Jenny borrowed $8000 at a rate of 9%, compounded semiannually. Assuming she makes no payments, how much will she owe after 10Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
SOLUTION
We will use the formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where\text{ } \\ A=amount\text{ after 10 years = ?} \\ P=money\text{ borrowed = \$8,000} \\ r=9\%=\frac{9}{100}=0.09 \\ t=time\text{ in years = 10} \\ n=compounding=semi-annualy=2 \end{gathered}[/tex]plugging in, we have
[tex]\begin{gathered} A=8,000(1+\frac{0.09}{2})^{2\times10} \\ A=8,000(1.045)^{20} \\ A=8,000\times2.4117140 \\ A=19,293.7121986 \end{gathered}[/tex]Hence the answer is $19,293.71
Related Questions
what is P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors.
Answers
So we have to write the following polynomial expression as a product of two factors:
[tex]P(x)=2x^3+5x^2+5x+6[/tex]In order to do this we should find one of its roots first i.e. a x value that makes P(x)=0. If we use r to label this root we can write P like:
[tex]P(x)=(x-r)\cdot(ax^2+bx+c)[/tex]Where a, b and c are numbers that we can find using Ruffini's rule. So first of all let's find a root. We can use the rational root theorem. It states that if P(x) has rational roots then they are given by the quotient between a factor of the constant term (i.e. the number not multplied by powers of x) and a factor of the leading coefficient (i.e. the number multiplying the biggest power of x). In this case we have to look for the factors of 6 and 2 respectively. Their factors are:
[tex]\begin{gathered} 6\colon6,-6,3,-3,2,-2,1,-1 \\ 2\colon2,-2,1,-1 \end{gathered}[/tex]And the quotients and possible values for r are:
[tex]6,-6,3,-3,2,-2,\frac{3}{2},-\frac{3}{2},1,-1,\frac{1}{2},-\frac{1}{2}[/tex]So one of these numbers make P(x) equal to zero. For example if we take x=-2 we get:
[tex]\begin{gathered} P(-2)=2\cdot(-2)^3+5\cdot(-2)^2+5\cdot(-2)+6 \\ P(-2)=-16+20-10+6=0 \end{gathered}[/tex]So -2 is a root of P(x) which means that we can take r=-2.
Now we can use Ruffini's law. On the first row we write the coefficients of P(x). Then the first one is repeated in the third row:
Now we multiply 2 by -2 and we write the result under the second coefficient. Then we add them:
Now we do the same with the 1:
And then we multiply 3 and -2 and add the result ot the last coefficient:
The numbers 2, 1 and 3 are the values of a,b and c respectively. Then we can write P(x) as a product of two factors and the answer is:
[tex]P(x)=(x+2)(2x^2+x+3)[/tex]The boats rate is ____ mph(Type an integer or decimal)
Answers
Let
x ----> rate of the boat in still water (mph)
y ---> rate of the current (mph)
Remember that
The speed is equal to dividing distance by the time
speed=d/t
d=speed*time
so
Upstream
speed=x-y
time=5 hours
100=(x-y)*5
x-y=20 --------> equation 1
Downstream
speed=x+y
time=4.5 h
100=(x+y)*4.5
x+y= 100/4.5 --------> equation 2
Adds equation 1 and equation 2
x-y=20
x+y= 100/4.5
-----------------
2x=20+(100/4.5)
2x=190/4.5
x=190/9
x=21.11 mph
therefore
The answer is 21.11 mphFind f.Write your answer in simplest radical form. ___ units
Answers
Answer:
The value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]Explanation:
Given the triangle in the attached image.
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]from the given figure;
[tex]\begin{gathered} \theta=30^{\circ} \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} \tan 30=\frac{f}{3\sqrt[]{6}} \\ f=3\sqrt[]{6}\tan 30 \\ f=3\sqrt[]{6}(\frac{\sqrt[]{3}}{3}) \\ f=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]√121 = ?
i need help
Answers
Answer:
11 and -11. Usually you only want the positive form
Step-by-step explanation:
[tex]\sqrt{121}[/tex] is asking what number times itself is 121? 11
11 x 11 = 121
-11 x -11 = 121
What’s the answer?? Just a part of a homework practice
Answers
The functions are
[tex]h(x)=0.42x^2+0.3x+4\text{ and }r(x)=-0.005x^2-0.2x+7[/tex]Multiply both functions s follows.
[tex]h(x)\times r(x)=(0.42x^2+0.3x+4)\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2-0.2x+7)+0.3x\times(-0.005x^2-0.2x+7)+4\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2)+0.42x^2\times(-0.2x)+0.42x^2\times7+0.3x\times(-0.005x^2)+0.3x\times(-0.2x)+0.3x\times7+4\times(-0.005x^2)+4\times(-0.2x)+4\times7)[/tex][tex]=-0.0021x^4-0.084x^3+2.94x^2-0.0015x^3-0.06x^2+2.1x-0.02x^2-0.8x+28[/tex][tex]=-0.0021x^4-0.084x^3-0.0015x^3+2.94x^2-0.06x^2-0.02x^2+2.1x-0.8x+28[/tex][tex]=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the required product is
[tex]q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the first option is correct.
From the diagram below, if side AB is 36 cm., side DE would be ______.
Answers
Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
Sales tax in South Carolina is 5%. Mr. Smith bought a new car there for $18,700. What did he pay in sales tax?
Answers
Answer: $935
Step-by-step explanation:
Mr. Smith paid $935 in sales tax
keith lives 5/6 mile north of the school Karen lives 2/3 Mile North of the school what is the distance from Keith's house to Karen's house?
Answers
The distance from Keith's house to Karen's house is
= 5/6 - 2/3
= 5/6 - 4/6
= 1/6 miles
Chase and his brother want to improve their personal information for when they startapplying to colleges of their choice. To accomplish this they decide to help the SalvationArmy with delivering hot meals to senior citizens. About a month ago, they decided tokeep track of how many successful deliveries they have each completed. As of today,Chase has successfully delivered 18 out of the 30 meals to senior citizens.Part AHow many more meals would Chase have to deliver in a row in order to have a 75%successful delivery record? Justify your answer.Part BHow many more meals would Chase have to deliver in a row in order to have a 90%successful delivery record? Justify your answer.PartAfter successfully delivering 18 out of 30 meals would Chase ever be able to reach a100% successful delivery record? Explain why or why not.
Answers
Part A.
Chase has successfully delivered 18 out of the 30 meals to senior citizens.
We have to calculate how many more meals (lets call it x) she has to deliver to have a 75% successful delivery record.
In order to do that, (18+x) meals have te be delivered successfully out of (30+x), and the successful meals (18+x) divided by (30+x) has to be 0.75:
[tex]\begin{gathered} \frac{18+x}{30+x}=0.75 \\ 18+x=0.75(30+x) \\ 18+x=22.5+0.75x \\ x-0.75x=22.5-18 \\ 0.25x=4.5 \\ x=\frac{4.5}{0.25} \\ x=18 \end{gathered}[/tex]Chase has to deliver 18 more meals successfully in order to have a 75% success delivery record.
Part B.
We apply the same analysis but we replace 0.75 with 0.9 as the delivery record.
[tex]\begin{gathered} \frac{18+x}{30+x}=0.9 \\ 18+x=0.9(30+x) \\ 18+x=27+0.9x \\ (1-0.9)x=27-18 \\ 0.1x=9 \\ x=\frac{9}{0.1} \\ x=90 \end{gathered}[/tex]Chase has to deliver 90 more meals successfully in order to have a 90% success delivery record.
Part C.
She won't be able to achieve 100% successful delivery record. We can prove it mathematically, but we already know as there are 12 meals that weren't successfully delivered, so we can get close to 100% but it can't never be reached.
Mathematically we have:
[tex]\begin{gathered} \frac{18+x}{30+x}=1 \\ 18+x=30+x \\ x-x=30-18 \\ 0=12 \end{gathered}[/tex]This solution is not valid, so there is no valid solution for x.
How do you find the range in a graph like this?
Answers
Answer
y can take on any real number value except around 1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Explanation
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
From the graph attached to this question, we can see that the function has different forms at different values of x.
But it is also evident that y can take on any real number value except around
1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Hope this Helps!!!
Helen has a box of marbles. 1/2 of the marbles are yellow. 1/8 of the
marbles are red. The rest of the marbles are blue. Helen pulls one marble
out of the box at random, records its color, replaces it, and mixes up the
marbles again. If she does this 400 times, how many blue marbles should
she expect to pull out?
Answers
Answer:
150 blue marbles
Step-by-step explanation:
Hello!
If 1/2 of the marbles are yellow, and 1/8 of the marbles are red, then 3/8 of the marbles should be blue.
The percentages are as given:
Yellow = 50%Red = 12.5%Blue = 37.5%To calculate the possible number of blue marbles out of the 400 marbles, we can find 37.5% of 400, as there is a 37.5% chance of getting blue for each turn.
Calculate37.5% of 4000.375 * 400150Helen should expect to pick out 150 blue marbles.
1+1=? Need Help! Asap
Answers
By definition, Addition is a mathematical operation.
In this case, you have the following Addition given in the exercise:
[tex]1+1[/tex]In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?A. 0.3040B. 0.4060C. 0.5060D. 0.2060
Answers
Given:
Number of boys=10
Number of girls=12
Out of 22 members, 4 members is need to be selected.
To find probability to form a committee consisting of 2 boys and 2 girls:
So, we get
[tex]\begin{gathered} \frac{^{10}C_2\times^{12}C_2}{^{22}C_4}=\frac{\frac{10\times9}{2\times1}\times\frac{12\times11}{2\times1}}{\frac{22\times21\times20\times19}{4\times3\times2\times1}} \\ =\frac{5\times9\times6\times11}{11\times7\times5\times19} \\ =\frac{9\times6}{7\times19} \\ =\frac{54}{133} \\ =0.4060 \end{gathered}[/tex]Hence, the correct option is B.
Assume the random variablex is normally distributed with mean p=85 and standard deviation o=5. Find the indicated probabiliP73
Answers
Remember that
z =(x - μ)/σ
we have
μ=85
σ=5
For x=73
Find out the value of Z1
z1=(73-85)/5
z1=-2.4
For x=76
Find out the value of Z2
z2=(76-85)/5
z2=-1.8
using a z-scores table values
we have that
P(73Find the volume of the composite figure.First, find the volume of the cylinder.Use 3.14 for it.CylinderVolume = [?] cm9 cm9 cmCube6 cmVolume = [ ]cm4 cmTotal Volume ofComposite Figure = [] cm3=9 cm
Answers
Solution
- The question gives us a composite figure made up of a cylinder and a cube.
- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.
- The formulas needed for this calculation are:
[tex]\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\ \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\ \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\ \end{gathered}[/tex]- With the information above, we can proceed to solve the question
Volume of the Cylinder:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{ \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\ \\ \therefore V=\pi\times3^2\times4 \\ \\ V=36\pi cm^3 \end{gathered}[/tex]Volume of Cube:
[tex]\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}[/tex]Volume of Composite Figure:
[tex]\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\ \\ V=36\left(3.14\right)+729 \\ \\ V=842.04cm^3 \end{gathered}[/tex]Final Answer
The volume of the composite shape is 842.04 cm³
use a power reducing formula to to simplify 20cos^4x
Answers
We can replace trigonometric terms in formulas with trigonometric terms of smaller powers using the trigonometric power reduction identities. This is significant for using calculus to integrate the powers of trigonometric expressions, among other applications.
Explain about the power reducing?2cos2 will be equal to 1 plus cos 2. We arrive at an equation for cos2 by dividing by 2. Because they enable us to reduce the power on one of the trig functions when the power is an even integer, these are commonly referred to as "power reduction formulae."
An integral problem can be solved using a reduction formula by first breaking it down into simpler integral problems, which can then be broken down into simpler problems, and so on.
P = E/t is the equation, where P stands for power, E for energy, and t for time in seconds. According to this equation, power is defined as the amount of energy consumed per unit of time.
The Equivalent expression for Cos 4x= 8cos4(x) - 8 cos2(x) + 1.
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Need help !! Geometry unit 3 parallel and perpendicular lines
Answers
ANSWER;
Converse; Exterior alternate angles are equal
[tex]x\text{ = 3}[/tex]EXPLANATION;
Here, we want to get the value of x given that the lines l and m are parallel
From the diagram given, we can see that;
[tex]15x\text{ +29 = 26x-4}[/tex]The reason for this is that they are a pair of exterior alternate angles
Mathematically, exterior alternate angles are equal
From here, we can proceed to solve for the value of x;
[tex]\begin{gathered} 26x-15x\text{ = 29+4} \\ 11x=33 \\ x\text{ = }\frac{33}{11} \\ x\text{ = 3} \end{gathered}[/tex]0.2x + 0.21x - 0.04 = 8.16Solve for "x".
Answers
Given the folllowing equation:
[tex]0.2x+0.21x-0.04=8.16[/tex]You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:
[tex]\begin{gathered} 0.2x+0.21x-0.04+(0.04)=8.16+(0.04) \\ 0.2x+0.21x=8.2 \end{gathered}[/tex]2. Now you need to add the like terms on the left side of the equation:
[tex]0.41x=8.2[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:
[tex]\begin{gathered} \frac{0.41x}{0.41}=\frac{8.2}{0.41} \\ \\ x=20 \end{gathered}[/tex]The answer is:
[tex]x=20[/tex]Elana has 80 unit squares. What is the volume of the largest cube she can build with them? Need to show work to explain to my son, having a hard time with this.
Answers
Answer: The largest cube has volume of 64 cubic units, and the sides are 4 units long.
Step-by-step explanation:
Elena has 80 unit cubes and she has to build the largest cube using the unit cubes she has
Unit cube has a dimension of 1 unit on each side (Cube has all sides equal)
To make the largest cube, she needs to calculate the maximum volume which is near 80 units of cubes
Therefore,
We have a cube with each side 4 units whose volume is 64 and a cube with each side 5 units whose volume is 125
Elena has only 80 unit cubes to build the maximum-sized cube
Therefore she will be able to build a cube with each side as 4 units with a volume of 64 units with 16 spare cubes
You use substitution to solve a system of equations and after simplifying end with a statement that says 7=7 discrible what this statement means about the number of solutions and about the graph of the system
Answers
Hence there are infinite solutions and the graphs of the system are concurrent.
If the system used straight lines then they would be on top of each other.
The number of inequality’s and signs can be changed by the way
Answers
Linear Optimization
It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.
We'll use the graphic method to solve the problem.
The problem is as follows:
Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.
The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:
x + y ≤ 130 (1)
She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:
3.75x + 6y ≥ 600
Multiply this inequality by 4:
15x + 24y ≥ 2400
And divide it by 3:
5x + 8y ≥ 800 (2)
We are given a final condition that she can sell a minimum of 80 burritos, thus:
y ≥ 80 (3)
There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:
x ≥ 0 (4)
y ≥ 0 (5)
Let's put this all together:
x + y ≤ 130 (1)
5x + 8y ≥ 800 (2)
y ≥ 80 (3)
x ≥ 0 (4)
y ≥ 0 (5)
The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).
We need to graph all five lines in one common grid. It's shown below.
According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos
Teresa surveyed 100 students about whether they like pop music or country music. Outof the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both popandcountry, and 9 do not like either pop or country. Complete the two-way frequency table.
Answers
SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Total number of student surveyed=100} \\ \text{like pop only=42} \\ \text{like country only=34} \end{gathered}[/tex][tex]\begin{gathered} \text{like both pop and country=15} \\ Do\text{ not like any =9} \end{gathered}[/tex]Construct the two- way frequency table
It takes Evelyn, traveling at 36 mph, 20 minutes longer to go a certain distance than it takes Sarah traveling at 60 mph. Find the distance
traveled.
Answers
The distance travelled by both Evelyn and Sarah is 30 miles.
Given,
The speed travelled by Evelyn = 30 mph
Time taken by Evelyn to cover a distance = 20 minutes
Speed travelled by Sarah = 60 mph
We have to find the distance travelled by both of them.
Speed = distance / time
Then,
Distance = speed x time
Lets take x as the distance.
Then,
36 × (x + 20) = 60x
36x + 720 = 60x
60x - 36x = 720
24x = 720
x = 720/24
x = 30
That is,
The distance travelled by both Evelyn and Sarah is 30 miles.
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!!PLEASE ANSWER FAST PLEASE!! Given f(x)=(1/4)(5-x)² what is the value of f(11)
Answers
Answer:
f(11) = 9
Explanation:
The equation for f(x) is:
[tex]f(x)=\frac{1}{4}(5-x)^2[/tex]To know the value of f(11), we need to replace x by 11 and solve, so:
[tex]\begin{gathered} f(11)=\frac{1}{4}(5-11)^2 \\ f(11)=\frac{1}{4}(-6)^2 \\ f(11)=\frac{1}{4}(36) \\ f(11)=9 \end{gathered}[/tex]Therefore, the value of f(11) is 9.
Given the formula for the perimeter of a rectangle, p=2l+2wwhich answer would you get if you solve for l? p−2w 2 p/w-2 p/2−2w p−2l/2
Answers
If we have:
[tex]p=2w+2l[/tex]To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:
[tex]\begin{gathered} p=2w+2l \\ 2w+2l=p \\ 2w-2w+2l=p-2w \\ 2l=p-2w \end{gathered}[/tex]Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:
[tex]\begin{gathered} 2l=p-2w \\ \frac{2l}{2}=\frac{p-2w}{2} \\ l=\frac{p-2w}{2} \end{gathered}[/tex]So, the answer we would get is
[tex]\frac{p-2w}{2}[/tex]The following relation defines y as a one-to-one function of x x y3.0 7.45-8.4 -8.072.4 -9.16-1.5 7.45TrueFalse
Answers
One-to-one functions are the ones that each value of "y" is related to only one value of "x". So we need to check in the provided values if that applies.
We have a group of 4 different values of "y". For these the value y = 7.45 is related to the x values of 3 and -1.5, therefore it is not a one-to-one function.
Simplify this fraction: 30/36
Answers
To simplify this fraction, we will have to find the common factors of both the numerator and denominator, then divide.
Common factors of 30 and 36 are: 2, 3, and 6
Now both numerator and denominator by the highest common factor which is 6:
[tex]\frac{30}{36}\text{ = }\frac{5}{6}[/tex]
After simplifying the fraction, we have:
[tex]\frac{5}{6}[/tex]Given that the shape below is a rectangle, we know that the diagonals, lines AD and CB, are ____.
Answers
The given information is the shape is a rectangle.
About the diagonals of rectangles, there are two known properties:
- The diagonals of a rectangle bisect each other
- Both diagonals have the same length
Then, the answer is option C. They have the same length
The adult skeleton consist of 206 Bones in the school and 30 bones in the arm and legs. Out of the 28th skull bones, 14 are facial bones. Six or ear bones and eight are cardinal bones. How many more bones are there in the arm and legs than in the faceA) 2B) 6C) 14D) 16
Answers
We need to compare the number of bones in the arms and legs with the number of bones in the face.
The question says that there are 30 bones in the arms and legs.
The question also says that there are 14 bones on the face.
So, the difference between these will be how many more bones there are in the arms and legs than in the face:
[tex]30-14=16[/tex]X) *11.4.14 Find the volume of the cylinder in terms of it and to the nearest tenth. 2 in 1 in The volume in terms of it is V= in3
Answers
We can calculate the volume of the cylinder as the product of the area of the base and the height of the cylinder.
[tex]V=A_b\cdot h[/tex]The area of the base is equal to:
[tex]A_b=\pi r^2=\pi\cdot2^2=4\pi[/tex]Then, the volume becomes:
[tex]V=A_b\cdot h=4\pi\cdot1=4\pi\approx12.6\text{ in}^3[/tex]Answer:
The volume in function of π is V = 4π in^3.
The volume rounded to the nearest tenth is 12.6 in^3.
