A principal of $4700 is invested at 6% interest compounded annually. How much will the investment be worth after 12 years Use the calculator provided and round your answer to the nearest dollar.
Find the first five terms of the sequence described by the following recursive formula: an = an – 1 + an – 2 where a1 = 1.2 and a2 = 2.3
1.2, , , ,
Find the first six terms of the sequence described by the following recursive formula:
an = an – 1 + an – 2
where a3 = -5 and a4 = 3
,
,
,
,
,
The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five or six terms, we substitute the given initial conditions into the formula and repeatedly apply it to find subsequent terms.
Explanation:The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five terms, we begin with a1 = 1.2 and a2 = 2.3. Then we use the formula to find the next terms:
a3 = a2 + a1 = 2.3 + 1.2 = 3.5a4 = a3 + a2 = 3.5 + 2.3 = 5.8a5 = a4 + a3 = 5.8 + 3.5 = 9.3So the first five terms of the sequence are 1.2, 2.3, 3.5, 5.8, and 9.3.
Similarly, to find the first six terms of the sequence with a3 = -5 and a4 = 3, we use the formula:
a5 = a4 + a3 = 3 + (-5) = -2a6 = a5 + a4 = -2 + 3 = 1So the first six terms of this sequence are -5, 3, -2, 1, -1, and 0.
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The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
What can you conclude about the slope of the values in the table? Check all that apply.
The slope is 3.
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
The conclusion that can be drawn from the slope of the values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
First, let's determine the value of the slope by applying the slope formula using two points given from the table, say, (1000, 20) and (1000, 23):Slope formula = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,[tex](1000, 20) = (x_1, y_1)\\\\(1000, 23) = (x_2, y_2)[/tex]
Substitute:[tex]slope(m)=\frac{23 - 20}{1,000 - 1,000}\\\\slope (m) =\frac{3}{0}[/tex] (undefined)
Zero cannot divide 3 hence, the slope is undefined.Slope that are vertical have rise but no run, thus, their slope is undefined.(see attachment for image showing an example of how an undefined slope looks like on a graph.)
Therefore, the conclusion that can be drawn from the slope of values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
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what divides an angle into two congruent angles
The value of a camcorder bought new for $2000 decreases 20% each year. Identify the function for the value of the camcorder. Does the function represent growth or decay?
A) V(t) = 2000(0.8)t; growth
B) V(t) = 2000(0.8)t; decay
C) V(t) = 2000(1.2)t; decay
D) V(t) = 2000(1.2)t; growth
Answer: V(t) = 2000(0.8)t; decay
Step-by-step explanation:
Which one of the binomials is a factor of this trinomial?
x^2-13x+40
A. x-8
B. x+8
C. x-4
D. x+4
Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).
You buy a commemorative coin for $110. Each year, t, the value V of the coin increases by 4%
Part a: Write a function that can be used to find the coin’s value after t years.
Part b: If the coin’s value continues to grow 4% per year, what will the approximate value be in 8 years? Round to two decimal places.
Answer:
$136.86
Step-by-step explanation:
Please Help!!!
which statement is true about the system x-3y = 5 and y = x - 7 ?
A certain forest covers an area of 1800 km2. Suppose that each year this area decreases by 8.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.
[tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, a certain forest covers an area of [tex]1800[/tex] [tex]km^{2}[/tex]. Each year this area decreases by [tex]8.5[/tex]%.
We have to find the area after 14 years.
Area after 14 years can be found using the below formula
[tex]A=I(1-r)^{t}[/tex]
[tex]=1800(1-0.085)^{14}[/tex]
[tex]=1800[/tex]×[tex]0.288[/tex]
[tex]=519km^{2}[/tex]
Hence, [tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
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What is the value of the 11th term of the sequence 1, -2, 4, -8, ...?
4,096
1,024
-2,048
-1,024
The formula is used to find the area of a parallelogram. if the base of a parallelogram is doubled and its height is doubled, how does this affect the area?
How many zeros are there at the end of 100!?
Final answer:
The number of zeros at the end of 100! is determined by counting the multiples of 5 in the factorization, including higher powers like 25. The result is a total of 24 zeros at the end of 100!.
Explanation:
To determine how many zeros are at the end of the factorial of 100 (100!), we need to know how many times the number 10 can be factored within that number. Since 10 is the product of 2 and 5, we should count the number of 2s and 5s in the prime factorization of 100!. The number of zeros at the end of 100! will equal the smaller of these two counts. However, because there are more 2s than 5s in the prime factorization, we only need to count the number of 5s as every 5 will have a corresponding 2 to form a 10.
For 100!, we count how many multiples of 5 there are within that range, including the multiples of 25 (since 25 includes an extra 5), and possibly higher powers of 5 if applicable. For example, 5 is counted once, 25 is counted twice (as 25 = 5×5), and so on.
Therefore, the number of zeros at the end of 100! equals the sum of the integer division of 100 by 5, plus the integer division of 100 by 25, and so on for any higher powers of 5. However, since 100 < 125, we do not need to consider any higher powers than 25.
We calculate:
100 ÷ 5 = 20,
100 ÷ 25 = 4.
Adding these together (20 + 4), we find that there are 24 zeros at the end of 100!.
Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +…
20
Does not exist
22
24
We can see that for every increment, the number gets doubled positively. Since we are looking for the value when the repetition is made infinite, therefore the value at that point would also be infinite. Since infinite is imaginary, therefore the correct answer is:
Does not exist
The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle. 12 cm 18 cm 10 cm 6 cm
How is the graph of y = 8x^2 − 1 different from the graph of y = 8x^2?
Answer:
1 up⊕⊕⊕⊕⊕⊕⊕⊕
Step-by-step explanation:
Use the graph below to fill in the blank with the correct number:
f(−2) = _______
Numerical Answers Expected!
Answer for Blank 1:
Issac is standing 174 feet from the base of the South Carolina State House in Columbia. The angle formed by the ground and the line segment from his position to the top of the building is 46°. How tall is the SC State House? Round to the nearest foot.
Using the tangent function of trigonometry, the height of the South Carolina State House is calculated to be approximately 180.2 feet. When rounded, the building stands at an estimated 180 feet tall.
To calculate the height of the South Carolina State House, we can use trigonometry. Given that Issac is standing 174 feet from the base and the angle of elevation to the top of the building is 46°, we can use the tangent function to determine the height of the building. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the building in this case) to the adjacent side (the distance from Issac to the building).
Using the formula:
tangent (angle) = opposite/adjacent
The equation would be:
tangent (46°) = height of building / 174 feet
Solving for the height of the building:
height of building = 174 feet * tangent (46°)
Using a calculator with the tangent function:
height of building = 174 * 1.035530 (approx value of tangent (46°))
So:
height of building ≈ 180.2 feet
Rounded to the nearest foot, the height of the South Carolina State House is approximately 180 feet.
Choose the correct simplification of the expression (7x − 3)(4x2 − 3x − 6).
28x3 − 33x2 − 33x − 18
28x3 + 33x2 − 33x + 18
28x3 − 51x2 − 33x + 18
28x3 − 33x2 − 33x + 18
a b c d
Answer:
The expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
Step-by-step explanation:
As given the expression in the question be as follow .
= (7x − 3) × (4x² − 3x − 6)
= 7x × (4x²- 3x - 6) - 3 × (4x² - 3x - 6)
Now open the bracket
= 7x × 4x² + 7x × -3x + 7x × -6 -3 × 4x² -3 × -3x - 3 × -6
= 28x³ -21x² -42x -12x² + 9x +18
= 28x³ -21x² - 12x² -42x + 9x + 18
= 28x³ - 33x² - 33x + 18
Therefore the expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
help me please!! Find the measure of angle 2. Image attached
opposite angles = 180
180-49 = 131
angle 2 = 131 degrees
Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.
If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
c.3x + 4 = 28
b.3(x + 4) = 28
a.3x = 4 + 28
x = number
the equation to use is: 3x+4=28
3x+4=28
3x=24
x-24/3 =8
x=8
What is best definition of combining like terms
Which ordered pairs make both inequalities true? Check all that apply.
(–2, 2)
(0, 0)
(1,1)
(1, 3)
(2, 2)
Answer:
the answers are c and e 1,1 and 2,2
Step-by-step explanation:
Answer:
(1,1) (2,2)
Step-by-step explanation:
Graph y = log8^x and its inverse
Answer:
Third one will be correct.
Step-by-step explanation:
Given : y =[tex]log_{8}(x)[/tex].
To find : Graph and its inverse.
Solution : We have given that
y =[tex]log_{8}(x)[/tex].
For x - intercept , y =0.
y = 0
0 =[tex]log_{8}(x)[/tex].
x = 1
(1,0)
Inverse of y =[tex]log_{8}(x)[/tex].
Interchange the x and y.
x = [tex]log_{8}(y)[/tex].
Solving for y
y = [tex]8^{x}[/tex].
Then For x = 0
y = [tex]8^{0}[/tex].
y = 1
For inverse ( 0 ,1)
Then we can see from given graphs Third one will be correct.
Therefore, Third one will be correct.
Type the correct answer in the box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar. Simplify the expression. tan(-x) cos(-x) =
Answer:
The correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Step-by-step explanation:
The given expression is:
[tex]tan(-x){\times}cos(-x)[/tex]
Now, simplifying the above given expression, we get
=[tex]\frac{sin(-x)}{cos(-x)}{\times}cos(-x)[/tex] (because [tex]tanx=\frac{sinx}{cosx}}[/tex])
=[tex]sin(-x)[/tex]
Also, we know that [tex]sin({-\theta})=-sin{\theta}[/tex], tehrefore teh expression becomes
=[tex]-sinx[/tex]
Hence, the correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
rounded to the nearest second would be 28 degrees 43 minutes and 30 seconds
The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive on a gallon of gasoline. Marcel converts the frequency table to a conditional relative frequency table by row. Which value should he use for Y? Round to the nearest hundredth. 0.19 0.45 0.82 0.90
Answer:
Its D on Ed2022
Step-by-step explanation:
a restaurant offers 3 kinds of bread 4 kinds of meat and 3 kinds of cheese
Answer:
36 combos
Step-by-step explanation:
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