It will take 12.8047 years for Jari's investment to double
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:
A is the future value of the investment/loan, including interestP is the principal investment amount (the initial deposit or loan amount)r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forJari invests in a CD with an annual interest rate of 5.45% compounded quarterly. We need to find how many years it will take for Jari's investment to double.
∵ The annual interest rate is 5.45%
∴ r = 5.45% = 5.45 ÷ 100 = 0.0545
∵ The interest rate is compounded quarterly
∴ n = 4
∵ The Jari's investment is doubled in t years
∴ A = 2P
- Substitute these values in the rule above
∵ [tex]2P=P(1+\frac{0.0545}{4})^{4t}[/tex]
- Divide both sides by P
∴ [tex]2=(1+\frac{0.0545}{4})^{4t}[/tex]
∴ [tex]2=(1+0.013625)^{4t}[/tex]
∴ [tex]2=(1.013625)^{4t}[/tex]
- Insert ㏒ to both sides
∴ [tex]log(2)=log[(1.013625)^{4t}][/tex]
- Remember [tex]log(a)^{n}=nlog(a)[/tex]
∴ ㏒(2) = 4t ㏒(1.013625)
- Divide both sides by 4 ㏒(1.013625) to find t
∴ t = 12.8047 years
It will take 12.8047 years for Jari's investment to double
Learn more;
You can learn more about compound interest in brainly.com/question/4361464
#LearnwithBrainly
add 9 and 3, then add 6 to the result
Answer:
Step-by-step explanation:
18
9+3=12+6=18
Answer:
18
Step-by-step explanation:
Add 9 and 3;
9 + 3 = 12
Then add 6 to the result
12 + 6 = 18
Deja spends 25% of her monthly salary on her rent. Her rent is $650 a month. What is dejas monthly salary
Answer:
Monthly Salary = $2,600
Step-by-step explanation:
Monthly rent on monthly salary = 25%
Monthly rent = $650.
To determine the monthly sale, we have to use the unitary method.
25% monthly rent on monthly salary means out of $100, Deja spends $25 on her rent.
Therefore,
Deja spends $25 on her rent, when the monthly salary = $100
Deja spends $1 on her rent, when the monthly salary = [tex]\frac{100}{25}[/tex]
Deja spends $650 on her rent, when the monthly salary = [tex]\frac{100*650}{25}[/tex]
= [tex]\frac{65000}{25}[/tex]
= $2,600
Her monthly salary is $2,600.
HELP An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the investor's total profit was $104, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 5% was $(blank). The amount invested in the mutual fund that earned 3% was $(blank). (show your work)
Answer:
The amount invested in the mutual fund that earned 5% was $1,000
The amount invested in the mutual fund that earned 3% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested in the mutual fund that earned 5%
y ----> the amount invested in the mutual fund that earned 3%
we know that
[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A
[tex]5\%=5/100=0.05[/tex]
[tex]3\%=3/100=0.03[/tex]
[tex]0.05x+0.03y=104[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.05x+0.03(2,800-x)=104[/tex]
Solve for x
[tex]0.05x+84-0.03x=104[/tex]
[tex]0.05x-0.03x=104-84[/tex]
[tex]0.02x=20[/tex]
[tex]x=\$1,000[/tex]
Find the value of y
[tex]y=2,800-x[/tex]
[tex]y=2,800-1,000=\$1,800[/tex]
therefore
The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800
Use addition to solve the linear system of equations y=2x-5 3x+3=y
Answer:
(-8, -21)
Step-by-step explanation:
y=2x-5
3x+3=y
------------
2x-5=3x+3
2x-3x-5=3
-x-5=3
-x=3+5
-x=8
x=-8
y=2(-8)-5=-16-5=-21
Answer: x=-8, y=-21.
Jasmine has 3/4 cup of flour in a mixing bowl. After adding more flour to the mixing bowl, Jasmine says that she now has 5/8 cup of flour.
Why is her statement incorrect?
Answer:
6/8
Step-by-step explanation:
3/4 into eighths would be 6/8. She said she had 5/8 cups of flour.
Caleb paid $26.70, including a 7% sales tax, for a security wallet. How much did the wallet itself cost?
Answer:
24.36
Step-by-step explanation:
26.7 / 1.07 = 24.36
determina la medida de cada uno de los angulos del triángulo ABC si se conoce que (3x+1)° (3x+4)° y (2x-1)°
Answer:
∠A=67°
∠B=70°
∠C=43°
Step-by-step explanation:
The correct question in English is
Determines the measurement of each of the angles of the triangle ABC if it is known that A=(3x+1)°,B=(3x+4)° and C=(2x-1)°.
we know that
The measure of the interior angles in a triangle must be equal to 180 degrees
so
∠A+∠B+∠C=180°
substitute the given values
[tex](3x+1)\°+(3x+4)\°+(2x-1)\°=180\°[/tex]
solve for x
[tex](8x+4)\°=180\°[/tex]
[tex]8x=180-4[/tex]
[tex]x=22[/tex]
Find the measure of each angle
∠A=(3(22)+1)=67°
∠B=(3(22)+4)=70°
∠C=(2(22)-1)=43°
someone please help with 17!! leave work below
Answer:
The amount charged is proportional to the ears of corn
Step-by-step explanation:
Now I'm going to explain, but write it in your own words. It's proportional because the amount charged is completely reliant on how many ears of corn you are buying.
So for every 1 ear of corn, you pay about 33 cents
or
For every 2 ears of corn, you pay about 67 cents
The amount you pay completely relies on how many you're buyingThe width of a rectangle is 3/8 the length x of the rectangle. What is the perimeter of the rectangle?
Answer:
(11/4)x units
Step-by-step explanation:
for a rectangle,
perimeter = 2(length) + 2(width)
given:
length = x
width = (3/8)x
hence,
perimeter = 2(length) + 2(width)
perimeter = 2x + 2(3/8)x
perimeter = 2x + (3/4)x
perimeter = [2 + (3/4)]x
perimeter = (11/4)x
x|x integars between 4 & 8 lost the elements in the set
Answer:
The set of integer between 4 and 8 = { 5, 6, 7 }.
Step-by-step explanation:
Set:
A set is a well-defined collection of distinct objects, elements encloses in curly bracket.
For example.
set of vowels = { a, e, i, o, u }
set of any three Capital alphabets = { A, B ,Z }
set of cars = { Ferrari, Volvo, Mercedes, Audi }
Now we want set of integer between 4 and 8
Integer: All the positive and negative natural numbers are called integers.
-1, -2, -3, 1, 2, 3, 4, 5, 6 ,7 , 8 ..
The set of integer between 4 and 8 = { 5, 6, 7 }.
Determine the intercepts of the line.
y=-3x+12y=−3x+12
Answer:
x-intercept=4 and y-intercept = 12
Step-by-step explanation:
To find the x-intercept, make the y=0:
0 = -3x+12
3x = 12
x=12/3
x=4
To find the y-intercept, make the x=0:
y = -3(0) +12
y = 0 +12
y = 12
Hope this helps!
Please mark brainliest if you think I helped! Would really appreciate!
Answer:
y=12,0
x=4,0
Step-by-step explanation:
for those who were just as confused as i was <3
To divide a number by 100, move the decimal point _____.
two places to the right
three places to the left
two places to the left
three places to the right
Answer:
c. two places to the left
Step-by-step explanation:
Answer:
two places to the left
Step-by-step explanation:
The difference of 2 times a number and 3/4 is 1/2. Determine the number
Answer:
5/8
Step-by-step explanation:
if I understand correctly the problem is
(2*X)-(3/4)=1/2
to solve for x we need to isolate it, the first step in doing so is getting rid of the 3/4
2*X-3/4+3/4=1/2+3/4
simplify
2*X=1 1/4
the next step is getting rid of the 2
(2*X)/2=(1 1/4)/2
simplify
X=5/8
5 different mathematics books, 4 different French books and 2 different biology books are to be arrange on a shelf. How many different arrangements are possible, if
1. The books in each particular subject must all stand together?
2. Only the mathematics books must stand together.
Problem 1
A = 5! = 5*4*3*2*1 = 120 ways to arrange the math books
B = 4! = 4*3*2*1 = 24 ways to arrange the French books
C = 2! = 2*1 = 2 ways to arrange the biology books
D = 3! = 3*2*1 = 6 ways to arrange the three blocks of books, each block a different subject
E = A*B*C*D = 120*24*2*6 = 34560 different ways to arrange the books such that the subjects stick together
-------------
Answer: 34560========================================
Problem 2
Group all the math books to form one "book". This is the same as taking out the 5 math books and replacing it with one single math book. This single math book acts as a placeholder for all of the five books together as one block.
We have
1 math "book"
4 French books
2 biology books
So there are 1+4+2 = 7 "books" total and
7! = 7*6*5*4*3*2*1 = 5040 different ways to arrange those "books"
Within the math block of books, there are 5! = 120 ways to arrange things.
So overall we have 120*5040 = 604800
-------------
Answer: 604800ANSWER MY QUESTION PLEASE
Here is a linear equation: y = 1/4x + 5/4. Find the x-intercept of the graph of the equation.
Hint: the y-value will be 0 at the x-intercept.
write your answer
To find the x-intercept of the linear equation y = 1/4x + 5/4, substitute y = 0 into the equation and solve for x. The x-intercept is -5.
Explanation:To find the x-intercept of the graph of the equation y = 1/4x + 5/4, we need to set the y-value to 0 and solve for x.
So, by substituting y = 0 into the equation, we get 0 = 1/4x + 5/4.
Now, we can solve for x by isolating x on one side of the equation. Subtracting 5/4 from both sides gives us -5/4 = 1/4x. Multiplying both sides by 4 gives us -5 = x, or x = -5.
Therefore, the x-intercept of the graph is -5.
Learn more about x-intercept here:https://brainly.com/question/27887128
#SPJ2
Your get a haircut that cost $23.if you tip the barber 10%,what is the final bill?
Answer:
$25.30
Step-by-step explanation:
The final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
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.
It is given that:
You get a haircut that cost $23.if you tip the barber 10% of the total hair cut cost.
Let x be the final bill amount.
The value of x can be found as follows:
x = $23 + 10% of $23
x = 23 + (10/100)23
x = 23 + 0.1(23)
x = 23 + 2.30
x = $25.30
Thus, the final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
cos(t)=24/25, what does sin(t)=?
Answer:
The value of sin t is [tex]\frac{7}{25}[/tex]
Step-by-step explanation:
Given as :
cos (t) = [tex]\frac{24}{25}[/tex]
Since sin² t + cos² t = 1
So, sin² t = 1 - cos² t
or, sin² t = 1 - ([tex]\frac{24}{25}[/tex])²
or, sin² t = [tex]\frac{25^{2} - 24^{2} }{25^{2} }[/tex]
Or, sin² t = [tex]\frac{625 - 576}{625}[/tex]
Or , sin² t = [tex]\frac{49}{625}[/tex]
Or, sin t = [tex]\sqrt{\frac{49}{625} }[/tex]
So, sin t = [tex]\frac{7}{25}[/tex]
Hence The value of sin t is [tex]\frac{7}{25}[/tex] Answer
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown on the right, making the one day sale price of the ski set $328. Find the original selling price of the ski set.
The original selling price of the ski set is $585.71.
Explanation:Step 1: Determine the final sale price after the first markdown
The one-day sale price of the ski set is $328, and the first markdown is 20%. To find the final sale price after the first markdown, we can set up the equation:
0.80 × Original Price = $328
Solving for the original price, we get:
Original Price = $328 / 0.80 = $410
Therefore, the final sale price after the first markdown is $410.
Step 2: Determine the original selling price
The final sale price after the first markdown is $410, and the second markdown is 30%. To find the original selling price, we can set up the equation:
0.70 × Original Price = $410
Solving for the original price, we get:
Original Price = $410 / 0.70 = $585.71
Therefore, the original selling price of the ski set is $585.71.
Evelyn is using her grandmother's pancake recipe, but she wants to make 40% more pancakes than the recipe usually prepares. If her grandmother's recipe calls for 1/2 cup of flour, how much flour will Evelyn need to use? Show Work!
(A) 3/10 cup
(B) 1/2 cup
(C) 7/10 cup
(D) 1 3/10 cup
(C) 7/10 cup is the correct answer
Step-by-step explanation:
First of all we will calculate the 40% of grandmother's recipe then add it to the given flour in grandma's recipe
So,
The amount of flour in grandma's recipe = F_g = 1/2 cups
Calculating percentage
[tex]=40\%\ of\ \frac{1}{2}\\=\frac{40}{100}*\frac{1}{2}\\=\frac{2}{10}[/tex]
So Evelyn needs to add 2/10 cups more to the original quantity.
So,
Flour used by Evelyn:
[tex]=\frac{1}{2}+\frac{2}{10}\\\\=\frac{5+2}{10}\\\\=\frac{7}{10}\ cups[/tex]
Hence,
(C) 7/10 cup is the correct answer
Keywords: Percentage, Quantity
Learn more about percentage at:
brainly.com/question/11286417brainly.com/question/11566221#LearnwithBrainly
it took jack 360 seconds to walk home from school how many min did it take him
1 minute has 60 seconds. So dividing the number of seconds jack has to walk from school to home by 60 will give us minutes.
[tex]t=\dfrac{360\mathrm{s}}{60}=\boxed{6\mathrm{min}}[/tex]
Hope this helps.
Which two points on the number line represent numbers that can be combined to make zero? C
Answer:
The are infinite
Step-by-step explanation:
some are 1,-1
2,-2
3,-3
10000,-10000
Answer:
It’s a
Step-by-step explanation:
Avery bought 5 packs of pencils there were eight pencils in each back if every team line pencils to her friends how many pencils does Avery have left
Answer:
31
Step-by-step explanation:
Avery has 31 left
5 x 8 = 40
40 - 9 = 31
therefore avery has 31 pencils left
4. How much time will it take for a bug to travel 7.5 meters across the floor if it is traveling at 1 m/s?
It will take the bug 7.5s to travel across the floor.
Step-by-step explanation:
Distance = 7.5 meters
Speed = 1 m/s
The formula for speed is
[tex]Speed = \frac{Distance}{Time}\\\\Time = \frac{Distance}{Speed}\\Time=\frac{7.5}{1}\\Time=7.5\ s[/tex]
It will take the bug 7.5s to travel across the floor.
Keywords: distance, speed
Learn more about distance at:
brainly.com/question/4460262brainly.com/question/4464845#LearnwithBrainly
what is the sign of 3/5 + 3/5
Final answer:
The sum of two positive numbers always has a positive sign, so the sum of 3/5 + 3/5 is positive.
Explanation:
The question what is the sign of 3/5 + 3/5 involves understanding the rules of addition for numbers with the same sign. According to the rules of addition:
When two positive numbers add, the answer has a +ve sign.
Since both fractions 3/5 and 3/5 are positive, their sum will also have a positive sign. Therefore, the sign of the sum 3/5 + 3/5 is +ve, which means the answer is also positive.
Write an inequality for the graph.
Answer:
x ≤ 3
This is because it is a closed circle.
-3 2/7 times .14 as a decimal and a fraction
Answer:
-0.46 or -23/50
Step-by-step explanation:
We note that 0.14 is easily divisible by 7, so we can do this using the distributive property:
(-3 2/7)(0.14) = (-1)(3 + 2/7)(0.14)
= (-1)(3×0.14 +2/7×0.14)
= (-1)(0.42 +0.04)
= -0.46 . . . . . decimal form
= -46/100 . . . . place value
= -23/50 . . . . remove common factor of 2; fraction form
The product is -0.46 or -23/50.
Can someone please explain to me HOW to transform this equation to determine if its an identity (8x+12y)^2+(6x+9y)=(10x+15y)^2
Answer:
See explanation
Step-by-step explanation:
Given
[tex](8x+12y)^2+(6x+9y)^2=(10x+15y)^2[/tex]
Note
[tex](8x+12y)^2=(4(2x+3y))^2=16(2x+3y)^2\\ \\(6x+9y)^2=(3(2x+3y))^2=9(2x+3y)^2\\ \\(10x+15y)^2=(5(2x+3y))^2=25(2x+3y)^2[/tex]
Since
[tex]16(2x+3y)^2+9(2x+3y)^2=(2x+3y)^2(16+9)=25(2x+3y)^2,[/tex]
this is an identity
A loan of $46,000 is made at 7% interest, compounded annually. After how many years will the amount due reach $65,000 or more?
After 5.11 years, amount due reach $65,000 or more
Solution:
Given that a loan of $46,000 is made.
Rate of interest charged is 7% compounded annually
Need to determine number of years in which the amount due reach $65,000 or more.
In our case
Amount due A = $65000
Loan Amount that is principal P = $46000
Rate of interest r = 7%
Formula for Amount compounded anually is as follows:
[tex]\mathrm{A}=P\left(1+\frac{r}{100}\right)^{n}[/tex]
Substituting the values in above formula we get
[tex]\begin{array}{l}{65000=46000\left(1+\frac{7}{100}\right)^{n}} \\\\ {\frac{65000}{46000}=\left(\frac{107}{100}\right)^{n}} \\\\ {\Rightarrow 1.4130=(1.07)^{n}}\end{array}[/tex]
Applying log on both sides, we
[tex]\begin{array}{l}{\ln 1.4130=n \ln 1.07} \\\\ {=>\frac{\ln 1.4130}{\ln 1.07}=\mathrm{n}} \\\\ {=>\mathrm{n}=\frac{0.34571}{0.067658}=5.1096=5.11}\end{array}[/tex]
Hence after 5.11 years , amount due reach $65,000 or more
A satellite travels 29 1/2 miles every 4 1/3
seconds. What is its unit rate of speed?
Answer:
The speed at which the satellite travel is 6.80 miles per second
Step-by-step explanation:
Given as :
The distance cover by satellites = 29 [tex]\frac{1}{2}[/tex] miles
Or, The distance cover by satellites = [tex]\frac{59}{2}[/tex] miles
The Time taken by satellite to travel with this speed = 4[tex]\frac{1}{3}[/tex] sec
Or, The Time taken by satellite to travel with this speed = [tex]\frac{13}{3}[/tex] seconds
Let the Speed with which the satellite travel = s miles per second
Now, As we know
Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]
Or, s = [tex]\frac{\frac{52}{2}}{\frac{13}{3}}[/tex]
or, s = [tex]\frac{59\times 3}{2\times 13}[/tex]
∴ s = 6.80 mps
So, speed = s = 6.80 miles per second
Hence The speed at which the satellite travel is 6.80 miles per second Anwser
In a recipe for double chocolate every 1/2 cup of milk calls for 2 cups of chocolate. if the recipe were increased to include 4 cups of chocolate, how much milk would be needed?
Answer:1 C milk
Step-by-step explanation:
1/2 C milk = 2 C chocolate
1 C milk = 4 C chocolate
Answer:
1 cup of milk
Step-by-step explanation:
If 1/2 cup of milk is needed for 2 cups of chocolate, and you need to find how much milk is needed for 4 cups, then you'd follow the same steps as going from 2 cups to 4, multiplying by 2.
2 cups chocolate x 2 = 4 cups chocolate
1/2 cup milk x 2 = 1 cup