Answer:
10 weeks
Step-by-step explanation:
40 books= ? weeks
4 books. = 1 week
so do 40/4 and get 10
Answer:
10 weeks
Step-by-step explanation:
Daniel already snacked on a almonds. Then he snacked on another 8 almonds. Write an expression that shows how many almonds Daniel snacked on in all.
a + 8. This expression represents the total number of almonds that Daniel snacked on in all.
What is the difference between expression and equation?
An expression is a mathematical phrase that contains numbers, variables, and operations. It can be evaluated to produce a single numerical value or another expression. Expressions do not contain an equal sign (=), and they do not represent a statement that is either true or false.
An equation, on the other hand, is a mathematical statement that shows the equality between two expressions. It contains an equal sign (=) and represents a statement that is either true or false. Equations typically contain variables that can take on different values, and they can be used to solve for an unknown variable by manipulating the equation using algebraic operations.
To summarize, expressions are mathematical phrases that do not contain an equal sign and can be evaluated to produce a value, while equations are mathematical statements that do contain an equal sign and represent a relationship between two expressions that is either true or false.
We can use addition to represent the total number of almonds that Daniel snacked on. If Daniel snacked on an initial amount of almonds, say "a", and then snacked on an additional 8 almonds, we can write the expression:
a + 8
This expression represents the total number of almonds that Daniel snacked on in all.
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Can someone answer this just read the picture? Right answers only please!
Answer:
8,192
Step-by-step explanation:
20/100*80 =16 apply tjis in every step as they asked 4 times
J
14
20
K
22.4
AKLS-
T
32
L
Similar By:
S
Determine if the triangles are similar. If similar.state how and complete the similarity statement
The triangles JTK and KSL are not congruent. So we cannot complete a similarity statement.
what is congruent ?
In geometry, two figures are said to be congruent if they have the same shape and size. In other words, if all corresponding angles are congruent and all corresponding sides are of equal length, then the two figures are congruent.
For example, two triangles are congruent if all three pairs of corresponding angles are congruent and all three pairs of corresponding sides are of equal length. Similarly, two circles are congruent if they have the same radius.
According to the question:
To determine if the triangles JTK and KSL are similar, we need to check if their corresponding angles are congruent and their corresponding sides are in proportion.
First, we can see that angle JTK and angle KSL are congruent because they are both right angles.
Next, we can use the Pythagorean theorem to find the length of side TK:
[tex]TK^2 = JK^2 - JT^2[/tex]
[tex]TK^2 = 14^2 - 2^2[/tex]
[tex]TK^2 = 192[/tex]
TK = sqrt(192)
TK = 8*sqrt(3)
Now, we can compare the ratios of the corresponding sides to see if they are equal:
JT : JK : TK = 2 : 14 : 8*sqrt(3)
KS : KL : SL = 32 : 22.4 : 15.2
We can simplify these ratios by dividing by the greatest common factor, which is 2:
JT : JK : TK = 1 : 7 : 4*sqrt(3)
KS : KL : SL = 8 : 5.6 : 3.8
We can see that these ratios are not equal. Therefore, the triangles JTK and KSL are not similar.
Since the triangles are not similar, we cannot complete a similarity statement.
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45 cm
36 cm
38 cm
= the volume
bonjours
oui sa est égale au volume
Siegell's Locksmith Shop is taking out a mortgage on a new building. It is going to be an interest-only, 12-year balloon mortgage for $350.000. The APR is 3.35%. The last payment will be the balloon payment of the full
principal.
a. Find the total number of monthly payments, not including the final balloon payment.[
b. Find the amount of each monthly payment if the payments are interest-only. Round to the nearest cent
c. Find the difference between the regular monthly payment and the balloon payment, to the nearest hundred dollars.
d. If the mortgage was not a balloon mortgage, what would be the amount of the monthly payment, rounded to the nearest cent?
Monthly payment is $973.52, difference is $349,000 and monthly payment for a fully amortizing mortgage would be $3,331.87.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the total number of monthly payments, we need to multiply the number of years by 12 (the number of months in a year) and subtract 1 (for the final balloon payment).
So the total number of monthly payments is:
12 x 12 - 1 = 143
b. To find the amount of each monthly payment, we can use the formula
First, we need to convert the APR to a monthly interest rate by dividing by 12:
Monthly Interest Rate = 0.0335 / 12 = 0.002792
Monthly Payment = (350000 x 0.002792) / (1 - (1 + 0.002792)⁻¹⁴³)
= $973.52
The monthly payment is $973.52.
c. The balloon payment is simply the full principal amount of $350,000. The difference between the regular monthly payment and the balloon payment is:
Balloon Payment - Monthly Payment = $350,000 - $973.52 = $349,026.48
The difference is $349,000.
d. To find the monthly payment for a 12-year, fully amortizing mortgage, we can use the same formula as in part b, but with a different Total Number of Payments:
Total Number of Payments = 12 x 12 = 144
Monthly Payment = (350000 x 0.002792) / (1 - (1 + 0.002792)⁻¹⁴⁴) = $3,331.87
The monthly payment for a fully amortizing mortgage would be $3,331.87.
Hence, monthly payment is $973.52, difference is $349,000 and monthly payment for a fully amortizing mortgage would be $3,331.87.
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pls help, it on khan academy
Answer:
25.12cm²
Step-by-step explanation:
Hope it helps. Have a nice week.
The mean amount of money spent on lunch per week for a sample of 273
students is $22
. If the margin of error for the population mean with a 98%
confidence interval is 2
, construct a 98%
confidence interval for the mean amount of money spent on lunch per week for all students.
The true mean amount of money spent on lunch per week for all students falls within the range of $20.12 to $23.88.
Define the term "margin of error"?Margin of error is a statistical term that refers to the amount of random sampling error that is present in a survey or statistical estimate. In other words, it is the amount of uncertainty or variation that is inherent in any statistical measurement or survey result.
To construct a 98% confidence interval for the mean amount of money spent on lunch per week for all students, we need to use the formula:
Confidence interval = sample mean ± (z-score)(standard error)
Here, the sample mean is $22, the margin of error is 2, and the sample size is 273. To find the z-score for a 98% confidence interval, we can use a standard normal distribution table or calculator. The z-score for a 98% confidence interval is approximately 2.33.
To calculate the standard error, we need to use the formula:
[tex]Standard Error = \frac{standard Deviation}{\sqrt{sample Size} }[/tex]
Since the standard deviation is not given, we can estimate it using the sample standard deviation. Let's assume that the sample standard deviation is $8. The Standard Error calculated as:
[tex]Standard Error = \frac{8}{\sqrt{273} }[/tex] ≈ 0.48
Substituting the values into the formula for the confidence interval, we get:
Confidence interval = $22 ± 2.33(0.48) ≈ $20.12 to $23.88
Therefore, we can be 98% confident that the true mean amount of money spent on lunch per week for all students falls within the range of $20.12 to $23.88.
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A vending machine has 6 different colors of gumballs (red, blue, pink, yellow, green, purple) and an equal chance of dispensing each. Martin buys 6 gumballs. What is the probability of Martin getting exactly 3 pink gumballs?
The prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is expressed as a number between 0 and 1, with 0 indicating an impοssible event and 1 indicating a certain event. The prοbability οf an event can be calculated by dividing the number οf favοrable οutcοmes by the tοtal number οf pοssible οutcοmes.
In the given scenariο, there are 6 different cοlοrs οf gumballs, and each has an equal chance οf being dispensed. Therefοre, the prοbability οf getting any particular cοlοr is 1/6.
Tο find the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6, we need tο use the binοmial prοbability fοrmula:
[tex]\mathrm{P(X=k) = C(n,k) \times p^k \times (1-p)^{(n-k)}}[/tex]
where:
P(X=k) is the prοbability οf getting exactly k successes
n is the tοtal number οf trials (in this case, 6)
k is the number οf successes we want (in this case, 3)
p is the prοbability οf success (in this case, the prοbability οf getting a pink gumball, which is 1/6)
C(n, k) is the number οf cοmbinatiοns οf n things taken k at a time, which can be calculated as n! / (k! × (n-k)!).
Plugging in the values, we get:
P(X=3) = C(6,3) × (1/6)³ × (5/6)³
= (6! / (3! × 3!)) × (1/6)³ × (5/6)³
= 20 × (1/216) × (125/216)
= 0.1608
Therefοre, the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.
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tommmy earns $140 in interest after 5 years on a pricipal of $400 jane earned $132 after 4 years on principal of $600 use the intrest rate to justify which bank would you rather use tommys or janes
Comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for less principal amount.
What is meant by the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Given,
Interest earned by Tommy SI = $140
Time t = 5 years
Principal amount P = $400
Interest earned by Jane SI = $132
Time t = 4 years
Principal amount P = $600
Simple interest SI = (P × r × t)/100
where r = interest rate
For Tommy,
140 = ( 400 × r × 5) /100
r = 7%
For Jane,
132 = ( 600 × r × 4) / 100
r = 5.5%
Therefore comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for the less principal amount.
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The ice cream above is going to melt.
When it does, will it fit in the cone or
will it overflow? Explain.
The spherical ice cream scoop and the
right cone have a radius of 3 cm.
The height of the cone is 7 cm.
Show all your work.
Answer:
well...it depends how much ice cream ia in the cone...if its 3 or more it Will definently overflow.
Mr. Shaw is building a walk away from the corner of his house out to his vegetable garden in the corner of the yard. The dimensions of the yard and the garden are shown. What is the length of the walkway, w, to the nearest foot?
A 24 foot
B 34 foot
C 46 foot
D 58 foot
Ummi chose C as the correct answer. How might she had gotten that answer?
Answer:
34 Foot
Step-by-step explanation:
You're basically just doing the pythagorean theory: a^2+b^2=c^2
You just are not directly being given a or b and instead you have to find them which you do by subtracting how big the garden is from the total length: 50-20=30(a) 30-14=16(b). After that you just do the normal theory getting 30^2+16^2=c^2 which leads to 900+256=c^2 then 1156=c^2 so you take the square root of both sides in order to turn c^2 into plain c or the length of the walk way which will get you 34 feet.
Which step is incorrect?
Answer:
c step 3
Step-by-step explanation:
from the correct x^(2/5) do we suddenly get to
x^(5/2).
1/x³ = x^(-3) is a correct identity, and using it has no impact on x^(2/5). that should still stay x^(2/5).
the correct step 3 is then
x^(2/5)x^(-3)
step 4 is then
x^(2/5 - 3) = x^(2/5 - 15/5) = x^(-13)/5
A community theater held auditions for their summer musical. There were 42 performers accepted in the cast. That was 60% of all those who auditioned. How many people auditioned for the musical?
Answer:
64 people
Step-by-step explanation:
I'm not so sure but I think its right.
Here's how I figured it out:
60x2=120
42x2=84
120-20=100%
84-20=64
the wind speed y (in miles per hour) of a tropical storm is y = 2x + 66, where x is the same number of hours after the storm enters the gulf of mexico "15 by 15 graph first quadrant" A: Complete the table (show work) B: Graph the equation C: When does the storm become a hurricane
Answer:
Step-by-step explanatio
A. To complete the table, we need to plug in different values of "x" into the equation y = 2x + 66 and solve for "y". We can choose any values of "x", but it's usually helpful to choose values that are easy to calculate. Here's the table with "x" values ranging from 0 to 7:
x y
0 66
1 68
2 70
3 72
4 74
5 76
6 78
7 80
B. To graph the equation, we can plot the points from the table on a coordinate plane. We can use the x-axis to represent the number of hours after the storm enters the Gulf of Mexico (x), and the y-axis to represent the wind speed in miles per hour (y). The points should fall on a straight line with a slope of 2 and a y-intercept of 66. We can plot the points and draw the line as follows:
C. The wind speed of a tropical storm becomes a hurricane when it reaches or exceeds 74 miles per hour. Looking at the graph, we can see that the wind speed reaches 74 miles per hour when x = 4. Therefore, the storm becomes a hurricane 4 hours after entering the Gulf of Mexico.
The point (-sqrt2/2, sqrt2/2) is the point at which the terminal ray of angle theta intersects the unit circle. What are the values for cosine and cotangent functions for angle theta
Hence, the values of cοsine and cotangent functions for angle theta are -√(2)/2 and -1, respectively.
What precisely does a degree angle mean?Angles between 0 and 90 degrees are cοnsidered acute. Obtuse angles fall within this range and vary frοm 90° to 180°. A right angle is knοwn as an angle with a 90-degree angle (= 90°).
The pοint (-√(2)/2, √(2)/2) lies on the unit circle in the second quadrant, which means that the cοrresponding angle theta has a reference angle of pi/4.
The cοsine of theta is the x-coordinate of the point on the unit circle corresponding to theta. Since the x-coοrdinate of the given point is -√(2)/2, we have:
cοs(θ) = -√(2)/2
The cοtangent of theta is the ratio of the cosine of theta to the sine of theta. We can find the sine of theta by using the Pythagοrean theorem, since the pοint (-√(2)/2, √(2)/2) lies on the unit circle:
sin(θ) = √(1 - cos²(θ)) = √(1 - (-√(2)/2)²) = √(2)/2
Therefοre, we have:
cot(θ) = cos(θ) / sin(θ) = (-√(2)/2) / (√(2)/2) = -1
Hence, the values of cοsine and cotangent functions for angle theta are -√(2)/2 and -1, respectively.
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A man walks for 40 minutes at 60km/h. he then travels for two hrs in a minibus at 80 km/h. Finally he travel by but for an one hour at 60km/h - Find his speed for the whole journey?
Answer: 71km/h
Step-by-step explanation:
He traveled 260km according to what you gave and 100 km using 60 km/h and 160km using 80km/h Also is this man has rocket since he walked 60km/h. His whole journey take 3h40m. Just take 260 divide by 3h40m so you got the final answer about 71km/h
In one year, 30,000 sheep on his property in the next year because of the drought the farmer reduced his flock by 37% The number of sheep he has after the fall in numbers is
Answer:
11,100
Step-by-step explanation:
1% of 30,000 is 300 so if we times 300 by 37 we get 11,100
there is 11,100 sheep in 37%.
hope this helps :)
which values in the set {1,2,3,4,5} are a solution to 4x - 2 < 15?
please give me an answer guys
Answer:
Values from the set = 1, 2, 3, 4.
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The inequation is,
→ 4x - 2 < 15
Then the value of x will be,
→ 4x - 2 < 15
→ 4x < 15 + 2
→ 4x < 17
→ x < 17/4
→ [ x < 4.25 ]
Hence, the answer is x < 4.25.
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
23 53 67 61 66 91 27 85 98 44 73
Question content area bottom
Part 1
Range= enter your response here (Round to one decimal place as needed.)
Part 2
Sample standard deviation= enter your response here (Round to one decimal place as needed.)
Part 3
Sample variance= enter your response here (Round to one decimal place as needed.)
Part 4
What do the results tell us?
A.
Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
B.
The sample standard deviation is too large in comparison to the range.
C.
Jersey numbers on a football team do not vary as much as expected. D Jersey numbers on a football team vary much more than expected.
Answer:
Part 1:
Range = 98 - 23 = 75
Part 2:
First, find the sample mean:
Mean = (23 + 53 + 67 + 61 + 66 + 91 + 27 + 85 + 98 + 44 + 73)/11 = 61.9
Then, find the sum of the squared differences between each jersey number and the mean:
(23-61.9)^2 + (53-61.9)^2 + (67-61.9)^2 + (61-61.9)^2 + (66-61.9)^2 + (91-61.9)^2 + (27-61.9)^2 + (85-61.9)^2 + (98-61.9)^2 + (44-61.9)^2 + (73-61.9)^2 = 12388.4
Sample variance = 12388.4/10 = 1238.84
Sample standard deviation = √1238.84 = 35.17
Part 3:
Sample variance = 1238.84
Part 4:
The results tell us that there is a relatively large range in jersey numbers, with a difference of 75 between the highest and lowest numbers. The sample variance and standard deviation also indicate that there is a considerable amount of variability in the data, with jersey numbers varying significantly from the mean. This suggests that there is no pattern or structure to the jersey numbers on the football team, and that they are assigned somewhat randomly.
Step-by-step explanation:
to make coldrink 1 must mix concentrate with water in a ratio of 1:3
if I have 400ml of concentrate how much water must I use?
Answer:
1200ml or 1.2l of water
Step-by-step explanation:
concentrate:water
1:3
400:x
3×400=1200
400:1200
1200ml or 1.2l of water
8.) SAT CORNER: Gatsby leaves his dock and takes his
motorboat due east for 0.5 miles to pick up Daisy. Then,
they motor 1.2 miles north to a private island in the
middle of the sound. What is the straight-line distance,
in miles, from the island to Gatsby's dock?
The distance from the island to Gatsby's dock is 1.3 miles.
What is a Pythagoras theorem?A Pythagoras theorem is a principle that can be used to determine the unknown side of a right angled triangle when the other two sides are known.
Applying the Pythagoras theorem to the given question, let the distance from island to Gatsby's dock be represented by s. Then;
/Hyp/^2 = /Opp/^2 + /Adj/^2
s^2 = 1.2^2 + 0.5^2
= 1.44 + 0.25
= 1.69
s = 1.69^1/2
= 1.3
Thus, the straight-line distance from the island to Gatsby's dock is 1.3 miles.
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Select the equation that is true. A. 2 2 3 × 4 = 8 2 3 B. 2 2 3 × 5 8 = 1 2 3 C. 2 2 3 × 2 3 = 2 4 9 D. 2 2 3 × 4 3 5 = 8 6 15 its fractions im lazy thats all
The equation 2 2/3 × 2/3 = 2 4/9 is true.
What are fractions?A fraction represents a part of a whole or a ratio between two quantities. It is written as a/b, where "a" is the numerator and "b" is the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or the ratio.
The equation that is true is:
C. 2 2/3 × 2/3 = 2 4/9
To solve the problem, we can convert the mixed numbers to improper fractions, and then multiply:
2 2/3 = 8/3
2/3 = 2/3
8/3 × 2/3 = 16/9
We can then convert the improper fraction back to a mixed number:
16/9 = 1 7/9
Therefore, the equation 2 2/3 × 2/3 = 2 4/9 is true.
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How do I find the vertex of the equation
The vertex of the equation (x - 1)^2 - 9 = 0 is (1. 9)
How to determine the vertex of the equationThe vertex of a quadratic equation is the point at which the graph of the equation reaches its maximum or minimum value.
For a quadratic equation in standard form, y = ax^2 + bx + c, the vertex is located at the point (-b/2a, f(-b/2a))
From the question, we have the following parameters that can be used in our computation:
(x - 1)^2 - 9 = 0
A quadratic equation is represented as
a(x - h)^2 + k = 0
Where the vertex is
Vertex = (h, k)
Using the above as a guide, we have the following:
Vertex = (h, k) = (1, 9)
Hence, the vertex is (1, 9)
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Complete question
How do I find the vertex of the equation
(x - 1)^2 - 9 = 0
Which color has the highest frequency? Which color has the lowest frequency? WHY?
I know I put it in the wrong subject but math is the most looked at and I know I'll get an answer faster.
Answer: Violet color light has the highest frequency. The frequency of violet color light is. 5 × 10 14 Hz . red color light has the lowest frequency. Red light has a frequency around 430 terahertz. This is all based on the order by wavelength.
mark me brainliest please :)
Step-by-step explanation: In order from lowest frequency to highest, they are red, orange, yellow, green, blue, indigo, and violet. Because of the inverse relationship, they are reversed in order by wavelength. The color with the highest frequency is violet.
What is the value of b?
10
16
20
26
Answer:
the value of b is 10 +151620 but we have; to check
The value of b in the equation is 13/12
How to determine the value of bFrom the question, we have the following parameters that can be used in our computation:
x^2/24 - y^2/b^2 = 1
The equation of a hyperbola with center at the origin and semi-axes lengths a and b can be written as:
x^2/a^2 - y^2/b^2 = 1
Comparing this equation with the given equation, we have:
a^2 = 24.
The directrix of the hyperbola is given as
x = 576/26
For a hyperbola with center at the origin, the distance between the center and the directrix is a^2/b.
So, we have:
a^2/b = 576/26
Substituting the value of a^2, we get:
24/b = 576/26
So, we have
b = 13/12
Hence, the value of b is 13/12
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Josh is at a park. He knows that the distance from the picnic table to a tree is 124 feet. Josh also knows the angle formed by a segment from his location to the picnic table and a segment from his position to the tree is 54 degrees and that triangle formed by his position, the picnic table, and the tree is a right triangle, with a right angle at the picnic table. Does josh have enough to find how far he is from the picnic table.
Answer:
Yes, Josh has enough information to find how far he is from the picnic table. Josh is 90.1 ft from the picnic table (to the nearest tenth).
Step-by-step explanation:
Yes, Josh has enough information to find how far he is from the picnic table.
From the given information, we can model this as a right triangle where the angle is 54°, the side opposite the angle is the distance between the picnic table and the tree, and the side adjacent the angle is the distance between Josh and the picnic table. (See attached diagram).
To calculate the distance between Josh and the picnic table (labelled "x" on the attached diagram), use the tangent trigonometric ratio.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]
Substitute the values into the tan ratio:
[tex]\implies \tan 54^{\circ}=\dfrac{124}{x}[/tex]
[tex]\implies x=\dfrac{124}{\tan 54^{\circ}}[/tex]
[tex]\implies x=90.09127...[/tex]
[tex]\implies x=90.1\; \sf ft\;(nearest\;tenth)[/tex]
Therefore, Josh is 90.1 ft from the picnic table (to the nearest tenth).
- The water level in a retention pond started at 5 ft (60 in.) and decreased at a rate of 2 in./day during a 14-day drought. A tropical depression moved through at the beginning of the 15th day and produced rain at an average rate of 2.5 in./day for 5 days. Write a piecewise-defined function to model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought.
The piecewise function that models model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought is given as follows:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.L(x) = 30 + 5x, 15 ≤ x ≤ 19.How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which;
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.A piecewise function is a function with different definitions, based on the input of the function.
For the first 14 days, the parameters are given as follows:
b = 60 -> water level during day 0.m = -2 -> each day the amount decreased by 2 in.Hence:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.
For the last 5 days, the parameters are obtained as follows:
b = 60 - 2(15) = 30.m = 5, as each day the amount increased by 2 in.Hence:
L(x) = 30 + 5x, 15 ≤ x ≤ 19.
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pleas find the area of the figure.
Answer:
41
Step-by-step explanation:
we can get this answer because:
3(3)=9
4(8)=32
and u add 32 and 9 together and get 41
How can i simplify 1½-⅓÷⅔+1
Answer:
2
Step-by-step explanation:
you first follow the BODMAS law then you divide 1/3÷2/3 It will give you 1/2 so you 3/2-1/2 +1 it will give you 2
Consider an investment of $2800 at an APR of 5% compounded monthly. Use the formula that gives the exact doubling time to determine exactly how long it will take for the investment to double.
Express your answer in terms of the number of whole years and remaining months it will take the investment to double. Give your answers as whole numbers.
It will take {log(1 - r/n)/n} years to exactly double your investment.
What is the formula to calculate compound interest?The formula for compound interest is -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
Given is that an investment of $2800 made at an APR of 5% compounded monthly.
The formula for compound interest is -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
For A = 2P, we can write -
Substituting 2P = A, we get -
2P = P(1 + r/n)^nt
2 = (1 + r/n)^nt
log 2 = log {(1 + r/n)^nt}
log 2 = (nt) log(1 + r/n)
(log 2)/log(1 + r/n) = nt
{t} = log{2 - 1 - r/n}/n
{t} = log{1 - r/n}/n
Therefore, it will take {log(1 - r/n)/n} years to exactly double your investment.
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