Given : Invested amount = $5000.
Rate of interet = r% compunded monthly.
Number of years = 4 years.
Total interest received = $1866.
Therefore, total amount after 4 years = 5000+1866 = $6866.
We know, formula for compound interest :
[tex]A=P(1+\frac{r}{n})^{t\times n}[/tex], where P is the invested amount, n is the number of monthly installments in an year.
Number of months in an year are 12.
Plugging n=12, P=5000, t=4 in the formula now, we get
[tex]6866=5000{(1+\frac{r}{12})^{12\times 4}[/tex]
[tex]6866=5000{(1+\frac{r}{12})^{48}[/tex]
Dividing both sides by 5000, we get
[tex]\frac{6866}{5000} =\frac{5000}{5000} {(1+\frac{r}{12})^{48}[/tex]
[tex]\frac{6866}{5000} = {(1+\frac{r}{12})^{48}[/tex]
[tex]1.3732= {(1+\frac{r}{12})^{48}[/tex]
Taking 48th root on both sides, we get
[tex]\sqrt[48]{1.3732} = \sqrt[48]{(1+\frac{r}{12})^{48}}[/tex]
[tex]\sqrt[48]{1.3732}=\left(1+\frac{r}{12}\right)[/tex]
[tex]1.00662903758=1+\frac{r}{12}[/tex]
Subtracting 1 from both sides, we get
0.00662903758 = [tex]\frac{r}{12}[/tex]
Multiplying by 12 on both sides, we get
r=0.07954845101
r≈0.0795
Or 7.95%.
A) The value of r is 7.95% compounded monthly.Now, we need to find the interest after four years if the rate of interest is 3.6% compounded quarterly.
There are 4 quarters in an year.
So, n=4 and r=3.6%= 0.036.
Plugging values in compound interest formula now, we get
[tex]A=5000{(1+\frac{0.036}{4})^{4\times 4}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{0.036}{4}=0.009[/tex]
[tex]A=5000\times \:1.009^{16}[/tex]
[tex]A=5000\times \:1.15414\dots[/tex]
[tex]=5770.70222\dots[/tex]
A≈5770.70
Subtracting 5770.70 -5000.00 = 770.70.
B) Therefore, the total interest he received at the end of the four years upto two decimal places is $770.70.(A)
We are given
Mr tan invested 5000 Swiss francs(CHf) bank
so,
[tex]P=5000[/tex]
nominal annual interest rate of r% compounded monthly
so, n=12
t=4
total interest he received was 1866 CHF
I=1866
we can use formula
[tex]I=P(1+\frac{r}{n} )^{nt}-P[/tex]
now, we can plug values
[tex]1866=5000(1+\frac{r}{12} )^{12*4}-5000[/tex]
now, we can solve for r
[tex]r=0.0795[/tex]
so, interest rate is 7.95%..........Answer
(B)
we are given
P=5000
r=0.036
n=4
t=4
so, we can use interest formula
[tex]I=P(1+\frac{r}{n} )^{nt}-P[/tex]
now, we can plug values
[tex]I=5000(1+\frac{0.036}{4} )^{4*4}-5000[/tex]
now, we can simplify it
and we get
[tex]I=770.702[/tex]
The total interest is 771 CHF...........Answer
Test Number Score
________________
1 86
_________
2 84
_________
3 79
_________
4 87
_________
5 75
_________
6 84
_________
7 89
_________
8 90
_________
9 88
_________
10 92
_________
Sara has been using an online review program to take practice tests for her upcoming graduation exam. Her scores are shown in the table. What is the range of the data set?
A) 17
B) 79
C) 85.4
D) 86.5
Answer:
17
Step-by-step explanation:
86 , 84 , 79, 87 , 75 , 84, 89, 90, 88, 92
The lowest and highest grades are shown above.
92 - 75 = 17
Answer:
17
Step-by-step explanation:
86 , 84 , 79, 87 , 75 , 84, 89, 90, 88, 92
The lowest and highest grades are shown above.
92 - 75 = 17
Maryland’s snowfall total for December was 1.43 inches and for January it was 12.67 inches. What was the total snowfall for December and January together?
14.1 inches is the total snowfall for Dec. and Jan. together.
Jack has g golf balls. The balls came in 8 packages. How many golf balls were in each package?
HELP ME PLEASE!!! 2(b+3)-(7+b)=-7 ??
2(b + 3) - (7 + b) = -7
2b + 6 - 7 - b = -7
b = -6 + 7 - 7
b = -6
To solve this first distribute the 2, and then distribute the negative sign.
2(b+3)-(7+b)=-7
2b+6-7-b=-7
Combine like terms.
2b+(-b)=b
6+(-7)=-1
b-1=-7
Add 1 on both sides of the equation.
b-1+1=-7+1
b=-6
Can someone help me on this pls
Identify the property that is being applied at each step to simplify the expression
We are given
First expression:
[tex]4^{-5} \cdot (4 \cdot 9)^{5} \cdot 9^{-3}=4^{-5} \cdot (4^{5} \cdot 9^{5}) \cdot 9^{-3}[/tex]
We used property
power rule-II:
Product to power distribute to each base
[tex](a \cdot b)^m=a^m \cdot b^m[/tex]
Second expression:
[tex]=(4^{-5} \cdot 4^{5}) \cdot ( 9^{5}) \cdot 9^{-3})[/tex]
we used property
associative property of multiplication:
[tex]a \cdot b \cdot c \cdot d =(a \cdot b) \cdot (c \cdot d)[/tex]
Third expression:
[tex]=4^0 \cdot 9^2[/tex]
we used property
Product Rule:
Same base add exponents
[tex]a^m \cdot a^n =a^{m+n}[/tex]
Fourth expression:
[tex]=1 \cdot 9^2[/tex]
we used property
Zero Exponent :
Anything to the zero power (except 0) is one
[tex]a^0=1[/tex]
Fifth expression:
[tex]= 9^2[/tex]
we used property
Multiplicative identity:
[tex]1 \cdot a=a[/tex]
Sixth expression:
[tex]= 81[/tex]
We used simplification
to make a shade of plant called Jasper Green, Mix 4 quarts of green paint with 2/3 cups of black paint. how much green paint should be mixed with 4 cups of black paint to make Jasper Green?
Answer
24 quarts of green paint should be mixed with 4 cups of black paint.
That is (96 cups)
Step by step explanation
Jasper Green mix 4 quarts of green paint with 2/3 cups of black paint.
Let's convert 4 quarts into cups.
1 quart = 4 cups
4 quarts = 16 cups
Here mix 16 cups of green paint with 2/3 cups of black paint.
Let's use the proportion
Green paint Black paint
16 2/3
x 4
16/x =2/3 divided by 4
[tex]\frac{16}{x} = \frac{2/3}{4}[/tex]
Cross multiplying, we get
16*4 = 2/3 x
64 = 2/3 x
x = 64/(2/3)
x = 64 * 3/2
x = 192/2
x = 96 cups
96 cups of green paint should be mixed with 4 cups of black paint.
We can covert 96 cups into quarts by dividing by 4
96/4 = 24 quarts
24 quarts of green paint should be mixed with 4 cups of black paint.
Thank you.
To make Jasper Green with 4 cups of black paint, you need to create a proportional relationship and solve for the amount of green paint needed, which is 96 cups.
Explanation:To solve this, we need to set up a proportional relationship between the amounts of green paint and black paint. In the first mixture, we have 4 quarts of green paint for every 2/3 cups of black paint. Converting 4 quarts to cups (since 1 quart = 4 cups), we get 16 cups of green paint.
Then we can set up the proportion: (16 cups green / 2/3 cups black) = (x cups green / 4 cups black). Cross multiplying and solving for x, we get x = 96 cups of green paint. So, to make Jasper Green with 4 cups of black paint, you need to mix in 96 cups of green paint.
Learn more about Proportional Relationship here:https://brainly.com/question/29765554
#SPJ11
hiking up a mountain,you notice that the air temperature drops 10°c for every 1,000 meters increase in elevation to represent the decrease in temperature if you hike up the mountain 2,000 meters. Then evaluate the expression and explain it's meaning
Answer: A-500 meters
Step-by-step explanation:
A store sells 2 1/4 pounds of tomatoes in a package for $4.45. The expression 4.45p represents the cost of the tomatoes for a number of packages. What does the variable p represent?
Answer:
The variable p represent the number of packages.
Step-by-step explanation:
As 4.45 is the cost of tomatoes, and 4.45p represents the cost of the tomatoes for a number of packages, we can say that p represent the number of packages.
What value of y will make this expression equal to 2.45?
What is the expression?
Any value of y, except when y = -4.9, will make the expression equal to 2.45.
i need help please and thanks
1. 3p: Add 6 to negative 3, and carry over the "p"
3. 6x: Subtract 1 from 7 and carry over the "x"
5. -4v: Add 6 to negative 10 and carry over the "v"
7. -4r + 9: Add 5 to -9 and carry over the "r". Then put "+9" after the variable, since the other 9 was by itself.
9. 14n: Add 5 to 9 and carry over the "n".
I hope this helps!
Solve for x: 3|x − 3| + 2 = 14 (5 points)
x = 0, x = 7
x = −1, x = 7
No solutions
x = −1, x = 8.3
[tex]Solution, solve\:for\:x,\:3\left|x-3\right|+2=14\quad :\quad x=-1\quad \mathrm{or}\quad \:x=7[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}, 3\left|x-3\right|+2-2=14-2[/tex]
[tex]\mathrm{Simplify}, 3\left|x-3\right|=12[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3, \frac{3\left|x-3\right|}{3}=\frac{12}{3}[/tex]
[tex]\mathrm{Simplify}, \left|x-3\right|=4[/tex]
[tex]|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a, x-3=-4\quad \quad \mathrm{or}\quad \:\quad \:x-3=4[/tex]
[tex]x-3=-4\quad :\quad x=-1[/tex]
[tex]x-3=4\quad :\quad x=7[/tex]
[tex]\mathrm{Combine\:the\:ranges}, x=-1\quad \mathrm{or}\quad \:x=7[/tex]
The correct answer is B. x=-1, x=7
Hope this helps!!!
Admission to the circus cost x dollars for an adult and y for a child find the total cost of 6 adults and 4 children
10 points!
Find the domain and range.
The domain is the first x of each ordered pair. The domain is 1, -30, -12, -11
The range is the y value : -27,30,21,4
Suppose 48 out 120 people like baseball. Of the people who like baseball, 3 out 5 play baseball. If you ask 500 people, how many would you expect to play baseball?
Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked the poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1 1/3 inches. What is the scale factor as a fraction (and how would I do this!?)
[tex]\frac{3 (ft)}{2(in)} by \frac{2(ft)}{\frac{4}{3}(in)}[/tex]
= [tex]\frac{3 (ft)}{2(in)} by \frac{2(3)(ft)}{4(in)}[/tex]
= [tex]\frac{3 (ft)}{2(in)} by \frac{3(ft)}{2(in)}[/tex]
Scale factor is: [tex]\frac{3(ft)}{2(in)}[/tex]
Answer:
9/16 is the scale factor.Step-by-step explanation:
Every transformation has an original figure and a transformed figure.
In order to find the scale factor fo the transformation, we need to divide the transformed dimensions by the original ones.
So, in this case, the poster originally had 3 feet by 2 feet. Then, the reproduced artwork has 2 inches by 1 1/3 inches. Before we divide, we need to transform feet to inches.
We know that 1 feet equals 12 inches, that means
[tex]3ft \frac{12in}{1ft} =36in[/tex]
[tex]2ft\frac{12in}{1ft}=24in[/tex]
Then, we do the divisions
[tex]\frac{36in}{2in}=18\\\frac{24in}{1\frac{1}{3}in }=\frac{24in}{\frac{4}{3}in }=\frac{96}{3}=32[/tex]
Therefore, the scale factor is [tex]\frac{18}{32}=\frac{9}{16}[/tex]
A bag contains 6 blue marbles, 10 red marbles, and 9 green marbles. If two marbles are drawn at random without replacement, what is the probability that two red marbles are drawn?
Answer:Your Answer of the probability would determindedly be 3/25.
Step-by-step explanation:
How can i write this in standard form? (7x^3+2x-1)+(8x^2-6+2x-x^3)
7x^3 +0x^2 + 2x -1
+ -x^3 +8x^2 +2x -6
----------------------------------------
6x^3 +8x^2 +4x -7
standard form is from largest exponent to smallest exponent
how many more miles is it to travel to Jakarta 10,053 than to london 3,471?
It would be 6,582 more miles to travel to Jakarta than it would to travel to London.
Hope this helps :)
Factor 3x2 − 12x − 36 completely.
a) 3(x − 6)(x + 2)
b) (3x + 6)(x − 2)
c) 3(x + 4)(x − 3)
d) (3x − 4)(x + 3)
The answer would be A, 3(x-6)(x+2)
The height of a baseball thrown from the catcher to first base is modeled by the function h(t)=-0.08t^2+0.72t+6, where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds. The ball is in the air for 10 seconds before being caught. What’s the initial height of the ball?
A. 4.2 feet
B. 5.72 feet
C. 6 feet
D. 9 feet
answer is C. 6 feet.
A olympic runner set a récord for the 100m dash. The time was sixsty-two hundred seconds.How Would you write this as a number
sixty-two hundred= This would be 6200.
What is the LCM between 12,7
Hello there!
You had to find the prime factorization of 12
3*2*2=12
Then you find the prime factorization of 7.
7*1=7
7*3*2*2=84
Answer⇒⇒84
The least common multiple of 12 and 7 is 84.
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
Three friends all have same ages that are consecutive integers. The sum of their ages is 180. What is the age of the oldest friend?
a) 61
b) 59
c) 62
d) 60
Answer:
a) 61
The friend's ages are consecutive, therefore they are each one year apart. There are 3 friends whose ages add up to 180 in total.
[tex]180 / 3 = 60[/tex]
In order to make three consecutive numbers, subtract one and add one to 60.
[tex]60 - 1 = 59\\60 + 1 = 61[/tex]
You get 59, 60, and 61.
61 is the oldest age, that's your answer.
Kayla want to build a fence around her backyard for her dogs to play in. Her backyard is squared and has an area of 24 m²
4 * √24
with √24 you find a side, per 4 and you have the perimeter of the square
4 * √24
4* 4.9=
19.6
A T-shirt department store cost 7.50.the total cost in dollar of a T-shirt is givien by the function C(a)=7.5a
Given cost function C(a) = 7.5a, where a is the number of T-shirts.
Let us complete table.
We need to plug a=1,2,3,4 in above function to get the costs to complete the table.
For a =1
C(1)= 7.5(1) = 7.50
For a =2
C(2)= 7.5(2) = 15.00
For a =3
C(3)= 7.5(3) = 22.50
For a = 4
C(4)= 7.5(1) = 30.00
In order to find the common difference we need to find the diffrences of costs 15-7.50 = 7.50
22.50-15.00=7.50.
Therefore, common difference is 7.5.a represents the number of T-shirts.
Domain of a is the numbers we can take for a.
So, we can take value for a as 0 or greater value.
Therefore, domain for a would be a is gerater than or equal to 0.
Domain : a≥0Abby has
2
4
5
245
lb of potting soil. She needs
2
1
2
212
times that amount for her plants.
How much potting soil does she need?
Abby needs 2940 total and has 245, therefore she needs 2695 lbs
you would do 245x212= 51,940
OR
212x212= 44,944
Hope that helps its one oth those but i want to say its the first one 245x212=51,940
Not sure on this one can someone help plz
Oscar and Julie Ashton are celebrating their 15th anniversary by having a reception at a local reception hall. They have budgeted $2,000 for their reception. If the reception hall charges a $90 cleanup fee plus $31 per person, find the greatest number of people that they may invite and still stay within their budget.
To determine the greatest number of people Oscar and Julie can invite within their budget, we can set up an inequality and solve for the variable 'x'. The total cost equation is $90 + $31x ≤ $2,000. Solving this inequality, we find that the greatest number of people they can invite is 61.
Explanation:To determine the greatest number of people that Oscar and Julie may invite and still stay within their budget, we need to set up an inequality based on the given information. Let's denote the number of people they invite as 'x'. The total cost of the reception hall is $90 (cleanup fee) + $31 (per person) * x (number of people). This should be less than or equal to their budget of $2,000. So, the inequality is 90 + 31x ≤ 2000. To solve for 'x', we need to isolate the variable. Subtracting 90 from both sides, we have 31x ≤ 1910. Dividing both sides by 31, we find x ≤ 61.935. Since we can't have a fraction of a person, the greatest number of people they can invite is 61.
Calcule:
a) (+9) + (-5) =
b) (+3) + (-4) =
c) (-8) + (+6) =
a) 9 + -5 = 9-5 = 4
b) 3 +-4 = 3 -4 = -1
c) -8 + 6 = -2
The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g?
g(x)=f(x3)
g(x)=3f(x)
g(x)=13f(x)
g(x)=f(3x)
Answer: The correct option is second, i.e., [tex]g(x)=3f(x)[/tex].
Explanation:
A functions g(x) is stretch or compressed of graph of function f(x) is defined by the equation,
[tex]g(x)=kf(x)[/tex]
Where, k is a constant and it shows the compress or stretch factor.
If k>0, then it is a stretch factor and the graph of f(x) is stretched by factor of k.
If k<0, then it is a compress factor and graph of f(x) is compressed by factor k.
Since the graph of g(x) is a vertical stretch of the graph of function f(x) by a factor of 3, therefore,
[tex]g(x)=3f(x)[/tex]
So, the option second is correct.