nth term of a sequence is n(n+1) what term is 240? is 55 a term in the sequence?
Answers
Answer:
a₁₅ = 240 55 is not term in the sequenceStep-by-step explanation:
\(n(n+1)=240\\\\n^2+n-240=0\\\\n=\dfrac{-1\pm\sqrt{1-4(-240)}}{2}=\dfrac{-1\pm\sqrt{1+960}}{2}=\dfrac{-1\pm31}{2}\quad\wedge\quad n\in N_+\\\\n=15\)
if n is even number then (n+1) is odd number and if n is odd number then (n+1) is even number
The product of numbers where one of them is even will always be even.
55 is odd number so it is not term of this sequence.
Related Questions
What is the x intercept of the line x = 3.5
Answers
Answer:
x=3.5
Y=None
Step-by-step explanation:
identify the end behavior and the zeros of function h
h(x) = -x^3-9x^2+4x+96
based on these key features which statement is true about the graph representing function h
a. the graph is positive on the intervals (-8, -4) and (3, infinity)
B. the graph is negative on the intervals (- infinity, -8) and (-4,3)
C. the graph is negative on the intervals (-3, 4) and (8, infinity)
D. the graph is positive and intervals (- infinity, -8) and (-4, 3)
Answers
Answer:
The graph is positive on the intervals (-infinity,-8) and (-4,3).
Step-by-step explanation:
I got the answer right and I checked the graph. I'm correct.
Answer:
The correct answer is:
D. The graph is positive on the intervals (-infinity, -8) and (-4, 3).
Step-by-step explanation:
I got it right on the Edmentum test.
Mohammed is trying to find angle h. He finds angle g first and then he finds angle h from angle g.
a) Which angle fact does he use to find angle g
b) which angle fact does he then use to find angle h
Answers
a. The angle fact that Mohammed can use to find angle g is alternate angles
b) The angle fact that he then use to find angle h is alternate interior angles.
What is an alternate angle?When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.
When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.
In this case, it should be noted that the angles will be 137° based on the illustration.
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Someone please help me with this
Answers
I’m not sure if this is correct but I hope this helps✨❤️
Identify the y-intercept for the line 4x – 2y = 4
Give your answer as a coordinate.
PLEASE HELP ASAP
Answers
Answer: (0,-2)
Step-by-step explanation: uhdehdwhehehhH
WILL GIVE BRAINLESS IF YOU GOT IT CORRECT
Answers
Answer: 2.79 x 10 to the 5th power
Step-by-step explanation: Your welcome :)
Answer:
2.79 x \(10^{5} }\)
Step-by-step explanation:
7.9 x \(10^{4}\) = 79000
2 x \(10^{5}\) = 200000
79000 + 200000 = 279000
279000 = 2.79 x \(10^{5} }\)
Hope this helps, I'm sorry about the earlier question but I fixed it:)
Let P(n) be the statement that 12+22+⋯+n2=n(n+1)(2n+1)/6 for the positive integer n. a) What is the statement P(1) ? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f) Explain why these steps show that this formula is true whenever n is a positive integer.
Answers
a) The statement P(1) is that 12 = 1(1 + 1)(2(1) + 1)/6.
b). 12 is equal to 1, P(1) is true.
c). The inductive hypothesis is that for some positive integer k, the statement P(k) is true.
d). we need to show that 12+22+⋯+k2+(k + 1)2=(k + 1)((k + 1) + 1)(2(k + 1) + 1)/6.
e). we add (k + 1)2 to both sides of the equation in the inductive hypothesis: 12+22+⋯+k2+(k + 1)2 = k(k + 1)(2k + 1)/6 + (k + 1)2
f). the formula 12+22+⋯+n2=n(n+1)(2n+1)/6 is true whenever n is a positive integer.
a) The statement P(1) is that 12 = 1(1 + 1)(2(1) + 1)/6.
b) To show that P(1) is true, we substitute n = 1 into the given equation and simplify:
12 = 1(1 + 1)(2(1) + 1)/6
12 = 1(2)(3)/6
12 = 6/6
12 = 1
Since 12 is equal to 1, P(1) is true.
c) The inductive hypothesis is that for some positive integer k, the statement P(k) is true. In other words, assume that 12+22+⋯+k2=k(k+1)(2k+1)/6 holds.
d) In the inductive step, we need to prove that if the statement P(k) is true, then the statement P(k + 1) is also true. So, we need to show that 12+22+⋯+k2+(k + 1)2=(k + 1)((k + 1) + 1)(2(k + 1) + 1)/6.
e) To complete the inductive step, we add (k + 1)2 to both sides of the equation in the inductive hypothesis:
12+22+⋯+k2+(k + 1)2 = k(k + 1)(2k + 1)/6 + (k + 1)2
Using algebraic simplification and factoring, we get:
(k + 1)((k + 1) + 1)(2(k + 1) + 1)/6.
f) By completing the basis step and the inductive step, we have shown that the statement P(n) holds for the positive integer n.
Therefore, the formula 12+22+⋯+n2=n(n+1)(2n+1)/6 is true whenever n is a positive integer.
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qs 14-18 determining components of costs of goods manufactured
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Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.
Direct Materials: It includes the cost of raw materials used in manufacturing a product.
Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.
Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process
Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.
To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.
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1) In the market for apartment housing, the quantity of available apartments is observed to be less than the number of renters who are willing and able to pay the market price of an apartment. In this scenario, the market is said to be _____.(1 point)
A in equilibrium because there is a surplus of apartments on the market
(B) in equilibrium because there is a shortage of apartments on the market
C in disequilibrium because there is a shortage of apartments on the market
D in disequilibrium because there is a surplus of apartments on the market
1) B
2) For a given market, the equilibrium quantity of the good or service will decrease if _____.(1 point)
A demand increases and supply decreases
B demand decreases and supply increases
(C) demand decreases and supply decreases
D demand increases and supply increases
2)C
3) Price Quantity Supplied Quantity Demanded
$10 1,000 2,500
$20 2,000 2,000
$30 3,000 1,500
$40 4,000 1,000
The equilibrium price for this market is _____.
(1 point)
A $10
(B) $20
C $30
D $40
3) B
4) In a given market, the market equilibrium price and quantity are $120 and 5 million units, respectively. At a price of $100, 4.8 million units are supplied, and 5.2 million units are demanded. It can be said that at a price level of $100 there is a _____.(1 point)
A a surplus of 0.4 million units
(B) a shortage of 0.4 million units
C a shortage of 0.2 million units
D a surplus of 0.2 million units
4) B
5)The supply and demand curves for a market are graphed below with price in dollars and quantity in thousands.
Two intersecting lines are graphed. The horizontal axis labeled Quantity goes from 0 to 70 in increments of 10. The vertical axis labeled Price goes from 0 to 50 in increments of 10. A line with a negative slope is labeled D and a line with a positive slope is labeled S. The lines intersect at approximately left parenthesis 33.7 comma 30 right parenthesis. A horizontal dashed line extends from left parenthesis 0 comma 30 right parenthesis to the point of intersection.
Which of the following would result from an increase in the supply curve?
(1 point)
(A) a market equilibrium price less than $30
B a market equilibrium quantity less than $30
C a market equilibrium quantity greater than $30
D a market equilibrium price greater than $30
5) A
5/5 Good job
Answers
Answer:
Hey
Step-by-step explanation:
Hey did you find the answers to this? i really need it. im desperate!
1. The market is said to be in disequilibrium because there is a shortage of apartments on the market
2. The equilibrium quantity of the good or service will decrease if demand decreases and supply decreases
3. The equilibrium price for this market is $20
4. It can be said that at a price level of $100 there is a a shortage of 0.4 million units
Equilibrium is the point at which quantity demanded equal quantity supplied
The price at this point is referred to as the equilibrium price.
Above equilibrium, there is a surplus - quantity supplied exceeds quantity demanded. As a result of the surplus, price would fall until equilibrium is reached.
Below equilibrium, there is a shortage - quantity demanded exceeds quantity supplied. As a result of the shortage, price would rise until equilibrium is reached.
A decrease in demand would lead to a leftward shift of the demand curve. As a result, quantity and price decreases. A decrease in supply would lead to a leftward shift of the supply curve. This leads to a decrease in quantity and an increase in price. Taking these two effect together, equilibrium quantity would decrease and there would be an indeterminate effect on equilibrium price
Equilibrium price is $20. This is because this is the price at which quantity demanded exceeds quantity supplied
There is a shortage because quantity supplied is less than quantity demanded
Shortage = 5.2 million - 4.8 million = 0.4 million
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Find the y-intercept of the line: x + 4y + 8 = 0
Answers
Answer:
y intercept is -2
Step-by-step explanation:
y intercept is when x is 0.
original equation:
If you want to make it into something solvable, you want to move everything but y to one side.
1. x+4y+8=0
2. 4y+8=-x
3. 4y=-x-8
4. y=-1/4x-2
5. Since this is a linear function, all you have to do to find the y intercept is plug x in with 0. (mentioned above)
6. y=-1/4(0)-2
7.y=-2
8. y int=-2
In which quadrant does 694 lie?
Answers
Answer: C. quadrant l
Step-by-step explanation:
Angle 694° lies Quadrant IV which is correct option (D)
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values
What is the quadrant?A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.
For Quadrant I : the value of x and y both are positive ( +,+ )
For Quadrant II : the value of x is negative and y is positive ( -,+ )
For Quadrant III : the value of x is negative and y is negative ( -, - )
For Quadrant IV : the value of x is positive and y is negative ( +, - )
Locate the quadrant of the angle.
If the angle is greater than 360°,
Subtract 360° until the angle is less than 360°.
⇒ 694 - 360
⇒ 334°
Hence, angle 694° lies Quadrant IV
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Help! 100 points! Evaluate the function at: x=3
Answers
Answer: When x=3 y=-3
Step-by-step explanation:
(2x+5)(x-4)=0 in standard form and value of a,b, and c
Answers
hi
A = (2x+5)(x-4)=0
A = 2x²-8x +5x-20
A = 2x² -3x -20
as a quadratic equation is : ax² +bx +c
then a = 2 ; b = -3 and c = -20
Answer:
a = 2 ; b = -3 ; c = -20
Step-by- step explanation:
Use FOIL method.
(2x + 5)(x - 4) = 0
2x*x+ 2x*(-4 )+ 5*x + 5* (-4) = 0
2x² - 8x + 5x - 20 =0
Combine like terms,
2x² - 3x - 20 = 0
Standard form: ax² + bx + x = 0
a = 2
b = -3
c = -20
Prove or disprove the following statements.
a. If a, b, c and d are integers such that a|b and c|d, then a + d|b + d. b. if a, b, c and d are integers such that a|b and c|d, then ac|bd. e. if a, b, c and d are integers such that a b and b c, then a c.
Answers
a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.
b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.
c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.
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a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.
b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.
c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.
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When a child is more than two standard deviations underweight for his or her age, the child is suffering from a condition called _____.
Answers
If you are making broccoli cheese soup the ratio of cheese to broccoli to broth is 5:6:10 if there is 100 parts broth how many of each ingredient should you use
Answers
Answer: See explanation
Step-by-step explanation:
Since there are 100 parts broth, the number to use for each ingredients will be:
Cheese = 5 × 100/10 = 5 × 10 = 50
Broccoli = 6 × 100/10 = 6 × 10 = 60
Broth = 100
Which of the following correlation coefficients represents the strongest relationship between two variables? -.75 +.60 .00 +.30
Answers
The correlation coefficient that represents the strongest relationship between two variables is -0.75.
In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.
The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.
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HELP given l || m || n, find the value of x
Answers
Answer:
56°
Step-by-step explanation:
The step by step is this below:
It is 180-124=56°
Please 16 points. And will mark as a brainlest
Answers
Answer:
A, B, C, and E are your answers
Step-by-step explanation:
order 5.13‚5.07,5.009,5.203 least to greatest
Answers
Answer:
. 5.009, 5.07, 5.13, 5.203
hope this helps :)
What is the solution to 31-3x + 9) = -18?
Ox=-5
O x=5 or x= 1
O x= -5 or x=1
O no solution
Hurry please
Answers
Step-by-step explanation:
31-3x+9=-18
31-3x+9+18=0
58-3x=0
-3x=-58
x=-58/-3
x=19.33
so the answer is no solution
not sure about the answer
express ratio as a fraction in simplest form
a. 10 yards to 10 feet
hint *there are 3 feet in every 1 yard
Answers
Answer:
\(\frac{3}{1}\)
Step-by-step explanation:
The dimensions must be the same
10 yards = 10 × 3 feet = 30 feet
ratio = \(\frac{30}{10}\) = \(\frac{3}{1}\)
what is the mean of 72,74,70,64,80
Answers
Answer:
64,70,72,74,80
Step-by-step explanation:
hahahahaahhaahhaah
Explanation=72+74+70+64+80=360, 360/5 = 72
A town council wants to conduct a survey on town policies using a random sample of residents.
Which method would result in a random sample?
A
Ask all residents having lunch at a local restaurant
B Ask the first 5 residents who visit town hall after it opens
С
Draw slips of paper with names of residents out of a large box.
D
Print survey forms on postcards and have residents mail their responses
Answers
Answer:
Step-by-step explanation:
Answer:
The correct answer is C. Draw slips of paper with names of residents out of a large box.
Step-by-step explanation:
Hope it helps-
An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion who are not satisfied.
(a) Past studies suggest that this proportion will be about 0.17. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015. (You will need a critical value accurate to at least 4 decimal places.) Sample size:
(b) Using the sample size above, when the sample is actually contacted, 25% of the sample say they are not satisfied. What is the margin of the error of the confidence interval? MoE:
Answers
The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.
(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = critical value (corresponding to the desired confidence level)
p = estimated proportion of the population
E = margin of error
In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.
Plugging these values into the formula, we have:
n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2
n ≈ 1901.63
Therefore, the sample size needed is approximately 1902.
(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:
MoE = Z * sqrt((p * (1-p)) / n)
Where:
MoE = margin of error
Z = critical value (corresponding to the desired confidence level)
p = proportion of the sample
n = sample size
Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:
MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)
MoE ≈ 0.014
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The ratio of 1.4 to 26 is the same as the ratio of 2.8 to ____.
Answers
How can I solve this?
4x+6/2 = 3x-15/3
Answers
Answer:
x=-8
Step-by-step explanation:
try using this app called cymath it helps with questions like this
find f(t) for the function f(s)= 5s³+20s²-49x-108/s²+7s+10. assume that k(t)=δ′(t) .
Answers
The function f(t) is given by (15t² + 40t) / (2t + 7) when k(t) is replaced by the derivative of the Dirac delta function, denoted as δ'(t).
the derivative of f(s) is taken by differentiating each term separately. The derivative of 5s³ is 15s², the derivative of 20s² is 40s, and the derivative of -49x is 0 since x is not involved.
The derivative of -108 is also 0.
Moving on to the denominator
the derivative of s² is 2s, the derivative of 7s is 7
and the derivative of 10 is 0. Therefore, the derivative of f(s) with respect to s is (15s² + 40s) / (2s + 7).
we substitute k(t) with δ'(t), which is the derivative of the Dirac delta function δ(t).
The Dirac delta function is defined as 0 for all values of t except at t = 0, where it is infinite.
Its derivative, δ'(t), is 0 for all values of t except at t = 0, where it is not defined.
Therefore, the resulting expression for f(t) is (15t² + 40t) / (2t + 7). This is the final answer for f(t) in terms of t, obtained by differentiating f(s) and substituting k(t) with δ'(t)
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A shopkeeper sells a DVD player at a price RM 2,500. If the cost price of the DVD player was RM 3,500, find the profit/loss in which the shopkeeper is. Also, find the percent for the same.
Answers
Answer:
see explanation
Step-by-step explanation:
Since the player was sold for less than what was paid then a loss is made.
loss = 3500 - 2500 = 1000
percent loss = \(\frac{loss}{cost}\) × 100% , thus
percent loss = \(\frac{1000}{3500}\) × 100% ≈ 28.6% ( to 1 dec. place )
ʏᴏᴜ’ᴠᴇ ʟᴇᴀʀɴᴇᴅ ᴀʙᴏᴜᴛ ꜰᴜɴᴄᴛɪᴏɴ ɴᴏᴛᴀᴛɪᴏɴ ɪɴ ᴘʀᴇᴠɪᴏᴜꜱ ʟᴇꜱꜱᴏɴꜱ, ʙᴜᴛ ᴄᴏᴜʟᴅ ʏᴏᴜ ᴜꜱᴇ ꜰᴜɴᴄᴛɪᴏɴ ɴᴏᴛᴀᴛɪᴏɴ ᴛᴏ ᴀᴅᴅ ᴛᴡᴏ ꜰᴜɴᴄᴛɪᴏɴꜱ? ʜᴏᴡ ᴅᴏ ʏᴏᴜ ᴛʜɪɴᴋ ʏᴏᴜ ᴄᴏᴜʟᴅ ꜱɪᴍᴘʟɪꜰʏ ꜰ(x) + ɢ(x) ɪꜰ ꜰ(x) = 3x + 2 ᴀɴᴅ ɢ(x) = 4x? ᴡʜᴀᴛ ᴀʙᴏᴜᴛ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ᴏꜰ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ꜱᴜᴄʜ ᴀꜱ ꜰ(ɢ(x))? ʜᴏᴡ ᴅᴏ ʏᴏᴜ ᴛʜɪɴᴋ ꜰ(ɢ(x)) ᴄᴏᴜʟᴅ ʙᴇ ꜱɪᴍᴘʟɪꜰɪᴇᴅ? ᴡʜᴀᴛ ꜱɪᴛᴜᴀᴛɪᴏɴꜱ ᴄᴀɴ ʏᴏᴜ ᴛʜɪɴᴋ ᴏꜰ ᴡʜᴇʀᴇ ᴄᴏᴍʙɪɴɪɴɢ ꜰᴜɴᴄᴛɪᴏɴꜱ ᴡᴏᴜʟᴅ ʙᴇ ᴜꜱᴇꜰᴜʟ?
different font because filter
Answers
Yes, function notation can be used to add two functions. we can compose the two functions to get the velocity as a function of time.
To add two functions f(x) and g(x), we simply add their output values for the same input value x. So, (f+g)(x) = f(x) + g(x).
In the given example, f(x) = 3x + 2 and g(x) = 4x. Therefore, (f+g)(x) = 3x + 2 + 4x = 7x + 2.
We can also compose functions, such as f(g(x)) which means applying function g to x and then applying function f to the result. In the given example, f(g(x)) = f(4x) = 3(4x) + 2 = 12x + 2.
Function composition can be useful in situations where we want to model complex systems as a series of simpler functions. For example, in physics, the position of an object may be modeled as a function of time, and the velocity of the object may be modeled as the derivative of the position function with respect to time. In this case, we can compose the two functions to get the velocity as a function of time.
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