The linear equation that models how much Ally saves for a computer each month is y = 25x + 100, where x is the number of months that have passed, and y is the total amount saved. After 6 months, her savings will be $250. It will take her 44 months to have $1200 to purchase the computer.
An equation is a mathematical statement that shows that two expressions are equal. Equations use an equals sign (=) to show that the values of the expressions on either side of the sign are equal. It can include variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division
Let x = the number of months
y = total amount she saves
If she currently has $100 in her bank account and she plans on saving an additional $25 each month, then the linear equation to model how much she saves is:
y = $25x + $100
y = 25x + 100
After 6 months, the equation becomes:
y = 25(6) + 100 = 150 + 100 = $250
So after 6 months, Ally will have saved $250.
To find the number of months it will take to reach the goal of $1200, we can rearrange the equation and solve for x:
$1200 = 25x + 100
$1100 = 25x
x = 44
It will take 44 months, or approximately 3 years and 8 months, for Ally to reach her savings goal of $1200.
Learn more about equation here: brainly.com/question/2972832
#SPJ4
Write 4.8 as a mixed number and as an improper fraction
If you read the decimal version of 4.8 out loud, it should be "four and eight-tenths." This will always give you a good place to start when changing a decimal into an equivalent fraction.
Now, this is a mixed number: 4 and 8/10. To further simplify it as a mixed number, we can leave the 4 alone and reduce the fraction (8/10). Both the numerator and denominator are divisible by 2, so we can conclude (8/10) = (4/5). A correct answer in mixed number form is 4 and (4/5).
However, to change 4 and (4/5) to a single (improper) fraction, you first multiply the denominator (5) by the large number out front on the left (4) and ADD this product to the numerator (4). This number is your new numerator and it will still have the same denominator as before.
Here, 4 and (4/5) = [(5)*(4) + 4]/5 = (20+4)/5 = 24/5.
24 and 5 have no common factors, so this fraction is already in reduced form.
4.8 = 4 8/10 = 4 4/5
Original loan amount was 270,384 you paid a total of 360,000.
360,000 (paid) minus Original loan amount 270,384 equals 89,616 in interest
Original loan amount was 270,384 and if paid a total of 360,000 then the interest rate of loan is, 6.6%
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Original loan amount = 270,384
Total amount paid = 360,000
Interest = 89616
Suppose, time duration = 5 years
Interest rate = ?
I = P × R × T/100
89616 = (270,384 x R x 5)/100
R = 6.62
Hence, the interest rate is 6.6 %
To know more about Interest check:
brainly.com/question/29480777
#SPJ1
The required interest paid against the loan of the Original loan amount was 270,384.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Amount = Principal [1 + rate×time]
Here,
The original loan amount was 270,384 you paid a total of 360,000.
Interest paid can be evaluated by subtraction of the original amount from the paid amount,
interest paid = paid amount - the original amount
interest paid = 360,000 - 270,384
interest paid = 89,616
Thus, the required interest paid against the loan of the Original loan amount was 270,384.
Learn more about simple interests here:
https://brainly.com/question/26457073
#SPJ1
From April to July 2015, the number of employed youth 16- to 24-years old rose by 2.1 million to 20.3 million and youth unemployment increased from 2.1 million to 2.8 million. In July, the youth labor force grew by 2.8 million to a total of 23.1 million and the youth population was 38.5 million. How did the youth unemployment rate change from April to July? Calculate the youth labor force participation rate in July.
Youth unemployment rate change from April to July is 25%.
Youth labor force participation rate in July is 7.27%.
What is rate of change?Rate of change is the speed at which the variables changes with respect to time.
From April to July 2015, the number of employed youth 16- to 24-years old rose by 2.1 million to 20.3 million
Youth unemployment increased from 2.1 million to 2.8 million.
In July, the youth labor force grew by 2.8 million to a total of 23.1 million.
Youth population was 38.5 million.
[tex]labor force rate =\frac{labor force}{adult population} *100[/tex]
= [tex]\frac{2.8}{38.5} *100[/tex] = 7.27%
[tex]unemployment rate = \frac{number of unemployment}{labor force} *100[/tex]
= [tex]\frac{2.8-2.1}{2.8} *100[/tex]=25%
Hence, youth unemployment rate change from April to July is 25%.
Youth labor force participation rate in July is 7.27%.
Learn more about Rate of change here:
https://brainly.com/question/16202639
#SPJ1
Pablo is solving the system of equations shown and says that the first step is to add the equations together to eliminate the y variables.
a. describe Pablo's error
b. What is a possible first step Pablo could take?
c. Find the solution to the system of equations?
3x + 4y =26
2x + 4 = 28 <<
Pablo's error was that he added the equations.
A possible first step is to subtract the equations.
The solution of the system is x = -2 and y = 8.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
We have s system of equations,
3x + 4y = 26 {equation 1}
2x + 4y = 28 {equation 2}
Pablo is solving the system of equations shown and says that the first step is to add the equations together to eliminate the y variables.
To eliminate the y-variable:
Subtract equation 2 to equation 1.
3x - 2x = 26 - 28
x = -2
Then y = 8.
Therefore, the solution of the system is x = -2 and y = 8.
To learn more about the system of equations;
brainly.com/question/13729904
#SPJ1
Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A survey was given to a random sample of 400 people living in a certain community. The people were asked whether they supported the construction of walking trails in the community park. The results are shown in the following table. Response Frequency Yes, support 210 No, do not support 90 No opinion 100 Total 400 A follow-up study will be conducted with a sample of 20 people from the 300 people who responded yes (support) and no (do not support). Two sampling methods have been proposed: a simple random sample and a stratified random sample with the survey response as strata. (b) If the stratified random sample is used, what is the number of people that will be selected from those who responded yes? Support your answer by showing your work. Upload files (PDF, JPG, GIF, PNG, TXT, Word, Excel, Powerpoint, file formats supported) 0/2 File Limit (c) Describe a statistical advantage of using the stratified random sample instead of the simple random sample for the follow-up study.
(b) The number of people to be selected from those who responded "yes" in the stratified random sample is 14.
(c) A statistical advantage of using the stratified random sample instead of the simple random sample is that it ensures a proportional representation of each stratum (in this case, "yes" and "no" responses) in the sample, reducing the risk of bias and increasing the accuracy of the results.
The calculation is determined by dividing the total number of samples (20) by the number of strata (2) plus 1, then multiplying by the number of samples for each stratum. The result of 20 / (2 + 1) * 2 is
20 / 3 * 2
= 40 / 3
= approximately 13.33, which is rounded up to 14 people.
In a simple random sample, the individuals selected may not accurately reflect the proportions of the two responses in the population. This can result in incorrect conclusions and decision-making. With the stratified random sample, the proportions of "yes" and "no" responses in the sample are maintained, providing a more accurate representation of the population.
Additionally, stratified random sampling allows for separate analysis of each stratum, which can provide additional insights into the population. Overall, stratified random sampling is a more robust method for obtaining accurate and representative results in a survey setting.
Learn more about simple random samples here:
https://brainly.com/question/13219833
#SPJ4
it is for a grade and i need 4 more questions done
Drag each number tile to the box with the matching expression. 3 1 2 3 1 3 3 1 4 3 1 6 3 2 3 12 1 2 − 9 1 4 5 3 4 − 2 5 12
Answer:
ggggghhytyhhh
Step-by-step explanation:
ghdhb
Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
f(x) =
1 + x2 if x ≤ 0
2 − x if 0 < x ≤ 2
(x − 2)2 if x > 2
x =
continuous from the right continuous from the left neither
On the basis of x-value at x = 0 function is left continuous and at x = 2 function is continuous from left and right both.
Function 'f' is continuous from the right, or from the left, or neither:
x = 0 (smaller value )
[tex]\lim_{x \to 0-} f(x)[/tex]
= [tex]\lim_{x \to 0-}[/tex] ( 1 + x² )
= 1+ 0
= 1
[tex]\lim_{x \to 0+} f(x)[/tex]
= [tex]\lim_{x \to 0+}[/tex] ( 2 - x)
= 2 - 0
= 2
[tex]\lim_{x \to 0} f(x)[/tex]
= f(0)
= 1 + 0²
= 1
[tex]\lim_{x \to 0-} f(x)[/tex] = f(0)
It is left continuous.
x = 2 (larger value )
[tex]\lim_{x \to 2-} f(x)[/tex]
= [tex]\lim_{x \to 2-}[/tex] ( 2 - x )
= 2 - 2
= 0
[tex]\lim_{x \to 2+} f(x)[/tex]
= [tex]\lim_{x \to 2+}[/tex] ( x - 2)²
= ( 2- 2)²
= 0
[tex]\lim_{x \to 2} f(x)[/tex]
= f(2)
= 2 - 2
= 0
[tex]\lim_{x \to 2-} f(x) = \lim_{x \to 2+} f(x)[/tex] = f(2)
It is continuous from both right and left.
Therefore, the function is continuous from left at x= 1 and x = 2 it is continuous from both left and right side.
The above question is incomplete ,the complete question is:
Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
f(x) = 1 + x² if x ≤ 0
2 − x if 0 < x ≤ 2
(x − 2)² if x > 2
x = (smaller value)
continuous from the right, or continuous from the left, or neither
x = (larger value)
continuous from the right, or continuous from the left, or neither.
Learn more about continuous here
brainly.com/question/24898810
#SPJ4
Of digoxin has a half life of 35hrs, how long will it take for a toxic plasma concentration of 8ng/ML to decline to a therapeutic plasma concentration of 2ng/ML?
70hrs, 5 hrs, 130hrs,180hrs ?
Digoxin has a half-life of 35 hours, so it takes 70 hours for the toxic plasma concentration to decline to a therapeutic plasma concentration of 2ng/ML.
What is digoxin?Digoxin has a half-life of 35 hours, which means it takes 35 hours for the quantity of digoxin in the body to be decreased by half. The dangerous plasma concentration of 8ng/ML must be decreased to a therapeutic plasma concentration of 2ng/ML in this circumstance.
To calculate how long this will take, we need to use the formula:
Time = (Toxic Concentration - Therapeutic Concentration) / (0.5 x Half-Life)
Time = (8ng/ML - 2ng/ML) / (0.5 x 35hrs)
Time = 6ng/ML / (17.5hrs)
Time = 0.342hrs
Time = 70hrs
As a result, the dangerous plasma concentration of 8ng/ML will take 70 hours to decrease to a therapeutic plasma concentration of 2ng/ML.
To know more about digoxin, visit
brainly.com/question/15180878
#SPJ1
Complete the proof that \triangle LMN\sim \triangle OPN△LMN∼△OPNtriangle, L, M, N, \sim, triangle, O, P, N. Two triangles L M N and N O P share the same point N. Side length P N is eight. Side Length L N is five. Sides L M and O P are parallel. Two triangles L M N and N O P share the same point N. Side length P N is eight. Side Length L N is five. Sides L M and O P are parallel. Statement Reason 1 \overline{LM}\parallel\overline{OP} LM ∥ OP start overline, L, M, end overline, \parallel, start overline, O, P, end overline Given 2 \angle L\cong\angle O∠L≅∠Oangle, L, \cong, angle, O When a transversal crosses parallel lines, alternate interior angles are congruent. 3 4 \triangle LMN\sim \triangle OPN△LMN∼△OPNtriangle, L, M, N, \sim, triangle, O, P, N similarity
The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem
What is the SSS Congruence Theorem?According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.
here, we have,
In the image given, we have:
ON ≅ MN
LO ≅ LM
LN ≅ LN (reflexive property)
This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:
A. SSS.
Learn more about the SSS congruence theorem on:
brainly.com/question/2102943
#SPJ2
a bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.
The linear speed of the bicycle is 20891.59 inches / min
The bike moving in 19.78 mph
As per the given data:
A bicycle with 20-in.-diameter wheels
Determine the speed that needs to be determined either angular or linear. Determine the given speed and radius.
Determining the linear speed is the task at hand. The indicated angular speed is 190 rpm.
To find the linear speed when the angular speed and the radius of the circular object are given, k revolutions per minute [tex]$ =\frac{k \text { revolutions }}{1 \text { minute }} \times \frac{2 \pi}{1 \text { revolution }} \\[/tex]
[tex]$=\frac{2 \pi k}{\text { minute }}[/tex]
For every cycle of the 7-inch sprocket, the 4-inch goes around
[tex]$\frac{7}{4}$[/tex] = 1.75 times.
Therefore 190 × 1.75+ π × 20 = 20891.59 inches / min
Therefore the linear speed of the bicycle is 20891.59 inches / min
Now, determine how fast the bike is moving in mph.
[tex]$\frac{20891.59}{12} \times \frac{60}{5280}$[/tex]
= 19.78 mph
Bike moving in 19.78 mph.
For more questions on linear speed
https://brainly.com/question/19568162
#SPJ4
A bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.
Find the linear speed of the bicycle (correct to at least two decimal places) in/min
How fast is the bike moving in mph (to two decimal places)?
can someone help me whit this factor[tex](\frac{2x}{7}- \frac{1}{4})^{2}[/tex]
The simplified expression (2x/7 - 1/4)² is given as follows:
(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.
How to simplify the expression?The expression for this problem is defined as follows:
(2x/7 - 1/4)².
The square of a subtracted binomial notable product is given as follows:
(a - b)² = a² - 2ab + b².
The parameters for this problem are given as follows:
a = 2x/7.b = 1/4.Hence the terms of the expression are given as follows:
a² = (2x/7)² = 4x²/49.2ab = 2 x 2x/7 x 1/4 = x/7.b² = (1/4)² = 1/16.Hence the simplified expression is defined as follows:
(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.
More can be learned about simplification of expressions at https://brainly.com/question/723406
#SPJ1
What is the range of the function y= ^3 square root y
Answer:
y= 3 y =0
Step-by-step explanation:
find the derivative
PLEASE HELP!!!! A rectangle has sides measuring (3x + 5) units and (6x + 11) units.
Part A: What is the expression that represents the area of the rectangle?
The expression that represents the area of the rectangle is 18x² + 63x + 55.
What is the multiplication of polynomials?
Multiplying polynomials is a basic concept in algebra. Multiplication of two polynomials will include the product of coefficients to coefficients and variables to variables.
The area is just length times width:
(3x + 5)(6x + 11) = 18x² + 63x + 55
The degree of the expression is the highest power which is in 18x²
Above we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials
Hence, the expression that represents the area of the rectangle is 18x² + 63x + 55.
To learn more about the multiplication of polynomials visit,
https://brainly.com/question/28841024
#SPJ1
Recall the definition of covariance for two random variables, X and W: Cov(X,W) =
E(X − E(X))(W − E(W)).
Prove or disprove
Cov(aX + b, cW) = ac Cov(X,W)
where a, b, and c are constants. Start with applying the covariance definition to Cov(aX +
b, cW), proceed by applying appropriate properties of expectation operator, and see if your
simplified expression is the same as ac Cov(X,W).
Answer:
The statement Cov(aX + b, cW) = ac Cov(X,W) is true.
Step-by-step explanation:
Starting with the definition of covariance:
Cov(aX + b, cW) = E((aX + b) - E(aX + b))(cW - E(cW))
Using linearity of expectation:
Cov(aX + b, cW) = E(a(X - E(X)) + (b - E(b)))(c(W - E(W)))
Expanding and rearranging the product:
Cov(aX + b, cW) = acE(X - E(X))(W - E(W)) + E(b - E(b))E(c(W - E(W)))
Since the expectation of a constant is the constant itself and E(b - E(b)) = 0, the above expression simplifies to:
Cov(aX + b, cW) = ac Cov(X,W)
Determine which of the following best describes the statement below.
"The temperature on randomly selected days throughout the year was measured"
Answer options:
experimental study
observational study
Answer:
observational study to see honestly but this is correct but I don't know the exact reason
I have 1/5 bag of beads leftover from a craft project. My 3 friends and I are going to split the leftover bag of beads. How much of the bag will each person get?
Each person get 4/5 of the e leftover bag of beads.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
From the question,
The total number of leftover beads is 1/5
4 people are to share the leftover beads
so,
the ratio will be 1/5 ÷ 1/4
1/5 x 4
=4/5
Hence, each person will get 4/5 of the beads
Learn more about ratio at:https://brainly.com/question/2914376
#SPJ1
22. Probability have values between _________________ and _________________.
Probability has values between 0 and 1.
What is the Probability?
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
0 represents an impossible event and 1 represents a certain event.
A probability of 0 means that an event will not occur, and a probability of 1 means that an event will certainly occur.
Probabilities between 0 and 1 represent the likelihood of an event occurring, with values closer to 1 indicating a higher likelihood of the event occurring and values closer to 0 indicating a lower likelihood.
Hence, Probability has values between 0 and 1.
To learn more about Probability visit,
https://brainly.com/question/24756209
#SPJ1
A water tank already contains 55 gallons of water when Baxter begins to fill it.
Water flows into the tank at a rate of 8 gallons per minute. Write a linear equation to model this situation. Find the volume of water in the tank 25 minutes after Baxter begins filling the tank.
Answer: 55+ (8* M)
Step-by-step explanation: I think that's the answer
Simplify the expression:
2+2+3+s+ 9 - 10
Answer:
6s
Step-by-step explanation:
2+2+3+S+9-10
first we can put these in different group to find out, like number to number, variable to variable. so it will be 2+3+2+9-10=6
second they only one s, so answer is 6s
i hope is helpful
Maths pls help someone
Using the
slope from the previous
problem, find the
equation of the line
passing through the
points (-2,1) and
(2,-11). The slope is -3
The answer is,
(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]
What is slope?A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. The slope of a line is how steep it is going from LEFT to RIGHT. Slope is the proportion of a line's ascent, or vertical change, to its run, or horizontal change. The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.(i) (-3,2) and (1,4) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{1-(-3)}=\frac{2}{4}=\frac{1}{2}$[/tex]
(ii) [tex]$\left(a_1^2, 2 a_1\right)$[/tex] and [tex]$\left(a t_2^2, 2 a_2\right)$[/tex] Slope of line
[tex]& \frac{y_2-y_1}{x_2-x_1}=\frac{2 a t_2-2 a t_1}{a t_2^2-a t_1^2} \\[/tex]
[tex]& =\frac{2 a\left(t_2-t_1\right)}{a\left(t_2-t_1\right)\left(t_2+t_1\right)}=\frac{2}{t_2+t_1}[/tex]
(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]
The complete question is,
Find the slope of a line passing through the following points:
(i) (-3,2) and (1,4)
(ii) [tex]$\left(a t_1^2, 2 a_1\right)$[/tex]and [tex]$\left(a t_2^2, 2 \mathrm{at}_2\right)$[/tex]
(iii) (3,-5), and (1,2)
To learn more about slope refer to:
https://brainly.com/question/16949303
#SPJ1
En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor
Tomando cocientes veremos que:
a) La probabilidad es 0.84
b) En este caso es 0.16
¿Como encontrar las probabilidades?
Primero queremos encontrar la probabilidad de que una bolsa tenga el peso correcto, la probabilidad esta dada por el cociente entre el numero de bolsas con el peso correcto y el numero total de bolsas analizadas, entonces tendremos:
P = 2100/2500 = 0.84
b) Ahora lo mismo, pero con una bolsa de peso menor o mayor, tenemos:
125 que pesan mas
275 que pesan menos
Por un total de 125 + 275 = 400
Entonces la probabilidad es:
P = 400/2500 = 0.16
Aprende más sobre probabilidad en:
https://brainly.com/question/25870256
#SPJ1
La pregunta completa es:
En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor
a) ¿Cuál es la probabilidad de que tenga el peso correcto?
b) ¿Cuál es la probabilidad de que tenga un peso menor o mayor?
Find the value of sin D rounded to the nearest hundredth, if necessary.
E90°
F
E√13
E
D√87
Answer:
below
Step-by-step explanation:
Need the diagram......
A survey asked people of different ages wether they get their news by reading the paper. what is the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper if necessary, round .
The probability that a person surveyed gets the news by reading the paper, given that he or she is under 40 is 10%. The Option A is correct.
How do we arrive at 10% as our probability?We are given that number of people who read paper and under 40 is 4 and number of people who are under 40 is 40.
We need to find the probability that a person surveyed gets the news by reading the paper given that he or she is under 40.
We will use the "Conditional probability": P (Person that read the paper given that he or she is under 40) is given by:
= P(read the paper and under age 40) / P(person who are under age 40)
= 4 / 40
= 0.1
= 10%
Full questions"A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed gets the news by reading the paper, given that he or she is under 40? If necessary, round your answer to the nearest percent. A.10% B.14% C.5% D.90%
Read more about probability
brainly.com/question/24756209
#SPJ1
HELP !!!!!!!! Jahaksgshshshshshsgshhaehhehee
On using the formula for compound interest the amount of time it will take until the account of Gracie has a balance of $0 is 4 years.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The initial deposit made by Gracie is P = $30,000
The rate at which the interest is earned r = 3.1% = 3.1/100 = 0.031
The withdrawal amount is W = $150
The number of times interest is compounded n = 52 weeks
The formula for compound interest becomes -
P = W[1 - {1 + (r/n)}^(-nt)] / (r/n)
Substitute the values into the equation -
30000 = 150[1 - {1 + (0.031/52)}^(-52)t] / (0.031/52)
Divide both sides with 150 and simplify -
200 = [1 - ({1 + 0.00059}^(-52)t)]/0.00059
200 = [1 - (1.00059)^(-52)t)]/0.00059
Multiply both sides with 0.00059 -
0.118 = 1 - (1.00059)^(-52)t
(1.00059)^(-52)t = 1 - 0.118
(1.00059)^(-52)t = 0.882
Using one to one property, and power property -
-52t log 1.00059 = log 0.882
t = (log 0.882/log 1.00059) / -52
t = (-0.0545/0.000256) / -52
t = -212.890625/ -52
t = 4.09 ≈ 4
Therefore, the time value is obtained as 4 years.
To learn more about compound interest from the given link
https://brainly.com/question/28020457
#SPJ1
expand (2x2^+3)(4x+5)-8x(x2^-2)
Answer: Expanding the expression:
(2x * 2^+3) * (4x + 5) - 8x * (x^2^-2)
Start with the first set of parentheses:
2x * 2^+3 = 2x * 8 = 16x
Next, the second set of parentheses:
16x * (4x + 5) = 16x * 4x + 16x * 5 = 64x^2 + 80x
Finally, the third set:
-8x * (x^2^-2) = -8x * x^2^-2 = -8x * (1/x^2) = -8/x
So the final expanded form is:
64x^2 + 72x - 8/x
Step-by-step explanation:
a box containing 8 shock absorbers and 10 brake pad sets weighs 101.6 lb
Answer:
10.16 lb
Step-by-step explanation:
This is a classic example of a problem that can be solved using dimensional analysis. To find the weight of a single shock absorber or brake pad set, you need to divide the total weight by the number of items in the box.
Weight of a single shock absorber = Total weight of shock absorbers / Number of shock absorbers in the box
= 101.6 lb / 8
= 12.7 lb
Weight of a single brake pad set = Total weight of brake pad sets / Number of brake pad sets in the box
= 101.6 lb / 10
= 10.16 lb
Therefore, a single shock absorber weighs 12.7 lb and a single brake pad set weighs 10.16 lb.
an investor can design a risky portfolio based on two stocks, a and b. stock a has an expected return of 12% and a standard deviation of return of 18.0%. stock b has an expected return of 8% and a standard deviation of return of 3%. the correlation coefficient between the returns of a and b is 0.50. the risk-free rate of return is 6%. the proportion of the optimal risky portfolio that should be invested in stock a is . question 7 options: 0% 50% 32% 56%
To calculate the proportion of the optimal risky portfolio that should be invested in stock A, we need to use the formula for a two-stock portfolio.
Let x be the proportion of the portfolio invested in stock A, then [tex](1 - x)[/tex]is the proportion invested in stock B.
The expected return of the portfolio,[tex]E(Rp)[/tex], can be calculated as:
[tex]E(Rp) = x * E(Ra) + (1 - x) * E(Rb)[/tex]
The standard deviation of the portfolio, σp, can be calculated as:
[tex]σp = sqrt(x^2 * σa^2 + (1 - x)^2 * σb^2 + 2x * (1 - x) * σa * σb * ρab)[/tex]
where σa is the standard deviation of stock A, [tex]σb[/tex] is the standard deviation of stock B, and [tex]ρab[/tex] is the correlation coefficient between the returns of A and B.
Substituting the given values, we get:
[tex]E(Rp) = x * 0.12 + (1 - x) * 0.08 = 0.1σp = sqrt(x^2 * 0.18^2 + (1 - x)^2 * 0.03^2 + 2x * (1-x) * 0.18 * 0.03 * 0.50)[/tex]
The optimal risky portfolio is the one that has the maximum Sharpe ratio, which is defined as:
Sharpe ratio =[tex](E(Rp) - Rf) / σp[/tex]
where Rf is the risk-free rate of return.
By equating the derivative of the Sharpe ratio to zero and solving for [tex]x[/tex], we can find the optimal proportion of the portfolio to be invested in stock A. So, the proportion of the optimal risky portfolio that should be invested in stock A is 56%.
To know more about standard deviation
brainly.com/question/23907081
#SPJ4
Please help with this problem
[tex]-\sqrt{9y^2} = -1\cdot \sqrt{9}\cdot \sqrt{y^2}[/tex]
I assume you're good with [tex]\sqrt{9}=3[/tex], so this gives us:
[tex]= -3\cdot \sqrt{y^2}[/tex]
Now the trick on the variable portion is that since y<0, when you square y, you turn it from being a negative number into a positive [tex]y^2[/tex] value. And when you take the square root of that, you keep the positive value. So effectively, [tex]\sqrt{y^2} = |y|[/tex], since it just makes the negative number become positive.
[tex]= -3|y|[/tex]
