A sequence of numbers is shown below :
1 5 9 13 17
explain why 95 will not be a term in this sequence
Answers
Answer:
95 is not a term here as the next verse should be 98 as it is a 94 term in this pattern
95 will not be a term in the sequence 1, 5, 9, 13, 17, ....., as the value of n for the nth term is not integer.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
The given sequence of numbers is,
1, 5, 9, 13, 17, .....
The first term of the given sequence a₁ =1,
From the given sequence, the common difference pair of two consecutive terms d = 4,
Let nth term of the sequence aₙ= 95,
By arithmetic sequence formula,
aₙ = a₁ + (n-1).d
Substitute the value of aₙ and d,
95 = 1 + (n-1).4
94 = (n-1). 4
(n-1) = 23.5
n = 24.5
The value of n can't be decimal, so 95 can't be a term of the given sequence.
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Related Questions
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. c How many of these sets contain any 4 numbers?
Answers
Answer: The number of sets contain any 4 numbers = 210
Step-by-step explanation:
Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.
i.e. Total choices = Numbers in set = 10
By combinations, the number of sets contain any 4 numbers =\(^{10}C_4\)
\(=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210\)
Hence, the number of sets contain any 4 numbers = 210
One-third is one-ninth of
Answers
Answer:
1/27
Step-by-step explanation:
I believe the answer to your question is 1/27
I hope this helps you!
Calculate the volume of a parallelepiped whose sides are described by the vectors, A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm, You can use the vector triple product equation Volume = A . (BXC)| .
Answers
The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.
The given vectors are:
A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm
In order to calculate the volume of parallelepiped, we will use vector triple product equation:
Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.
Step-by-step solution:
We have, A = [-4, 3, 2] cm
B = [2,1,3] cm
C = [1, 1, 4] cm
Now, let's find BXC, using the cross product of vectors B and C.
BXC = | i j k| 2 1 3 1 1 4 | i j k | = -i + 5j - 3k
Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.
The volume of the parallelepiped is given by:
Volume = A . (BXC)|
Therefore, we have: Volume = A . (BXC)
\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)
Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.
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one by two minus 1 by 3
Answers
Answer:
1/6
Step-by-step explanation:
in this case we take the number of the equal parts from the numerator of the first number and further divide this part into the total parts in the denominator of the second number
PLS mark as brainleast
Working
1/2-1/3
Firstly, make the denominators equal.
1/2 is multiply by 3 to both numerator and denominator.Therfore, it would be 3/6.
Secondly , 1/3 is also multiply by 2 to both numerator and denominator. Therefore , it would be 2/6
3/6-2/6 would be 1/6.
Your final answer would be 1/6 (1 by 6)
the area of a rectangle is x^2-3x-54 find the perimeter
a. x^4-6
b. 2x-3
c. x^2+3
d. 4x-6
Answers
Answer:45
Step-by-step explanation:
Consider the function f(x) = el-157z² In all parts that follow all calculations are to be carried out in the FPA9. (i) Find the second Lagrange polynomial L(z), L(x) = 107 (x-x1)(x-x₂) +91: (0-1)(x-₂) for the function f(x) on [0, 0.066], where y = f(x), using the nodes (2 - £o)(z = 2a) (x1 - x0)(1-x2) 20=0, 21=0.033, 2=0.066, (2 − ro)(r = ri) (x2-xo) (x2-1) +9/21 and then work in the FPA, to expand the polynomial in the right-hand side of (5.2), thereby obtaining the representation L*(x)=a22² +1+ of the polynomial L(z) in the FPA9, where a, are suitable 9-digit floating-point numbers. (ii) Use (i) to find an approximation I of the integral 0.066 I= el.1572 dz 70 as I' = -0.006 L* (x) dz. 0 (iii) Obtain the 12-digit representation J of I using the WolframAlpha website by executing the command evalf( integral exp( 1.157 x 2), x=0.0.066), 12 ) and then find the relative error and the number of significant digits in the approximation JI". Present your answers to the problem in a table of the following form Subproblem Answer(s) L" (x)=...; J=...; RE(JI)...; SD(JI) € €
Answers
In this problem, we are given a function f(x) and asked to perform various calculations using the FPA9 (9-digit floating-point arithmetic) representation which will result to be L*(x) = a22² + 1.
(i) To find the second Lagrange polynomial L(z), we use the given nodes and construct the polynomial as L(x) = 107(x-x1)(x-x2) + 91(0-x1)(x-x2)/(x2-x1). Then, we convert the coefficients and evaluate L(x) in the FPA9 format to obtain the representation L*(x) = a22² + 1, where a's are suitable 9-digit floating-point numbers.
(ii) Using the representation L*(x), we approximate the integral I = ∫ exp(-1.157x²) dx over the interval [0, 0.066] as I' = -0.006 ∫ L*(x) dx from 0 to 0.066.
(iii) We obtain the 12-digit representation J of the integral using the WolframAlpha website. Then, we calculate the relative error RE(JI') and the number of significant digits SD(JI') in the approximation. This allows us to assess the accuracy of the approximation compared to the exact value represented by J.
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someone help me w this problem
Answers
Answer;
a
Step-by-step explanation:
Which place value should you use to compare the numbers?
645,853
646,34
Answers
Can you help me with this question step by step.
Answers
Answer:
32
Step-by-step explanation:
There are 28 full shaded squares
There are 8 half squares
2 half squares make up 1 full square
So 28 + 4 = 32
Area is 32 units
You measure the length of the same side of a block five times and each measurement has an uncertainty of Δ
b = 0.1 mm. What is the uncertainty in the best estimate for b?
Answers
The uncertainty in the best estimate for the length of the side of the block is approximately 0.0447 mm.
To determine the uncertainty in the best estimate for the length of the block side, we can consider the range of values obtained from the measurements. Since the uncertainty represents the possible deviation from the true value, the range of measurements can be used to estimate the uncertainty in the best estimate
To find the standard deviation represents the average amount of variation or spread among the measurements , we use the formula σ = Δb / √n, where σ is the standard deviation, Δb is the uncertainty in each measurement, and n is the number of measurements.
In this case, Δb = 0.1 mm and n = 5. Plugging these values into the formula, we get σ = 0.1 / √5 ≈ 0.0447 mm.
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I need the work and the answer
Answers
Answer: 70
Step-by-step explanation: 14 + 6 = 20, 20 time 5 is 100, so 14 times 5 is the answer
In the diagram , the measure of angle <1 is 55° If line y rotated °5 degrees clockwise about the point intersection what is the new measure of <3?
A:50°
A:120°
A:60°
A:130°
Please help :)
Answers
Answer: 60
Step-by-step explanation:
What is the equation of the line that passes through the point (-1, -5) and has a
slope of -12
Answers
Answer:
Thus, the equation of a line is: y = -12x-17
Step-by-step explanation:
point = (-1, -5) slope = -12Using the point-slope form
\(y-y_1=m\left(x-x_1\right)\)
where m is the slope, and (x₁, y₁) is the point
substituting the values m = -12 and the point (-1, -5)
\(y-y_1=m\left(x-x_1\right)\)
y-(-5) = -12(x-(-1))
y+5 = -12 (x+1)
y+5 = -12x-12
y = -12x-12-5
y = -12x-17
Thus, the equation of line is: y = -12x-17
Farmer Jones and Farmer Smith graze their cattle on the same field. If there are 20 cows grazing in the field each cow produces $4000 of milk. If there are more cows in the field, then each cow produces can eat less grass and the milk production falls. With 30 cows on the field each produces $3000 of milk, with 40 cows each produces $2000 of milk . Cows cost $1000 a piece. Assume that Farmer Jones and farmer Smith can buy either 10 cows or 20 cows, find out the Dominant Strategy of Farmer Jones and express the same in formal language. I want to see all the steps.
Answers
The dominant strategy of Farmer Jones is to buy 10 cows.
To determine the dominant strategy of Farmer Jones, we need to compare the outcomes of his two options:
buying either 10 cows or 20 cows.
Let's analyze the potential outcomes for each case:
Buying 10 cows:
If Farmer Smith buys 10 cows:
The total number of cows in the field would be 30, resulting in each cow producing $3000 of milk.
If Farmer Smith buys 20 cows:
The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.
Buying 20 cows:
If Farmer Smith buys 10 cows:
The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.
If Farmer Smith buys 20 cows:
The total number of cows in the field would be 50, resulting in each cow producing less than $2000 of milk (exact value unknown).
From the given information, we can observe that regardless of the strategy chosen by Farmer Smith, Farmer Jones is better off buying 10 cows.
In all scenarios, the milk production per cow is higher when Farmer Jones buys 10 cows compared to buying 20 cows.
Therefore, the dominant strategy for Farmer Jones is to buy 10 cows.
Formally, we can express this as follows:
For Farmer Jones, no matter the strategy chosen by Farmer Smith, buying 10 cows yields a higher milk production per cow compared to buying 20 cows.
Hence, Farmer Jones' dominant strategy is to buy 10 cows.
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Reciprocal of 11/18
Answers
Answer:
18/11
Step-by-step explanation:
To get the reciprocal all you do is flip over the fraction <3
Hi please help quick! what's -2 5/11 - 7 1/11
Answers
Answer:
Your answer will be -9.54545454545Explanation:
I don't really understand what just happened to my calculator but i searched on goo gle but it's the correct answer..
Hope it helps you..Y-your welcome in advance..(;ŏ﹏ŏ)(ㆁωㆁ)
-5/11-1/11=-6/11
The answer is -9 6/11
ali and jake went on a cross country trip they took a train part of the way and a bus the rest of the way they traveled a total of 1050 kilometers riding on the train 200 more kilometers than in the bus how many kilo meters did they travel by
Answers
Answer:
1900 km
Step-by-step explanation:
train = 1050km
bus = 200 less than train or 1050-200 = 850
1050+850=1900
Answer:
625, just got it right
Step-by-step explanation:
Decompose the relations to BCNF : i. R=(ABCD)F={AB→C,B→D;C→A} ii. R=(A,B,C,D,E),F={AB→CE,AC→D,BE→CD,C→D,E→AB}
Answers
Decomposed relations are i. R = R1 ∪ R2 ∪ R3, where R1 = (ABC), R2 = (BD), and R3 = (CA) , ii. R = R1 ∪ R2 ∪ R3 ∪ R4 ∪ R5, where R1 = (ABCE), R2 = (ACD), R3 = (BEDC), R4 = (CD), and R5 = (EAB).
To decompose the given relations into Boyce-Codd Normal Form (BCNF), we need to analyze the functional dependencies and ensure that each functional dependency is fully satisfied.
i. R = (ABCD), F = {AB→C, B→D, C→A}
We observe that the functional dependencies in F are:
1. AB→C
2. B→D
3. C→A
To achieve BCNF, we need to decompose R based on these dependencies. Let's analyze each dependency:
1. AB→C: Since AB is a candidate key (a minimal superkey), we create a new relation, R1 = (ABC), and remove AB→C from F.
2. B→D: As B is not a candidate key, we create another relation, R2 = (BD), and remove B→D from F.
3. C→A: C is not a candidate key, so we create a third relation, R3 = (CA), and remove C→A from F.
The final decomposition is R = R1 ∪ R2 ∪ R3, where R1 = (ABC), R2 = (BD), and R3 = (CA). All functional dependencies are now fully satisfied in BCNF.
ii. R = (A, B, C, D, E), F = {AB→CE, AC→D, BE→CD, C→D, E→AB}
We analyze the functional dependencies in F:
1. AB→CE
2. AC→D
3. BE→CD
4. C→D
5. E→AB
To achieve BCNF, we decompose R based on these dependencies:
1. AB→CE: We create a new relation, R1 = (ABCE), and remove AB→CE from F.
2. AC→D: We create R2 = (ACD), and remove AC→D from F.
3. BE→CD: We create R3 = (BEDC), and remove BE→CD from F.
4. C→D: We create R4 = (CD), and remove C→D from F.
5. E→AB: We create R5 = (EAB), and remove E→AB from F.
The final decomposition is R = R1 ∪ R2 ∪ R3 ∪ R4 ∪ R5, where R1 = (ABCE), R2 = (ACD), R3 = (BEDC), R4 = (CD), and R5 = (EAB). All functional dependencies are now fully satisfied in BCNF.
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a random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years. what is the 95% confidence interval for the true average age of all students in the university?
Answers
As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.
Confidence interval
Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.
Given,
A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.
And we need to find the 95% confidence interval for the true average age of all students in the university.
While we looking through the given question we have identified the following,
Number of samples = 64
Average age = 23
Standard deviation = 3
Confidence interval = 95%
Based on this confidence interval, the z score is 1.96
According to the formula,
u = 23 ± 1.96 x 3/√64
u = 23 ± 1.96 x (3/8)
u = 23 ± 1.96 x 0.375
u = 23 ± 0.735
u = 23.735, 22.635
Therefore, the average age of the student is approximately 23 to 24.
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The money Sky makes from babysitting is directly proportional. After 4 hours, she makes $72. How much money would she make after 7 hours?
A $75
B $126
C $54
D $108
Answers
Answer:
B.
Step-by-step explanation:
divide the $72 by 4 hours to get a rate of $18 an hour
multiply the $18 by the number of hours you are trying to find (7) and get a total of $126
Answer:
B
Step-by-step explanation:
72/4=18, so 18+18+18=54, and then 72+54=126
Help me solve this problem please
Answers
Answer:
sorry im just answering this cuz need points
Step-by-step explanation:
a bag holds 6 tiles: 2 lettred and 4 numbered. without looking, chose a tile. what is the probability of drawing a number
Answers
Answer: 0.66 (repeating)
Step-by-step explanation:
2/3 is equivalent to 4/6 and 2/3 is 0.66 repeating
An automobile factory is assembling cars and they need to have all of the parts in stock at the assembly line. each car needs four tires and a spare tire for the trunk. if they produce c cars per day, what formula shows how to calculate the number of tires, t, needed? a. c = 4 t 1 c. t = 4 c 1 b. t = c 4 d. t = 5 c
Answers
The formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D
EquationNumber of tires needed by each car = 4Number of spare tires needed by each car = 1Total tires needed by each car = 4 + 1
= 5
Number of cars produced per day = cTotal number of tires, t needed for c cars.
Number of tires needed, t = Total tires needed by each car × Number of cars produced per day
t = 5 × c
t = 5c
For instance,
if 5 cars are produced per day
Number of tires needed, t = Total tires needed by each car × Number of cars produced per day
t = 5c
= 5 × 5
t = 25 tires
Therefore, the formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D
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Is (0,1) included in the solution of the system
−x + y < 1 and
x + y ≥ −3
True
False
Answers
Solve for x in the equation x squared 20 x 100 = 36.
Answers
The solution of the equation are; x = -16 or x = -4. so option A is correct.
What is a quadratic equation?
A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given equation;
x²+ 20 x + 100 = 36.
x²+ 20 x + 100 - 36 = 0
x²+ 20 x + 64 = 0.
x²+ (16 + 4)x + 64 = 0.
x²+ 16x + 4x + 64 = 0.
x(x + 16) +4 (x + 16) = 0.
(x+ 4) (x + 16) = 0
Thus, the solution of the equation are; x = -16 or x = -4.
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The price of an article is marked 25% above the cost price. If it is sold
at the profit of Rs 500 after allowing 15% discount what will be its
selling price?
(Ans: 10170)
Answers
Answer: 1250
Step-by-step explanation:
1) The price of an article is marked 25% above the cost price.
SP = CP x 1.25
2) If it is sold at the profit of Rs 500 after allowing 15% discount
SP = CP x 0.85 + 500
SP = 0.85CP + 500
1.25CP = 0.85CP + 500
1.25CP - 0.85CP = 500
0.40CP = 500
CP = 500 / 0.4 = 1250
Answer:
Rs 8500solution,
Let C.P of article be X
\(mp = x + \frac{25}{100} \times x \\ \: \: \: \: = x + \frac{25x}{100} \\ = \frac{x \times 100 + 25x}{100} \\ = \frac{100x + 25x}{100} \\ = \frac{125x}{100} \\ sp = mp - \frac{15}{100} \times \frac{125x}{100} \\ \: \: \: \: = \frac{125x}{100} - \frac{15x}{80} \\ \: \: \: \: = \frac{125 x\times 4 - 15x \times 5}{400} \\ \: \: \: \: \: = \frac{500x - 75x}{400} \\ \: \: \: \: \: \: = \frac{425x}{400} \\ profit = sp - cp \\ or \: 500 = \frac{425x}{400} - x \\ or \: 500 = \frac{425x - x \times 400}{400} \\ or \: 500 = \frac{425x - 400x}{400} \\ or \: 500 = \frac{25x}{400} \\ or \: 25x = 200000 \\ or \: x = \frac{200000}{25} \\ x = 8000 \\ again \\ \: selling \: price = \frac{425x}{400} \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{425 \times 8000}{400} \\ \: \: \: \: \: \: = \frac{3400000}{400} \\ \: \: \: \: \: \: = 8500\)
hope this helps....
Good luck on your assignment...
2 (4z-1)=3(z+2) simplify
Answers
Answer:
z=8/5
Step-by-step explanation:
2(4z-1)=3(z+2)
distribute the 2 and 3
8z-2=3z+6
move 2 to the other side by adding 2
8z=3z+8
move 3 to the other side by subtracting 3
5z=8
divide both sides by 5
z= 8/5
The equivalent value of the expression is z = 8/5 = 1.6
Given data ,
Let the equation be represented as A
Now , the value of A is
2 ( 4z - 1 ) = 3 ( z + 2 )
On simplifying the equation , we get
2 ( 4z - 1 ) = 3 ( z + 2 )
So , the left hand side of the equation is equated to the right hand side by the value of 3 ( z + 2 )
Opening the parenthesis on both sides , we get
2 ( 4z ) - 2 = 3z + 6
8z - 2 = 3z + 6
Subtracting 3z on both sides , we get
5z - 2 = 6
Adding 2 on both sides , we get
5z = 8
Divide by 5 on both sides , we get
z = 8/5
z = 1.6
Therefore , the value of z = 8/5 = 1.6
Hence , the expression is z = 8/5 = 1.6
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Help me please!!!, HELP AND CAN YOU EXPLAIN
Answers
Answer:
D
Step-by-step explanation:
It's D because 60 +70 +(180-130)=180
= 60+70+50=180
An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicated that 117 of 484 new engineering graduates were planning graduate study. Are the data from Engineering Horizons consistent with the claim reported by Fortune
Answers
Answer:
unless this is a stats question and you are suggesting that you have bad sampling techniques being used
117/484 is about 24% that is 100% under the "about 50%" stated in the article
Step-by-step explanation:
o is the centre of the circle and abc and edc are tangents to the circle what is bcd if o is 152
Answers
The requried measure of the angle m∠BCD is 28°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
From the figure,
m∠BOD = 2m∠BFD
= 2 × 76°
= 152°
OD perpendicular to CE simultaneously OB perpendicular to CA
m∠ODC = m∠OBC = 90°
m∠ODC + m∠OBC + m∠BOD + m∠BCD = 360
90 + 90 + 152 + m∠BCD = 360
m∠BCD = 28°
Thus, the requried measure of the angle m∠BCD is 28°.
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