Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.
To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money, $1,500).r is the annual interest rate (decimal, so 6.75% becomes 0.0675).n is the number of times that interest is compounded per year (since it's annual, n = 1).t is the number of years.We rearrange the formula to solve for t:
t = (log(A/P) / log(1 + r/n)) / n
Plug in the known values:
t = (log(7300/1500) / log(1 + 0.0675)) / 1
Calculate the logarithms:
t ≈ (log(4.8667) / log(1.0675))
t ≈ (0.6887 / 0.0281)
t ≈ 24.53
It will take approximately 24.53 years for the investment to grow to $7,300.
Use the Rational Zeros Theorem to write a list of all potential rational zeros
f(x) = x3 - 10x2 + 4x - 24
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±2, ±3, ±4, ±24
±1, ±2, ±3, ±4, ±6, ±12, ±24
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
How many distinct arrangements can you make using the letters in the word DEGREE
Answer: 120
Step-by-step explanation:
The number of ways to arrange n things of which 'a' things are identical , 'b' things are identical and so on...... :-
[tex]\dfrac{n!}{a!\ b!......}[/tex]
Given Word : DEGREE
Total letters = 6
Here letter E is repeated 3 times.
Then, the number of unique ways to arrange the letters in the word "DEGREE " will be :-
[tex]\dfrac{6!}{3!}=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]
Hence, the number of distinct arrangements for the letters in the word "DEGREE "=120
What is the mean median mode and range of the numbers 31 28 30 31 30 ...?
what is the product of 3x4 y2 and 2xy3?
If total Revenue is $3000, Cost of Goods is $1500, and total Selling Expense is $500; what is the Profit for the business?
Explain why the product of any four consecutive integers is divisible by 24.
...?
how do I solve : CSC pi/6 ...?
Rational irrational0.01π 100 π √100 √1100
1. What are the next two terms of the following sequence?
1,5,9.........
A: 27, 211
B: 10, 11
C: 12, 15
D: 13, 17 *****
2. what is the common difference of the following Arithmetic sequence
102, 100, 98, 96....
A: 2
B: -2*****
C: -1
D: 102
3. What is the ninth term of the arithmetic sequence defined by the rule below?
A(n( = -14 + (n-1)(2)
A: 232
B: 230
C:2****
D: 4
4. Which function below represents the arithmetic sequence
3, 7 , 11, 15....?
A: F(n) = 4+3(n-1)
B: F(n) = 4+3n
C: F(n) = 3+4n
D: F(n) = 3+4(n-1)******
Answer:
1. 13, 17 Option D
2. -2 Option B
3. 2 Option C
4. F(n) = 3+4(n-1) Option D
Step-by-step explanation:
1.
Given sequence is: 1, 5, 9....
Common difference = 5-1 = 9-5 = 4
Next term is :
9+4 = 13
and
13+4= 17
So, next two terms are: 13 & 17.
2.
Given sequence is :
102, 100, 98, 96....
Common difference = 100 - 102 = 98 -100 = 96 - 98 = -2
3.
Given rule is :
Aₙ = -14 + (n - 1)(2)
Find the 9th term
so, we put n = 9
A₉ = -14 + (9-1)*2
A₉ = -14 + 8*2 = -14 + 16
A₉ = 2
Ninth term is 2.
4.
Given sequence is:
3, 7, 11, 15.....
Write the nth term
Formula is :
F(n) = a₁ + (n-1)d
Where a₁ is first term
n is number of terms
d is common difference
a₁ = 3
d = 7-3 = 11-7 = 15 - 11 = 4
So nth term is :
F(n) = 3 + 4(n-1)
That's the final answer.
Answer:
1. 13, 17 Option D
2. -2 Option B
3. 2 Option C
4. F(n) = 3+4(n-1) Option D
Step-by-step explanation:
A group of 483 students is taking a field trip. one bus is needed for every 50 students. how many buses are needed?
Devil has 39 toy blocks what is the value of the digit nine in this number
Will upvote. What is the area of a circle whose radius is 4 ft
4TTft^2
8TTft^2
16TTft^2
64TTft^2
solve the equation for y 2x+6y=13
.
Which of the following is the correctly abbreviated SI unit describing the amount of a substance?
M
kg
mol
g
HELLPP MEE PLEAASSEEE!!????
Is ABC DEF?
If so, name the postulate that applies.
A. congruent - SAS
B. congruent - ASA
C. congruent - SSS
D. might not be congruent
The data set represents the number of miles Mary jogged each day for the past nine days. 6, 7, 5, 0, 6, 12, 8, 6, 9 The outlier of the data set is
Your answer for this question is 0
The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?
what is the highest common factor of 630 and 1560
Brianna cut 351 fresh flowers to make bouquets if she wants to place an equal number of flowers and each bouquet how many groups should she use
a. 2 groups
b. 4 groups
c.6 groups
d. 9 groups
AB is tangent to O. If AO = 24 and BC = 27, what is AB?
Choices:
45
69
54
51
The measure of the side AB will be 45. The correct option is A.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Use the Pythagorean theorem to calculate the length of AB as below,
OB² = AB² + OA²
(BC + OC)² = AB² + OA²
(27 + 24)² = AB² + 24²
AB² = 51² - 24²
AB = 45 units
Therefore, the correct option is A. The value of length AB is 45.
To know more about the Pythagorean theorem follow
https://brainly.com/question/13080921
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A table factor of .7312 from a present value table of $1 means that a certain rate of interest for a certain period of time it will equal? ...?
What is the multiplicative rate of change for the exponential function f(x) = 2(5/2)–x(to the negative X)?
A.0.4
B.0.6
C.1.5
D.2.5
Answer:
A. 0.4
Step-by-step explanation:
If A is uniformly distributed over [-12,16] , what is the probability that the roots of the equation
x^2+Ax+A+3=0
are both real?
Final answer:
The probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real is approximately 0.6786. Then we calculate the length of the range [-3, 16] divided by the length of the entire interval [-12, 16].
Explanation:
To find the probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real, we need to determine the range of values for A that will result in real roots. For real roots, the discriminant (b^2-4ac) must be greater than or equal to 0. In this case, the equation can be rewritten as [tex]x^2+(1+A)x+(A+3)=0[/tex], so a = 1, b = (1+A), and c = (A+3). The discriminant is (1+A)^2 - 4(A+3), which must be greater than or equal to 0.
Expanding and simplifying, we get (A^2 + 2A + 1) - 4A - 12 ≥ 0. Combining like terms, we have [tex]A^2 - 2A - 11 > 0[/tex].
To solve the inequality, we can find the values of A that make the equation equal to 0. Factoring, we get (A - 4)(A + 3) ≥ 0. The solutions are A ≤ -3 or A ≥ 4.
Therefore, the probability that the roots of the equation are both real is the probability of A taking values in the interval [-12, -3] or [4, 16]. To find this probability, we divide the length of the interval [-3, 16] by the length of the entire interval [-12, 16].
P(A is in [-3, 16]) = (16 - (-3)) / (16 - (-12)) = 19 / 28 ≈ 0.6786.
Which number sentence should be used to solve this problem? Ethan collected 30.4 pounds of recycling in June. He collected 35.5 pounds in July.
How many more pounds of recycling did Ethan collect in July than June?
A.
30.4 + 35.5 = ?
B.
35.5 - 30.4 = ?
C.
30.4 - 35.5 = ?
D.
35.5 + 30.4 = ?
whats the anserr becuse i got this wrong on a home work sheet
SERIOUSLY NEED HELP WITH THIS QUESTION.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
800 cubic feet
1,000 cubic feet
1,200 cubic feet
2,000 cubic feet
Answer: 1000 ft³.
Step-by-step explanation:
Since, The volume of a cube = ( side )³
⇒ 1000 = (side)³ ⇒ side = 10
Hence, the side of the given cube = 10 feet
Since, the base of a cube = square having side 10 feet.
When we tilted the cube by 2 units,
Then, the base of the new solid = Rhombus having height 10 meters and base 10 feet,
Since, the square and rhombus are lying in the same base ( Shown in diagram)
Area of rhombus (Base of new solid) = Area of square having side 10 feet = 100 ft²
Since, the height of new solid is also 10 feet. the volume of new solid = Area of its base × height
= 10 × 100
= 1000 ft
eremy is working at 2 jobs to save money for his college education. He makes $8 per hours working for his uncle at Pizza Pie busing tables and $10 per hour tutoring peers after school in math. His goal is to make $160 per week. Part c- After researching the costs of colleges, Jeremy decides he needs to make more than $160 each week. Write an inequality in two variables to represent the amount of money Jeremy needs to make. Then graph.
Final answer:
Jeremy needs to create an inequality to represent his new earning goal higher than $160 a week, leading to the inequality 8x + 10y > 160. This can be graphed by first converting to intercept form, plotting the intercept and slope, drawing a dashed boundary line, and shading the region above this line.
Explanation:
Jeremy is working two jobs to save for his college education and needs to create an inequality to represent the amount he needs to make each week, now more than $160. Let's denote the number of hours Jeremy works busing tables as x and the number of hours he spends tutoring as y. He makes $8 per hour busing tables and $10 per hour tutoring.
To express Jeremy's goal of making more than $160 a week, we can write the following inequality:
8x + 10y > 160
To graph this inequality:
First, rewrite the inequality as y > (-4/5)x + 16 to get the intercept form.
Plot the y-intercept at (0, 16) on the graph.
Use the slope of -4/5 to determine another point. From (0, 16), move 5 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point.
Draw a dashed line through the two points to represent the boundary of the inequality (dashed because the inequality is strict and does not include the line itself).
Shade above the line to indicate that all solutions to the inequality lie in this area, where Jeremy would be earning more than $160.
A test for the presence of a certain disease has probability 0.2 of giving a false-positive result (indicating that an individual has the disease when this is not the case) and probability 0.1 of giving a false-negative result. Suppose that 10 individuals are tested, 5 of whom have the disease and 5 whom do not. Let X be the number of positive readings that result.
a. Explain why X does not have a binomial distribution.
b. Find the probability that exactly 3 of the 10 test results is positive?
What describes each face on a dodecahedron?
A. equilateral triangle B. equilateral pentagon C. circle D. square ...?
You roll a blue die and a yellow die. What is
P(the sum of the dice is at least 6 | the blue die shows a 3)?
Write fractions using the slash ( / ) key. Reduce fractions to their lowest terms. ...?