Find the first six terms of the sequence. 1) \( a_{1}=3, a_{2}=1 \); for \( n \geq 3, a_{n}=a_{n-1}-a_{n-2} \) Evaluate the sum. Round to the nearest hundredth, if necessary. 2) \( \sum_{k=1}^{4} \fra
Answers
The first six terms of the given sequence are 3, 1, -2, -3, -1, 2. The sum of the sequence is 0.
To find the first six terms of the given sequence, we start with the initial values\(\( a_{1} = 3 \) and \( a_{2} = 1 \),\) and then use the recursive formula \(\( a_{n} = a_{n-1} - a_{n-2} \)\)for \(\( n \geq 3 \)\). Let's calculate the first six terms:
\(\( a_{1} = 3 \)\( a_{2} = 1 \)\( a_{3} = a_{2} - a_{1} = 1 - 3 = -2 \)\( a_{4} = a_{3} - a_{2} = -2 - 1 = -3 \)\( a_{5} = a_{4} - a_{3} = -3 - (-2) = -1 \)\( a_{6} = a_{5} - a_{4} = -1 - (-3) = 2 \)\)
Hence, the first six terms of the given sequence are 3, 1, -2, -3, -1, 2.
To evaluate the sum of the sequence, we add up all the terms: 3 + 1 + (-2) + (-3) + (-1) + 2 = 0. Therefore, the sum of the given sequence is 0.
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Related Questions
A man walks at the rate of 88 paces to the minute .if the average length of his pace is 0.875 m, find the time he takes to walk 2.31km
Answers
Answer:
0.02
Step-by-step explanation:
I believe this is pretty easy but it's: solve for x using common denominators 3/4(x+2)=x/(x+3) Answer choices below:
Answers
Answer:
x = \(\frac{3}{4}\)
Step-by-step explanation:
Given
\(\frac{3}{4(x+2)}\) = \(\frac{x}{x+2}\)
multiply numerator/ denominator of \(\frac{x}{x+2}\) by 4, thus
\(\frac{3}{4(x+2)}\) = \(\frac{4x}{4(x+2)}\)
Since the denominators are common , equate the numerators, that is
4x = 3 ( divide both sides by 4 )
x = \(\frac{3}{4}\)
Pedro paid $1.44 for a dozen eggs. How much would it be for 7 eggs?
Answers
Answer:
7 eggs = $0.84
Step-by-step explanation:
dozen = 12
cost of one egg = 1.44/12 = 0.12
cost of 7 eggs = 0.12x7 = 0.84
Answer:
$0.84 for 7 eggs
Step-by-step explanation:
$1.44 = a dozen (12)
1.44 / 12 = $0.12 = 1 egg
$0.12 * 7 = $0.84 = 7 eggs
7. A box contains 16 cards bearing numbers 1, 2, 3, 4, .... 15, 16 respectively. A card is drawn
at random from the box. What is the probability that the
number on the card is:
(ii) a prime number?
(ii) a number divisible by 3?
(iv) a number not divisible by 4?
(i) an odd number?
Answers
Answer:
9/16
6/16
10/16
8/16
Step-by-step explanation:
briefly explain the goal for defining and measuring variability. a measure of variability describes the degree to which the scores in a distribution are . variability also measures the .
Answers
Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution
What is variability ?Variability also measure how accurately individual score or sample represent the entire population
When the standard deviation is 0 , the scores have no variability.
Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.
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Q2) For total cost: TC(q)=10−6q+q2 determine: a. the production level (q∗) that minimizes total cost. b. The amount of Total cost for the q∗, in other words TC(q∗) ? (10 pints)
Answers
The amount of total cost at q* is 1.
To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):
TC(q) = 10 - 6q + q^2
To find the minimum point, we differentiate TC(q) with respect to q:
d(TC(q))/dq = -6 + 2q
Setting the derivative equal to zero and solving for q:
-6 + 2q = 0
2q = 6
q = 3
So the production level q* that minimizes the total cost is 3.
To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):
TC(q*) = 10 - 6(3) + (3)^2
TC(q*) = 10 - 18 + 9
TC(q*) = 1
Therefore, the amount of total cost at q* is 1.
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charlotte is driving at 64.3 mi/h and receives a text message. she looks down at her phone and takes her eyes off the road for 3.36 s. how far has charlotte traveled in feet during this time?
Answers
Speed is regarded as the rate at which a particular distance is traveled over time. 138.92 miles has charlotte traveled in feet during this time
From the information given:
The speed at which charlotte is driving = 64.3 ml/h
The time which she took of her eyes from the road = 3.36 s
During the entire journey, the time at which she took her eyes off the road, she is probably not driving.
∴We will have to convert the 64.3 mi/h to m/s
Since 1 mi/hr = 0.44704 m/s
64.3 mi/h will be:
= (64.3 mi/hr × 0.44704 m/s) ÷ 1 mi/hr
= 30.39872 m/s
Now, using the relation:
Speed = distance/ time
30.39872 m/s = (distance) / 3.36 s
By Cross multiplying
Distance = 30.39872 m/s × 3.36 s
Distance = 138.92 m
in conclusion, Charlotte traveled by feet for 138.92 m during this time
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A: {-4, -2 -1, 2}
B: {-4, 4}
C: {-3, -2, 0, 2}
D: {-4, -2, -1, 0, -2}
Answers
Answer:this is soooo compli
Step-by-step explanation:
Please name these last two shapes
Answers
Answer:
Step-by-step explanation:
Square, Irregular shape
look at the photo and solve what goes in the boxes that say choose.
Answers
Answer:
120
Step-by-step explanation:
Split up the boxes to help you achieve the answer.
Find an angle that is positive, less than 360° , and coterminal with 395° . Subtract 360° 360 ° from 395° 395 ° .
Answers
Given an angle that is positive, less than 360°, and coterminal with 395° is 35°.
Subtract 360° from 395°.
We know that 1 revolution is equal to 360°.
Therefore, a positive angle that is less than 360° and coterminal with 395° is 35°.
When an angle is less than 360° and shares the same terminal side with another angle that is less than 360°, then the angle is referred to as a coterminal angle.
In other words, the two angles have the same initial side and terminal side but can be either positive or negative.
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very fast
Show, by induction, that \( T(n)=10 n^{2}-3 n \quad \) if \( n=1 \)
Answers
Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that \($$\(T(n)=10n^2-3n\)$$\) if ( n= 1). The given statement is true for all positive integers n
Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.
Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)
Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) = \(10(k+1)^2-3(k+1)\).
Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that \($$\(T(n)=10n^2-3n\)$$\) if (n=1). Therefore, the given statement is true for all positive integers n.
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anyone know the answer? its algrebra
Does the equation represent an exponential function?
y = 4 • 5x
Yes
No
Answers
Answer:
yes is rhe anwers that was that i put
3 Rewrite using rational exponent. Assume all variables are positive. Find all real solutions. 7x-9-4=0 See the rational equation. 61 3 S + x-4x+3 Xx+3x²-x-12 10
Answers
The rational exponent form of the given equation is \(7x^{-\frac{9}{4}} = 4\).
Step 1: To rewrite the equation using rational exponents, we need to express the variable \(x\) with a fractional exponent.
Step 2: We start with the given equation \(7x - 9 - 4 = 0\). First, we move the constant term (-9) to the right side of the equation by adding 9 to both sides: \(7x - 4 = 9\).
Step 3: Next, we rewrite the equation using rational exponents. The exponent \(-\frac{9}{4}\) can be expressed as a rational exponent by applying the rule that states \(a^{-\frac{m}{n}} = \frac{1}{a^{\frac{m}{n}}}\).
Step 4: By applying the rule mentioned above, we rewrite the equation as \(7x^{\frac{9}{4}} = \frac{1}{4}\).
Step 5: Now we have the equation in rational exponent form, which is \(7x^{\frac{9}{4}} = \frac{1}{4}\).
Step 6: To find the real solutions, we can isolate \(x\) by raising both sides of the equation to the power of \(\frac{4}{9}\).
Step 7: Raising both sides of the equation to the power of \(\frac{4}{9}\) gives us \(7^{\frac{4}{9}}(x^{\frac{9}{4}})^{\frac{4}{9}} = \left(\frac{1}{4}\right)^{\frac{4}{9}}\).
Step 8: Simplifying further, we get \(7^{\frac{4}{9}}x = \left(\frac{1}{4}\right)^{\frac{4}{9}}\).
Step 9: Finally, we can solve for \(x\) by dividing both sides of the equation by \(7^{\frac{4}{9}}\), which gives \(x = \frac{\left(\frac{1}{4}\right)^{\frac{4}{9}}}{7^{\frac{4}{9}}}\).
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One pump can drain a pool in 8 minutes. when a second pump is also used, the pool only takes 4 minutes to drain. how long would it take the second pump to drain the pool if it were the only pump in use
Answers
Answer:
8 minutes
Step-by-step explanation:
The first pump can drain in 8 minutes, therefore:
Rate of the first pump = 1/8
Working together, they can drain the pool in 4 minutes, therefore:
Rate of both pumps = 1/4
Let the time taken by the second pump =t
Rate of the second pump = 1/t.
We then have:
\(\dfrac{1}{8}+ \dfrac{1}{t}=\dfrac{1}{4}\\$Collect like terms$\\\dfrac{1}{t}=\dfrac{1}{4}-\dfrac{1}{8}\\\dfrac{1}{t}=\dfrac{2-1}{8}\\\dfrac{1}{t}=\dfrac{1}{8}\\$Therefore:\\t = 8 minutes\)
It would take the second pump 8 minutes to drain the pool alone.
Identify the location of the values square root of 12, square root of 15, and twenty two ninths on the number line.
Number line with points plotted at two and four tenths labeled Point A, three and five tenths labeled Point B, and three and nine tenths labeled Point C.
Point A is square root of 12, point B is square root of 15, and point C is twenty-two ninths.
Point A is twenty-two ninths, point B is square root of 15, and point C is square root of 12.
Point A is square root of 12, point B is twenty-two ninths, and point C is square root of 15.
Point A is twenty-two ninths, point B is square root of 12, and point C is square root of 15.
Answers
The location of the values square root of 11, square root of 8, and twenty two ninths on the number line is illustrated below.
What is a number line?It should be noted that a number line simply means a straight line that serves as an abstraction for real numbers.
As square root of 12 will be 3.4641.
The square root of 15 is 3.872 and twenty two ninths on the number line will be around 20.22.
So, we can conclude that Point A is twenty-two ninths, point B is square root of 12, and point C is square root of 15.
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write 37/99 as a decimal .
Answers
Answer:
Fraction Decimal Percentage
40/99 0.404 40.4%
39/99 0.3939 39.39%
38/99 0.3838 38.38%
37/99 0.3737 37.37%
Step-by-step explanation:
Answer:
0.3737
Step-by-step explanation:
Determine the force in members gf, fc, and cd of the bridge truss using method of sections. state if the members are in tension of compression. assume all members are pin connected 15 ft 30 ft 40 ft-40 ft40 ft40 ft 10 k 15 k
Answers
While fc is in compression, members gf and cd are in average tension. Gf has a force of 10k, fc of 15k, and cd of 5k.
The method of sections can be used to calculate the force in members gf, fc, and cd of the bridge truss. While members fc and cd are in compression, member gf is in tension. In comparison to fc's 15k and cd's 5k, the force in gf is 10k. By assuming that the total sum of the forces in each part is equal to zero, this may be ascertained. The force on gf is 10k and the force on fc is 15k for the left section, the middle section has a 15k fc and a 5k cd force, and the right section has a 5k cd force. The dimensions of each member—15 feet, 30 feet, 40 feet, 40 feet, and 40 feet—are considered to be pin linked.
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What is the number that when you multiply by 6 then subtract 4 from the product you get 32?
Answers
Answer:
6
Step-by-step explanation:
6x6=36
36-4=32
Answer:
6
Step-by-step explanation:
6x6=36
36-4=32
Hope this helps!
What is the ordered pair representing the y intercept of the line containing he points (4,8) and (2, -4)?
Answers
Answer:
(0,-16)
Step-by-step explanation:
Find the number of distinguishable arrangements of the letters of each word. 1) C O M M I S S I O N. 2) H E E B I E - J E E B I E S.
Answers
The number of arrangements of letters of given words
(1) COMMISSION is 226800 ,
(2) HEEBIE-JEEBIES is 2162160 .
Part(a) : The word "COMMISSION" has 10 letters, with 2 each of M, I, O, and S, and 1 each of N and C.
The number of "distinguishable-arrangements" of letters is calculated as :
⇒ N = 10!/(2! × 2! × 2! × 2!)
⇒ 226800
So, there are 226800 "distinguishable-arrangements" of letters in word "COMMISSION".
Part(b) : The word "HEEBIE-JEEBIES" has 13 letters, but there are 6 "E"s and 2 "B"s, and 2 "I"s which are repeated.
So, the total number of distinguishable arrangements is :
⇒ 13!/(6! × 2! × 2!),
⇒ 12162160.
So, there are 2162160 "distinguishable-arrangements" of letters in word "HEEBIE-JEEBIES".
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If f(x) =
(3 + x)
(x-3)
what is f(a + 2)?
Answers
Answer:
(a^2)+4a-5
Step-by-step explanation:
(3+a+2)(a+2-3)
(a+5)(a-1)
use FOIL or box method
5a-5+(a^2)-a simplifyes to
(a^2)+4a-5
Evaluate the expression for the given values of the variables.- k2 – (2k – 5n) + 3n; k= - 3 and n= -5For k= - 3 and n= - 5, – k? - (2k – 5n) + 3n=).
Answers
Answer
The answer is -43.
Explanation
The question wants us to evaluate the expression using the given variables
-k² - (2k - 5n) + 3n
if k = -3, n = -5
So, to solve this, we would just substitute the given values for k and n
-k² - (2k - 5n) + 3n
= -(-3)² - [(2 × -3) - (5 × -5)] + (3 × -5)
= -(9) - [-6 - (-25)] - 15
= -9 - (-6 + 25) - 15
= -9 - (19) - 15
= -9 - 19 - 15
= -43
Hope this Helps!!!
THREE QUESTIONS 21POINTS HELP!!!
8. Six boys have heights of 1.53 m, 1.49 m, 1-60 m, 1.65 m, 1.90 m and 1.43 m. (a) Find the mean height of the six boys. (b) Find the mean height of the remaining five boys when the shortest boy leaves.
9. In a maths test the marks for the boys were 9, 7, 8, 7, 5 and the marks for the girls were 6, 3, 9, 8, 2, 2. (a) Find the mean mark for the boys. (b) Find the mean mark for the girls. (c) Find the mean mark for the whole class.
10. Five different drinks have an average (mean) price of £1.50. When a sixth drink is added the new average price is £1.60. How much did the sixth drink cost?
Answers
I'll do problem 8 to get you started.
Part (a)
To find the mean, we first add up the values
1.53+1.49+1.60+1.65+1.90+1.43 = 9.6
Then divide over 6 since this is the number of values in the set.
9.6/6 = 1.6
Answer: 1.6 meters==================================================
Part (b)
The shortest boy is 1.43 meters tall. If he leaves the group, then we have these heights leftover
1.53, 1.49, 1.60, 1.65, 1.90
Adding them up gets us
1.53+1.49+1.60+1.65+1.90 = 8.17
Then divide by 5
8.17/5 = 1.634
Answer: 1.634 metersWhich represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
the answer is C ;D
Step-by-step explanation:
Solve for x.
A) - 9
C) -5
B) -11
D) 10
Answers
Answer: D) 10
Step-by-step explanation:
All angles in a triangle adds up to 180°
60° + 50° + 7x = 180°
7x = 180° - 60° - 50° = 180°- 110° = 70°
x = (70 ÷ 7)° = 10°
For nitrogen to be a liquid, its temperature must be within 12.78 °F of -333.22 °F. Which equation can be used to
find the maximum and minimum temperatures at which nitrogen is a liquid, x?
The equation that can be used to find the maximum and minimum temperatures is
x +
Answers
Answer:
X+333.22=12.78.
Step-by-step explanation:
Please check the attached picture, please answer thoroughly!
Answers
The selection depends on individual needs, preferences, and the intended use of the tiny house.
a) To find the amount of space inside each house, we need to calculate the volume for each design.
House on the left:
Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³
Triangular house:
Volume of a triangular prism = (base area x height) / 2
Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²
Volume = (20 m² x 7 m) / 2 = 70 m³
b) When comparing the environmental impacts of each house, several factors need to be considered:
Positive impacts:
1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.
2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.
3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.
Negative impacts:
1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.
2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.
3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.
c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:
The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.
The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.
Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.
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Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one sentence summary comparing the blue line to the black line. Hint: Find the y-intercept. Then count up and over (y/x) to the next point on the line to determine the slope.
Answers
Answer:
y=1/2x+2(2 is the y-intercept)
The blue line and black line have the same y-intercept, but the black line has a slope 1/6 greater than the blue line.
Hope it helps <3
Answer:
\(\boxed{y=\frac{1}{2} x+2}\)
Step-by-step explanation:
Let's take any of the coordinates of blue line to find the slope
The coordinates are (4,4) and (0,2)
Slope = \(\frac{y2-y1}{x2-x1}\)
Slope = \(\frac{2-4}{0-4}\)
Slope = \(\frac{-2}{-4}\)
Slope = m = 1/2
Y-intercept = b = 2 (Because here x= 0)
So, the slope intercept equation becomes:
=> \(y = mx+b\)
=> \(y = \frac{1}{2} x+2\)
For the function f ( x ) = − 3 x 2 − 5 x − 8 , evaluate and fully simplify each of the following.
f(x+h)=
f(x+h)−f(x)/h=
Answers
Therefore, the fully simplified values are f(x + h) = -3x² - 6hx - 3h² - 5x - 5h - 8f(x+h) - f(x)/h = -6x - 3h - 5
The function f(x) = −3x² - 5x - 8Given the function, we are to evaluate and fully simplify each of the following: f(x+h)f(x+h) - f(x)/h To find the value of f(x + h), we will replace x with (x + h) in the given function: f(x + h) = -3(x + h)² - 5(x + h) - 8= -3(x² + 2hx + h²) - 5x - 5h - 8= -3x² - 6hx - 3h² - 5x - 5h - 8
To find the value of f(x + h) - f(x)/h, we will first find the value of f(x):f(x) = -3x² - 5x - 8Now, we will subtract f(x) from f(x + h) and divide by h: f(x+h) - f(x)/h = [-3x² - 6hx - 3h² - 5x - 5h - 8 - (-3x² - 5x - 8)]/h= [-3x² - 6hx - 3h² - 5x - 5h - 8 + 3x² + 5x + 8]/h= (-6hx - 3h² - 5h)/h= -6x - 3h - 5.
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