Given:
Annual interest rate = r%
Growth factor : x = 1 + r
The below function gives the amount in the account after 4 years when the growth factor is x .
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
To find:
The total amount in the account if the interest rate for the account is 3% each year and initial amount.
Solution:
Rate of interest = 3% = 0.03
Growth factor : x = 1 + 0.03 = 1.03
We have,
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.
[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]
[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609 )+618[/tex]
[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]
[tex]A(1.03)=2431.311498 [/tex]
[tex]A(1.03)\approx 2431.31 [/tex]
Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.
For initial amount the rate of interest is 0.
Growth factor : x = 1 + 0 = 1
Substitute x=0 in the given function to find the initial amount.
[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]
[tex]A(1)=800+350+500+600[/tex]
[tex]A(1)=2250[/tex]
Therefore, 2250 was put into the account at the beginning.
Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. Fr example, if your solution is 12%, you would enter 0.12.
Answer:
0.05
Step-by-step explanation:
we are given the formula
I = Prt, where
I = interest earned = $450
P = Principal amount = $3000
t = time = 3 years
r = rate (we are asked to find this_
Simply substitute the known values into the equation
I = Prt
450 = 3000 x r x 3
450 = 9000r
r = 450/9000
r = 0.05
Answer:
0.05
Step-by-step explanation:
Find the volume of the prism.
6 cm
5 cm
7 cm
5 cm
6 cm
Answer: Possibly, 105 cm³ if it is a triangular prism, or
Possibly 210 cm³ if it is a rectangular prism
Step-by-step explanation: Without knowing exactly what kind of prism it is, it is impossible to give an exact answer.
If the bases are triangles with altitude and and base of 5 and 6, anf the height of the prism is 7, the volume is
(6×5)/2 × 7
30/2 ×7
15 × 7 = 105 cm³ for a triangular prism
If the bases are rectangles with length and and width of 6 and 5, and the height of the prism is 7, the volume is
6×5×7 = 210 cm³ for a rectangular prism
Using compatible numbers to estimate, which expression has a quotient of about 70?
O A. 3, 424 : 49
OB. 5,358 - 89
O C. 6,409 - 79
O D. 5,238 : 89
Answer:
A is the correct answer
Step-by-step explanation:
Hoped this helped :)
Answer: im positive its A me and my class did this at school
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HEEEEEEELLLLLLPPPPPPPP!!!
THIS IS DUUEEEE TTTOOOODDDAAAYYYYY.
Question 1:
-|7-2x|+11= -8
Question 2:
9-7|-x-3|= -61
Question 3:
13|-2x+1|-10=159
Answer:
-|7-2x|+11= -8
x=-6 0r x=13
9-7|-x-3|= -61
x=-13 or x=7
13|-2x+1|-10=159
x=-6 or x=7
Step-by-step explanation:
-|7-2x|+11= -8
-|7-2x|=-8-11
either :
7-2x=-19
-2x=-19-7
x=-26/2
x=13
Or: 7-2x=19
-2x=19-7
-2x=12
x=-12/2
x= - 6
9-7|-x-3|= -619−7(|−x−3|)=−61
−7(|−x−3|)=−61-9
−7(|−x−3|)=−70
|-x-3|=-70/-7
|-x-3|=10
either :
-x-3=10 or -x-3=-10
-x=13 -x=-7
x=-13 x=7
13|-2x+1|-10=15913|-2x+1|=159+10
13|-2x+1|=169
|-2x+1|=169/13
|-2x+1|=13
either or
-2x+1=-13 -2x+1=13
-2x=-14 -2x=12
x=-14/-2 x=12/-2
x=7 x=-6
A water tower holds 26400 gallons of water. The water company can fill the tower at a rate of 20 gallons per minute,
How many hours would it take the water company to all the tower if it is completely empty?
o 22 hours
24 hours
220 hours
0 440 hours
Answer:
22 Hours
Step-by-step explanation:
26400/20 = 1320m
1320m = 22h
22 Hours
2. Describe the process used to solve an equation with variables on both sides.
Answer:
After simplifying, the first step in solving an equation with a variable on both sides is to Get The Variable On One Side. This is done by reversing the addition or subtraction of one of the terms with the variable. In other words, we must add to both sides or subtract from both sides one of the quantities that contains the variable. It is generally easier to add or to subtract the smaller quantity from the larger quantity, so we are working with positive coefficients, but either way works
Model the unknown number situation by writing an algebraic expression.
the difference of a number and one hundred
n-100
100 - n
n + 100
100 +n
Answer:
number 1 or A i got it
Step-by-step explanation:
Answer: The answer you are looking for is A on edge
Step-by-step explanation: Pls Mark me Brainilist! I know that this is for sure Right!
PLEASE HELP WORTH 40 POINTS! ANSWER QUICK PLEASEEE
(a) Does each triangle have the same change in x-values? Explain.
(b) Does each triangle have the same change in y-values? Explain.
(c) Does each triangle have the same ratio of change in y-values over change in x-values? Explain
Answer:
SPLEASE HELP WORTH 40 POINTS! ANSWER QUICK PLEASEEE
(a) Does each triangle have the same change in x-values? Explain.
(b) Does each triangle have the same change in y-values? Explain.
(c) Does each triangle have the same ratio of change in y-values over change in x-values? Explain
tep-by-step explanation:
There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is 5: 7. Is Lonnie correct?
Here are four logos.
Which two logos have more than one line of symmetry?
Answer:
A and C
Step-by-step explanation:
A and C
Thank you
The logos have more than one line of symmetry are Option(c) and Option (1)
What is a line of symmetry?
A line of symmetry is a line that cuts a shape exactly in half. This means that if you were to fold the shape along the line, both halves would match exactly. Equally, if you were to place a mirror along the line, the shape would remain unchanged. A square has 4 lines of symmetry, as shown below.
According to the question
Logos have more than one line of symmetry
are option A and Option C
As in Option A if we cuts the shape exactly in half along lines marked in circle
There half will be same
so , there are 3 lines of symmetry in option A.
Now, In option 4
if we cuts the shape exactly in half along the middle of horizonal and vertical side of square figure
There half will be same
So , there are 2 lines of symmetry in option C.
Hence, The logos have more than one line of symmetry are Option(c) and Option (1) .
To know more about line of symmetry here:
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Find 3 ratios that are equivalent to the given ratio. 6/9
Answer:
2:3
12:18
18:27
Step-by-step explanation:
Answer:
In order to get equivalent ratios, we can just multiply by a factor! Lets use the factors of 2, 3, 4.
So we have:
[tex]2 * \frac{6}{9}=\frac{2*6}{2*9}=\frac{12}{18}[/tex]
As well as:
[tex]3 * \frac{6}{9}=\frac{3*6}{3*9}=\frac{18}{27}[/tex]
And finally:
[tex]4 * \frac{6}{9}=\frac{4*6}{4*9}=\frac{24}{36}[/tex]
In a survey of 600 students 80 percent said they liked pop music.How many students liked pop music
Answer:
600 × .8 = 480
480 Students
Inductive Reasoning
Write the next two numbers in the pattern
400, 200, 100, 50, 25,
Answer:
12.5, 6.25
Step-by-step explanation:
The answer halfs every time
Answer:
Step-by-step explanation:
After 400 ,800,1600
Before 25,12.5,6.25
5+(×-2)=-8 need help with answer
Answer:
x = -11
Step-by-step explanation:
5 + (x - 2) = -8
Subtract 5 from both sides.
x - 2 = -13
Add 2 to both sides.
x = -11
PLEASE ANWSER RIGHT AND U WILL GET BRAINLIEST the fraction 5/4 is an example of an improper fraction a proper fraction or a mixed number
Answer:
It is a proper fraction
Step-by-step explanation:
Juan needs to rent a car for his road trip to Savannah, GA. Juan asks his friends if he knows how much the car rental costs. Nadia says she paid $50 for a two-day car rental. Johanna says she paid $75 for a three-day rental, and Kristine paid $100 for a four-day rental.
Juan made the table below to help him visualize how much his car rental will cost.
Answer:
ok whats the question?
Step-by-step explanation:
i only see the explanation
Draw a histogram for the intervals 2-4, 5-7, 8-10, and 11-13 using the following data: 11,3,13,4,2,2,13,3,6,4,6,11,4,13,7,3,3,3,10,2
A
B
C
D
are you in statistics because I took it and I'm good at it. pet me see if I can figure it out. give me a minute
please help me ASAP :)
c.) 1/2³ i got it right on assignment
Diego is selling raffle tickets for $1.75 per ticket. How many tickets would Diego need to sell to earn $140?
Answer:
Diego would need to sell 80 tickets.
Step-by-step explanation:
Divide 140 by 1.75 to get your answer. To double-check multiply 1.75 by 80, and you should get 140.
Answer:
Diego would sell 80 tickets.
Step-by-step explanation:
Solve for X. 8(x + 2) = 40 Simply your answer as much as possible. = x 6
Answer:
x = 3
Step-by-step explanation:
8(x+2) = 40
8x + 16 = 40
8x = 24
x = 3
County day scholarship fund receives a gift of $130,000 the money is invested in stocks, bonds and CDs. CDs pay 2% interest, bonds pay 2.9% interest, and stocks pay 9.9% interest. country day invests $25000 more in bonds than in CDs. if the annual income from the investment is $8885, how much was invested in each vehicle?
country day invested $______ in stocks.
country day invested $______ in bonds.
country day invested $______ in CDs.
Answer:
$15,000 was invested in CDs.
$40,000 was invested in bonds.
$75,000 was invested in stocks.
Step-by-step explanation:
Let C be the amount invested for CDs, B be the amount invested for bonds, and S be the amount invested for stocks.
We know that the total amount invested must be $130,000 because that was the amount given to the Scholarship Fund. So:
[tex]C+B+S=130000[/tex]
We know that CDs pay 2% or 0.02 interest; Bonds pay 2.9% or 0.029 interest; and Stocks pay 9.9% or 0.099 interest. In total, the investment earned $8,885. So:
[tex]0.02C+0.029B+0.099S=8885[/tex]
Let's remove the decimals by multiplying everything by 1000. This yields:
[tex]20C+29B+99S=8885000[/tex]
Now, we know that $25000 more was invested in bonds than CDs. So:
[tex]B=25000+C[/tex]
We have a triple system of equations. We can solve this using substitution. Let's substitute our third equation into the second equation. This yields:
[tex]20C+29(25000+C)+99S=8885000[/tex]
We want to isolate the C variable. Here, we removed the B but we still have an S.
So, to remove the S, we can go back to our first equation. We have:
[tex]C+B+S=13000[/tex]
Subtract C and B from both sides:
[tex]S=130000-C-B[/tex]
We can now substitute this for S:
[tex]20C+29(25000+C)+99(130000-C-B)=8885000[/tex]
We got a B again. But, we already know what B is. Substitute:
[tex]20C+29(25000+C)+99(130000-C-((25000)+C))=8885000[/tex]
So, our equation is now in terms of C. Solve for C. Distribute on the far right:
[tex]20C+29(25000+C)+99(130000-C-25000-C)=8885000[/tex]
Combine like terms:
[tex]20C+29(25000+C)+99(105000-2C)=8885000[/tex]
Distributive Property:
[tex]20C+725000+29C+10395000-198C=8885000[/tex]
Combine like terms:
[tex](20C+29C-198C)+(725000+10395000)=8885000[/tex]
Add:
[tex]-149C+11120000=8885000[/tex]
Subtract 1112000 from both sides:
[tex]-149C=-2235000[/tex]
Divide both sides by -149:
[tex]C=15000[/tex]
So, a total of $15,000 was invested in CDs.
Since $25,000 more was invested in bonds than in CDs, this means that a total of $25000+$15000 or $40,000 was invested in bonds.
To find out how much was invested in stocks, we can use our first equation again:
[tex]C+B+S=130000[/tex]
Substitute 15000 for C and 40000 for B:
[tex]15000+40000+S=130000[/tex]
Add:
[tex]55000+S=130000[/tex]
Subtract 55000 from both sides:
[tex]S=\$75000[/tex]
So, $15,000 was invested in CDs, $40,000 was invested in bonds, and $75,000 was invested in stocks.
And we're done!
Answer:
$15,000 was invested in CDs.
$40,000 was invested in bonds.
$75,000 was invested in stocks.
Step-by-step explanation:
What is an equation of the line that passes through the points (1, 2) and (2, -1)?
Answer: m = -3
............................
The width of a classroom is 4 meters less than the length, and the area is 192 m^2. If the length is x m, find an equation in x and hence, find the dimensions of the classroom.
Answer:
length-x
width-x-4
area-- length* width
192=X*(X-4)
x^2-4x-192=0
x^2-16x+12x-192=0
X(x-16)+12(x-16)=0
(x-16),(X+12)
X= 16 because X cannot be negative like (-12)
the dimensions of the classroom will be
length = 16
width = 12
I hope this will help everyone
PLS Answer these questions! I have a test!
Answer:
ZDM is not a name for the angle, 6 square units is the area, A the cylindar, 26 degrees
Step-by-step explanation:
Area of triangle is 1/2 base x height
116-90 = 26 degrees to angle ABC
WHAT IS 12X124
PLEASE ANSWER ASAP FIRST TO ANSWER GETS BRAINLY
Answer:
1488 (✿◕‿◕✿)
Step-by-step explanation:
Answer:
1488
step-by-step explanation:
124
12 when multiplied equal 1488
What are the partial products of 73 × 8
The partial products of 73 x 8 is = 584
What is partial product?The partial products algorithm allows students to multiply two long numbers fast and easily by breaking down a more challenging product into a series of simpler problems.
Steps to calculating the partial product for 73 x 8(70 +3 ) * (8)
= 70 x 8 = 560 and ;
= 3 x 8 = 24
Step 2 - Add all the products together
560 + 24 = 584
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If 3t^2 and -4t are multiplied, the product
Is
Answer:
-36
bc my brain say write dis
When estimating you should use what numbers
Odd
Even
Large
Round
Answer:
Round
Step-by-step explanation:
©C a r n e g ie L e a r n in g 6.1 Picture Algebra • 3093. The members of a small town’s local arts council are selling raffle tickets. The art council decides that the top three raffle ticket sellers will share a portion of the profits. The second-place seller will receive twice as much as the third-place seller. The first-place seller will receive $20 more than second-place seller. How much will each of the top three sellers receive if the profit portion they will share is $200?
Answer:
1st - $92
2nd - $72
3ed - $36
Step-by-step explanation:
save 20 dollars for first place, because they are going to get that no matter what.
200 - 20 = 180
we'll need to divide 180 into 5 parts, one for 3ed place, two each for 1st and second.
180 / 5 = 36
3ed place gets $36
2nd gets twice that, $72
1st gets the same as 2nd +$20, so $92
to check our answer, add up all their profit and make sure it's 200 even.
Sandra spent $32 for a purse and buys aCD for $15. Write an expression to represent this problem
Answer:
x - ($32 + $15); or x - $32 + $15
Step-by-step explanation:
Spending on the purse and a CD means less cash then the starting amount, x.
Answer:
$32+ $15=$47
Step-by-step explanation: