Suppose chang places $7000 and an account that pays 2% interest compounded each year. Assume that no withdraws are made from the account.Follow the instructions below. Do not do any rounding
Answers
In general, the compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ n\rightarrow\text{ number of times the interest is applied per period of time \lparen t\rparen} \\ t\rightarrow\text{ years} \end{gathered}[/tex]In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,
[tex]A=7000(1+\frac{0.02}{1})^{1*t}=7000(1.02)^t[/tex]a) Set t=1
[tex]\begin{gathered} t=1 \\ \Rightarrow A(1)=7000(1.02)^t=7140 \\ \end{gathered}[/tex]The answer to part a) is 7140b) Set t=2,
[tex]A(2)=7000(1.02)^2=7282.8[/tex]The answer to part b) is 7282.8Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.
Related Questions
2. A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that
the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
a. What price yields the maximum profit?
b. What is the maximum profit?
Answers
Based on the given function,
a) The price that yields the maximum profit is $20.
b) The maximum profit is $6,050
Function
Function defines the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Given,
A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
Here we need to find the price that yields maximum profit and the amount of maximum profit.
In order to find the price that yield the maximum profit, we have to find the value of t, that can be obtained by using the formula,
t = -b/2a
According to the given function the values of a = -15 and the value of b = 600
Apply these values on the given function then we get,
t = -600/ 2(-15)
t = -600/-30
t = 20
Therefore, the price that yields the maximum profit is $20.
Now, we need to find the maximum profit, by apply the value of t as 20 in the given function then we get,
p = -15(20)² + 600(20) + 50
P = -15(400) + 12000 + 50
p = -6000 + 12000 + 50
p = 6000 + 50
Therefore, the maximum profit is $6,050.
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please help! where it says “select” the options are 1997-2006
Answers
We can find the average rate of change of change using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]for the period betwen 1999 and 2002, we have the following:
[tex]\begin{gathered} m=\frac{1483-1336}{2002-1999}=\frac{147}{3}=49 \\ \Rightarrow m=49 \end{gathered}[/tex]therefore, the average rate of change of population between 1999 and 2000 is 49.
Next, we do the same for the period between 2001 to 2005:
[tex]\begin{gathered} m=\frac{801-1591}{2005-2001}=-\frac{790}{4}=-197.5 \\ \Rightarrow m=-197.5 \end{gathered}[/tex]thus, the average rate of change of population between 2001 and 2005 is 197.5
Finally, notice that the population increased from 1997 to 2001, while it decreased from 2002, to 2006
help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
The ratio of the number of apple trees to the number of lemon trees in a farm is 9:5. There are 45 lemon trees in the farm. How many apple trees are there in the farm?
Answers
5x9=45
9x9=81
you’re welcome
Identify all pairs of congruent corresponding parts.Then write another congruence statement for the polygons.AABC ~ADEF
Answers
1) Congruent parts possess the same length, or measure (if angles).
2) As we can see, by the marks on the angles notation within each triangle we can state the following:
[tex]\begin{gathered} AB\cong ED \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]Note that was possible since we could base ourselves on the measure of those angles.
3) Thus, we can state that these triangles as we can see, fall under the case of:
SSS - Side Side Side Congruence
Given that those three sides are congruent to each other.
What is the solution of the system of equations?
13x-6y=2
3x-4y=-10
(Write as ordered pair)
Answers
Step-by-step explanation:
let's multiply the first equation by 2 and the second equation by -3, and then we add them together :
26x - 12y = 4
-9x +12y = 30
-------------------------
17x 0 = 34
x = 2
and now we use one of the original equations to solve for y :
3×2 - 4y = -10
6 - 4y = -10
-4y = -16
y = 4
the solution is (2, 4).
The population P of Phoenix, Arizona (in thousands) from 1970 through 2000 can be modeled by the equation P = 590e ^ (0.027t) where r represents the year, with t = 0 corresponding to 1970. According to this model, when will the population reach 1.5 million.
Answers
The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
In the question ,
it is given that ,
the equation , modelling the the population P of Phoenix, Arizona (in thousands) from 1970 through 2000 is
P = 590[tex]e^{0.027\times t}[/tex]
where t represents the year corresponding to 1970 .
we need to find the time required for the population to reach 1.5 million.
since population is represented in thousands , so ,
1.5 million = 1500000 will be taken as 1500 .
Substituting P = 1500 in the equation ,
we get ,
1500 = 590[tex]e^{0.027\times t}[/tex]
1500/590 = [tex]e^{0.027\times t}[/tex]
2.5423 = [tex]e^{0.027\times t}[/tex]
taking ㏑ both the sides , we get
㏑(2.5423) = (0.027t)×㏑(e)
0.93306 = 0.027×t
t = 0.93306/0.027
t = 34.55 years
t ≈ 35 years
the year will be 1970 + 35 = 2005 .
Therefore , The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
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9. Charlie has 6 more quarters than dimes in a jar and a total of $9.20. Which system of
equations can be used to determine the number of each type of coin Charlie has if
q= the number of quarters and d = the number of dimes?
A. [q=d+6
10d + 25q = 920
B. [d=q+6
10d + 25q = 920
C. [d+q=6
10d + 25q = 920
D. q=d+920
10d + 25q = 6
Answers
In linear equation the number of dimes 10d + 25q = 920 .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18. A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.if
q= the number of quarters and d = the number of dimes
d = q + 6
10d + 25q = 920
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Gavin has a points card for a movie theater. He receives 20 rewards points just for signing up. He earns 9.5 points for each visit to the movie theater. He needs 77 points for a free movie ticket. Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?
Answers
Explanation:
If he already has 20 to start you subtract 77-20, leaving you with 57 more point to earn. If each visit is worth 9.5 points then you can either do 57/9.5 to give you 6 visits or 9.5 multiplied by 6 which gives you 57 visits, so he ends up with a free movie ticket.
Find the equation of a line perpendicular to y = -3x + 5 that passes through the point (6,7)
Answers
789
Answer:
Step-by-step explanation:
At any time t (in hours), there are 216(t +18) of Type A bacteria in a sample and 362t + 8 of Type B bacteria in a sample. After how many hours will the number of type A bacteria be less than the type B bacteria?
Answers
1. The given situation can be described in the following inequality:
[tex]216^{(t+18)}<36^{(2t+8)}[/tex]2. To solve the prevous inequality, proceedas follow:
write 216 as 6^3 and 36 as 6^2, then, apply log_6 both sides:
[tex]\begin{gathered} 6^{3(t+18)}<6^{2(2t+8)} \\ \log _66^{3(t+18)}<\log _66^{2(2t+8)} \\ 3(t+18)<2(2t+8) \end{gathered}[/tex]then, solve for t, as follow:
[tex]\begin{gathered} 3t+54<4t+16 \\ 3t-4t<16-54 \\ -t<-38 \\ t>38 \end{gathered}[/tex]Hence, from t = 38 hours the number of type A bacteria will be less than the type B bacteria
3. In a number line, you obtain:
what is the volume of the cone? use 3.14 for Pi and round to the nearest hundredth
Answers
The volume of the cone:
[tex]V\text{ = }50.24in^3[/tex]Explanations:The radius of the cone, r = 2 in
The height of the cone, h = 4 in
The volume, V, of a cone is given by the formula:
[tex]V\text{ = }\pi r^2h[/tex]Substituting r = 2, h = 4, and π = 3.14 into the formula for calculating the volume shown above:
[tex]\begin{gathered} V=3.14\text{ }\times2^2\text{ }\times\text{ 4} \\ V\text{ = 3.14 }\times\text{ 4 }\times\text{ 4} \\ V\text{ = }50.24in^3 \end{gathered}[/tex]a random sample of 2 measurements is taken from the following population of values: 1, 2, 4, 5, 8. what is the probability that the range of the sample is 7?
Answers
The probability of the sample required where the range is 7 is 0.1 .
The range of a sample is the difference of the maximum and minimum values.
The range of the sample to be 7, the maximum and minimum values should be 8 and 1.
The outcomes required are (8,1).
The total probability of the sample for 2 measured values:
P=[tex]C_{5,2}[/tex]
P=5!/(2!(5-2)!)
P=5!/(2![tex]\times[/tex]3!)
P=20/2
P=10
The probability of the outcome desired,
=(required outcomes)/(total outcomes)
=1/10
=0.1
The probability of the outcome required is 0.1 .
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I really need help I'll take a picture of the question
Answers
To plot the graph of the function:
[tex]h(x)=8|x+1|-1[/tex]According to your graphing software, we need to find the smallest value of the function, and any point at the positive slope side of the function. Let's start with the minimum point. Let's use the general formula for an absolute value function:
[tex]f(x)=a|x+b|+c[/tex]The coefficients 'b' and 'c' determinates how much the function was translated from the origin. The 'b' determinates in the x-axis, and the 'c' determinates in the y-axis.
If the 'b' is positive, the function translated to the left, if it is negative the function translated to the right.
If the 'c' is positive the function went up, and if it is negative it went down.
Now let's analyze our h(x) function. Our coefficients are:
[tex]\begin{cases}b=1 \\ c=-1\end{cases}[/tex]Which means our minimum point is
[tex](-1,-1)[/tex]Now, we just need to calculate any point to the right of x = -1.
Let's calculate for x = 0.
[tex]h(0)=8|0+1|-1=8-1=7[/tex]The second point is (0,7)
What transformations map the figure onto itself? Select all that apply.
A.
Reflection over line y
B.
Reflection over point P
С.
Rotation 180 degrees
D.
Reflection over line m
E.
Rotation 270 degrees
Answers
Answer:
Step-by-step explanation:
C because its right
find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.
Answers
Remember that
If f is continuous over [a,b] and differentiable over (a,b), then there exists c∈(a,b) such that
[tex]f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}[/tex]In this problem, we have the function
[tex]f(x)=\frac{9}{x^3}[/tex]over the interval [1,3]
so
f(a)=f(1)=9/(1)^3=9
f(b)=f(3)=9/(3)^3=1/3
substitute
[tex]f^{\prime}(c)=\frac{\frac{1}{3}-9}{3-1}=\frac{-\frac{26}{3}}{2}=-\frac{26}{6}=-\frac{13}{3}[/tex]Find out the first derivative f'(x)
[tex]f^{\prime}(x)=-\frac{27}{x^4}[/tex]Equate the first derivative to -13/3
[tex]\begin{gathered} -\frac{27}{x^4}=-\frac{13}{3} \\ \\ x^4=\frac{27*3}{13} \\ \\ x=1.58 \end{gathered}[/tex]therefore
The value of c is 1.58 (rounded to two decimal places)Samuel has 10 coins that add up to $3.80. Some are 50 cent and the rest are 20 cent coins. How many 50 cent coins does he have?
Answers
Answer:
6 coins of 50cent
Step-by-step explanation:
Information we have:
1. x number of 50cent and y number of 20cent added up to 380cent.
2. x and y is 10coins
eq1 : 50x + 20y = 380
eq2: x + y = 10
write eq2 to y in term of x
y = 10 - x -> eq3
replace eq3 into eq1
50x + 20(10 - x) = 380
50x + 200 - 20x = 380
50x -20x = 380 -200
30x = 180
x = 180/30 = 6
Solve the equation 7x = 91 for x.
−98
84
−13
13
Answers
Your answer will be D 13
Learning Diagnostic Analytics Math Skill plans Recommendations Fifth grade > Z.11 Parts of a circle Q7N The radius of a circle is 12 feet. What is the circle's diameter? feet Submit
Answers
Given:
The radius of the circle = 12 feet
The circle diameter = two times of the radius
so, the diameter = 2 * 12 = 24 feet
So, the answer is 24 feet
What is -2(-x+5y-4) (simplify equation)
Answers
Using the distributed property, the simplified form of -2(-x+5y-4) is 2x-10y+8.
In the equation question,
The given expression is -2(-x+5y-4).
We have to simplify the given expression.
We simplify the given expression using the distributed method.
In the distributed method we have to multiply the number outside the bracket to all the terms that are inside the bracket.
As a(b+c) = ab+bc
In the given question there is -2 outside the bracket and -x+5y-4 is inside the bracket.
To simplify the given expression we multiply -2 to each term inside the bracket.
-2(-x+5y-4) = (-2)×(-x)+(-2)×5y-(-2)×4
Simplifying
-2(-x+5y-4) = 2x+(-10)y-(-8)
Simplifying the bracket
-2(-x+5y-4) = 2x-10y+8
Hence, the simplified form of -2(-x+5y-4) is 2x-10y+8.
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Which of the following expressions is equivalent to the one shown below?(-5.4)How do I solve this and what’s the answer ?
Answers
Option B
Using the law of indices
[tex]undefined[/tex]10 less than 7 times a number is the same as 3 times the number plus 18
Answers
Answer:
yes, it is the same
Step-by-step explanation:
7x - 10 = 3x + 18
7x-10+10 = 3x + 18 + 10
7x = 3x + 28
7x - 3x = 3x - 3x + 28
4x = 28
4x ÷ 4 = 28 ÷ 4
x=7
Plug x back in and check the answer.
7x-10 = 3x+18
7(7)-10 = 3(7)+18
49-10 = 21+18
39 = 39
So, YES they are the same.
After Batman brought the Joker to justice, the crime rate in Arkham City decreased by 12\%12%12, percent. Previously, the crime rate was ccc incidents per 100010001000 people.
Answers
0.88 is the new crime rate in Arkham City.
What is crime rate?The number of offenses reported to law enforcement authorities per 100,000 people in a population is referred to as the crime rate. By dividing the total number of reported offenses by the population, the crime rate is determined.
Given,
The crime rate in Arkham City decreased by 12% when Batman managed to capture the Joker.
In the past, there were c occurrences of crime per 1000 persons.
How can one create an expression that models the issue?
A drop in the percent of crime is subtracted from the prior crime rate, which was defined as incidences per 1000 persons.
c the number of recent crimes per 1,000 individuals;
New crime rate = previous crime rate - decrease in crime %.
New crime rate = c - 12%c
New crime rate = c - 0.12c
New crime rate = 0.88c
Hence, the new crime rate is 0.88c.
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The complete question is:
"After batman brought the joker to justice , the crime rate in arkham city decreased by 12%. Previously the crime rate was c incidents per 1000 people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?
a. 22/25 c
b. 0.12c
c. -0.12
d. 0.88c
e. c/1.12"
Mr. Kilgore made a pot of gumbo with 72 ounces of okra and 2 lbs of shrimp. He made another pot
of gumbo with the same amount of okra, but three times as many lbs of shrimp. How many ounces
of okra did he use per lb of shrimp in the second pot of gumbo
Answers
Answer:
12
Step-by-step explanation:
72 / 2 =36
36 / 3 = 12
12, 24, 36, 48, 60, 72.
Simplify each expression. (–5x2y)(3x4)a. 15x6yb. –15x2yc. –15x6yd. –15x8y
Answers
The given expression is
[tex](-5x^2y)(3x^4)[/tex]We will multiply at first -5 by 3
[tex]-5\times3=-15[/tex]Then we will multiply x^2 by x^4 by adding their powers
[tex]x^2\times x^4=x^{2+4}=x^6^{}[/tex]And multiply y by 1 as there is no y in the second bracket, then
[tex](-5x^2y)(3x^4)=-15x^6y[/tex]The answer is C
Julia ran 1,000 meters in 9 minutes. How many meters/minute did she run?
Answers
Answer:
111.11111111111111111
Step-by-step explanation:
if dyllan makes 7 out of 10 free throws on any given day what is the probability he will make his next free throw? ( write your answers as a precent.)
Answers
Answer:
70%
Explanation:
The probability can be calculated as the number of free throws that Dylan makes divided by the total number of free throws.
So, if Dylan makes 7 out of 10 free throws, the probability can be calculated as:
[tex]P=\frac{7}{10}=0.7[/tex]Then, to know the probability as a percent, we need to multiply 0.7 by 100% to get:
P = 0.7 x 100% = 70%
Therefore, the answer is 70%
What is 3 to the 9th power times 3 to the 5th power
Answers
Answer:
3^14
Step-by-step explanation:
Multiplication of two values with same base and different exponent:
When we are multiplicating two values with the same base and different exponents, we keep the base and add the exponents. For example:
[tex]x^a\ast x^b=x^{a+b}[/tex]In this question:
[tex]3^9\ast3^5=3^{9+5}=3^{14}[/tex]A population numbers 11,000 organisms initially and decreases by 9% each year.
Answers
Answer:
Step-by-step explanation:
11000*0.91=10010
10010*0.91=9109.1(approximately 9109)
keep going until you find the year you want
2. An account is opened with $28000 earning12% interest compounded yearly. What is thebalance in the account after 4 years?
Answers
The principal is $28000 with rate 12% compounded yearly .
To determine the balance after 4 years,
[tex]SI=\frac{P\times R\times T}{100}[/tex][tex]SI=\frac{28000\times12\times4}{100}[/tex][tex]SI=13440[/tex]The balance in the account after 4 years is the sum of principal and simple interest.
[tex]A=\text{ 28000}+13440[/tex][tex]A=41440[/tex]Thus, the balance in the account after 4 years is 41440 dollar.