Answers
Answer:
An = 74(1.07)^n-1
Step-by-step explanation:
Here, we want to get the explicit rule
We are told that the sequence is geometric
At hour 4, we have that this is the 4th term
With conformance to the rule of geometric progression;
T4 = ar^3
90 = ar^3
for the 6th hour, this is the sixth term
103 = ar^5
dividing the 6th term by the 4th term, we have that
103/90 = ar^5/ar^3
103/90 = r^2
r = 1.07
To get a, we simply use any of the terms to substitute
using;
ar^3 = 90
a = 90/r^3
a = 90/1.07^3
a = 73.5 which is approximately 74
So the explicit rule is as follows;
An = 74(1.07)^n-1
Related Questions
3 1/4 - 4 1/2 show your work
Answers
If I did the math correct, the answer is -1 1/4, i'll attach a ss in a second.
I need help!!
Simplify this complex fraction
Answers
Help please i’m terrible at maths !!
Answers
A car dealer offers a discount of 15% off the normal price of a car for cash.
Emma pays £6120 cash for a car.
Calculate the normal price of the car.
Answers
Answer:
7200
Step-by-step explanation:
100/(100-15) * 6120 = 7200
How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).
Answers
Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:
100 * (1+1.07)x = 400
Then we will take 400 and divide it by 100 getting:
1.07X = 4
Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X
Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.
2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula
where:
P (principal) is equal to hypothetical $100
E (e) is a mathematical constant, which is approximately 2.718
R (rate) is the interest rate, in our case it is 5.5%
T (time) is the time required for money to grow
A (amount) is the final amount desired, which is 4 times larger of $100, thus $400
We have the following:
400 = 100 * e0.055t
400/100 = e0.055t
4 = e0.055t
Then we will apply natural log to both sides of the equations and get the following:
ln(4) = ln(e0.055t)
Since e is the base of ln(x) the equation simplifies to:
ln(4) = 0.055t
Using the calculator to find ln(4) we are getting:
1.38629 = 0.055t
Lastly find t
t = 1.38629/0.055
t = 25.20535202
Plug the answers back to the original equation to verify the answers.
1st part of the question answer: t = 20.4895
2nd part of the question answer: t = 25.20535202
What is the constant in the expression -18 - 3a
Answers
Answer:
'-18' is the constant in the expression -18 - 3a.
Step-by-step explanation:
We know that in an algebraic expression the constant term has a fixed value and it can not be changed.
For example,
The expression x + 2 contains two terms, x and 2. Here, '2' is a constant term because it has a fixed value and cannot be changed.
IN OUR CASE,
Given the expression
-18 - 3a
As '-18' is a fixed number and its value can not be changed.
Therefore, '-18' is the constant in the expression -18 - 3a.
The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located
at (9, –8). What are the values of h and k?
Answers
9514 1404 393
Answer:
(h, k) = (9, -8)
Step-by-step explanation:
The function g(x) is "vertex form" for a quadratic whose vertex is (h, k). We are told the vertex is (9, -8), so we have ...
(h, k) = (9, -8) . . . . the values of h and k
A fish is swimming at a constant rate toward the ocean floor. The equation y = -7x - 3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming.
Answers
Complete question :
A fish is swimming at a constant rate toward the ocean floor. The equation y = -7x - 3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming
Which statement best describes the depth of the fish
From a starting position of 7 meters below sea level, the fish is descending 3 meters per second.
From a starting position of 7 meters below sea level, the fish is ascending 3 meters per second.
From a starting position of 3 meters below sea level, the fish is descending 7 meters per second.
From a starting position of 3 meters below sea level, the fish is ascending 7 meters per second.
Answer:
From a starting position of 3 meters below sea level, the fish is descending 7 meters per second.
Step-by-step explanation:
Given the equation :
y = - 7x - 3
y = depth of fish in meters ; x = Number of seconds fish has been swimming
From the equation ; which is written according to the slope - intercept equation, ; y = mx + c
The slope, m = - 7 is the rate of change in y per unit of x
c = intercept, constant, value of y when x = 0
Hence, the true statement in the equation is :
-7 represents descent and meams fish descents at a rate of 7 m per second
At x = 0, the fish is at a depth of 3 m
A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs.
To the nearest whole percent, what is the probability that a car is an SUV, given that it is white?
9%
15%
21%
57%
Answers
Answer:
15%
Step-by-step explanation:
please help
g(x) = -x - 1
Answers
Answer:
g(x) = -1
Hope this helps.
Step-by-step explanation:
What is the radius if you drew a new circle with a scale facter of 3
Answers
Answer:
it is 5
20-5-10=5 and there is your answer
What is the value − 3 1/4 ∙ 2 1/3
Answers
Answer:
the value of this is-217÷4 = -54.25
please help me!!!!!
one month Ahmad rented 3 movies and 5 video games for a total of $42. The next Month he rented 9 movies and 7 video games for a total of $72 . find the rental cost for each movie in each video game
Answers
Answer:
The rental cost of one movie is $2.25 and the rental cost of one video game is $6.25
Step-by-step explanation:
Let the rental cost of 1 movie be m.
Let the rental cost of 1 video game be v.
Step-by-step explanation:
A king owned land outside of his castle he has partitioned the land to give as gifts to his 5 sons what fraction of land did the king give to each of his sons
Answers
Answer:
1/5
Step-by-step explanation:
since there is 5 sons they divide the land in 5.
Evaluate the expression 36.6 – 24 x 22 ÷ 3
Answers
Answer:
-139.4
Step-by-step explanation:
36.6 - 528 ÷ 3 = 36.6 - 176
= -139.4
Evaluate
2-8÷-2-3-12÷-6×-2
Answers
Answer:
7
Step-by-step explanation:
2-8÷-2-3-12÷-6×-2
2 - -4 - 3 - 2 x -2
2 + 4 + -3 - -4
6 + -3 + 4
3 + 4
7 :)
Find the equation of the line shown
Answers
Step-by-step explanation:
at 3=3
at 0=9
at 4=1
[tex]y = ax + b[/tex]
[tex]1 = 4a + b \\ 3 = 3a + b \\ 2 = - a \\ a = - 2 \\ 1 = - 4 \times 2 + b \\ b = 1 + 8 = 9 \\ y = - 2x + 9[/tex]
Answer:
y=-2x+9
Step-by-step explanation:
From looking at the line you can already tell that the slope is going to be negative, and the y-intercept is going to be 9, since that's where y is when x is 0. You can see that when x is one, y is 7. When x is 2, y is 5. And when x is 3, y is 3.
So:
0: 9
1:7
2:5
3:3
And the difference of y over the difference of x is the slope
-2/1=-2
So the slope is -2
Therefore, putting the equation together makes:
y=-2x+9
Hope this helps!
5.) g(x) = -4x + 2. Find x when g(x) = 22.
I'm on a timed test and I wasn't able to study because of personal reasons
Answers
Answer:
x = -5
Step-by-step explanation:
If g(x) = 22 and g(x) = -4x + 2, then -4x + 2 = 22.
Isolate x.
-4x = 22 - 2
= -4x = 20
= x = 20 ÷ -4
= x = -5
Find the value of 64 3/2
Answers
Answer:
65 1/2 or 65.5
Step-by-step explanation:
3/2 = 1.5 or 1 1/2
Answer:
65 1/2
Step-by-step explanation:
Multiplying binomials using area model.
Answers
Answer:
4x²+35x+24
Step-by-step explanation:
FOIL the binomials and simplify
4x^2 + 35x + 24
That's all I know.
solve for x 2|x|+5=11
Answers
Answer:
Solve for x over the real numbers:
abs(x) = 3
Hint: | Eliminate the absolute value.
Split the equation into two possible cases:
Answer: x = 3 or x = -3
Step-by-step explanation:
3. Q3) What is the smallest number of identical squares
that will fit in this rectangle?
Answers
Answer:
Minimum 3 squares.
Step-by-step explanation:
Let the number of identical squares that will fit in the rectangle = x
Sum of the area of the squares = Area of the given rectangle
x(Side length of the square)²= (length of the rectangle × width of the rectangle)
x(S)²= (40 × 90)
x(S)²= 3600 cm²
For the minimum numbers of the squares,
If x = 1,
S = √3600 = 60 cm
But the length of the rectangle is 40 cm, so can't be fitted in the rectangle.
If x = 2,
2S² = 3600
S² = 1800
S = √1800
S = 42.43 cm
Since, length of the rectangle is 40 cm, so the given square can't be fitted in the rectangle.
If x = 3,
3S² = 3600
S² = 1200
S = √1200
= 34.64 cm
Therefore, minimum 3 squares can be fitted in the given rectangle.
In a video store, a DVD that sells for $20 is marked down to $14. What is the
percent discount? *
Explain how you got your answer.
Answers
Your thrteater company sells tickets to their holiday showing off the nutcracker. Tickets cost $5 each. Tickets for adults cost $8 each. The total sales on opening night is $720. Write an equation to show the total sales as a combanation of kid tickets and adult tickets sold.
Answers
Answer:
5x + 8y = 720
Step-by-step explanation:
Let the :
Number of kid tickets sold = x
Number of adult tickets sold = y
Hence:
Tickets for kids cost $5 each.
Tickets for adults cost $8 each.
The total sales on opening night is $720.
The equation to show the total sales as a combanation of kid tickets and adult tickets sold is:
$5 × x + $8 × y = $720
5x + 8y = 720
Therefore, the equation to show the total sales as a combanation of kid tickets and adult tickets sold is
5x + 8y = 720
Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets
and sold each of them for $9.00.
a. Write an expression that represents the profit Althea made.
b. Evaluate the expression. Name the property used in each step.
Answers
Answer:
I have the same question
Step-by-step explanation:
message me if anyone helps I need it too
I WILL GIVE BRAINLIEST TO RIGHT ANSWER
write an equation of the line in a slope intercept form has a slope of -1/2 and passes through the point (2, 3)
Answers
Answer:
y = -¹/₂ x + 4Step-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
m = -¹/₂
(2, 3) ⇒ x₀ = 2, y₀ = 3
The point-slope form of the equation:
y - 3 = -¹/₂ (x - 2)
So:
y - 3 = -¹/₂ x + 1 {add 3 to both sides}
y = -¹/₂ x + 4 ← the slope-intercept form of the equation
Phyllis has $1,400 in her savings account. If the bank pays 2.25% interest per year
on savings, how much interest does she earn in one year?
Answers
Answer:
1400/100 x 2.25 = $31.50
Express this number in scientific notation.
31 billion
Answers
Hope this helps
Answer:
3.1 * 10^10
Step-by-step explanation:
we know 1 billion is 1,000,000,000
In scientific notation
1,000,000,000=1 * 10^9
To find the value of 31 Billion
Multiply the value of one billion for 31
so
31 * 1 * 10^9 = 31 * 10^9
= 3.1 * 10^10
What is the value of x?
Answers
Answer:
answer is 6............
100-64= x
36=x
then take the square root of 36
x=6
Which of the following expression(s) are fourth-degree trinomials? Select all that apply.
A. 3x²y + 5x3y + 6yA
B. 6y + 5x3 + 1
C. 5xy - 5x?y2 + 7
D. 3y2 + 3x3y2
Answers
Answer:
Options A and B are polynomial of the fourth degree
Step-by-step explanation:
In this problem, option
A. 3x2y + 5x3y + 6y4
Is a Polynomial of the fourth degree because of the 6y⁴ term which is the highest degree
Also the option
B. 6y4 + 5x3 + 1 has a 6y⁴ term which indicates that the polynomial is a fourth degree polynomial
What is the degree of a polynomial?
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer
