Answer:
51 hope this helps!!!!!!!!!!
Step-by-step explanation:
Final answer:
The nth term for the given sequence 1, 7, 15, 25, 37 is derived to be n² + n - 1, which fits the pattern of the sequence accurately.
Explanation:
The sequence given is 1, 7, 15, 25, 37. To find the nth term of this sequence, let's first identify the pattern of differences between the terms. Observing the differences, we see they are 6, 8, 10, and 12, which suggests an arithmetic sequence in the differences. This indicates the original sequence is quadratic.
Using the general formula for the nth term of a quadratic sequence, An² + Bn + C, we can substitute the first few terms to solve for A, B, and C. However, there's a quicker method given the pattern of differences seen in the second layer (6, 8, 10, 12, ...) that increases by 2 each time, suggesting that 2n is involved.
Through analysis, the nth-term formula can be derived as n² + n - 1.
Here's why:
considering n=1 for the first term, we get 1+1-1=1;
for n=2, the formula yields 2^2+2-1=7; and so forth, matching the given sequence precisely.
Construct a polynomial function of least degree possible using the given information.
Real roots: -2, 1/2 (with multiplicity 2) and (-3, f(-3))=(-3,5)
Suppose investment of $6200 doubles in value every 13 years how much is the ivestment worth after 78 years
A vendor sold 72 hotdogs and hamburgers during a football game if the ratio of hotdogs to hamburgers sold was 8:1 how many of each food did vendor sell?
Factor the following
A small train at an amusement park is carrying passengers. Half of the passengers are 6 years old, 1 over 10 are 7 years old, 1 fifth are 8 years old, and 1 fifth are 9 years old.
What is the expected age for one of the passengers on the train?
6 years
7.1 years
8 years
8.5 years
The expected age for one of the passengers on the train is 7.1 years. This can be explained by following steps:
Following are the calculation for the expected age given
½ = 6 years old
1/10 = 7 years old
1/5 = 8 years old
1/5 = 9 years old
With the help of the above information, expected age can be calculated as follows:
Expected age = ½*6+1/10*7+1/5*8+1/5*9
= 6/2+7/10+8/5+9/5
=3+0.7+1.6+1.8
= 7.1
Therefore, the correct answer is 7.1 years old.
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Michael did 45 pushups in 3 minutes. Michelle did 36 pushups in 2 minutes.Who did pushups at a faster rate? How much faster was that person? Answer with supporting work.
20 points and brainliest to the fastest, right answer!
Please answer ASAP: Use cross products to determine which of the following proportions are equivalent to each other.
Select all situations that apply.
a/b=c/d
a/c=b/d
a/d=c/b
b/a=d/c
d/a=c/b
what are the term in the expression 4x^2-2x-x^2+3x+1
how many meters does it take to make 1 kilometer
Write a function perfect that determines whether parameter number is perfect number
PLEASE HELP WILL GIVE BRAINLIEST!!
What is 0.69 expressed as a fraction in simplest form?
If total liabilities are $200,000 and total assets are $325,000, owner's equity would be: 2)
a. $525,000
b. $200,000
c. $125,000
d. impossible to determine from the given data
A homeowner is draining her swimming pool. The volume of water in the pool changes by −12 gallons every minute.
What is the change in volume over 60 minutes?
So, water decreases by 12 gallons EVERY minute.
How much water will decrease in 60 minutes?
[tex]12*60=720[/tex] gallons
So, the volume changes by 720 gallons in 60 minutes.
ANSWER: Volume decreases 720 gallons in 60 minutes.
If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of is . Point lies on .
The perimeter of a rectangle is 36 yards. The width is 18 yards less than twice the length. Find the length and the width of the rectangle
The length of the rectangle is 12 yards and the width is 6 yards. The problem is solved with algebra using the formulas for the perimeter of a rectangle and given relation between the length and width.
Explanation:This problem involves the use of algebra in solving geometrical problems. The question provides information about the perimeter and the relationship of length to width using algebraic expressions. To find the length and the width, we can use the formulas for the perimeter of a rectangle (P=2L + 2W) and the given width (W=2L-18).
Let L represent the length. Then, 2L+W=18 represents the width. Setting 2L + 2W equal to the given perimeter of 36, we get 2L + 2(2L - 18) = 36.
Solving this equation gives: L = 12, and substituting L=12 into W=2L - 18, we get: W=6. Hence, the length is 12 yards and the width is 6 yards.
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Curve passes through the point (0,8)(0,8) and has the property that the slope of the curve at every point pp is four-times the y-coordinate. what is the equation of the curve
Harry worked seven hours last week this is 1/3 as many hours as Aiden worked how many hours did Aidan work
doreen needs 1/2 of the remaining 3/4 bag of flour to bake a cake. what fraction of the entire bag does she need?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. Then 3/8 of the entire bag does she need.
What is Fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
It is given that doreen needs 1/2 of the remaining 3/4 bag of flour to bake a cake. We need to find the fraction of the entire bag does she need.
When Some fraction of another fraction means a fraction is multiplied with the another fraction.
1/2 of the remaining 3/4
one by two times of three by four.
1/2 × 3/4
While multiplying fractions, the numerators are multiplied and the denominators are multiplied.
So 1 and 2 are multiplied on numerator and 2 and 4 are multiplied on denominator.
1×3/2×4
3/8
Hence 3/8 of the entire bag does she need.
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You can buy 4 pounds of peaches for $5.96. What do 4 1/2 pounds of peaches cost?
Write an equation of the line that passes through (0, 5) and (−1.5, 1)
The equation of the line that passes through (0, 5) and (−1.5, 1) is y = 8/3 x + 5
The equation can be represented as follows:
y = mx + b
where
m = slope
b = y-intercept
lets find the slope
(0, 5) (−1.5, 1)
m = 1 - 5 / -1.5 - 0 = - 4 / -1.5 ≈ 8 / 3
we multiplied the numerator and denominator by 2
b = 5, b is the value of y when x = 0.
Therefore, the equation will be as follows:
y = 8/3 x + 5
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For the x-values 1,2,3, and so on, y-values...
Answer:
decreasing linear
Step-by-step explanation:
Veronique and Lily compare their investment accounts to see how much they will have in the accounts after seven years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Veronique $1,000 5% 7 Once a year Lily $1,800 9% 7 Once a year mc017-1.jpg Which pair of equations would correctly calculate their compound interests? Veronique: mc017-2.jpg, Lily: mc017-3.jpg Veronique: mc017-4.jpg, Lily: mc017-5.jpg Veronique: mc017-6.jpg, Lily: mc017-7.jpg
Answer:
A
Step-by-step explanation:
The pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
What is the compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n)^(nt)
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
For Veronique, we have:
A = 1000(1 + 0.05/1)⁷ = $1,407.10
For Lily, we have:
A = 1800(1 + 0.09/1)⁷ = $3290.47
To calculate the compound interest for each account, we subtract the principal amount from the final amount:
For Veronique:
Interest = A - P = $1,407.10 - $1,000 = $407.10
For Lily:
Interest = A - P = $3,290.47 - $1,800 = $1,490.47
Therefore, the pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
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In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. 2a, 2a2b, 2a3b2, 2a4b3. . .
Answer:
a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Step-by-step explanation:
Given: A Sequence 2a , 2a²b , 2a³b² , [tex]2a^4b^3[/tex]
To find: a). Given Sequence is finite or infinite
b). Pattern of the sequence
c). Sixth term
a). Since, there is no detail about no. of terms of the sequence.
Therefore, It implies it is an Infinite Sequence.
b). Given 1st term = 2a , 2nd term = 2a²b , 3rd term = 2a³b²
First we find the difference of 1st and 2nd term
d = 2a²b - 2a ⇒ d = 2a (ab - 1)
Now, Difference of 2nd and 3rd term,
d = 2a³b² - 2a²b = 2a²b (ab - 1)
So, This Sequence is not a Arthematic Progression.
Now, we find the ratio of 2nd term to 1st term,
[tex]r\:=\:\frac{2a^2b}{2a}\,=\,ab[/tex]
Ratio of 3rd term to 2nd term,
[tex]r\:=\:\frac{2a^3b^2}{2a^2b}\,=\,ab[/tex]
Since, the ratio is common.
This sequence is Geometric Progression.
So, Pattern is next term of this sequence has 1 more in power of a and b
⇒ [tex]nth\,term\,of\,this\,GP\,=\,2a^{n}b^{n-1}[/tex]
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^{6}b^{6-1}[/tex]
[tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Therfore, a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.
Answer: [tex]x-2y+7=0[/tex]
Step-by-step explanation:
Given : The line[tex]L_1[/tex] has equation [tex]2x + y = 8[/tex]
In intercept form : [tex]y =-2x+8[/tex]
The slope of [tex]L_1[/tex] =-2 [in intercept form equation of line [tex]y =mx+c[/tex], m is slope ]
Let p be slope of [tex]L_2[/tex]
We know that when two lines are perpendicular then the product of their slopes is -1.
[tex]\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}[/tex]
The equation of line having slope 'm' and passing through (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , equation of line [tex]L_2[/tex] will be :-
[tex](y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7[/tex]
What's the answer? I need help. Thank you :)
Rya uses 4 gallons of gas ro drive 120 miles on the highway. If she gets that samw gas mileage, how many miles can she drive on 1 gallon of gas?
find the y-intercept of the line represented by 6x-7y=12
Write the equation in standard form
x^2+y^2+6x+14y+37=0
Where is the answer to the image of finding the area of the irregular shape that I emailed last night?
You and your frend step into identical row-boats. you notice that your boat sinks into the water twice as far as your friends. what can you say about your friend's weight compared with yours? your friend weighs twice as much as you your friend weighs the same as you your friend weighs half as much as you your friend weighs one fourth your weight