Answer:
The deposit required is $6633.62 and the interest earned is $366.38
Step-by-step explanation:
Compound interest occurs when the interest earned is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It's given the final amount A=$7700 after t=3 years of investment in an account that pays an APR of r=5%=0.05. Since the interests compound quarterly and there are 4 quarters in a year, then n=4.
To find the principal P, we solve the previous equation for P as follows:
[tex]{\displaystyle P=A\left(1+{\frac {r}{n}}\right)^{-nt}}[/tex]
Substituting:
[tex]{\displaystyle P=7700\left(1+{\frac {0.05}{4}}\right)^{-4\cdot 3}}[/tex]
[tex]{\displaystyle P=7700\left(1+0.0125}\right)^{-12}}[/tex]
P=$6633.62
The interest earned is:
I = A - P = $7700 - $6633.62 = $366.38
The deposit required is $6633.62 and the interest earned is $366.38
Lin runs 5 laps around a track in 6 minutes. How many minutes per lap is that?
Answer:
one minutes and 12 seconds
Step-by-step explanation:
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Faith is driving to a concert and needs to pay for parking. There is an automatic fee of $7 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Faith have to pay for parking if she left her car in the lot for 3 hours? How much would Faith have to pay if she left her car in the lot for tt hours?
Cost for 3 hours:
Cost for tt hours:
Answer: 13
Step-by-step explanation:
cost for 3 hours: 7+2(3)=13
cost for t hours: 7+2t
Answer:
13
Step-by-step explanation:
the sum of 4 consecutive even integers is -164. what is the value of the greatest integer
Answer:
The value of the greatest integer is -38
Step-by-step explanation:
Let's make
x = the first even integer
x + 2, x + 4, x + 6 are the following even integers.
Recall even numbers are counted every other number.
The sum of all the numbers is -164:
x + x + 2 + x + 4 + x + 6 = -164
Simplifying:
4x + 12 = -164
Subtracting 12:
4x = -164 - 12 = -176
Dividing by 4:
x = -176 / 4 = -44
Thus, the greatest of them all is x + 6 = -44 + 6 = -38
The value of the greatest integer is -38
In the orchestra, there
are eight violinists in the
front row. How many
different ways can
they be seated?
Explanation:
We have 8 choices for the first slot, 7 for the second, and so on. We count our way down until we have 1 choice left for the eighth slot.
We'll get 8*7*6*5*4*3*2*1 = 40,320 different permutations.
You could use the nPr formula
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
with n = 8 and r = 8 to get the same result. The exclamation marks indicate factorials.
The 8 violinists can be seated in 40,320 ways.
What is permutation?A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given In the orchestra, there are eight violinists in the front row,
the sitting arrangement of violinists is done with the help of permutation,
ⁿPₓ = n!/(n - x)!
here n = 8 and x = 8
(n - x)! = (8 - 8)!
(n - x)! = = 0! = 1
⁸P₈ = 8!/1
⁸P₈ = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1
⁸P₈ = 40,320
Hence they can be seated in 40,320 ways.
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∠A and ∠B\angle B∠B are supplementary angles. If m∠A=(8x−27)∘\angle A=(8x-27)^{\circ}∠A=(8x−27)∘ and m∠B=(4x+3)∘\angle B=(4x+3)^{\circ}∠B=(4x+3)∘, then find the measure of ∠A\angle A∠A.
Answer:< B = 15°
Step-by-step explanation:
If m\angle A=(x+16)^{\circ}∠A=(x+16) and m\angle B=(3x-14)^{\circ}∠B=(3x−14), then find the measure of \angle A∠A.
Maria deposited $5,700 in an account that earns 8% simple interest. How much will be in her account after 6 years?
Answer:
,$456 paid in her account after 6 year
Find the probability of selecting an heartt out of a
standard deck of cards.
Answer:
4/9
Step-by-step explanation:
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a) Four gallons of water weigh 33.4 lb
How much do 7.5 gallons of water weigh?
b) Four gallons of water weigh 33.4 lb
Find the constant of variation.
Answer: a) 62.591 lb b) 7.5
Step-by-step explanation:
Answer:
a) 62.625 lb
b) 8.35
Step-by-step explanation:
a) Use a proportion.
4 gal is to 33.4 lb as 7.5 gal is to x lb.
4/33.4 = 7.5/x
4x = 33.4 * 7.5
4x = 250.5
x = 62.625
Answer: 62.625 lb
b) 33.4/4 = 8.35
Tada!!!!!
What is the slope and y-intercept of the equation on this graph
Answer:
C.
Step-by-step explanation:
What is the absolute value of -8.35
Answer:
8.35
Step-by-step explanation:
To get absolute value, just make it the opposite
Answer: |-8.35| = 8.35
Step-by-step explanation: |-8.35| = 8.35
1. At Store A, the price for pineapples is $5.00 for 2 pineapples.
2. At Store B, the price for pineapples is $8.00 for 4 pineapples.
Which store is offering the lower price per pineapple? Show your work or explain your answer.
Answer:
Store B
Step-by-step explanation:
If you divide 5 by 2, you get the unit price for Store A which is $2.50.
If you divide 8 by 4, you get the unit price for store B which is $2.00
Store B has a lower unit price than store A therefore Store B is offering the lower price per pineapple.
What is 5 to the 3 power simplifyed
Answer: 125
Step-by-step explanation:
5^3=5*5*5=125
Answer:
125
Step-by-step explanation:
5^3 = 5 times 5 times 5
5 times 5 = 25
25 times 5 = 125
When multiplying more than two integers, describe how you know the sign of the product
Answer:
The number of negative integers given determines the sign of the product.
Step-by-step explanation:
The sign of the product could either be negative or positive. This depends on the number of negatively directed integers in the given integers to be multiplied. Since all integers are directed numbers i.e either positive whole numbers or negative whole numbers.
Thus to know the sign of the product, if the number of negative integers is even, then the product would be positive. But if the number of negative integers is odd, the product would be negative.
Therefore, the number of negative integers given determines the sign of the product.
Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded.
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians.
What is the area of the shaded sector?
36Pi units squared
72Pi units squared
144Pi units squared
324Pi units squared
The area of the sector in circle R is: C. 144Pi units squared
How to Find the Area of a Sector of a Circle?Area of sector = (1/2) × r²θ.
Given the parameters:
θ = 8π/9Radius (r) = 18Plug in the values
Area of sector = (1/2) × (18²)(8π/9)
Area of sector = 144π units²
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Find the area of each square. Each grid square represents 1 square unit.
The dairy used 50 pounds of milk to make 5 pounds of
cheddar cheese.
How many pounds of cheddar cheese would 30 pounds
of milk make?
Answer:
3 pounds
Step-by-step explanation:
Find the unit rate by using the equation 50/5 = 10. That means you need 10 pounds of milk to make 1 pound of cheddar cheese. 10 x 3 = 30, so you need to do 1 x 3 = 3.
Assume that the population proportion is 0.46. Compute the standard error of the proportion, σp, for sample sizes of 500,000; 1,000,000; 5,000,000; 10,000,000; and 100,000,000. (Round your answers to five decimal places.)sample size of 500,000 __________sample size of 1,000,000_________sample size of 5,000,000_________sample size of 10,000,000_________sample size of 100,000,000 ___________
Answer:
a) 0.00070
b) 0.00050
c) 0.00022
d) 0.00016
e) 0.00005
Step-by-step explanation:
Standard error for proportion formula
S.E = √P(1 - P)/n
Where P = proportion
n = number of samples
Assume that the population proportion is 0.46. Compute the standard error of the proportion, σp, for sample sizes of a) 500,000
S.E = √P(1 - P)/n
= √0.46 × 0.54/500000
= √ 4.968 ×10^-7
= 0.0007048404
≈ 0.00070
b) 1,000,000
√P(1 - P)/n
= √0.46 × 0.54/1000000
= 0.0004983974
≈ 0.00050
c) 5,000,000
√P(1 - P)/n
= √0.46 × 0.54/5000000
= √ 4.968 ×10^-8
= 0.0002228901
≈ 0.00022
d) 10,000,000
√P(1 - P)/n
= √0.46 × 0.54/10000000
= √2.484 ×10^-8
= 0.0001576071
≈ 0.00016
e) 100,000,000
√P(1 - P)/n
= √0.46 × 0.54/100000000
= √2.484 × 10^-9
= 0.0000498397
= 0.00005
can someone answer these?
Answer:
1. SSS
2.SSA
3.ASA
Step-by-step explanation:
For number one there is three congruent sides with the on in the middle
For number two there is two sides and one angle congruent
And number three has an embedded side between the two angles
How much would $700 invested at 3% interest compounded annually be worth after 10 years
Answer: $940.74
Step-by-step explanation: Use the Calculator provided on money chimp or you can look up the formula. I like using the calculator
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Answer:
46
Step-by-step explanation:
it wouldn't change if it was to be rotated
Find the circumference of a circle with a radius of 19 inches. Give an exact answer.
Provide your answer below:
Answer:
119.38
Step-by-step explanation:
Answer:119.3805208 inches
Step-by-step explanation:
Expand the following expression
(9h+2k)^2
Simplify the given expression. Write your answer with positive exponents.
(See picture below to see problem)
Answer:
heres your answer
Step-by-step explanation:
here you go miss.
Please help me I need help
Which number line shows the solution to the inequality 5x + 3> - 17
At the middle school Vanessa attends, there are 240 Grade 6 students, 210 Grade students, and 200 Grade 8 students. Which ratio best compares the number of tudents in Grade 8 to the number of students in Grade 6 at Vanessa's school? A 5:6 ® 5:11 © 6:5 07:8
Answer:
A, 5:6
Step-by-step explanation: :)
Answer:
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Step-by-step explanation:
A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat’s heart beat per second?
Answer:
3 beats per second
Step-by-step explanation:
45÷15
Cat’s heart will beat 3 times per second.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a cat’s heart beats approximately 45 times in 15 seconds. The number of times a Cat's heartbeat in a second will be calculated as:-
15 seconds = 45 beats
1 second = 45 / 15
1 second = 3 beats
Therefore, Cat’s heart will beat 3 times per second.
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Penny used to drive 3.36 miles to school. Then, she moved 1.29 miles closer to
school. How far does Penny have to drive to school now?
о
Answer:
I think the answer is 2.07
Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = and y = , where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c, and d is shown. Statement Reason substitution Create common denominators. Simplify. Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
The question is missing parts. Here is the complete question.
Now that you've created your hypotheses, it's time to prove them. First look at the sum of two rational numbers. Let's say they are two rational numbers, x and y. Because they're rational, they can be written as a ratio of integers. Let [tex]x=\frac{a}{b}[/tex] and [tex]y=\frac{c}{d}[/tex], where a, b, c and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c and d is shown in the figure below.
Based on the sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answer: The sum of two rational numbers equals a rational number.
Step-by-step explanation: Rational number is defined as a number that can be made by dividing two integers.
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number, as demonstrated in the table below.
deduct 18.729 from the sum of 29.178 and 9.65
Answer:
Step-by-step explanation:
the sum of 29.178 and 9.65
29.178
+ 9.650
= 38.828
Sum =38.828
Deduct 18.729 from the sum
38.828
-. 18.729
=20.099
So the answer is 20.099