Answer:
-666
Step-by-step explanation:
a1 = 6
an = -5 an-1 +4
a2 = -5 a1 +4 = -5*6 +4 = -30 +4 = -26
a3 = -5 a2 +4 = -5 (-26) +4 = 130+4 = 134
a4 = -5 a3 +4 = -5 (134) +4 = -670+4 =-666
Question 6 of 40
Which recursive formula can be used to represent the sequence
2, 6, 10, 14, 18, ... ?
& - 2
O A.
&, - 87-704
ay - 2
O B.
an - 2n-1-4
C. &-0
an - 2n-1 + 4
D.
ay - 2
an - 8-1 + 4
Gays
Step-by-step explanation:
I cannot really identify and read the provided answer options.
the solution to the sequence 2, 6, 10, 14, 18, ... is
an = 4×(n-1) + 2
recursive that is
a1 = 2
an = an-1 + 4
please pick the right option in your original problem definition that fits to this solution.
The recursive formula that represents the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.
This fixed value is called the common difference, and it is the same for all terms in the sequence.
We have,
The given sequence has a common difference of 4 between its consecutive terms.
To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.
Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:
[tex]a_2 = a_1 + 4[/tex]
Similarly, we can represent the third term (a3) as:
[tex]a_3 = a_2 + 4[/tex]
Substituting the value of a2 from the above equation, we get:
[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]
We can continue this pattern to find the recursive formula for the nth term of the sequence:
[tex]a_n = a_{n-1} + 4[/tex]
where [tex]a_1[/tex]= 2
Thus,
The recursive formula for the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
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rule for 15,19,23 please I need it urgently
Answer:
[tex]a_{n}[/tex] = 4n + 11
Step-by-step explanation:
There is a common difference between consecutive terms, that is
19 - 15 = 23 - 19 = 4
This indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 15 and d = 4 , then
[tex]a_{n}[/tex] = 15 + 4(n - 1) = 15 + 4n - 4 = 4n + 11
You roll a die with the sample space s=1,2,3,4,5,6. you define A as (1,2,4) B as (2,3,4,5,6) C as (3,4) and D as (2,4,5). Determine which of the following events are exhaustive and/or mutually exhaustive.
Exhaustive Mutually exclusive
A and B
A and C
A and D
Band C
Answer:
A and B are exhaustive.
Step-by-step explanation:
Given
[tex]A = \{1,2,4\}[/tex]
[tex]B = \{2,3,4,5,6\}[/tex]
[tex]C =\{3,4\}[/tex]
[tex]D = \{2,4,5\}[/tex]
Solving (a): The mutually exclusive events
These are events that have no common or mutual elements
Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.
Solving (b): Exhaustive events.
Two events X and Y are said to be exhaustive if:
[tex]S = P(X\ n\ Y)[/tex]
i.e. if the sample space equals the intersection of X and Y
For events A to D, we have:
[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]
and the sample space is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
By comparison;
[tex]A\ n\ B = S[/tex]
Hence, A and B are exhaustive.
Jayden drives 22.5 miles in 30 minutes. If he drove one hour in total at the same rate, how far did he go? Before you try that problem, answer the question below. How many minutes did Jayden drive in total?
how far did he go in minutes?
Answer:
45 miles in 1 hour
Step-by-step explanation:
1 hour is 60 minutes
22.5 miles / 30 minutes * 2/2 = 45 miles / 60 minutes = 45 miles in 1 hour
Answer:
He drove 22.5 miles in 60 min. He drove 45 miles in 1 hour
Step-by-step explanation:
22.5 miles in 30 min
1 hour= 60 min
30+30=60
22.5+22.5=45 miles
Find the Surface Area and the Volume.
Answer:
Surface area = 850 cm²
Volume = 1000 cm³
Step-by-step explanation:
Applying,
A = h(a+b+c+d)................ Equation 1
Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.
From the diagram in the question,
Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm
Substitute these values into equation 1
A = 25(6+14+7+7)
A = 25(34)
A = 850 cm²
From the volume,
V = A'h...................... Equation 2
Where A' = Area of the base.
From the diagram,
A' = 1/2(6+14)4
A' = 40 cm²
Therefore,
V = 40×25
V = 1000 cm³
9 Two people start writing reports on the same day. Both write 200-page reports. Writer A averages 8 pages a day, and writer B averages 5 pages per day. How much sooner will Writer A finish her report than will Writer B?
Answer:
15 days
+
Step-by-step explanation:
A
200 pages / (8 pages / day) =
= 200 pages days / 8 pages =
= 200 days / 8 = 25 days
B
200 pages / (5 pages / day) =
= 200 pages days / 5 pages =
= 200 days / 5 = 40 days
40-25 = 15 days
A will finish 15 days sooner than B.
A will finish her report 15 days sooner than B.
What is the ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Writer A averages 8 pages a day,
Number of pages per day written by writer A = 8 per day
Writer A will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (8 pages / day)
⇒ 200 pages days / 8 pages
⇒ 200 days / 8
⇒ 25 days
Writer B averages 5 pages a day
Number of pages per day written by writer B = 5 per day
Writer B will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (5 pages / day)
⇒ 200 pages days / 5 pages
⇒ 200 days / 5
⇒ 40 days
Difference between both of time when they finished their report = 40-25 = 15 days
Hence, A will finish her report 15 days sooner than B.
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PLEASE CHECK MY WORK
The function given in the table is quadratic:
true***
false
Answer:
false
Step-by-step explanation:
The function given in the table is a linear function:
f(x) = 3x+2
Assume that the tunnel in Exercise 3.132 is observed during ten two-minute intervals, thus giving ten independent observations Y1, Y2,..., Y10, on the Poisson random variable. Find the probability that Y > 3 during at least one of the ten two-minute intervals
Answer: hello the exercise is missing from your question below is the missing exercise for reference
answer:
0.1745
Step-by-step explanation:
Determine P ( Y > 3 )
Given that y follows Poisson distribution with mean
P( Y = y ) = [tex]\frac{e^{-1} }{y!}[/tex]
assuming that yi represents number of autos that will enter the tunnel and
also let A represent Y > 3 at one of the ten two-minute interval
step 1 : hence finding P(A )
= P(Y > 3 ) = 1 - P( Y≤ 3 )
= 1 - [ [tex][\frac{e^{-1} }{0!} +\frac{e^{-1} }{1!} +\frac{e^{-1} }{2!} +\frac{e^{-1} }{3!} ][/tex]
= 0.018988
since the ten observations are independent
P(X≥ 1 ) = 1 - P( X = 0 )
= 1 - [tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right][/tex] * (0.018988)^0 ( 1 - 0.018988)^10-0
= 1 - 0.8255 = 0.1745
PROBIBILITY HELP ME PLZ Mike is playing a game where a ball is hidden under one of 5 cups. Mike guesses which cup contains the ball 20 times and chooses correctly 6 times. Mike wants to simulate the game to determine if his results are the same as what would be expected by random chance.
Answer:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
Step-by-step explanation:
Given
[tex]Cups = 5[/tex]
[tex]Ball=1[/tex]
[tex]Trials = 20[/tex]
See attachment
Required
Simulate the above experiment (fill in the gaps)
The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:
[tex]P(Correct) = \frac{Ball}{Cups}[/tex]
This gives:
[tex]P(Correct) = \frac{1}{5}[/tex]
The number of times (i.e. 6) he chose correctly is not a factor in his simulation
So, a correct simulation of the experiment is as follows:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
The selected ball represents the number of balls hidden (i.e. 1 ball).
The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)
The 20 times represent the number of times the experiment is repeated.
please help me Solve the following equations simultaneously:
solve for x and y
x+3y =6 and 2x+8y=-12
Answer:
x+3y =6
2x+8y=-12
The solutions to your equations are:
x= 42 and y= -12
lets check this
42+-36 =6
84+-96=-12
Hope This Helps!!!
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Types of restaurants (fast food, organic food, sea food, etc.)A. The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point. B. The nominal level of measurement is most appropriate because the data cannot be ordered. C. The interval level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting point. D. The ordinal level of measurement is most appropriate because the data can be ordered, but differences (obtained by subtraction) cannot be found or are meaningless.
Answer:
B. The nominal level of measurement is most appropriate because data cannot be ordered.
Step-by-step explanation:
Nominal scale is used when there is no specific order scale and data can be arranged according to name. Ordinal scale requires variables to be arranged in specific order. For fast food restaurant the best scale used is nominal scale as variables can be arranged according to their name without specific order.
if you are just given the two points it is the same formula. Find the midpoint between the points (4,−5) and (−4,5).
Answer:
[tex]M = (0,0)[/tex]
Step-by-step explanation:
Given
[tex](4,-5)[/tex] and [tex](-4,5)[/tex]
Required
The midpoint (M)
This is calculated as:
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
So, we have:
[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]
[tex]M = \frac{1}{2}(0,0)[/tex]
[tex]M = (0,0)[/tex]
8x – 3y = 1
–2x + 3y = 11
Solve a Linear System by Elimination
Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 16,12,17,8,15,15,10,11,19,18
Answer:
[tex]Range = 11[/tex]
[tex]\sigma^2 = 12.1[/tex]
[tex]\sigma = 3.5[/tex]
Step-by-step explanation:
Given
[tex]Data: 16,12,17,8,15,15,10,11,19,18[/tex]
Solving (a): Range
This is calculated as:
[tex]Range = Highest - Least[/tex]
Where:
[tex]Highest = 19[/tex]
[tex]Least = 8[/tex]
So:
[tex]Range = 19 - 8[/tex]
[tex]Range = 11[/tex]
Solving (b): The population variance
First, calculate the population mean using:
[tex]\mu = \frac{\sum x}{n}[/tex]
So:
[tex]\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}[/tex]
[tex]\mu = \frac{141}{10}[/tex]
[tex]\mu = 14.1[/tex]
So, the population variance is:
[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]
[tex]\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}[/tex]
[tex]\sigma^2 = \frac{120.9}{10}[/tex]
[tex]\sigma^2 = 12.09[/tex]
[tex]\sigma^2 = 12.1[/tex] --- approximated
Solving (c): The population standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{\sigma^2[/tex]
[tex]\sigma = \sqrt{12.09[/tex]
[tex]\sigma = 3.5[/tex]
I'm not good with ordering fractions from smallest to largest. Can help anyone help with this problem?
by selling 33m of cloth ,prabha gained the selling price 11 m.what is the gain percent
Answer:
The gain percent is 33.3 %
Step-by-step explanation:
Let the selling price of 1 m cloth is p.
Cost of 33 m = 33 p
gain = cost of 11 m = 11 p
The gain percentage is given by
[tex]\frac{11 p}{33 p}\times 100\\\\= 33.3 %[/tex]
The gain percent is 33.3 %.
Solve for H.[tex]V = \pi r^{2} h[/tex]
Answer:
h = [tex]\frac{V}{\pi r^2}[/tex]
Step-by-step explanation:
Given
V = πr²h ( isolate h by dividing both sides by πr² )
[tex]\frac{V}{\pi r^2}[/tex] = h
The rectangular ground floor of a building has a perimeter of 780 ft. The length is 200 ft more than the width. Find the length and the width.
The length is ___ and the width is ___
Answer:
L = 295ft
W = 95ft
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
If the length is 200 ft more than the width, then:
L = 200+W
Substitute
P = 2(200+W+W)
780 = 2(200+2W)
780 = 400+4W
4W = 780-400
4w = 380
W = 380/4
W = 95ft
Since L = 200+w
L = 200+95
L = 295ft
A company manufactures two products. Market research and available resources require the following
constraints:
• The number of units of product A manufactured, 2, is at most 500 units more than twice the number
of units of product B. y.
• The square of the company's profit is equal to the sum of 35 times the number of product A units
sold and 50 times the number of product B units sold.
If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these
constraints?
will give brainliest + 50 points :)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of product A and y represent the number of product B, hence:
x ≤ 500 + 2y (1)
Also:
35x + 50y > 22500² (2)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
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Find the area and circumference of each circle
Answer:
Step-by-step explanation:
Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]
Answer:
[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]
Explanation is attached to the picture
Hope this helps you.
A band played an encore at 2 of its last 4 shows. Considering this data, how many of the
band's next 14 shows would you expect to have an encore?
shows
The number of times that the band played an encore at 7 out of the next 14 shows.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.
We may use the following percentage to determine how many of the following 14 performances will likely have an encore:
1/2 = x/14
14 = 2x
x = 7
Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.
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You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford? Round your answer to the nearest dollar.
S
b) How much total money will you pay the loan company? Round your answer to the
nearest dollar.
C) How much of that money is interest? Round your answer to the nearest dollar.
S
Question Help: D Postito forum
Submit Question
9514 1404 393
Answer:
loan: $157,823repaid: $378,000interest: $220,177Step-by-step explanation:
For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...
A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495
Then the amount repaid after 360 payments is ...
360A = 2.39508898 . . . times the principal amount
__
a) For a monthly payment of $1050, the principal can be ...
$1050/0.00665302495 ≈ $157,823
__
b) The amount repaid to the loan company is ...
$157,823×2.39508898 ≈ $378,000
__
c) The amount that is interest is ...
$378,000 -157,823 = $220,177
3x-6y-2z=-17
−6x+4y+5z=13
−3x−4y−3z=22
Answer:
1) x = -17 +6y + 2z/3
2) x= -13 - 4y - 5z/6
3) x= -22 +4y + 3z/3
Step-by-step explanation:
1) 3x-6y-2z=-17
3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )
3x=-17+6y+2z
3x/3= -17/3 +6y/3 + 2z/3
x = -17 +6y + 2z/3
2) −6x+4y+5z=13
-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )
-6x=13-4y-5z
-6x/-6= 13/-6 - 4y/-6 - 5z/-6
x= -13 - 4y - 5z/6
3) −3x−4y−3z=22
-3x=22+4y+3z
-3x/-3 = 22/-3 + 4y/-3 +3z/-3
x= -22 +4y + 3z/3
In what time will #250 gain #120 at 2%
Answer: 24 years
Step-by-step explanation:
Based on the information given, we've been given,
Principal = #250
Interest = #120
Interest rate = 2%
Time = Unknown
Interest = PRT/100
120 = (250 × 2 × Time)
Cross multiply
120 × 100 = (250 × 2 × T)
12000 = 500T
Time = 12000/500
Time = 24
It will take 24 years.
How would I solve this?
Answer:
20°
Step-by-step explanation:
perpendicular from the center on a chord of a circle always bisects the chord.
AR=BR
∴m arcAC=m arc BC=20°
Một người gửi tiết kiệm tại ngân hàng một số tiền là 120 triệu đồng vào đầu mỗi năm theo thể thức lãi kép kỳ hạn một năm với lãi suất cố định 6,5%/ năm.
a) Hỏi sau 3 năm, số tiền gốc cộng lãi mà người đó nhận được là bao nhiêu ?
b) Hỏi sau bao nhiêu năm thì tổng số tiền nhận được lần đầu vượt quá 1,1 tỷ đồng.
Answer: lil t j
Step-by-step explanation:
I’m not a goat but I fit the description we walk around with then bands in my pocket
HELPP ASAP plzzz tyy!!!!
Answer:
The domain of a function is the input numbers that, when plugged into a function, the result is defined. In simple words, we can define the domain of a function as the possible values of x that will make an equation true.
The range of a function is defined as a set of solutions to the equation for a given input. In other words, the range is the output or y value of a function. There is only one range for a given function.
hope this helps!
Step-by-step explanation:
Which is an x-intercept of the continuous function in the
table?
-2
-1
0
1
2
3
f(x)
-10
48
46
44
-2
0
(0, -6)
(3.0)
O (-6.0)
(0, 3)
Answer:
The x-intercept is the value of the variable x when the value of the function is equal to zero
so
In the table we have
(-1, 0)(−1,0) is a x-intercept, because
For x=-1x=−1 the value of the function is equal to zero
(-6, 0)(−6,0) is a x-intercept, because
For x=-6x=−6 the value of the function is equal to zero
therefore
the answer is
the continuous function in the table has two x-intercepts
(-1, 0)(−1,0)
(-6, 0)(−6,0)
Find P(0), P(1) and P(2) for each of the following polynomial.
[tex]p(y) = 2 + y + 2 {y}^{2} - {y}^{3} [/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \sf \: p(y) = 2 + y + 2y {}^{2} - y {}^{3} [/tex]
[tex] \sf \: p(o) = 2 + (o) + 2(o) {}^{2} - (o) {}^{3} = 2 + 0 + 0 - 0 = 2 [/tex]
[tex] \sf \: p(1) = 2 + (1) + 2(1) {}^{2} - 1 {}^{3} = 2 + 1 + 2 - 1 = 4 [/tex]
[tex] \sf \: p(2) = 2 + 2 + 2(2) {}^{2} - 2 {}^{3} = 4 + 8 - 8 = 4 [/tex]
Write the next three terms in this pattern: 1, 4, 3, 6, 5, 8, 7, …
Answer:
10, 9, 12
Step-by-step explanation:
