Answer:
After 35 years balance in the account = $93429.71
Explanation:
We will applying the compound interest formula.
A = [tex] P(1 +\frac{r}{n})^{nt} [/tex]
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given that,
P = $6000
r = 8% = [tex] \frac{8}{100} [/tex] = 0.08
n = 2 (because of twice in a year)
t = 35 years
[tex] A= 6000(1 + \frac{0.08}{2}) ^{2*35} [/tex]
A = 6000[tex] (1.04)^{70} [/tex]
A= $93429.71 (Option D)
Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT
Answer:
1. 49
2. 169
3. 81
4. 100
5. 441
6. 36
Step-by-step explanation:
1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]
= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]
= 7×7 = 49
2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]
= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]
= 169
3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]
= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]
= 81
4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]
= 10²
= 100
5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]
= 21²
= 441
6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]
= 6²
= 36
3/4 of what number is 8?
table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?
Tldr: The answer is 9
help me please asap!!!!!!!
Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm
This one helps too.
Ur welcome.
Find the value of the missing side of a triangle practice
is -4 real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.)
99 POINT QUESTION!!!!!
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
express the perimeter of the rectangle as a polynomial. help please.
Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6
Ryanne is 14. her brother's age is three more than half her age. how old is her brother?
Answer:
10 years old
Step-by-step explanation:
I will use the letter r to denote Ryanne's age:
r = 14
And according to the problem, her brother's age is THREE MORE THAN HALF HER AGE
so, we start by finding how much is half of Ryanne's age:
r/2 = 14/2 = 7
and next, we find that three more than half her age is:
7 + 3 = 10
Her brother is 10 years old
What is the first error he made in computing the standard deviation?
A.Yuri failed to find the difference between each data point and the mean.
B.Yuri divided by n instead of n -1.
C.Yuri did not subtract 9 - 14 correctly.
D.Yuri failed to square -2 correctly.
Answer:
Step-by-step explanation:
Given is a sample with 4 items as
12,9,14,21
Mean = average of 4 = 14
s is the square root of sample variance
Sample variance is the sum of squares divided by n-1
But Yuri divided by 4 = n instead of 3 = n-1
That is the only mistake he did and all other steps are right.
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?
A pair of shoes that normally costs $75 is on sale for $55. What is the percent decrease in the price, to the nearest whole percent?
A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH
Nadia needs half of a dollar for bus fare. Which amount is equivalent to her bus fare?
what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..
a. 1,350
b. 150
c. 3
d. 53
Anybody know the answer to this?
Could someone explain this to me?
The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet. Find the dimensions of the garden.
The width of the garden is 12 feet and the length of the garden is 20 feet.
Explanation:Let's denote the width of the garden as 'w'. The length will then be 'w + 8'. Measurements are in feet. The garden is surrounded by a 4-foot sidewalk. Therefore, the total length of the garden including the sidewalk is 'w + 8 + 4 + 4 = w + 16', and the total width is 'w + 4 + 4 = w + 8'.
The area of the sidewalk surrounding the garden is the area of the large rectangle minus the area of the garden. So, we set up the following equation:
(w + 16)(w + 8) - (w)(w + 8) = 320.
After simplifying, we can get a quadratic equation: w² + 8w - 320 = 0 and then solve this equation, which gives us w = 12 or w = -28. We ignore the negative solution as the width cannot be negative. So, the dimensions of the garden are:
Width: 12 feet
Length: 20 feet.
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WILL GIVE BRAINLIEST
WILL GIVE BRAINLIEST AND 50 points
out of a port departed a steam boat with a speed of 36.8km/h. In 1.75 hours out of the same port and going the Sam direction departed a speed boat. In 1.8 hours after the the department of the speed boat, the distance between the speed boat and the steam boat was 86.9km. What was the speed boats speed in km/h?
Hi there!
My name is Chris and I'll be helping you today!
So your question states that a boat departed the port at 36.8 km/h.
After 1.75 hours, a second boat emerges from the port.
After 1.8 hours, the second boat is 86.9 km away from the first boat.
Also, remember that speed equals distance over time.
Therefore, your answer will be: The speed boat's speed in km/h was 24.3 km/h. Forgive me if I am incorrect.
Enjoy your day!
The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42
Answer:
Option A is correct
equation [tex]2(x+14)=42[/tex] could be used.
Step-by-step explanation:
Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.
Perimeter(P)of a rectangle in inches is given by:
[tex]P= (2l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.
Substitute the value of P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;
[tex]42 = 2 \cdot (14+x)[/tex]
Divide by 2 on both sides we get;
[tex]21 = 14+x[/tex]
On simplify, we get;
x = 21-14 = 7 inches
therefore, the width of the rectangle is, x = 7 inches
Check :
Substitute the value of x =7 in option A.
[tex]2(x+14) =42[/tex]
[tex]2(7+14)=42[/tex]
[tex]2\cdot 21 =42[/tex]
42 = 42
Hence, the only equation that could be used to find the width, x is, [tex]2(x + 14) = 42[/tex]
Pablo folds a straw into a triangle with side lengths of 4x -2 inches and 4x -1 inched . The perimeter of the triangle is 12x -6 inched . If x =1.5 what was the length of the straw before it was folded ?
Answer:
21
Step-by-step explanation:
which or the following will happen if you miss a monthly credit card payment?
A)You will be charged a late fee.
B)You loose reward points
C)Your APR will increase the next month
D)Both A & B
The square of the sum of two consecutive natural numbers is greater than the sum of the squares of these two numbers by 112. find the two numbers.
The two consecutive numbers are 7 and 8.
Consecutive numbers are numbers that follow each other. For example, 1,2,3,4 are consecutive numbers.
Let:
x = first number
(x + 1) = second number
From the question, this expression can be derived:
[(x) + (x + 1)] ²
This can be simplified to (2x +1)²
The second expression is : x² + (x +1)²
(2x +1)² - [x² + (x +1)²] = 112
expanding the bracket gives:
(4x² + 4x + 1) - [x² + (x² + 2x +1) = 112
4x² + 4x + 1 - 2x² - 2x - 1 = 112
Add like terms
2x² + 2x = 112
Divide both sides by 2
x² + x = 56
x² + x - 56 = 0
Factorise the equation
The factors of -56x² that add up to x are : 8x and -7x
(x² - 7x) (8x - 56) = 0
x(x - 7) 8(x -7) = 0
x = 7
or
x = -8
Since x cannot be a negative number, x is 7 and (x + 1) = 8
A similar question was solved here: https://brainly.com/question/14024870?referrer=searchResults
An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
Final answer:
The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
Explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)Using the given information, we can plug in the values and solve for r:
$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
The interest rate, for continuous compounding, is approximately 5.775%.
To find the interest rate for continuous compounding, we can use the formula for compound interest:
[tex]\[ A = P \times e^{rt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount of money,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),
- [tex]\( t \)[/tex] is the time the money is invested for (in years),
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
Given:
- [tex]\( P = $750 \)[/tex],
- [tex]\( A = $1500 \)[/tex],
- [tex]\( t = 12 \)[/tex] years.
We need to solve for [tex]\( r \)[/tex], the interest rate.
Step 1 :**Substitute the Given Values into the Formulaa :
[tex]\[ 1500 = 750 \times e^{12r} \][/tex]
Step 2 :**Divide Both Sides by 750**:
[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]
[tex]\[ 2 = e^{12r} \][/tex]
Step 3 :**Take the Natural Logarithm of Both Sides**:
[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]
[tex]\[ \ln(2) = 12r \ln(e) \][/tex]
[tex]\[ \ln(2) = 12r \][/tex]
Step 4 :**Solve for [tex]\( r \)[/tex]**:
[tex]\[ r = \frac{\ln(2)}{12} \][/tex]
[tex]\[ r = \frac{0.693}{12} \][/tex]
[tex]\[ r = 0.05775 \][/tex]
Step 5 :**Convert the Interest Rate to a Percentage**:
[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]
[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]
So, the interest rate is approximately 5.775%.
How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32
When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.
Explanation:To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.
4 x 1/8 = 4/8 = 1/2Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.
What is the approximate area of the circle shown below 60cm
Answer:
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Step-by-step explanation:
Given the diameter of circle 60 cm
we have to find the area of circle
Diameter=60 cm
Radius=30 cm
[tex]\text{Area of circle=}\pi r^2[/tex]
[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Option A is correct
Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?
The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel
The steps used to find the solution of the logarithm equation can be presented as follows;
The logarithm equation is; [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]
Converting the logarithm to the same base, we get;
[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]
[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]
[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]
2 × log₂(3·x - 1) = log₂(x + 8)
log₂(3·x - 1)² = log₂(x + 8)
(3·x - 1)² = (x + 8)
(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0
Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575
Plugging in the value of x = 1.353, we get;
log₂(3 × 1.353 - 1) ≈ 1.613
log₄(1.353 + 8) ≈ 1.613
The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353
Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353
Final answer:
To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.
Explanation:
To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.
At how many points does the graph of the function below intersect the x-axis?
y = 25x2 - 10x + 1
A. 0
B. 1
C. 2
Answer:
It is one.
Step-by-step explanation:
If you didn't get 1 re read the problem