Answer:
about 8.66 years
Step-by-step explanation:
The multiplier of account value when interest is compounded continuously is ...
k = e^(rt)
where r is the annual interest rate, and t is the number of years.
SetupWe want to find t when k=2 and r=0.08. Putting these values in the formula gives ...
2 = e^(0.08t)
SolutionTaking logs of both sides, we have ...
ln(2) = 0.08t
t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66
It takes about 8.66 years to double the amount.
__
Additional comment
If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...
t = 100·ln(2)/R ≈ 69.3147/R
Here, that is 69.3147/8 ≈ 8.66.
The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.
For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.
Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply.
p(x) = 14(x + 7)2 + 1
q(x) = –5(x + 10)2 – 1
s(x) = –(x – 1)2 + 0.5
g(x) = 2x2 + 10x – 35
t(x) = –2x2 – 4x – 3
The functions that have a maximum and are transformed are:
q(x) = –5(x + 10)2 – 1t(x) = –2x2 – 4x – 3What is a function?This is the rule in mathematics that is used to show the relationship that is in existence between variables.
In order to check for the minimum and the maximum, we have to check on the coefficient of the x square. When it is negative, we have a maximum. When it is positive it is a minimum.
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Answer: b and e
Step-by-step explanation: algebra edge 2022 :)
From the diagram below, if AD = 5, and DB = 10, what is the length of CD?
Answer:
20
Step-by-step explanation:
According to Euclidian theorem:
h^2 = AD*CD (h is the height, DB in this case)
rewrite the equation by using given values
10^2 = 5*CD find the square value of 10
100 = 5*CD divide both sides by 5
20 = CD
solve for the pattern 7, 11, 2, 18, -7, ?
Answer:
7, 11, 2, 18, -7, 25
Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
Answer:
r = 163 --> C
Step-by-step explanation:
In a right triangle, the remaining angle is = 180-73-90 = 17
Because n // p so acute angle created by n = 17
r+17 =180 --> r = 180-17 = 163
Of the
50
5050 U.S. states,
4
44 have names that start with the letter
W
Wstart text, W, end text.
What percentage of U.S. states have names that start with the letter
W
Wstart text, W, end text?
The 8% of us states have names that start with the letter w the answer is 8%.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The complete question is:
Of the 50 us states 4 have names that start with the letter w what percentage of us states have names that start with the letter w.
The percentage of the US states that have names that start with the letter W can be calculated:
Percentage = (No of US states starting with W/Total no of US states)×100
Percentage = (4/50)×100
Percentage = 8%
Thus, the 8% of us states have names that start with the letter w the answer is 8%.
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Which has a higher cost of credit, a $12,000.00 loan for 3 years at 21.2% interest or a $24,000.00 loan for 3 years at 10.6% interest?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. Both the cards have the same cost of credit.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The interest on $12,000 will be,
SI = $12,000 × 3 × 0.212 = $7,632
The interest on $24,000 will be,
SI = $24,000 × 3 × 0.106 = $7,632
Hence, both the cards have the same cost of credit.
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Graph F(x)=-6|x| how to graph this
See the graph in the attached image.
In the parallelogram above what is the value of x?Please explain for brainlest
E.36
F.18
G.6
H.5
Estimate 760 X 55 by first rounding each number so that it has only 1 nonzero digit.
Answer:
48000
Step-by-step explanation:
After rounding each number to the criteria stated, we get the question 800 * 60. Multiply the 8 and the 6 and add the same number of zeros that are there right now. this is 48 + "000" so 48000.
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 15 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 75 bolts. The sample mean bolt length was 15.07 centimeters. The population standard deviation is known to be a = 0.26 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of a 0.01?
The test statistic z is 2.33, the p-value corresponding to the test statistic z value is 0.0099.
What is Probability?Probability is the measure of the likeliness of happening of an event.
The mean of the data is 15.07 centimeters
The standard deviation of the data is 0.26 centimeters.
n = 75
Significance Level ∝ = 0.01
According to the null and alternative hypothesis
Hₐ : [tex]\rm \mu[/tex] ≤15 vs H₁ : [tex]\rm \mu[/tex] >15
The test statistic z is given by
[tex]\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}[/tex]
Z = ( 15.07 -15)/(0.26/√75)
Z = 2.33
The p-value corresponding to z value is 0.0099
as p-value < significance level, therefore the H₁ : [tex]\rm \mu[/tex] >15 is acceptable.
No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.
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La empresa ABC S.A.A tiene como saldo al 31 de marzo de 2021 en Servicios Contratados por Anticipado S/ 16 000 por cuatro meses de alquiler. A la fecha ya ha recibido el servicio de dos meses, los cuales aún no han sido registrados.
ABC S.A.A. debe registra el siguiente ajuste contable al 31 de marzo de 2021.
Answer:
its 20, because I said it
Step-by-step explanation:
so 5+5=10
30-10=20
Does anyone know the answer to this?
1) m∠1 = 62°, lines t and l intersect (given)
2) ∠1 and ∠4 are vertical angles (intersecting lines form vertical angles)
3) ∠1 and ∠4 are congruent (vertical angles are congruent)
4) m∠1 = m∠4 (congruent angles have equal measure)
5) 62° = m∠4 (substitution)
6) m∠4 = 62° (symmetric property of equality)
A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table.
A 2-column table with 7 rows. The first column is labeled x with entries 2, 3, 5, 6, 7, 8, 9. The second column is labeled f(x) with entries 12, 10, 10, 8, 9, 5, 6.
Using the equation for the line of best fit, what is a good approximation for the value of the function, f(x), when x = 18?
−5
−2
3
12
The required value of function F(x), when x=18 is -2
A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table
x = 2 3 5 6 7 8 9
F(x) = 21 10 10 8 9 5 6
What is line?
line, is curve showing the shortest distance between 2 points.
Now, putting x = 18 in f(x) ≈ −0.86x + 13.5
f(x) ≈ −0.86(18) + 13.5
= -1.98
≅ -2 (approximation)
Thus, the required values of x=18 in a line of best fit is -2.
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2. Find the largest value of s satisfying the condition
The required value of δ = 1/4.
0< |x-1| < δ
| f(x) - 4 | < 1/2 where f(x) = 6 - 2x
Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation
now
| f(x) - 4 | < 1/2
|6 - 2x - 4 | <1/2
| 2-2x | < 1/2
| 1 - x | < 1/4
| x - 1 | < 1/4
since modulus function always give positive values.
0 < | x - 1 | < 1 /4
The required value of δ = 1/4.
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If x varies directly as y, and x = 28 when y = 4, find x when y = 8.
Answer:
to find the value of x
x=(8x28)÷4
Answer: x=56
x/y 28/4=x/8
reduce 28/4 to 7/1
7/1 = x/8
cross multiply
x=56
Step-by-step explanation:
The graph shown below expresses a radical function that can be written in the form f(x)= a(x + k)^1/n +C. What does the graph tell you about the value of c in this function?
Answer:
C. c is less than zero
Step-by-step explanation:
The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.
Function transformationThe transformation of the parent function y=x^(1/n) into the function ...
f(x) = a(x +k)^(1/n) +c
represents the following transformations:
vertical scaling by a factor of 'a'left shift by k unitsup shift by c unitsApplicationThe location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...
k = 3c = -4The graph says the value of c is less than zero.
__
Additional comment
Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...
f(x) = 2(x +3)^(1/3) -4
Find the derivative of each function. Then,
determine whether the function has any local
extrema.
Using the quotient rule, the derivative of [tex]y[/tex] is
[tex]y' = \dfrac{(x^2-1) x' - x(x^2-1)'}{(x^2-1)^2} = \dfrac{(x^2-1) - x(2x)}{(x^2-1)^2} = -\dfrac{x^2+1}{(x^2-1)^2}[/tex]
as you're shown in the picture.
If [tex]y[/tex] has any local extrema, they occur at critical points where [tex]y'=0[/tex] or possibly when [tex]y'[/tex] is undefined.
In this case, [tex]y'[/tex] is undefined when [tex]x=1[/tex], but this is outside the domain of [tex]y[/tex] anyway, so we can ignore that.
That leaves us with the zero-case. For [tex]x\neq1[/tex], the denominator is always positive, so the numerator must be zero. But this never happens, since
[tex]-(x^2+1) = 0 \implies x^2 = -1[/tex]
but [tex]x^2\ge0[/tex] for all real [tex]x[/tex]. Therefore [tex]y[/tex] has no critical points and thus no extrema.
In a bag of 60 candies, 36 are green and 45 have caramel in them. If the events of
picking a green candy and picking a candy with caramel are independent, what
percent of the green candies have caramel in them?
Answer:
9/20
Step-by-step explanation:
Total number of candies =60
Number of Green candies, n(G)=36
Number of candies with caramel, n(C)=45
Since the events are independent, the probability of selecting two candies where the first is green and the second has caramel is given by:
P(GC)=P(G) X P(C)
\begin{gathered}=\dfrac{n(G)}{n(S)} X \dfrac{n(C)}{n(S)} \\=\dfrac{36}{60} X \dfrac{45}{60}\\ =\dfrac{9}{20}\end{gathered}=n(S)n(G)Xn(S)n(C)=6036X6045=209
The probability in its lowest form is 9/20.
ASAP PLEASE Given that
A friend asks to borrow $500 from you. She wishes to pay you back at the end of six months and agrees to pay 6% simple interest. How much interest will you earn? Round your answer to the nearest dollar. Do NOT round until you have calculated your final answer.
The interest you will earn from the loan of 500 dollars at rate of 6% and 6 months is $15.
How to find interest?He borrowed $500 and she will pay at the end of 6 months.
The interest rate is 6%.
Therefore,
I = prt / 100
where
p = principalr = ratet = time in yearsTherefore,
I = 500 × 6 × 0.5 / 100
I = 1500 / 100
I = $15
Therefore, the interest you will earn from the loan is $15.
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11) Gretchen purchased a dress that originally cost $89.99. It was marked down 30% off. What was the cost of the
dress?
O a.) $65.99
Ob.) $63.99
Oc.) $62.99
Od.) $64.99
The sum of three numbers is 12. If the second number is subtracted from the sum of the first and third numbers, the result is 2. If the third number is subtracted from the sum of the first and second numbers, the result is 4. Find the three numbers.
Answer:
the numbers are 3, 5, 4
Step-by-step explanation:
The given relations can be written as a system of equations. These are conveniently solved using elimination.
SetupLet the three numbers be represented by x, y, z. The given relations are ...
x +y +z = 12
x -y +z = 2
x +y -z = 4
SolutionSubtracting the second equation from the first gives ...
(x +y +z) -(x -y +z) = (12) -(2)
2y = 10 . . . . . . . . . simplify
y = 5 . . . . . . . . divide by 2
Subtracting the third equation from the first gives ...
(x +y +z) -(x +y -z) = (12) -(4)
2z = 8 . . . . . . . . . simplify
z = 4 . . . . . . . . divide by 2
Using these values of y and z in the first equation lets us find x:
x +5 +4 = 12
x = 3 . . . . . . . . . subtract 9
The numbers, in order, are (3, 5, 4).
Evaluate 3b²-c when b = 1/2 and c = 1/4
Answer:
1/2
Step-by-step explanation:
We are given the expression 3b²-c, and we want to evaluate it if b is 1/2 and c is 1/4.
Because b and c are given values, we can substitute them into the expression as so:
Replace b with 1/2 in the expression.
3(1/2)²-c
Now replace c with 1/4 in the expression.
3(1/2)²-1/4
Now to solve this, we need to use the order of operations, which is usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have different abbreviations.
Regardless, the order of operations tells us that we should start with what is inside parentheses (i.e. if we need to do anything, like multiplying or dividing any numbers that are inside parentheses).
In this case, we don't have anything. So, we should go next to exponents, and we do have an exponent here (1/2 is raised to the second power).
So let's evaluate that.
Raise 1/2 to the second power (multiply it by itself).
1/2 * 1/2 = 1/4
We can substitute (1/2)² with 1/4:
3(1/4) - 1/4
Next, we should take care of any multiplication / division, making sure that we should work left to right
There is one multiplication thing to do: the 3(1/4), which will be 3/4
Replace 3(1/4) with 3/4.
3/4 - 1/4
Now, we can subtract 1/4 from 3/4, as the final two things in PEMDAS are addition and subtraction (A and S). Note that even though while addition is written first, we should always be working left to right, so for example if we had 3 - 4 + 6, we should do 3 - 4 first, THEN add 6 to the result of that. The same is true for multiplication and division.
3/4 - 1/4 = 2/4 = 1/2
A decorator wants to line the bottom with through George with paper if the bottom each drawer measures 36“ x 20“ how many square inches of paper are needed
The amount of paper that are needed to line the bottom of 3 drawers with paper is equal to 2,160 square inches.
How to determine the amount of paper?First of all, we would calculate the area of the bottom of each drawer as follows:
Area = length × width
Area = 36 × 20
Area = 720 square inches.
Next, we would multiply this area by 3:
Total area = 720 × 3
Total area = 2,160 square inches.
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Complete Question:
A decorator wants to line the bottom of 3 drawers with paper. If the bottom of each drawer measures 36 inches by 20 inches, how many square inches of paper are needed?
A. 1,040
B. 1,080
C. 2,040
D. 2,160
Least common multiple of 10,20 35
Answer: 140
Step-by-step explanation:
Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds.
(n - 30) + n = 210
(n + 30) + n = 180
(n + 30) + n = 210
(n - 30) + n = 180
The equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210
Linear equationFrom the question, we are to write an equation for the given problem
From the given information,
n = Tom's weight in pounds
If Jim weighs 30 pounds less than Tom
Then,
Jim weighs (n - 30)
Thus,
The sum of their weight is
(n-30) + n
∴ (n-30) + n = 210
Hence, the equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210
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simplify the expression by using the distributive property and combining like terms
6(3y + 7) + 4(9+9y)
Answer:
54y+78
Step-by-step explanation:
6*3y+ 18y
6*7=42
4*9=36
4*9y=36y
18y+36y+42+36= 54y+78
Write 18,25% as a common fraction in its simplest form.
Step-by-step explanation:
1825%
and percentage means 100
so 1825/100=73/4
it is customary to give a 15% tip for a meal at a restaurant. what is 15% of $64.40
Answer:
$9.66 isb15% of $64.40
Step-by-step explanation:
64.40×15%
Which of the following is the graph of the inequality y-2>-2(x-1)?
A
B
C
(2.1)
(0, -3)
ACE
AD
(2.1)
(4,-1)
UN
(1.2)
(3,-2)
14TH
D
(1.2)
(3,-2)
The graph is shown in the attached image.