The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
To learn more about compounding, follow the link.
https://brainly.com/question/30460031
#SPJ1
Look at picture please
Answer:
EF this is the correct answer
Find x. Use law of sine. Round to the nearest tenth.
Answer:
9.5
Step-by-step explanation:
Law of sine:
[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]
Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°
∠Z° = 76°
∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]
Cross- multiplication is applied:
(x)(sin76°) = (14)(sin41°)
x has to be isolated and made the subject of the equation:
x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]
x = 9.466
x = 9.5 (Rounded to the nearest tenth)
Cory is a bird-watcher. He estimates that 30% of the birds he sees are
American robins, 20% are dark-eyed juncos, and 20% are song sparrows. He
designs a simulation.
Let 0, 1, and 2 represent American robins.
Let 3 and 4 represent dark-eyed juncos.
Let 5 and 6 represent song sparrows.
Let 7, 8, and 9 represent other birds.
The table shows the simulation results.
05716
16803
96568
32177
33855
76635
92290
88864
72794
14333
79019
05943
77510
74051
87238
97895
86481
94036
12749
24005
According to this simulation, what is the probability that at least one of the
next five birds he sees is a song sparrow?
The probability that at least one of the next five birds he sees is a song sparrow is 0.65
How to determine the probability from the simulationFrom the question, we have the following parameters that can be used in our computation:
05716 16803 96568 32177 33855
76635 92290 88864 72794 14333
79019 05943 77510 74051 87238
97895 86481 94036 12749 24005
Also, we have:
Let 0, 1, and 2 represent American robins.Let 3 and 4 represent dark-eyed juncos.Let 5 and 6 represent song sparrows.Let 7, 8, and 9 represent other birds.Using the above as a guide, we have the following individual representations of at least one sparrow bird
Yes Yes Yes No Yes
Yes No Yes No No
No Yes Yes Yes No
Yes Yes Yes No Yes
So, we have
At least one sparrow bird = 13
Total = 20
So, the probability is
P = 13/20
Evaluate
P = 0.65
Hence, the probability is 0.65
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Explain using general or slope form
PLS HELP
Answer:
y = 3x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{3}[/tex] x + 4 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute (- 1, - 3 ) into the partial equation
- 3 = 3(- 1) + c = - 3 + c ( add 3 to both sides )
y = 3x + 0 , that is
y = 3x
you deposit $1000 in an account that pays 3.5% annual interest compounded monthly. when is your balance at least $1200? round your answer to nearest hundredth.
The balance will be at least $1200 after 8.18 months, if you deposit $1000 in an account that pays 3.5% annual interest compounded monthly.
What is compound interest?The result of earning interest on a principal amount as well as the accumulated interest from earlier periods is known as compound interest. It occurs when money is reinvested rather being paid out, allowing interest to be generated on the principle and accrued interest over the next month.
The balance of an account with an initial deposit of $1000 earning 3.5% annual interest compounded monthly will reach $1200 after 8.18 months.
To find the time it takes for the balance to reach $1200, we can use the formula for compound interest, A = P[tex](1 + r/n)^{nt}[/tex],
where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = 1000, r = 0.035, n = 12 (because the interest is compounded monthly), and t is the unknown variable. We can rearrange the formula to solve for t:
t = (A/P) / (1 + r/n)
Plugging in the values, we get
t = (1200/1000) / (12(1 + 0.035/12))
which simplifies to
t = 8.18 months
Therefore, it will take 8.18 months for the balance of the account to reach $1200.
To know more about compound interest, visit
brainly.com/question/14295570
#SPJ1
a. Will he be able to make a right triangle with his fence? Why or why not?
Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Dimensions of triangle he has to use for fencing are
15 feet, 8 feet, and 20 feet.
For making it a right triangle it must satisfy the "Pythagoras theorem" which states that
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
H²=B²+P²
20²=15²+18²
400=225+64
400≠289
No, it will not be able to make a right triangle.
Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ9
The complete question is given below:
Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.
1. Will he be able to make a right triangle out of his fence? Why or why not?
Pat deposits $ 600 in a savings account at a simple interest rate of 6% per year for 5
years. how much will pat have earned in interest by the end of 5 years
Answer:
will earn in interest $ 180
Of the apps on Juan’s tablet, 3/4 are gaming apps,and 5/7 of the gaming apps are action games.what fraction of the apps on Juan’s tablet are action games?
On solving the provided question, we can say that By fraction, 3/4 times 5/7 is 15/28 and Action games are 15/28 of the apps.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
By fraction,
3/4 times 5/7 is 15/28.
Action games are 15/28 of the apps.
To know more about fraction visit:
https://brainly.com/question/10354322
#SPJ1
It takes Mrs. Ritts 3 hours to mow her back yard. This is 2 hours less than twice the time it takes her to mow the front yard. Write an equation that will show the time it takes her to mow the front yard. (use x as the variable)
Answer:
5/2 hours or 2 hours and 30 minutes
Step-by-step explanation:
The x represents the time it took Mrs. Ritts to mow the front yard. We don't know this time so put it as a variable. We also know that the time to mow her backyard is equal to 2 times the variable and then minus 2.
Equation: 3 = (2x) - 2
Now we just isolate the x. First, start by adding 2 to both sides.
5 = 2x
Now just divide both sides by 2.
5/2 = x
5/2 as a mixed number would be 2 and 1/2 so that means the time would be 2 and a half hours.
What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer.
The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0 .
We have to solve the algebraic expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.
So , we subtract "2" from both sides of expression ,
we get ;
⇒ 3x + 2 - 2 = 8 - 2 ;
Simplifying the left hand side, we get:
⇒ 3x = 6 ;
To solve for the variable x, we on divide both sides by 3 ;
⇒ 3x/3 = 6/3 ;
Simplifying, we get:
⇒ x = 6/3 = 2 .
Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.
Learn more about Expression here
https://brainly.com/question/17513857
#SPJ4
The given question is incomplete , the complete question is
What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.
For each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained.
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
What is dilation?Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.
From the diagram:
Scale factor = A'B' / AB = 6/3 = 2
Center = (6, -6)
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
Learn more about dilation at:
brainly.com/question/10253650
#SPJ1
The table below represents which equation?
x −1 0 1 2
y 1 −2 −5 −8
(Hari Bahadur sold a watch after allowing 20% discount and then adding 13% VAT. If the discount amount is Rs.192 more than VAT amount then find the marked price and selling price of the watch.)
Answer: Let's assume that the marked price of the watch is M.
The discount amount would be 20% of M, which can be calculated as:
0.2 * M = 0.2M
The selling price after the discount would be:
M - 0.2M = 0.8M
The VAT amount would be 13% of the selling price after the discount, which can be calculated as:
0.13 * 0.8M = 0.104M
Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:
0.2M = 0.104M + 192
0.096M = 192
M = 192 / 0.096 = 2000
So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.
Step-by-step explanation:
Translate the sentence into an inequality.
Seven subtracted from b is less or equal to -18
If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
What is meant by inequality?A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.
An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.
Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
To learn more about inequality refer to:
https://brainly.com/question/25275758
#SPJ1
Which statement best describes the functions represented here?
A.only function p is nonlinear
B. Neither function is nonlinear
C.only function q is nonlinear
D.both functions are nonlinear
Answer:
D
Step-by-step explanation: for p(x), the slope from 0 to 3 is 30, meaning if linear every time x increases by 3, the y value should as well, meaning that six as an x value to be linear should have been 90, but it was not.
For q(x), the slope from 0 to 3 is 90, and following the same thing from above, this means for every 3 units moved on the x, it should increase by 90 units on the y. This means 6 to be linear should have been 200 but instead was 380 making it also nonlinear
Suppose a turtle walks 3/8 of a mile in 50 minutes what is the unit rate
Answer:
3/400 per min
Explanation:
Divide the rate at which he can walk by the number how mins he can walk at that rate
Find the surface area of the pyramid. The side lengths of the base are equal.
The surface area of the pyramid is 116.4 sq. ft.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.
The area of the triangle is given as:
A = 1/2 (b)(h)
For the face of the pyramid:
b = 12 and h = 9
Substituting the values we have:
A = 1/2 (12)(9)
A = 54 sq. ft
The pyramid consists of three faces thus,
A = 3(54) = 162 sq ft
For the base of the pyramid:
b = 12 and h = 10.4 ft
A = 1/2(12)(10.4)
A = (6)(10.4)
A = 62.4 sq ft
The surface area of the pyramid is:
SA = 54 + 62.4
SA = 116.4 sq. ft
Hence, the surface area of the pyramid is 116.4 sq. ft.
Learn more about surface area here:
https://brainly.com/question/27847638
#SPJ1
Please, answer the question shown below.
D. $402 Million.
Using fitted curve, a similar new blockbuster would expect
C. 290 millionWhat is fitted curve?A fitted curve is a curve that is created to model a set of data points, such that the curve passes as closely as possible to the points. The process of finding a fitted curve is called curve fitting or regression analysis.
Tracing the fitted curve, we have that
week 1 = 150 million
Week 2 = 75 million
Week 3 = 40 million
Week 4 = 25 million
Adding up the amounts
= 150 + 75 + 40 + 25
= 290 million
Learn more about fitted curve at:
https://brainly.com/question/9248452
#SPJ1
11311 rounded off to the nearest 100
Answer:
11300
Step-by-step explanation:
The closest 100 to 11311 is 11300
If the number was 11351 you would round up to 11400
The jacket's original price is $65.00. It is on sale for 40% off. You have to pay 5% sales tax. What is the final price for the jacket?
Answer:
To find the final price for the jacket, we need to first calculate the amount of the discount and then add the sales tax.
The amount of the discount is $65.00 * 40% = $26.00. So the price after the discount is $65.00 - $26.00 = $39.00.
The sales tax is $39.00 * 5% = $1.95. So the final price for the jacket is $39.00 + $1.95 = $40.95.
Step-by-step explanation:
Answer:
he final price for the jacket is $40.95.
Step-by-step explanation:
First, let's calculate the discount for the jacket:
Discount = $65.00 * 40% = $26.00
The price of the jacket after the discount is:
$65.00 - $26.00 = $39.00
Next, let's calculate the sales tax:
Sales tax = $39.00 * 5% = $1.95
Finally, let's add the sales tax to the discounted price to find the final price:
Final price = $39.00 + $1.95 = $40.95
So, the final price for the jacket is $40.95.
evaluate expressions: a)10^5*10^6 b) 10^4*10^-2 c)10^8/10^4 d)10^9/10^-3
Simplify your answer. Type your answer using exponential notation.)
The solution to each of the exponent problems are;
a) 10¹¹
b) 10²
c) 10⁴
d) 10¹²
How to use laws of exponents?
The seven laws of exponents are;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
The given expressions are;
a) 10⁵ × 10⁶
= 10⁵⁺⁶
= 10¹¹
b) 10⁴ × 10⁻²
= 10⁴⁻²
= 10²
c) 10⁸/10⁴
= 10⁸⁻⁴
= 10⁴
d) 10⁹/10⁻³
= 10⁹⁻⁽⁻³⁾
= 10⁹⁺³
= 10¹²
Read more about Laws of Exponents at; https://brainly.com/question/11761858
#SPJ1
What is the slope of this line?
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Please help me with the question pleaseeee
Answer:
∠1 and ∠3
Step-by-step explanation:
The other pair of vertical angles are ∠2 and ∠4
can someone help me please fast
(a) In the figure below, m AB = 54° and m CD = 66°. Find m ZAEB.
A
B
E
C
D
m 2 AEB =
The measure of the angle m∠AEB, found using the angle of intersecting secant theorem, where the measure of the arcs intercepted by the secants are m[tex]\widehat{AB}[/tex] = 54°, and m[tex]\widehat{CD}[/tex] = 66° is; m∠AEB = 6°
What is the angle of intersecting secant theorem?The angle of intersecting secant theorem states that the measure of the angle formed by the intersection of two secant is half the positive difference of the arcs intercepted by the secants.
Please find attached the possible drawing in the question, obtained based on the specified parameters and on similar questions on the internet, created with MS Word.
The parameters indicates that we get;
m[tex]\widehat{AB}[/tex] = 54°
m[tex]\widehat{CD}[/tex] = 66°
The angle of intersecting secants theorem indicates that we get;
m∠AEB = (1/2) × (m[tex]\widehat{CD}[/tex] - m[tex]\widehat{AB}[/tex])
Therefore;
m∠AEB = (1/2) × (66° - 54°) = 6°
m∠AEB = 6°
Learn more on circle theorems here: https://brainly.com/question/28699728
#SPJ1
Examine the figure below, find the length of b, round to the nearest whole
number.
32°
L
b
M
The length of the side using cosine rule and approximating to a whole number gives 23
How to use Cosine Rule?The law of cosines is used to find the missing parts of an oblique triangle when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.
This is expressed as;
b² = a² + c² - 2ac cos b
Plugging in the relevant values gives;
b² = 28² + 41² - 2(28 * 41) cos 32
b² = 2465 - 1947.118
b² = 517.882
b = √517.882
b = 22.757 ≈ 23
Read more about Cosine Rule at; https://brainly.com/question/4372174
#SPJ1
If 15 + 3x is 10 more than 17, what is the value of 6x?
Line ℓ has equation y=-x+4. Find the distance between ℓ and the point F(-1 7)
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:
Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.
Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.
To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:
-x + 4 = x + 8
Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:
y = -6 + 4 = -2
So, the point of intersection between the two lines is (6, -2).
To find the distance between the point F and the line ℓ, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).
So, substituting the values into the formula:
distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3
Therefore, the distance between the line ℓ and point F is approximately 11.3 units.
An online company is making $60 profit every week. The company owes the bank 300 dollars for the start-up money. How much does the company need to pay the bank and make a profit of 150
Answer:
The company must make $450.
If the company must pay $300, then you will take 300, and since they want to make a profit, which means 1500 dollars more once they pay the 300, the you will add that to 300.
300 + 150 = 450
Now to find how many weeks it will take, you will divide 450 by 60:
450/60 = 7.5
It will take 7 1/2 (or round it to 8)weeks to gain $450, which is enough money to pay the bank $300, and make a profit of $150.
Step-by-step explanation:
Hope it helps! =D
d. 6.5
templi friebu
4. Mike can empty his pool with a small or large hose. The large hose can pump
triple as much as the small hose. The small hose pumps 20 gallons of water per
minute. He wants to empty his pool in 2 hrs. The pool holds 1200 gallons of water.
Determine the equation that represent this relationship.
a. 1200-60x=2
b. 30x +1200 = 2
c. 45x-1200=2
d) -1200-20x = 2
The relationship representing the amount of water remaining in the pool when using the large hose to pump out is
a. 1200 - 60x = y
How to determine the equationThe amount of water to be pumped out = 1200 gallons
The rate of pumping out using the small hose 20 gallons of water per minute. = -20x
let each minute be x, hence every minute 20x volume of water leaves the pond
The equation is represented as
water remaining = 1200 - 20x
in 2 hours, we have 120 minutes, when will the water finish
water remaining = 0 = 1200 - 20x
20x = 1200
x = 1200 / 20
x = 60 minutes hence 1 hour
For the large hose the rate of pumping out is tripled hence
water remaining = 1200 - 60x
y = 1200 - 60x
Learn more about linear functions at:
https://brainly.com/question/2030026
#SPJ1
