By using differential equations' concept, we get that there is no sugar in the beginning.
What is a differential equation?A differential equation is an equation that connects the derivatives of one or more unknown functions.
Given:
Pure water = 2840 litres
sugar = 0.01kg per liter
Rate of sugar entering the tank = 4liter/min
New solution drains out at the rate = 4 litre/min
To find: sugar in the beginning.
Finding:
(a) In the beginning, the tank contains only pure water and no solution of water with sugar.
Hence, the sugar is null for t = 0.
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Write the function rule for the function shown below reflected in the given axis. f(x) = 4x; x-axis Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)? g(x) =
The function rule for g(x) is g(x) = -4x
How to determine the function rule for g(x)?The function is given as
f(x) = 4x
The transformation is given as reflection across the x-axis
The rule of this transformation is
(x, y) = (x, -y)
So, we have
g(x) = -f(x)
This gives
g(x) = -4x
Hence, the function rule for g(x) is g(x) = -4x
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suppose that you decided to go skiing this weekend. it costs $50 for transportation, $50 for lodging, $50 for ski lift tickets and you could have earned $100 as a waiter at a job you love so much you would do it as a volunteer if you had nothing better to do. what is the total cost of the ski weekend?
The total cost of the ski weekend comes out to be $250.
What is the total cost of expenses?Total expenses for just a given period are the sum of all gross cash expenditures and furthermore any pending subsidiary items like operating expenses, reward fees, interest, & taxes.
Some key features regarding the total cost are-
In economics, total cost is the sum of all costs a company incurs in generating a certain output level. It is generally expressed as the sum of all fixed costs (for example, the costs of a construction lease and heavy machinery) that do not vary with the amount of output produced and all variable costs (for example, the costs of labor and raw materials) that change with the of output. If fixed costs are not changed (for example, by acquiring a larger building or more industrial equipment), the rate at which of variable costs to increasing output will become progressively greater with in long run, due to decreasing returns on additional units of production.Now, according to the question;
The cost of all spending are-
$50 for transportation
$50 for lodging
$50 for ski lift tickets
$100 for waiter.
Total cost = transportation cost + lodging cost + ski lift tickets cost + waiter cost.
Total cost = $50 + $50 + $50 + $100
Total cost = $250.
Therefore, the total spending in the ski weekend are $250.
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Answer please, thanks.
Answer:2
Step-by-step explanation:
9. Mr. Crowley bought lunch for himself and eight of his employees.
Each had a sandwich platter that costs $5.85 and a drink that
costs $1.25. Five of the employees had dessert that costs $1.50.
Mr. Crowley gave the delivery person $80 and told her to keep
the change as a tip. How much was the delivery person's tip?
Answer:
$8.60
Step-by-step explanation:
Let x = the tip
80 - x = 9(5.85 + 1.25) + 5(1.50)
80 -x = 63.90 + 7.5
80 - x = 71.40 Subtract 80 from both sides
-x = -8.60 Divide both sides by -1
x = 8.60
Eli wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. Eli only has $37 to spend.
Let n represent the number of notebooks that Eli buys.
Which inequality describes this scenario?
37<2n+24 , 37<2n+24
37≤2n+24 , 37 is less than or equal to 2 n plus 24
37>2n+24 37 is greater than 2 n plus 24
37≥2n+24
Answer: the second one
Step-by-step explanation:
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 2n + 24
Option D is the correct answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
Cost of the calculator = $24
Cost of a notebook = $2
Total amount to spend = $37
Number of notebooks = n
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 24 + 2n
The number of possible notebooks to buy:
37 24 + 2n
37 - 24 ≥ 2n
13 ≥ 2n
13/2 ≥ n
6.5 ≥ n
The number of notebooks can be 6 or fewer.
Thus,
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 2n + 24
Option D is the correct answer.
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A company makes a profit of $55 per software program and $45 per video game. The company can produce at most 225 software programs and at most 275 video games per week. Total production cannot exceed 450 items per week. How many items of each kind should be produced per week in order to maximize the profit?
Use linear programming to solve. Show all your work.
Answer:
they should produce 225 software programs and 225 video games per week.
Step-by-step explanation:
limit 450
there are 2 factors the software and video games.
450•2= 225
What are the key features of the quadratic function f(x) = 2(x - 3)2 + 4
The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
The given quadratic function is f(x) = 2(x - 3)² + 4.
We need to find the key features of the given quadratic function.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Now, the key features of the given quadratic function as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3, 4)
Focus: (3, 33/8)
Axis of Symmetry: x=3
Directrix: y=31/8
Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.
Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
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Graph the image of V(0, -2) after a rotation 180° clockwise around the origin.
Greetings from Brasil...
For rotation, we can use the expression:
V(X; Y) → V'(Xcos θ - Ysen θ; Xsen θ + Ycos θ)Let rotate 180° - specifically for this angle, 180°, either counterclockwise or clockwise
SEN 180 = 0 and COS 180 = - 1
V(X; Y) → V'(- X; - Y)
V(0; - 2) → V'(0; - (- 2))
V'(0; 2)___________________________________
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consider a certain type of nucleus that has a decay rate constant of 0.0250 min-1. calculate the time required for the sample to decay to one-fourth of its initial value.
It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
In the given statement is:
λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus
To solve this problem, we use
N(t) = [tex]N_{0}[/tex]e^-λt
and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set
N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]
We can substitute this in the decay equation:
0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt
Cancel the like terms
0.25 = e ^-λt
Take the natural logarithm of both sides:
㏑(0.25) =㏑(e^-λt)
㏑(0.25)= -λt
Solve for the time t:
t = - ㏑(0.25)/λ
Substitute the given rate constant :
t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]
t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]
t = 55.452mins
It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
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what trigonometric expression can be used to find the value of x? replace a and b with the correct values.
The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .
Given :
A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .
Trigonometric Formula for Tan θ
tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .
where θ = 25 , perpendicular = 12 , base = x .
Substituting values in above first formula ,
tan 25 = 12 / x
Therefore , x = 12 / tan ( 25 ) .
Hence , a = 12 and b = 25 .
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Raven is deciding between two plumbing services. service provider a multiplies the average number
Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:
Service provider A - $83.33Service provider B - $105What is the service cost?The Service cost for Service provider A is:
= 50 x 1.5 + (50 x ((1.75 / 1.5) - 1)
= $83.33
Service cost for Service provider B is:
= Number of hours x Cost per hour
= 60 x 1.75
= $105
The cheaper plumber is Service provider A.
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a bucket holds 10 liters.about how many gallons does the buket hold?round to the nearest tenth,if necessary
For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.
What is termed as units and unit conversion?A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.
Before performing any arithmetic operations on 2 variables, we should always convert all of their values to a common unit.Unit conversion is the process of converting one unit of measurement to another measurement unit for the same amount by multiplying/dividing by conversion factors.Scientific notation is used to express the units, which are then converted into numerical based on the quantities.Now, per the given question;
The total amount a bucket contains is 10 litres.
Noe, the conversion of litres in gallons is given as;
1 litres = 0.26 gallons.
Thus, 10 litres = 10×0.264
= 2.64 gallons.
Therefore, the bucket will contain 2.64 gallons.
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In 1975, a person earning minimum wage made $80 for a 40-hour work week. what was the minimum wage per hour in 1975?
The minimum wage per hour = $2
Here we need to find the value of minimum wage per hour in 1975
As is given that the earning minimum wage is $80 for working 40 hours.
40-hour work gives = $80
1-hour work gives = $80/40
= $2
Therefore the minimum wage per hour in 1975 is $2
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identify the set of values for which will be a real number. the set of values for which will be a real number is
Except for x = 3, the set of x values for that y will become a real number as per Y=8/x-3 contains all real numbers.
What is real number?A real number is any number which can be found with in real world. Numbers can be found all around us.
Natural numbers are used to count objects, rational numbers for fraction representation, irrational numbers for determining the square root of the a number, integers for temperature measurement, and so on. These various types of numbers combine to form a gathering of real numbers.The union of a set of rational numbers (Q) or the set of irrational numbers yields the set of real numbers (R).Now according to the question;
In actuality, the expression Y=8/x-3 stops producing a real numerical value for y when the denominator has become zero.
When the denominator is zero, the y value is undefined and thus not a real number.
As a result, if we set;
x - 3 = 0
x = 3
Therefore, except for x = 3, the set of x values for which y is a real number per the Y=8/x-3 includes all real numbers.
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The complete question is-
Y=8/x-3
Identify the set of values x for which y will be a real number
If A= [-2 14 9] and B= [0 -6 10], the A-3B=?
Answer:
(-2, 32, -21)
Step-by-step explanation:
You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)
ngozi earns \$24{,}000$24,000dollar sign, 24, comma, 000 in salary in the first year she works as an interpreter. each year, she earns a 3.5\%3.5%3, point, 5, percent raise.
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by [tex]S = 24000 * (1.035)^t[/tex].
What is a function?
A function in mathematics from a set X(ax) to a set Y allocates exactly one element of Y to each element of X(ax). A relation between a collection of inputs and labor is known as a function.You can use the fact that the raise is done on the previous year's salary.
Let the initial salary be P = $24000
After 1 year, her salary increased by R = 3.5% which, thus,
Total salary = P + increment
Similarly going on, we get
[tex]P_t = P(1+ \frac{R}{100})^t = S[/tex] (we can say)
Putting values of P(value of P) and R(value of R), we get
[tex]S = 24000(1 + 0.035)^t = 24000 *(1.035)^t[/tex]
Thus,
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by
[tex]S = 24000 * (1.035)^t[/tex]
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Solve the equation
A =2πr*2 + 2πrh, for h
Find the constant of variation where y varies directly as x if y = 30 when x = 8. Write your answer
as a decimal.
The value of constant v is 3.75 if y varies directly as x and when
x = 8 and y = 30.
Let v be any constant.
According to the given question.
y varries directly as x.
⇒ y ∝ x
⇒ y = vx (beacuse v is constant)
Here, it is give that x = 8 and y = 30.
Thereofre, the value of constant v when y = 30 and x = 8 is given by
y = vx
⇒ 30 = v(8)
⇒ 30/8 = v
⇒ v = 3.75
Hence, the value of constant v is 3.75 if y varies directly as x and when
x = 8 and y = 30.
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a researcher wants to know how the residents of a town feel about constructing a new road through the town
I need help asap (Fractions)
Answer:
Step-by-step explanation:
3 3/4 = 15/4
15/4 divided by 3/4 = 5
The sum of a number and its half is 27. Find the number.
Let the number be y
Answer:
Step-by-step explanation:
the number is y
you are told
y+0.5y=27
Therefore,
1.5y = 27.
If you divide by 1.5 on both sides, you'll get 18 which is your answer.
18+9=27
The Evans family drives 21 miles in the first miles in the first 20 minutes of their trip. what is their speed in miles per hour during this time? create a representation to show your work.
The measure of the speed during the time is 63. 64 miles per hour
How to determine the speedThe formula for speed is expressed as;
Speed = distance/ time
Given that;
Distance traveled = 21 milesTime = 20 minutesLet's convert the time in minutes to hour
60 minutes = 1 hour
20 minutes = x hour
cross multiply
x = 20/ 60
x = 0. 33 hours
Substitute the values
Speed = 21/ 0. 33
Speed = 63. 64 miles per hour
Thus, the measure of the speed during the time is 63. 64 miles per hour
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Kaylee drove 160 miles in 5 hours. If she continued at the same rate, how far would
she travel in 17 hours
Answer:
544 miles
Step-by-step explanation:
160 miles= 5 hours in order to see how much she traveled in 1 hour you need to divide so do 160 divided by 5 = 32 then do 32x17 which would be 544.
I hope it helps you!
~XxBells is a cute girlxX~
Kaylee would travel 544 miles in 17 hours if she continued at the same rate.
What is the distance?A mathematical number is known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
distance = rate × time
We know that Kaylee drove 160 miles in 5 hours, so her rate is:
rate = distance / time = 160 miles / 5 hours = 32 miles/hour
Now we can use this rate to find out how far she would travel in 17 hours:
distance = rate × time
distance = 32 miles/hour × 17 hours
distance = 544 miles
Therefore, Kaylee would travel 544 miles in 17 hours if she continued at the same rate.
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What is the slope of the line that passes through the points (5, -6) and (9, -6) Write your answer in simplest form.
Answer:
slope=y2-y1/x2-x1
=-6-(-6)/9-6
=0/3
any fraction in which numerator is 0 is 0.
What is the relationship of the edge length of the cube
to its volume?
Volume is equal to [tex]a^{3}[/tex] where an is the width or length of its edges.
The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes [tex]centimetres^{3}[/tex], [tex]metres^{3}[/tex], [tex]inches^{3}[/tex], [tex]feet^{3}[/tex], etc.
A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.
If a cube's length, breadth, and height are equal to "a," then;
Cube volume = a[tex]\times[/tex]a[tex]\times[/tex]a.
Therefore, Volume of cube is [tex]a^{3}[/tex] where a is the length of the edge.
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Select all the polynomials that have (x - 4) as a factor.
a
x3 - 13x - 12
b
x3 + 8x2 + 19x + 12
c
x3 + 6x + 5x -12
d
x3 - x2 - 10x - 8
e
x2 - 4
Polynomials which have (x-4) as a factor are a. x³ - 13x - 12 = 0 and c. x³ + 6x + 5x - 12 = 0.
What is a polynomial ?An algebraic equation having two or more than two terms is called a polynomial.
According to the given question we have determine which of the following polynomials have (x-4) as a factor.
One way is factoring each of these polynomials.
Another way is given x - 4 is a factor,
∴ x - 4 = 0
x = 4 must satisfy the polynomial which has a factor of (x-4).
Now we have to replace x with 4 in each of the given polynomials and if LHS = RHS then (x -4) is a factor.
a. x³ - 13x - 12 = 0
(4)³ - 13(4) - 12 = 0
64 - 52 - 12 = 0
64 - 64 = 0. (LHS = RHS).
b. x³ + 8x² + 19x + 12 = 0
(4)³ + 8(4)² + 19(4) + 12 ≠0
Here you don't need to calculate further because in LHS sum of these terms won't be zero.
c. x³ + 6x + 5x - 12 = 0.
x³ + 11x - 12 = 0.
64 + 44 - 12 ≠ 0.
d. x³ - x² - 10x - 8 = 0.
64 - 16 - 40 - 8 = 0.
64 - 64 = 0, (LHS = RHS).
e. x² - 4
16 - 4 ≠ 0.
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7+(2x3) 5-6(9 divided by 5)=
Answer:
26.2
Step-by-step explanation:
7 + (2x3) 5-6 (9/5)
7 + 6*5-6*1.8
7 + 30-10.8
37 - 10.8
26.2
Simplify (24)−1. one over two raised to the power of negative four one over two raised to the fourth power −24 23
The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).
The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
It is given that the expression is (2⁴)⁻¹
Now,
using the integer exponent properties,
=> (2⁴)⁻¹
=> (2)⁴* ⁻¹
=> (2)⁻⁴
=> 1/2⁴
Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.
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Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
Answer:
8 nickels and 14 pennies
Step-by-step explanation:
Let p = number of pennies
Let n = number of nickels
p + n = 22 .01p + .05n =.54
Take the second equation and multiple it through by 100 to clear the decimals.
100(.01p + .05n( = .54(100)
p + 5 n = 54 Multiply this through by -1 so that I can add it to the first equation.
-p -5n = -54
p + n = 22 Add these together
-4n = -32 Divide both sides by -4
n = 8 We have solved for n. We have 8 nickels.
Plug 8 in for n in the first equation and solve for p.
p + n = 22
p + 8 = 22 Subtract both sides by 8
p = 14 There are 14 pennies.
Check:
p + n = 22
14 + 8 = 22
22 = 22 Checks
.01p + .05n = .54
.01(14) + .05(8) = .54
.14 + .40 .54
.54 .54 check
90% of what number is 45?
Answer:
40.5
Step-by-step explanation: