Answer:
Multiply each side by −5, add 25 to each side.
Step-by-step explanation:
12. After 80 years of 5.8% interest compounded monthly, an account has $102,393.44. What was the
original deposit amount?
Answer:
12195508,42
Step-by-step explanation:
A(1-R) NA is the depositR is the % presentN is the time period (exponent)A(1-5.8%)80=102,393.44An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
What is meant by deposit?A deposit is money held at a bank. A deposit is a monetary transaction in which money is transferred to another party for safekeeping.A deposit is money placed in a bank account. Deposits are classified into two types: demand deposits and time deposits. Checking, savings, and money market accounts are all examples of demand deposit accounts. Certificates of deposit (CD) and individual retirement accounts are examples of time deposit accounts.Therefore,
Assume that each year has 52 weeks: then compounding occurs.
n = 52 × 80n
times and the rate for each compounding is
[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]
If the original deposit amount is
PV
then the future value
FV
is equal to
[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]
We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:
[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]
The simplest way to compute this is to use a calculator:
[tex]$P V \approx \$ 991.45 .$$[/tex]
We can simplify this expression with great precision just for fun. It is well known that
[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]
which easily implies that
[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]
Here,
[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]
That is, [tex]P V \approx F V e^{-4.64}$.[/tex]
Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
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Raven can walk 2 2/5 miles in 3/5 hour. At this rate, how far can she walk in 1 hour? You might want to change 2 2/5 to an improper fraction in order to make the math easier for you to do.
The distance traveled by Raven in 1 hour at the given rate is 4.0 miles.
The given parameters:
Distance traveled by Raven = 2 2/5 milesTime of motion, t = 3/5 hourThe speed of Raven motion is calculated as follows;
[tex]V = \frac{Distance}{Time} \\\\V = Distance\ \times \ \frac{1}{Time} \\\\V = 2\frac{2}{5} \ miles \ \ \times \ \ \frac{1}{3/5 \ hr} \\\\V = \frac{12}{5} \ miles \ \ \times \ \ \frac{5}{3 hr} \\\\V = 4 \ mph[/tex]
The distance traveled by Raven in 1 hour at the given rate is calculated as follows;
[tex]D = 4 \times 1\\\\D = 4 \ miles[/tex]
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The population of a slowly growing bacterial colony after t hours is given by
p(t) = 4t² + 27t + 150. Find the growth rate after 2 hours.
bacteria/hour
Submit Question
A function is an expression that defines a relationship between an independent variable and a dependent variable.
The number of bacteria colonies after 2 hours is 220.
What is a function?It is an expression that defines a relationship between an independent variable and a dependent variable.
We have,
P(t) = 4t² + 27t + 150
Where t = time
P(t) = population of a slowly growing bacteria colony after a particular time
The growth rate after 2 hours:
P(2) = 4 x (2)² + 27 x 2 + 150
P (2) = 16 + 54 + 150
P (2) = 220
Thus the number of bacteria colonies after 2 hours is 220.
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Find the area of the equilateral triangle.
Answer:
try 6.93 for answer on equilqteral triangle
(a) The area of a rectangular parking lot is 7050 m².
If the length of the parking lot is 94 m, what is its width?
(b) The perimetel of a rectangular pool is 356 m.
If the width of the pool is 82 m, what is its length?
Length of the pool: Im
Answer:
75 m, 96 m
Step-by-step explanation:
a. Area = length x width
7050 = 94 x width
7050/94 = w
75 m is width
b. perimeter = 2L + 2W
356 = 2L + 2(82)
356 = 2L + 164
192 = 2L
96 m = L
1. If you roll two fair dice, what is the probability that the sum of both rolls is 8?
Answer:
1/4
Step-by-step explanation:
Sample space = 12
Prob of sum = 8 is:
[2,6], [3,5]. [4,4]
That is 3/12 = 1/4
Prove that
sin 75-sin 15=cos 105+cos 15
Answer:
Step-by-step explanation
RHS = cos 105° + cos 15°
= cos (90° + 15°) + cos (90° – 75°)
= – sin 15° + sin 75°
= sin 75° – sin 15°
= LHS
Answer:
Step-by-step explanation:
sin75-sin15
=sin (90-15)-(-cos (90+15))
=cos 15+cos 105
The amount of money charged to borrow money, expressed as a percentage,
is called the
A. collateral
B. interest rate
O C. principal
D. loan term
Answer:
Interest rate
Step-by-step explanation:
The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.
The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm
The Formula of the relation is M = 8AT.
The mass of the metal sheet is 960 g.
The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).
Proportionality:
M ∝ ATRemoving the proportionality sign,
M = KATWhere:
K = constant of proportionality.make K the subject of the equation:
K = M/KT.................... Equation 1From the question,
Given:
M = 200 gA = 250 cm²T = 1 mm = 0.1 cmSusbtitute into equation 1
K = 200/(250×0.1)K = 8 g/cm³Formula:
M = 8AT................. equation 2Hence the formula of the relation is M = 8AT
If,
A = 400 cm²T = 3 mm = 0.3Substitute these values into equation 2
M = 8(400)(0.3)M = 960 gHence, the mass of the metal sheet is 960 g
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Please help!!!!!!!!!!!!!!
Answer:
The answer is A.
Step-by-step explanation:
1 plus 2x (276-5y) + 69= A.
Can someone please explain step by step on how I subtract fractions like for an a example!
7/8 - 3/8 ?
Keep the denominators the same and subtract the numerators. So for example in your example:
7/8 - 3/8
Leave the 8 alone. Subtract 3 from 7.
7 - 3 = 4
So answer is:
4/8
Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2
plz help me to answer
Answer:
H=2 r=1
Step-by-step explanation:
P= 2h+4r + πr = π+8
h= π+8- πr -4r/2
(pls give brainliest if helps!)
A car traveled 133 miles in 4 3/4 hours. What was the cars average speed in miles per hour?
4 3/4 = 19/4
133/(19/4) = 133(4/19) = 1197/19 = 63 mph
A projectile is thrown upward so that its distance above the ground after t seconds is h = -156 + 510t. What is its maximum height?
For the parabola:
h(t) = -at2 + bt, the maximum occurs at -b/2a
For h(t) = -16t2 + 576t that is -576/(-2)(-16), or -576/32, or 18.
The projectile is at its highest point at 18 seconds.
Suppose that sin a= 15/17 and 90 degrees
Carson bought 50 pounds of rice for his restaurant. He cooked the rice and wanted to evenly divide it into 9 containers to be served later. How many pounds of rice should Carson put in each container?
help plss
Answer:
Step-by-step explanation: there you go
help please
No links
Answer:
62-0.75x8
Step-by-step explanation
$6=discount
8 tickets
Total=62.00
0.75 multiplied by 8= 6
62-6=56
56 is before the discount
Equation would be 62-0.75x8
Choose the fraction that goes in the blank. 5/12< _____<3/4
Answer:
7/12 or 8/12 are both good options
Step-by-step explanation:
nvr mind, its 7/12 only
The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?
Answer:
Hayes family: 35 hoursRodrigues family: 40 hoursStep-by-step explanation:
Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.
15x +30y = 1725 . . . . . total liters of use
x + y = 75 . . . . . . . . . total hours of use
The second equation lets us write an expression for y:
y = 75 -x
This can be substituted into the first equation to give ...
15x +30(75 -x) = 1725
-15x + 2250 = 1725 . . . . . . simplify
-15x = -525 . . . . . . . . . . . subtract 2250
x = 35 . . . . . . . . . . . . . . divide by -15
y = 75 -35 = 40
The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.
Solve the inequality 15 ≥ q + 3
Answer:
[tex]q\le \:12[/tex]
Step-by-step explanation:
Solving
[tex]\mathrm{Switch\:sides}[/tex] (Not a required step)
[tex]q+3\le \:15[/tex]
[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]
[tex]q+3-3\le \:15-3\\=q\le \:12[/tex]
[tex]\bold{q\le \:12}[/tex]
Graphing
y = 30.078(1.003)*.
Question 1
? Question
Use the exponential model to make predictions about closing prices of this stock. Remember that x
represents the number of weeks since the first data point, so the value of x today would be 260.
Type the correct answer in each box. If necessary, round the answers to the nearest cent.
One week from today, the stock is predicted to close at $
One month from today, the stock is predicted to close at $
One year from today, the stock is predicted to close at $
Using the exponential function, it is found that:
One week from today, the stock is predicted to close at $65,734.37.One month from today, the stock is predicted to close at $66,327.75.One year from today, the stock is predicted to close at $76,584.35.The exponential function is:
[tex]y(x) = 30078(1.003)^x[/tex]
x represents the number of weeks since the first data point, so the value of x today would be 260.Hence, considering today as an starting point, the function is:
[tex]y(x) = 30078(1.003)^{x + 260}[/tex]
One week from now, we have y(1), hence:
[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]
One week from today, the stock is predicted to close at $65,734.37.
One month from now, we have y(4), hence:
[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]
One month from today, the stock is predicted to close at $66,327.75.
One year from now, we have y(52), hence:
[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]
One year from today, the stock is predicted to close at $76,584.35.
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Answer:
One week from today, the stock is predicted to close at $65,734.37.
One month from today, the stock is predicted to close at $66,327.75.
One year from today, the stock is predicted to close at $76,584.35.
Step-by-step explanation:
Choose a way to solve.
Write or draw to explain.
2. Greg has Il shirts.
3 have long sleeves.
The rest have short sleeves.
How many short-sleeve
shirts does Greg have?
Help please! Thank you in advance!!
Answer:
8 short sleeve shirts
Step-by-step explanation:
Subtract the total amount of of shirts by the number of shirts with long sleeves to find your answer.
I thought of a number. This number double is 7 less than 29. What is my number? hurry please
Answer:
11
Step-by-step explanation:
11*2=22
29-7 =22
Answer:
11
Step-by-step explanation:
Let x be your number
Is means equals
2x = 29-7
2x= 22
2x/2 = 22/2
x =11
1. Gavin buys 89 blue pansies and
86 yellow pansies. He will plant the flowers
in 5 rows with an equal number of plants
in each row. Draw a bar model to help you
find how many plants will be in each row,
O
17
Spiral Review
nose nilo que dise perdoooooooon xd
4.6 + 3.28 + 1.03 = ___
8.91
8.81
8.37
8.18
Answer: The answer is 8.91.
Answer : 8.91
Step - by - step explanation :
Sometimes if a question is to big for you - it's best to start off small . . .
4.60 + 3.28 = 7.88
7.88 + 1.03 = 8.91
Translate this sentence into an equation.
46 is the sum of 20 and Han's savings.
Use the variable h to represent Han's savings. I
Answer:
20+h = 46
Step-by-step explanation:
it doesn't ask to solve it so that's the answer
Answer :-
[tex]20 + h = 46[/tex]• 46 is the sum of 20 and Han's savings. .
So here Question tell that 46 is the sum of Han's Saving .Then it says that to write the equation in this sentence .
• Use the variable h to represent Han's savings.
So 20 and h = 20 + h = 46 .Hope this helps you !!Which triangle is a 30°-60°-90° triangle?
Answer:
-90
Step-by-step explanation:
it's right
Answer:
The first one.
Step-by-step explanation:
I took the quiz and got a 100, hope this helps :))
A2 + B2
Best answer gets a brainliest and thank and 5 star
Answer:
a+b)(a-b)
(Step-by-step explanation:
Assume running consumes 95 cal per mile. If you run 9- minute miles, what is your average power output in watts
What is the value of the expression
Answer:
C. 9
Step-by-step explanation:
K(3)=3*3=9........................