The expression for savings after t years, based on the principle amount and annual interest rate is 3000 + 105t.
The formula to be used for computation of savings is -
Interest = (Principal × Rate of interest × Time)/100
Keep the values in formula -
Interest = (3000 × 3.5 × t)/100
Performing division and multiplication
Interest = 10,500t/100
Performing division on Right Hand Side of the equation to find the interest
Interest = 105t
Now, savings will be sum of amount and the interest earned
Savings = 3000 + 105t
Thus, the savings will be 3000 + 105t.
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 negative X divided by negative one will be 
Answer:
x
Step-by-step explanation:
Determining Ordered Pairs
Piano lessons cost $30 per lesson. Find ordered pairs that represent the total cost for x number of lessons.
Check all that apply.
Check
□ (-1,-30)
□ (0,30)
(1,30)
(1.5,50)
(3,90)
Answer:
C) (1, 30) and E) (3, 90)-----------------------
Piano lessons cost $30 per lesson.
This can be expressed as function:
C(l) = 30l, where C- total cost, l - number of lessonsEvaluate the given ordered pairs:
A) (-1, - 30) - not applicable as number of lessons can't be negative,B) (0, 30) - incorrect as C(0) = 30*0 = 0, it should be (0, 0);C) (1, 30) - correct as C(1) = 30*1 = 30;D) (1.5, 50) - incorrect as C(1.5) = 30*1.5 = 45;E) (3, 90) - correct as C(3) = 30*3 = 90.A media download store sells songs for $2 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you can purchase. What are three combinations of numbers
of songs and movies you can purchase?
I dont understand this. could someone give me step by step what the answer would be If?
Questions: If one solution of a quadratic equation is 7-13i, what would the second solution be?
Question 2: solve these, step by step using indicated operations with work!
1. (4-3i) (-7+21)
2. (-7+6i)+(2-3i)+(4+5i)
3. (-6-i)/4-2i
4. (-2-7i)(-2+7i)
5. (5-3i)-(-2-6i)
Answer:
Below
Step-by-step explanation:
Question 1:
The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. If one solution of the equation is 7-13i, the other solution must be the complex conjugate of 7-13i, which is 7+13i. To find the complex conjugate of a complex number, you simply need to change the sign of the imaginary part of the number. In this case, the complex conjugate of 7-13i is 7+13i.
Question 2:
1. (4-3i) (-7+21)
To add two complex numbers, we need to add their real parts and imaginary parts separately. In this case, we have:
(4-3i) (-7+21)
= (4 - 7) + (-3i + 21)
= -3 + 18i
2. (-7+6i)+(2-3i)+(4+5i)
To add multiple complex numbers, we can add them one at a time using the same procedure as before. In this case, we have:
(-7+6i)+(2-3i)+(4+5i)
= (-7+2) + (6i - 3i) + (4 + 5i)
= -5 + 3i + 4 + 5i
= -1 + 8i
3. (-6-i)/4-2i
To divide two complex numbers, we need to multiply the numerator and denominator by the complex conjugate of the denominator. In this case, we have:
4. (-6-i)/4-2i
= (-6-i)(4+2i)/(4-2i)(4+2i)
= (-24 - 2i + 6i - i^2)/20
= (-24 + 4 -1)/20
= (-21)/20
= -1.05 - 0.05i
5. (-2-7i)(-2+7i)
To multiply two complex numbers, we use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms separately and then adding the results. In this case, we have:
(-2-7i)(-2+7i)
= (-2 * -2) + (-2 * 7i) + (-7i * -2) + (-7i * 7i)
= 4 + (-14i) + 14i + 49
= 4 + 49
= 53
6. (5-3i)-(-2-6i)
To subtract two complex numbers, we need to add the first number to the opposite of the second number. In this case, we have:
(5-3i)-(-2-6i)
= (5-3i) + (2 + 6i)
= 7 + 3i
This is the final answer for each of the problems.
Which factors plays a role in establishing the value of a country's currency?
Supply and demand are two factors that affect how much a country's currency is worth.
The supply and demand of a country's currency determine the value of that currency in a free-floating currency exchange market. A currency improves in value or appreciates when demand for it rises. A currency loses value or depreciates when there is less demand for it.
Money's demand determines how much it is worth. When there is still a strong demand for treasuries, the US dollar increases. The value of a currency determines both its supply and demand. For instance, if a nation prints a lot of currency, the value relative to other currencies will drop because supply exceeds demand. Inflation will happen if the cost of products rises or the value of money declines in comparison to other assets.
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the line that passes through (−2, 6) and (−1, 18) in slope-intercept form.
Answer:
To find the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18), we can use the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the coordinates of the points given in the problem, we have:
m = (18 - 6) / (−1 - (−2)) = 12 / 3 = 4
Next, we need to find the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which has an x-coordinate of 0. Substituting the slope and the coordinates of one of the points given in the problem, we can solve for b:
y = mx + b
6 = 4 * (−2) + b
6 = −8 + b
b = 6 + 8 = 14
Therefore, the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18) is y = 4x + 14.
Step-by-step explanation:
if a certain positive two-digit number has tens' digit w and units' digit x , what is the value of w x ?
A two-digit number 23 is written with its place values. The digit 2 is at tens place and stands for 20 and digit 3 is at ones place and stands for 3.
A two-digit number is a two-digit number that starts with 10 and ends with 99. We can't start from scratch. In that case, it is assumed to be a single digit. The tens digit can be any number from 1 to 9. For example, 45, 78, 12 are two digit numbers.
The digit value is the position of each digit in the number. When talking about single-digit numbers, there is only one place value. When it comes to two-digit numbers, there are two digit values, 1 and 10.
For example:
a.) 33 ⇒ 3 tens + 3 ones = (3 × 10) + (3 × 1) = 30 + 3 = 33
b.) 18 ⇒ 1 tens + 8 ones = (1 × 10) + (8 × 1) = 10 + 8 = 18
c.) 27 ⇒ 2 tens + 7 ones = (2 × 10) + (7 × 1) = 20 + 7 = 27
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a fair coin is tossed at random 100 times. what is the approximate probability that the number of heads will exceed 60? what is the approximate probability that the number of heads will be at least 40 but less than 60?
Therefore ,the probability that the number of heads will exceed 60 is 0.0176
What is probability ?The number of outcomes that could occur is the basis for the response is known as probability .To this question the outcome in this case might be either head or tail. Therefore, there is a 50% chance that the result will be a head.
Here,
The fair coin is tossed at random 100 times.
So we have to find probability that the number of heads will exceed 60
Thus,
=> P(number of heads will exceed 60) = [tex]\frac{C^{100} _{1} }{C^{2} _{60}}[/tex]
=> P(number of heads will exceed 60) = 0.01760010010885238
=> P(number of heads will exceed 60) = 0.0176
Therefore ,the probability that the number of heads will exceed 60 is 0.0176
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Explain how to solve for the volume of a rectangular box if you know the length, width, and height of the box.
Answer:
V= Base X Height X Length
Step-by-step explanation:
Base = 5
Length = 7
Height = 3
Volume = 105
How many times larger is 6.255 × 1010 than 1.5 × 108?
Answer:6,155.55
Step-by-step explanation: 6.255*1010=6,317.55
1.5*108=162
6,317.55-162=6,155.55
an athletic facility has 5 tennis courts. pairs of players arrive at the courts and use a court for an exponentially distributed time with mean 40 minutes. suppose a pair of players arrives and finds all courts busy and k other pairs waiting in queue. what is the expected waiting time to get a court?
The expected waiting time to get a court is 8(k + 1).
What is expected time?
The projected time is simply the time frame in which the Project is anticipated to be finished. When the parties to the project contract are signing it, they will either mutually agree upon this time or decide it together with the participation of all the stakeholders, contractors, and clients.
They need to wait for k+1 pairs to finish before they can start.
Since the exponential distribution is memoryless, the expected time for a given pair to finish once started is 40 minutes, and there are 5 courts,
the expected time for any of the 5 courts to finish is 40/5=8 minutes, and so their expected waiting time is 8(k+1) minutes.
Hence, the expected waiting time to get a court is 8(k + 1).
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Solve for x based on the diagram
Answer:
x=11
Step-by-step explanation:
2x+1=5x-32 ==> since the two triangles are congruent, their angle measures are congruent as well.
2x-2x+1=5x-2x-32
1=3x-32
1+32=3x-32+32
33=3x
x=11
Why do we find range?
When you have a distribution without extreme values, the range typically provides you with a decent indication of variability.
In the given question, we have explain why we find the range.
When you have a distribution without extreme values, the range typically provides you with a decent indication of variability. The range can provide information about the breadth of the distribution when combined with metrics of central tendency. But if your data collection contains outliers, the range may be deceptive.
The difference between both the highest and lowest numbers in a collection or set is known as the range. Put together all statistics in order before considering a range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.
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how to solve the volume of a frustum with a radius of 15 and height of 4
Answer: 26
Explanation: Well, by using the formula to find volume of frustum. (this can be shown in a easier way or harder i choose my own way)
Step 1: The hight is: h=15h=15
Step 2: The top radius of the frustum is: r=19r=19
Step 3: The lower base radius of the frustum is: R=26R=26
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one cubic meter equals 264 gallons. if you use 100 gallons of water per day, how many cubic meters of water will you use in a year?
The use of water in a year will be 138 cubic meter.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
one cubic meter equals 264 gallons.
if you use 100 gallons of water per day.
In a year it will take 365*100 = 36500.
So total water is = 36500/264 = 138.
Hence the use of water in a year will be 138 cubic meters.
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Describe the position of the function below relative to the graph of the indicated basic function.
Ax)=-2*+¹; relative to f(x) = 2*
a. moved up 1 unit; reflected across the y axis. c.
moved down 1 unit; reflected across the y
axis.
b. moved right 1 unit; reflected across the x d. moved left 1 unit; reflected across the x axis.
axis.
Please select the best answer from the choices provided
3
3
B
D
From the given the option moved left 1 unit; reflected across the x axis is the correct.
what is function?
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.
We have to describe the position of the function [tex]f(x) = -2^x^+^1[/tex] relative to the basic function [tex]2^x[/tex].
Let the parent function is [tex]2^x[/tex].
After shifting one unit right it becomes, [tex]2^x^+^1[/tex].
After reflection in x axis it becomes, [tex]-2^x^+^1[/tex].
Hence, from the given the option moved left 1 unit; reflected across the x axis is the correct.
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name examples of a divergent, a convergent, and a transform plate boundary. how are these boundaries different (6 points)?
Example of Divergent Plate: Mid Atlantic ridge, Red Sea Ridge, and Southeast Indian Ridge.
Example of Convergent Plate: The collision between the Eurasian Plate and the Indian Plate.
Example of Transform Plate: San Andreas Fault Zone of western North America.
Divergent Plate:In plate tectonics, a divergent boundary or divergent plate boundary (also called constructive or extensional boundary) is a linear feature that exists between two tectonic plates moving apart. Diverging boundaries within continents first create rifts that eventually become rift valleys. The most active diverging plate boundaries occur between oceanic plates and exist as mid-ocean ridges.
Recent research suggests that complex convective currents within the Earth's mantle allow matter to rise to the bottom of the lithosphere beneath each divergent plate boundary. This provides the region with a tremendous amount of heat and pressure reduction that melts rock from the asthenosphere (or upper mantle) below the rift region, forming large flood basalts or lava flows.
Continental Plate:When continental and oceanic plates collide, the thin, dense oceanic plate is overwritten by the thicker, less dense continental plate. The oceanic plate is being pushed into the mantle in a process known as "subduction." As the oceanic plate sinks, it is forced into a hotter environment. At a depth of about 160 km (100 miles), the material within the subducting plate begins to approach melting temperatures and the process of partial melting begins.
This partial melting creates a magma chamber above the subducting oceanic plate. These magma chambers are less dense and buoyant than the surrounding mantle material. A buoyant magma chamber begins to rise slowly through the material above it, melting and rupturing as it rises. The size and depth of these magma chambers can be determined by mapping the seismic activity around the magma chambers. When a magma chamber rises to the surface without solidifying, magma breaks through in the form of a volcanic eruption.
Transformation Plate:A third type of plate boundary is a deformation fault where plates slip past each other without creating or breaking the crust. Rocks facing each other on both sides of a fault are usually of different types and ages, because rocks are cut and displaced by movement in opposite directions. These structures are so-called strike faults.
As friction increases and the sliding motion of the blade stops at one point, stress builds up and can be released with abrupt slippage. These can lead to some of the most damaging earthquakes in the continental crust. The San Andreas Fault (western United States), the North Anatolia Fault (Turkey), and the Dolores-Guayaquil Mega Fault in the northern Andes are examples of massive strike faults that cut through the continental crust.
Mid-ocean ridges are also often offset by so-called transformation faults. However, due to its association with stress distribution centers and the varied nature of the oceanic crust, earthquakes occurring there are usually shallow and therefore weak.
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jiminy’s cricket farm issued a 30-year, 4.5 percent semiannual bond three years ago. the bond currently sells for 104 percent of its face value. the company’s tax rate is 22 percent.
a) Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = 3.315%
c) After tax cost of debt of 3.135% is more relevant.
Given:
FV = 100
Semiannual bond issued 3 years ago
Maturity = 27
Price, PV = 104
coupon rate = 4.5%
Tax rate = 22%
a) Semiannual bond issued 3 years ago
Maturity, n = 27 years × 2 = 54
Coupon C = 4.5%/2×100 = 2.25
Now,
Pretax cost of debt,
Cost of debt, I = [C+(FV-PV)/n] / (FV+PV)/2
= [2.25 +(100 - 104)/54] / [ 100+1040/2
= 2.12%
= 2.12×2
Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = cost of debt × (1-T)
= 4.25% × (1-22%)
After tax cost of debt = 3.315%
c) After tax cost of debt is more relevant.
Hence we get the required answer.
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what order is this in
Considering the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis, the signs for the slope are as follows;
The plane is cruising at an altitude of 37,000 feet above sea level: zero.The plane is descending at rate of 1000 feet per minute: negative.The plane is ascending at a rate of 2000 feet per minute: positive.What is a slope?In Mathematics, a slope is also referred to as gradient and it is typically used to describe both the ratio, direction, and steepness of the function of a straight line.
Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
In this scenario, the sign of the slope of the graph of this plane's equation, with time being represented on the horizontal axis and elevation on the vertical axis are as follows;
The plane is cruising: the slope of the graph would be zero because it is moving at a constant speed.The plane is descending: the slope of the graph would be negative because it is decelerating.The plane is ascending: the slope of the graph would be positive because it is accelerating.In conclusion, the slope of a graph would be positive because there is an increase in the variables on the cartesian coordinate.
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Complete Question:
Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
a. The plane is cruising at an altitude of 37,000 feet above sea level.
b. The plane is descending at rate of 1000 feet per minute.
c. The plane is ascending at a rate of 2000 feet per minute.
How do you represent a linear function?
The linear function can be represented by slope intercept form, point slope form and standard form.
Given,
Linear function;
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
We can represent linear function by;
The slope intercept form, point slope form, and standard form can all be used to express a linear function.
Slope intercept form;
The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Standard form;
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.
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The solution of a system of linear inequalities is the intersection of the solutions to each inequality. Every point in the intersection region satisfies all inequalities in the system. Describe how you know which region, if any, represents the solution to a system of linear inequalities
Answer:
To determine which region represents the solution to a system of linear inequalities, you need to graph each inequality on the same coordinate plane and then find the intersection of the regions that satisfy each inequality. This intersection is the solution to the system of linear inequalities, as every point in this region satisfies all of the inequalities in the system.
To graph the solution, you can use a number line for each variable and plot the inequalities as points or lines on the coordinate plane. For example, if the system of linear inequalities is given by the equations y > 2x + 3 and y < -x + 5, you can plot the lines y = 2x + 3 and y = -x + 5 on the coordinate plane and find the intersection of the two lines. This intersection represents the solution to the system of linear inequalities, as every point in this region satisfies both inequalities.
Another way to find the solution to a system of linear inequalities is by using algebra to solve the system. This involves writing the equations in standard form, eliminating variables, and solving for the remaining variable. The solution can then be written as a set of ordered pairs that represent the points on the coordinate plane that satisfy the system of linear inequalities.
In either case, the solution to a system of linear inequalities is the region of the coordinate plane that satisfies all of the inequalities in the system.
Step-by-step explanation:
Aldo’s art class is 8 hours long. How long is his class in minutes.
Answer:
480 minutes
Step-by-step explanation:
One hour is 60 minutes, so 8*60 will give you your answer.
Answer:
Step-by-step explanation:
Theres 60 minutes in 1 hour, and you are trying to find how many in 8 hours, so you would multiply 60 by 8. The answer would be 480 minutes
Which value for A satisfies the equation 3 - 4(1 + A) = 7
Answer:
3−4(1+a)=7Step 1: Simplify both sides of the equation.3−4(1+a)=73+(−4)(1)+(−4)(a)=7(Distribute)3+−4+−4a=7(−4a)+(3+−4)=7(Combine Like Terms)−4a+−1=7−4a−1=7Step 2: Add 1 to both sides.−4a−1+1=7+1−4a=8Step 3: Divide both sides by -4.−4a−4=8−4a=−2
Answer:a=−2
a hospital needs 0.100 gg of 133 54xe 54133xe for a lung-imaging test. if it takes 10 daysdays to receive the shipment, what is the minimal amount mxemxem xe of xenon that the hospital should order?
In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a minimum amount of 0.4 g of.
Given that:
A hospital needs 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex]
and it takes 10 days for the shipment to arrive:
the half life [tex]t_{\frac{1}{2}[/tex] = 5 days.
So, since the half life = 5 days ;
decay constant [tex]\lambda = \frac{In_{2} }{t_{\frac{1}{2} } } }[/tex]
where:
[tex]No=?[/tex]
[tex]N=0.100\\\\t=10days\\\\N(t)=N_{o} e^{-\lambda\ t} \\\\0.1=N_{o}e^{-In\ 4} \\\\0.1=N_{o}e^{In\ \frac{1}{4} }\\\\0.1=\frac{N_{o}}{4} \\\\N_{o}=01*4\\\\N_{o}=0.4\ g[/tex]
Therefore, In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a minimum amount of 0.4 g of.
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the risk-free return during the sample period was 3%. calculate the jensen measure of performance evaluation for sooner stock fund.
the jensen measure of performance evaluation for sooner stock fund will be 2.6%.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
the risk-free return during the sample period was 3%.
performance evaluation for sooner stock fund.
Expected return of Sooner Stock Fund = E(Rp) = 20%
Beta of stock = 1.8
risk free rate Rf = 3%
Market Return Rm = 11%
So, Jensen measure alpha = E(Rp) - Rf - beta*(Rm - Rf) = 20 - 3 - 1.8*(11-8) = 2.6%
Hence the Jensen measure of performance evaluation for the sooner stock fund will be 2.6%.
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Point M lies on AB, AB = 24 , and BM = 13 What is AM?
If Point M lies on AB, AB = 24 , and BM = 13, then the length of AM is; 11 units
What is the length of the line segment?
We are given the following parameters;
Length of line segment AB = 24
Length of line segment BM = 13
Now, we are told that M lies on the line segment AB and as such;
If BM = 13, then it means that;
AM + BM = AB
AM + 13 = 24
AM = 24 - 13
AM = 11 Units
We conclude that the length of AM is 11 units.
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a group of 52 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. the purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. in particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of u.s. college students in general, which is estimated to be 4.73. the group of 52 students in the study reported an average of 5.11 drinks per with a standard deviation of 3.79 drinks. find the p -value for the hypothesis test.
The p -value for the hypothesis test is; 0.4195
What is the p-value of the hypothesis test?Let us first define the hypotheses.
We are told that the mean of u.s. college students in general, is estimated to be 4.73. Thus;
Null Hypothesis; H₀: μ = 4.73
Alternative Hypothesis; Hₐ: μ ≠ 4.73
Since we have the standard deviation for the sample, we will use the t-distribution with the formula;
t = (x' - μ)/(s/√n)
Where;
x' is the sample mean.
μ is the value tested at the null hypothesis.
s is the standard deviation of the sample.
n is the sample size.
We are given;
x' = 5.11
μ = 4.73
s = 3.98
n = 52
Thus;
t = (5.11 - 4.73)/(3.98/√52)
t = 0.688
Using a t-distribution calculator, this p-value is 0.4195
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Zoe is starting her own snow plowing business. She will charge $11.00 per hour. If Zoe works 40.25 hours per week, how much money will she earn each week?
Answer:
$442.75
Step-by-step explanation:
40.25 x 11.00= 442.75
A factory has a batch of hand sanitizer with 50\%50%50, percent alcohol content.
How much pure (100\%100%100, percent concentration) alcohol should they include in a 600\,\text{mL}600mL600, start text, m, L, end text bottle to make a 68\%68%68, percent mixture?
We can determine that we need 216 mL of 100% alcohol and 384 mL of 50% alcohol using the percentage by volume of the solutions that have been provided.
What is the percentage by volume?Volume/volume percentage, often known as v/v percent or %v/v, is a unit used to express how much of a substance is present in a solution.
It is defined as the volume of the solute divided by the sum of the volumes of the solution, multiplied by one hundred.
So, we know that:
A + B = 600 mL
We also understand that the final solution's total alcohol content must equal:
0.68 * 600 mL = 408 mL
So, it follows that:
0.50 * A + B = 408 mL
We can infer the following from the first equation:
A = 600 mL - B
In the second equation, using that A, we obtain:
0.50 * (600 mL - B) + B = 408 mL
300 mL - 0.50 B + B = 408 mL
The result of rearranging this equation is:
B - 0.50 * B = 408 mL - 300 mL
0.50 * B = 108 mL
B = 108 mL / 0.50
B = 216 mL
A = 600 mL - 216 mL = 384 mL
Therefore, we can determine that we need 216 mL of 100% alcohol and 384 mL of 50% alcohol using the percentage by volume of the solutions that have been provided.
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A rectangular field is to have an area of and is to be surrounded by a fence. The cost of the fence is dollars per meter of length. What is the minimum cost this can be done for?.
The minimum cost for the area can be fenced is $1920
It is given that the area of the rectangular field is 900 m²
Let the length of one side of the field be x m
Therefore, the length of the other side will be
900/x
The perimeter of the rectangular field
= 2(length + breadth)
= 2(x + 900/x)
= 2x + 1800/x m
Therefore, the cost of fencing will be
$(32x + 28800/x )
Let f(x) = 32x + 28800/x
We need to minimize f(x)
Differentiating with respect to x and equating it to 0 gives us
32 - 28800/x² = 0
or, x² = 28800/32
or, x² = 900
or, x = 30
This is because the length cannot be negative hence -30 cannot be a value
Now
f''(x) = 57600/x³
f''(30) = 2/1333
Since f"(x) is positive, x = 30 is the minimum value of x for which the cost is minimum.
Hence, the minimum cost will be
f(30)
= 960 + 960
= $1920
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Complete Question
A rectangular field is to have an area of 900 m² and is to be surrounded by a fence. The cost of the fence is 16 dollars per meter of length. What is the minimum cost this can be done for?