expression ?
A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount.
and, Nasim have to pay to buy 3 pounds of coffee.
So, Nasim have to pay for 3 pounds of coffee.
= 3 x 4.75 - 3.50
= 14.25 - 3.5
= $10.75
and, the expression for p pounds of coffee is
= 4.75p - 3.5
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an auto dealer has 8 different cars and 4 different trucks. how many ways are there to select two vehicles?
There are 66 ways to choose two vehicles from the dealer's inventory.
A combination is a grouping of items from a larger set in which the order of the items is irrelevant. In other words, it is a method of selecting a subset of items from a larger set without regard for their order of selection.
The formula C(n, k) = n! / (k! (n - k)!) can be used to calculate the number of combinations.
where n represents the total number of items in the set and k represents the number of items in the combination.
The exclamation mark (!) represents the factorial function, which is the sum of all positive integers up to a certain number.
The number of ways to select two vehicles from 8 cars and 4 trucks is 8 + 4 = 12 vehicles.
To find the number of combinations, we use the formula for combinations, which is:
C(n, k) = n! / (k! (n - k)!)
where n is the total number of vehicles and k is the number of vehicles we want to choose.
So, for n = 12 and k = 2,
we have:
So, putting the value in above formula:
We will get it as:
C(12, 2) = 12! / (2! (12 - 2)!) = (12 * 11) / (2 * 1) = 66
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Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
A solution for the given system of linear inequalities is the shaded area below the solid line.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the cost of vegetarian meal and cost of meat meal, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the cost of vegetarian meal.Let the variable y represent the cost of meat meal.Since each vegetarian meal cost $2.25 to make while each meat meal cost $2.75 and Chef Malik can spend no more than $800, a linear inequality which represents this situation is given by;
2.25x + 2.75y ≤ 800
Additionally, Chef Malik wants to serve at least 400 meals;
x + y ≥ 400
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities.
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Complete Question:
Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
Write and solve the system of inequalities graphically.
WXYZ is a parallelogram. The position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively. Determine in the form (x,y) the vectors, WX, XY, WZ, OZ
In the parallelogram, the coordinates form of the vectors WX, XY, WZ, OZ are (18,3), (24, 21), (2x, y) and (0,0).
The term coordinate in math is known as the set of values that represents the exact position on the coordinate plane
Here we know that WXYZ is a parallelogram and the position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively.
Then the value of the coordinate vectors are calculated as,
=> WX = (2,1) x (6,3) = (18, 3)
And the value of XY is calculated as,
=> XY = (6,3) x (4,7) = (24, 21)
And we know that the value of Z is (x, y), then the vector is calculated as,
=> WZ = (2,1) x (x, y) = (2x, y)
Finally the value of OZ is calculated as,
=> OZ =(0,0) x (x , y) = (0, 0)
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what is D=8 cm and R =4.7 in ,
The circumference of the circles are 25.12 cm and 29.516 in
How to determine the circumference of the circleFrom the question, we have the following parameters that can be used in our computation:
(a) D = 8 cm and (b) R = 4.7 inches
Given the diameter, the circumference is
C = πD
So, we have
C = 3.14 * 8 cm = 25.12 cm
Given the radius, the circumference is
C = 2πR
So, we have
C = 2 * 3.14 * 4.7 in = 29.516 in
Hence, the circumference is 29.516 in
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Complete question
What is the circumference of the circle given its diameter (D) of its radius (R)
(a) D = 8 cm and (b) R = 4.7 inches
pls help fast it due today
Answer:
ch.1 = 12x1.2=14.4
ch.2=10.5x1.2=12.6
ch.3=39.3x1.2=47.16
Step-by-step explanation:
You just have to multiply all the chapters by 1.2
i think if im wrong im sorry
Answer: 14.4, 12.6, 49.16
Step-by-step explanation:
Multiply each number by 1.2
12x1.2=14.4
10.5x1.2=12.6
39.3x1.2=49.16
chapter 1 : 14.4
chapter 2: 12.6
chapter 3: 49.16
Find the indicated real n the root(s) of a. n=9, a=-512
[tex]\sqrt[9]{-512}\qquad \begin{cases} -512=-2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\\ \qquad 2^9 \end{cases} \\\\\\ \sqrt[9]{(-2^9)}\implies -2[/tex]
Evaluate the following. 4 x 5 - 18 divided 3 - 8
Answer: The answer would be
Step-by-step explanation:
28/3
in decimal form- 9.3 (3 keeps going)
Mixed Number- 9 1/3
the feather on an arrow form two congruent parallelograms. the parallelograms are reflection of each other over the line that contains their shared side show that m
Dustin’s math classroom has 2 bulletin boards side by side. The teacher said the length of one
board is 1. 25 yards, and the other is 1. 75 yards. What is the total length in feet of the two
bulletin boards side by side?
The total length in feet of the two bulletin boards side by side is 9 feet.
The total length of the bulletin boards when calculated side by side will be done using addition operation. The expression that will form for calculation is -
The total length = length of one bulletin board + length of second bulletin board
Keep the values in formula -
The total length = 1.25 + 1.75
Performing addition on Right Hand Side of the equation
The total length of the two bulletin boards = 3 yards
The total length in feet = 3 × (3 feet)
Performing multiplication
Total length = 9 feet
The total length in feet is 9 feet.
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solve for x.
2x°
24°
Answer: x = 33°
Step-by-step explanation: 2x° + 24°-24 = 90°-24 2x/2 = 66/2 x = 33°
Andy is using wooden boards that are 0. 45 feet wide to build a deck. How many rows of boards are needed to completely cover a space that is 21 feet wide?
Andy is using wooden boards that are 0. 45 feet wide to build a deck. The number of rows of boards are needed to completely cover a space is 47 rows of boards.
Divide the total width (21 feet) by the width of each board (0. 45 feet):
21 / 0. 45 = 46. 666666
Round the result up to the next whole number:
47 rows of boards
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
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Help meeee thx I don’t know how to do this
Answer:
There are 36 pink blocks in the bin
Step-by-step explanation:
[tex]45\% \text{ of } 80 = 0.45(80)= 36[/tex]
An amusement park is building a new water slide which is supported by beams of 40 feet and 25 feet. To support the weight of the ride effectively, a support beam (EF) needs to be added to hold the guide wires (AC and BD) in place. What will the height of the support beam need to be for this new ride?
As per the formula of area of triangle, the height of the support beam need to be for this new ride is 3.2 feet.
In math the term area is defined as “b” be the base and “h” be the height of a triangle, then the formula to find the area of a triangle is given by. Then the Area of triangle is calculated as,
=> A = (½) b h square units.
Here we have know that an amusement park is building a new water slide which is supported by beams of 40 feet and 25 feet.
Then based on the formula of area of triangle, the height of the support beam need to be for this new ride is calculated as,
=> 40 = 1/2 x 25 x h
=> h = 80/25
=> h = 3.2
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Can someone help me please? I'm struggling :(
Answer:
Ariel's plant is 1.6 inches taller than Dyani's.
It doesn't seem that you can multiply the measurement of Dyani's plant anymore than Ariel's. So I believe that would be 0 inches.
Step-by-step explanation: You can multiply Dyani's measurement with number like 1.0, 1.2, etc. You still wouldn't be able to multiply it anymore.
I hope this helps!