Answer:
f(n) = 8000(1.67)ⁿ⁻¹
Explanation:
The equation for exponential growth has the following form:
[tex]f(x)=a(1+r)^x[/tex]Where a is the initial amount, r is the growth rate and x is the variable.
In this case, we know the amount after the first year and the growth rate and the variable is the number of years. So, replacing a by 8,000 and r by 0.67 and x by (n-1) because we will not include the 1st year, we get:
[tex]f(n)=8000(1+0.67)^{n-1}[/tex]Therefore, the explicit equation for f(n) is:
[tex]f(n)=8000(1.67)^{n-1}[/tex]A railroad crew can lay 7 miles of track each day. They need to lay 196 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function.
L (d) = 196 - 7d
(a). How many days will it take the crew to lay all the track?
(b) How many miles of track does the crew have left to lay after 19 days?
The number of miles of track does the crew have left to lay after 19 days is 63 miles.
The given equation is L (d) = 196 - 7d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
a) Number of days will it take the crew to lay all the track = 196/7
= 28 days
b) Number of miles of track does the crew have left to lay after 19 days
L (d) = 196 - 7d
Put d=19 in the given equation
We get L=196 - 7(19)
= 196 - 133
= 63 miles
Therefore, the number of miles of track does the crew have left to lay after 19 days is 63 miles.
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determine the discriminat and use it to determine the number of x-intercepts for the graph of f(x) = 2x^2 - 8x + 9
Answer:
[tex]\begin{gathered} x=2+i14 \\ x=2-i14 \\ \text{ Complex answer, no x-intercepts} \end{gathered}[/tex]Explanation: The discriminant is the part of the quadratic formula underneath the square root symbol As we know that square root of any number is both plus and minus of a certain value:
[tex]\sqrt[]{a}=\pm c\Rightarrow(-c)^2=(+c)^2=a[/tex]Using this information about the discriminant we can determine the x-intercepts of the graph as follows:
[tex]f(x)=2x^2-8x+9=0\Rightarrow\text{ Solving this quadratic equation will give x-intercepts}[/tex]Quadratic equation solution:
[tex]\begin{gathered} f(x)=2x^2-8x+9=0\Rightarrow x=\frac{-B\pm\sqrt[]{B^2-4AC}}{2A} \\ \because\Rightarrow \\ A=2 \\ B=-8 \\ C=9 \\ \therefore\Rightarrow \\ x=\frac{-(-8)\pm\sqrt[]{(-8)^2-(4\times2\times9)}}{2\times(2)}=\frac{8\pm\sqrt[]{16^{}-72}}{4}=\frac{8\pm\sqrt[]{-56}}{4}=2\pm\frac{\sqrt[]{-56}}{4} \\ \therefore\Rightarrow \\ x=2\pm i14 \\ \rightarrow\text{ Complex answer} \\ x=2+i14 \\ x=2-i14 \end{gathered}[/tex]Graph
Note! The plot of f(x) above confirms that there are no x-intercepts of this function, so the reason for complex values of x. also discriminant is the square root of -56
a realtor make 6% commission on each sale how much commission will the realtor earn for selling a $140,000 home
Answer:
1&3239282882819&;&39303847
Answer:
$8,400
Step-by-step explanation:
6%x140,000
Looking at the graph, which point shows the constant of proportionality?
(2,1)
(2,4)
(,2)
(1,2)
Answer:
I forgot maybe someone else knows
Step-by-step explanation:
:) ;) <*)))))<
Determine whether the pair of polygons is similar using properties of similar polygons. Explain your reasoning.
The polygons are similar
What is a polygon?
A polygon (/pln/) in geometry is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain (or polygonal circuit). A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides. The vertices (plural: vertex) or corners of a polygon are the spots where two edges meet. A solid polygon's interior is sometimes referred to as its body. A polygon having n sides is known as an n-gon. A simple polygon is one that does not cross itself. Mathematicians are frequently interested simply in the bounding polygonal chains of simple polygons, and they frequently define a polygon in this manner.
The sides ratio is same in both polygons i.e. 1:2
and all the angles of the two polygons are congruent
So, the polygons are similar
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Tamarisk Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck (not the least of which is that it runs). The new truck would cost $56,619. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,100. At the end of eight years, the company will sell the truck for an estimated $28,500. Traditionally, the company has used a general rule that it should not accept a proposal unless it has a payback period that is less than 50% of the asset's estimated useful life. Thomas Anderson, a new manager, has suggested that the company should not rely only on the payback approach but should also use the net present value method when evaluating new projects. The company's cost of capital is 8%.
The cash Payback period is 6.66 years and the Net present value of the proposed investment is $5,329 (to see the calculation please refer the attached image.)
Computation of Payback Period
Cash Payback Period = Cost of truck/Annual cost savings.
Given that-
Cost of truck = $56,619
Annual cost savings = $8,100
Putting values, we get-
Cash payback period = ($56,619/$8,100) cash payback period
cash payback period = 6.66 years.
To calculate the PVF at 8% below is the formula
P = (1/[tex](1+r)^{n}[/tex])
Where,
P = the Present Value Factor.
r = the interest rate
n = the number of periods over which payments are made.
To calculate the Present Value = PVF at 8% x Amount.
Hence, As the Net Present Value is positive, Tamarisk corporation should purchase the truck.
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which function can be used to find y, total amount saved in, x weeks
Input data
Points
A = (0, 50)
B = (30,110)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} m=\frac{110-50}{30-0} \\ m=\frac{60}{30} \\ m=2 \end{gathered}[/tex]Now, what about b, the y-intercept?
[tex]\begin{gathered} b=y-mx \\ b=50-2\cdot0 \\ b=50 \end{gathered}[/tex]The equation of the line that passes through the points
[tex]y=2x+50[/tex]Write the correct equation for the following statement.
The quotient of x and seven is twelve
To get quotient we divide
in this case we divide x by 7 to get the quotient 12 as A RESULT
[tex]x \div 7 = 12[/tex]
HOPE THIS HELPS.
Which of the following is the correct mathematical expression
for:
The sum of x and 5
Answer:
Yes
Step-by-step explanation:
Yes
Need help please and also explain it
15 points if help
Answer:
60
Explanation:
1/2 of 80 is 40. 1/4 of 80 is 20. Add them and you get 60.
Mr. Shepard,The band teacher wanted to know if a certain type of Instruments are more appealing Who won grade level or another he conduct a survey and compiled the chart
So complete If I were to multiply 23 by 15, I would get 38
if one gender finds a certain sort of instrument more attractive than the other. In order to find out his pupils' choices, he organized a poll. The findings are shown in the table below. What percentage of girls preferred woodwind instruments? So girls who prefer woodwind instruments over boys would receive instruments? So, 30 2 19 would be the result. The same thing is said at the beginning of this one as well, but it asks for the number of ladies who prefer string instruments, which is 23 out of all the pupils that performed and preferred string instruments. So complete If I were to multiply 23 by 15, I would get 38.
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complete question:
'Mr Keen, a band teacher wanted to know if certain types of instruments are more appealing to one gender or the other. So he conducted a survey of his students preferences. The results are complied in the chart below: What is the ratio of the number of girls preferring woodwind instruments to the number of boys preferring woodwind instruments? * Instruments Boys Girls 15 23 Strings Woodwind 19 30 Brass 27 13 Percussion 32 25 Your answer P Mr Kccn; band tcacher wantea t0 know certain types 0i instumenlsare morc appealing [O onc gender or the other So he conducted & survey of his students preferences; Thc results are complied In Ihe chart below: What is the ratio of the number of girls preferring woodwind instruments t0 the number of boys preferring woodwind instruments? Inatuuments Roys he Strings Woodwlnd Brass Percusslon Your answer Mr Keen; band teacher wanted t0 know if certain types of instruments are more appcaling to ore gender or the other: So he conducted survey of his students preferences, The results are complied in the chart below: What is the rallo of the number of girls preferring string instrurents to the total number of students preferring strings Instruments?
What’s the correct answer answer asap for brainlist
Answer: A
Step-by-step explanation:
I NEED HELP ASAP!! i’m not sure how to do this.
Answer:
slope = -2/3
Step-by-step explanation:
Locations of points: (-3 , 2) and (3 , -2)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (-2 - 2) / (3 - (-3))
slope = -4/6
reduce:
slope = -2/3
Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has nn nickels and pp pennies?
As per given by the question,
There are given that 140 nickels and 130 pennies.
Now,
The number of nickels is 140 and number of pennies is 130.
So,
The total number of coin is:
[tex]140+130=270[/tex]Hence, 270 coins does she have if she has 140 nickels amd 130 pennies.
And,
The total coint that have n nickels and p pennies is:
[tex]n+p[/tex]The asnwer is:
[tex]\begin{gathered} (a)\text{ 270 coins} \\ (b)\text{ n+p coins} \end{gathered}[/tex]Joan invests $200. She earns interest at 3% per annum, compounded monthly.What is the future value of Joan’s investment after 1.5 years?
For this exercise you need to use the following formula:
[tex]FV=PV\mleft(1+r\mright)^n[/tex]Where "FV" is the future value, "PV" is the present value, "r" is the interest rate (in decimal form), and "n" number of periods.
In this case, analyzing the information given in the exercise, you can identify that:
[tex]PV=200[/tex]Remember that a percent can be written in Decimal form by dividing it by 100. Then:
[tex]\frac{3}{100}=0.03[/tex]Since she earns interest at 3% per annum and it is compounded monthly, you can determine that the interest rate per month is:
[tex]r=\frac{0.03}{12}=0.0025[/tex]Knowing that 1 year has 12 months, you know that:
[tex](12)(1.5\text{ }years)=18\text{ }months[/tex]Then:
[tex]n=18[/tex]Therefore, you can substitute all those values into the formula and then evaluate, in order to find the future value of Joan’s investment after 1.5 years:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=(200)(1+0.0025)^{18} \\ FV=(200)(1.0025)^{18} \end{gathered}[/tex][tex]FV\approx209.19[/tex]Hence, the answer is: $209.19 (approximately).
a submarine is situated at 45 feet below sea level and sing 75 ft what is the new position of the submarine?
Given
a submarine is situated at 45 feet below sea level
the submarine sink 75 ft
so, the new position will be = 45 + 75 = 120 feet below
which of the following graphs match the indicated rotation? Point “R” Rotated 90 degrees about the origin.
The rule for a 90° rotation about the origin is:
[tex](x,y)\rightarrow(-y,x)[/tex]then, if we select one of the points of the figure, A(-2,1), and apply the transformation,
[tex]A(-2,1)\rightarrow A^{\prime}(-1,-2)[/tex]do the same for the other three points,
[tex]\begin{gathered} B(3,3)\rightarrow B^{\prime}(-3,3) \\ C(4,0)\rightarrow C^{\prime}(0,4) \end{gathered}[/tex]select the graph with all three points.
Answer:
The correct answer is option 4.
Find slope and y-intercept12x = 2y+1
12x = 2y+1
First, express in slope-intercept form
y= mx +b
Where:
m = slope
b= y -intercept
So, we have to solve for y:
12x=2y+1
-2y= -12x+1
y= (-12x+1)/-2
y = 6x-1/2
So:
Slope = 6
Y-intercept = -1/2 or -0.5 (decimal form)
The measures of the angles of a triangle are 2x, 3x, and 4x. What is the degree measure of the largest angle of the triangle?o 20°o 60°o 80°o 100°
ANSWER
[tex]80\degree[/tex]EXPLANATION
We want to find the measure of the largest angle of the triangle.
The sum of angles in a triangle is 180 degrees. This means that:
[tex]2x+3x+4x=180[/tex]Simplify the equation and solve for x:
[tex]\begin{gathered} 2x+3x+4x=180 \\ 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]The largest angle is 4x. Therefore, the measure of the largest angle is:
[tex]\begin{gathered} 4\cdot20 \\ 80\degree \end{gathered}[/tex]At the ice cream factory you manage you have a rush order for 1200 gallons of wainut fudge ice cream. One machine can produce 100 gallons of ice cream every 80 minutes. If you start production on that machine at 6:00 am, about what time will be production run end end?
Given that the machine takes 80 minutes to produce 100 gallons of ice cream, so the rate of production (r) is given by,
[tex]\begin{gathered} r=\frac{100}{80} \\ r=1.25\text{ gallons/min} \end{gathered}[/tex]So the time required to produce 1200 gallons of the ice cream is calculated as,
[tex]\begin{gathered} t=\frac{1200}{r} \\ t=\frac{1200}{1.25} \\ t=960\text{ min} \end{gathered}[/tex]Thus, 960 minutes are required for producing 1200 gallons of ice cream.
Converting into hours,
[tex]\begin{gathered} 960\text{ minutes=}\frac{960}{60}\text{ hours} \\ 960\text{ minutes=}16\text{ hours} \end{gathered}[/tex]The time 16 hours after 6:00 am will be 22:00 which corresponds to 10:00 pm.
Therefore, the product run will end at 10:00 pm.
given:m<6=m<8b l l cprove:a l l b
1) From the data, we can see that
[tex]\angle6=\angle8[/tex]is given.
2) Next,
[tex]\angle6=\angle7[/tex]since they are alternate angles.
3) By substitution, these means that
[tex]\angle7=\angle8[/tex]4) Finally, a || b since
[tex]\angle7=\angle8[/tex]this is because, angle 7 and angle 8 are corresponding angles.
Corresponding angles are angles that are on the same corner at each intersection. For instance, 2 and 6
4 and 8, 1 and 5, 3 and 7
In our case, 7 and 8 are corresponding angles
Given points J(2,5), A(5,4), and R(4,2), graph AJAR and its reflection image across the given line.Ry-axis
after a reflection across the x-axis:
[tex]\begin{gathered} J\to(x,-y)\to J^{\prime}=(2,-5) \\ A\to(x,-y)\to A^{\prime}=(5,-4) \\ R\to(x,-y)\to R^{\prime}=(4,-2) \end{gathered}[/tex]Can you help me solve this problem I know how to do the others but I can’t really figure this one out
We have an inequality, this inequality is as follows
[tex]4x\ge112[/tex]To solve the inequality we must clear "x" and see what it tells us
[tex]\begin{gathered} x\ge\frac{112}{4} \\ x\ge28 \end{gathered}[/tex]The inequality indicates that "x" belongs to the set of numbers equal to or greater than 28
Of the set of numbers we have, the only ones that meet this condition are numbers 28 and 33
In conclusion, Only options D and F are correct
Evaluate the expression (c^2) + (d^3) for c = 3 and d = 3
ANSWER
36
EXPLANATION
We want to evaluate the expression for when c = 3 and d = 3.
The expression given is:
[tex]c^2+d^3[/tex]To do this, we will simply replace the values of c and d with the values given:
[tex]\begin{gathered} 3^2+3^3 \\ =\text{ 9 + 27} \\ =\text{ 36} \end{gathered}[/tex]That is the answer.
Jane spends $15 each time she travels the toll roads. She started the month with $240 in her toll road account. The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function.
How much money does Jane have left in the account after 8 trips on the toll roads?
(b) How many trips on the toll roads can she take until her account is empty?
$120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
What is Equation?
Two or more expressions with an equal sign is called equation.
Given that Jane spends $15 each time she travels the toll roads..
Jane started the month with $240 in her toll road account.
The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function
A(r)=240-15r.
Now for 8 trips the amount she left is
A(8)=240-15(8)
=240-120
=120
So $120 money does Jane have left in the account after 8 trips on the toll roads.
$240/15
=16.
She has to make 16 trips to make her account empty.
Hence $120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
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-5x + 3 > (-7x) - 12
Solve the inequality
-5x + 3 > (-7x) - 12
We want to move the variables to the left side and the numbers to the right side. The (-7x) can be eliminated from the right side by adding 7x on both sides.
Add 7x to both sides:
-5x + 3 + 7x > -12
We need to move the 3 from the left to the right side. So we subtract 3
Subtract 3 to both sides:
-5x + 7x > -12 - 3
Joining like terms:
2x > -15
Solving:
x > -15/2
The solution is every real number greater than -15/2
In interval notation, it can be written as:
[tex]\mleft(-15/2,+\infty\mright)[/tex]The left parentheses are used because the endpoint is not included in the solution
If the endpoint was included, we'd use a bracket [
solve this please ???
Answer:
I am a little confused because it says the point-slope formula, but then tells you to solve for y and to distribute. Attached , I put the answer in the point slope form, but if they want the equations solves for y, then the answer would be in the slope intercept form. Below the answers are in point slope form, but I will put the answer in slope intercept form here.
1 y = 2x -1
2. y = 1/2x +3
3. y = 2/3x + 4
4. y = -3/4x -7
5.y = -2x + 1
6. y = 1/3x -5
7. y = -5/3x + 7/3
8 y = 3x + 1
Step-by-step explanation:
find the surface area of a square pyramid with side length 3km and slant height 5km
Explanation
the surface area of a square pyramid is given by:
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ \text{where A is the area of the base} \\ p\text{ is the perimeter of the base} \\ s\text{ is the }slant\text{ heigth} \end{gathered}[/tex]so
Step 1
area of the base
the baseis a square, so the area is
[tex]\begin{gathered} Area=side^{^2} \\ Area_{base}=3km\cdot\text{ 3}km \\ Area_{base}=\text{ 9(}km^2) \end{gathered}[/tex]Step 2
perimeter of the base
the perimeter of a square is given by:
[tex]\begin{gathered} \text{Perimeter}=\text{ 4}\cdot side \\ sp \\ \text{Perimeter}=\text{ 4}\cdot3km\text{ =12 }km \\ \text{Perimeter}=12km \end{gathered}[/tex]Step 3
finally, let
[tex]\text{slant heigth=5}km[/tex]now, replace in the formula
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ sa=9(km^2)+\frac{1}{2}(12km)(5km) \\ sa=9(km^2)+30(km^2) \\ sa=39(km^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{ 36 }km^2[/tex]I hope this helps you
Differentiate the equation to find the functions for
Velocity v= ds/dt
Differentiation from First Principles is a formal method for determining a tangent's gradient.
What is meant by differentiation?Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.
According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.
Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.
s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c
substituting the values t = 3, we get
s(-3) = (-cos(-3π))/π + c = 0
simplifying the above equation, we get
(-cos(3π))/π + c = 0
1/π + c = c
c = -1/π
Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.
The complete question is:
Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0
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Suppose Rachel and Nadia buy a house and have to take out a loan for $183500. If they qualify for an APR of 3.75% and choose a 30 year mortgage, we can find their monthly payment by using the PMT formula. If Rachel and Nadia decide to pay $1500 per month, we can use goal seek to see how many years it will take to pay off the loan. Use the PMT function and goal seek (as needed) to answer the following questions about Rachel and Nadia's mortgage. a. What is their monthly payment on the 30 year loan? $ 15 year loan, what will the new monthly payment be?
We have that the PMT formula is given by:
[tex]\text{PMT}=p(\frac{\frac{r}{n}}{1-(1+\frac{r}{n})^{-ny}})[/tex]Where p is the initial principal (Loan ammount), r is the interest rate period, n is the total number of payments or periods, y is the number of years, PMT is the monthly payment.
Now, replacing the data in the formula, we will get:
*The payment will be due for 30 years, that is 12 months each year [That is our n] and y will be 30, r is 0.0375.
p will be $183500, that is:
[tex]\text{PMT}=(183500)(\frac{\frac{0.0375}{12}}{1-(1\pm\frac{0.0375}{12})^{-(12)(30)}})[/tex]Then, we will have that the monthly payment for the 30 years, should be:
[tex]\text{PMT}=849.8171105[/tex]If she wishes to pay $1500 each mothn, we then replace in the formula:
[tex]1500=(183500)(\frac{(\frac{0.0375}{12})}{1-(1+\frac{0.0375}{12})^{-12y}}[/tex]Now, solving for Y, we will have:
[tex]-12y=\frac{\ln(\frac{593}{960})}{\ln(\frac{321}{320})}\Rightarrow y\approx12.86643229[/tex]From this, we have that if they pay a monthly morgage of 1500, they would take 13 years to pay the total cost.
If they wanted to pay the morgage in 15 years, then we replace in the formula as follows:
[tex]\text{PMT}=(183500)(\frac{(\frac{0.0375}{12})}{1-(1\pm\frac{0.03755}{12})^{-12(15)}})[/tex]That is:
[tex]\text{PMT=1334.453182}\Rightarrow PMT\approx1334.45[/tex]They would have to pay $1334.45 each month in order to pay the morgage in 15 years.