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]
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
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The equation of the line passing through (2, 3) with a slope of 5 is y = [] x - []
what are the answers to []
Answer:
y = 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, then
y = 5x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 10 + c ⇒ c = 3 - 10 = - 7
y = 5x - 7 ← equation of line
what does the equation inverse of the function found in part b represent in the contract of the problem ? explain your answer .
context to question - At a carnaval , you pay $15 for admission plus $3 for each ride that you go on .
Answer:
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The inverse function is to calculate the number of rides; given the amount paid
Step-by-step explanation:
Given
[tex]Admission = 15[/tex]
[tex]Ride = 3[/tex] per ride
Required
Explain the inverse function
First, we calculate the function
Let x represents the number of rides
So:
[tex]f(x) = Admission + Ride * x[/tex]
[tex]f(x) = 15 + 3 * x[/tex]
[tex]f(x) = 15 + 3x[/tex]
For the inverse function, we have:
[tex]y = 15 + 3x[/tex]
Swap x and y
[tex]x = 15 + 3y[/tex]
Make 3y the subject
[tex]3y = x - 15[/tex]
Make y the subject
[tex]y =\frac{x}{3} - 5[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The above is to calculate the number of rides; given the amount paid
santino is renting a canoe from a local shop that charges a $10 fee, plus an hourly rate of $7.50. For how long can santino rent a canoe if he pays a total of $70
Answer:
Santino rented the canoe for 8 hours.
Step-by-step explanation:
The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,
where h is the number of hours over which the canoe is rented.
If the total bill is $70, then $70 = $10 + ($7.50/hour)h.
Solve this for h. Start by subtracting $10 from both sides, obtaining:
$60 = ($7.50/hour)h.
Dividing both sides by ($7.50/hour), we get:
$60
h = --------------------- = 8 hours
($7.50/hour)
Santino rented the canoe for 8 hours.
What is the value of x in the triangle?
3/2
X
help please<3
Answer:
x = 3
Step-by-step explanation:
Assuming the acute angle are 45degrees
Hypotenuse = 3√2
Opposite = x
According to SOH CAH TOA
Sin 45 = opposite//hypotenuse
Sin 45 = x/3√2
1/√2 = x/3√2
Cross multiply
√2x = 3√2
x = 3
Hence the value of x is 3
Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?
Answer:
silly question...I used technology to "cheat"
it is 11/23
34155 32775 33649 34485
72105 72105 72105 72105
Step-by-step explanation:
En una escuela hay 200 estudiantes. Si la razón entre hombres estudiantes y mujeres
estudiantes es de 3:5, ¿cuántos estudiantes son hombres y cuántas son mujeres?
Answer:
75 hombres y 125 mujeres
Step-by-step explanation:
lo siento, yo no hablo español bien
In a geometric sequence, the term an+1 can be smaller than the term ar O A. True O B. False
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Answer:
True
Step-by-step explanation:
In a geometric sequence, the terms a[n+1] and a[n] are related by the common ratio. If the sequence is otherwise unspecified, two sequential terms may have any a relation you like.* Either could be larger or smaller than the other.
__
* If one is zero, the other must be as well. Multiplying 0 by any finite common ratio will give zero as the next term.
ASAP!!! There are three marbles in a bag. One is red and two are black. What is the probability of picking a red marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answer:
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Step-by-step explanation:
Hey there!
The probability of first getting a red marble is 1/3 since we have 1 red marble out of 2 + 1 = 3 total.
We put the marble back. The probability of then choosing a black marble is 2/3, since we have 2 black marbles out of 3 total.
So we get 1/3 * 2/3 = 2/9
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Hope this helps, please mark brainliest if possible. Have a nice day. :)
DJ Jacqueline is making a playlist for work; she is trying to decide what 9 songs to play and in what order they should be played. If she has her choices narrowed down to 6 jazz, 19 reggae, and 7 blues songs, and she wants to play an equal number of jazz, reggae, and blues songs, how many different playlists are possible
Which of the following phrases would represent this expression?
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3
Answer:
the quotient of x and 3
Step-by-step explanation:
x divided by 3
division answers are called quotients
Answer:
Step-by-step explanation:
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3 is correct. We are dividing x into 3, not 3 into x.
The square root of -2 rounded to nearest 100th?
Answer:
√-2 ≈ 1.41i
Step-by-step explanation:
√-2 = i√2 = i × 1.414.. ≈ 1.41i
Consider the following data representing the price of plasma televisions (in dollars).
1325, 1266, 1123, 1233, 1387, 1249, 1120, 1140, 1347, 1337, 1402, 1259, 1421, 1351, 1452, 1277, 1309, 1232, 1112, 1243, 1429
Copy Data Price of Plasma Televisions (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency
1067–1126 1127–1186 1187–1246 1247–1306 1307–1366 1367–1426
Determine the class width of the classes listed in the frequency table.
Answer:
[tex]Width = 59[/tex]
Step-by-step explanation:
Given
The above data
Required
The class width
To do this, we simply calculate the difference between the class limits of any one of the classes.
Taking 1187–1246 as a point of reference, the class width is:
[tex]Width = 1246 - 1187[/tex]
[tex]Width = 59[/tex]
find the volume of pyrmaid
Answer:
37
Step-by-step explanation:
In the given figure the angles are vertically opposite angles so ;
4x + 2 = 150
or, 4x = 148
or, x = 37 ans .
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
The sample space,S,of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.
Answer: Bottom left corner
=======================================================
Explanation:
There are only four possible outcomes here
A) we get all tails, ie getting 0 headsB) we get exactly one head (the rest tails)C) we get exactly 2 headsD) we get all three headsBased on this so far, the answer is either the table in the bottom left corner or in the top right corner. It's not possible for X = 4 since we only flipped 3 coins.
The probability of case A happening is 1/8 since we have 1 scenario that's all tails (TTT) out of 8 items in the sample space. Similarly, the probability for case D is the same probability. We only have one HHH out of 8 total items.
The probabilities of cases B and C are the same. Both are 3/8. Note that for case B, we have HTT, THT, TTH which is three occurrences in which we get exactly 1 head. So that explains the 3/8.
4. Write an equation for the line that is parallel to the given line and that passes
through the given point.
y = 5/2x-10;(-6,-29)
Answer:
[tex]y=\frac{5}{2}x-14[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]y=\frac{5}{2}x-10[/tex]
In the given equation, [tex]\frac{5}{2}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of [tex]\frac{5}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{5}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{5}{2}x+b[/tex]
Plug in the given point (-6,-29) and solve for b
[tex]-29=\frac{5}{2}(-6)+b[/tex]
Simplify -6 and 2
[tex]-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b[/tex]
Add 15 to both sides to isolate b
[tex]-29+15=-15+b+15\\-14=b[/tex]
Therefore, the y-intercept is -14. Plug this back into [tex]y=\frac{5}{2}x+b[/tex]:
[tex]y=\frac{5}{2}x-14[/tex]
I hope this helps!
why do you think that increasing the number of people in a sample creates a normal curve?
Answer:
Increasing the number of people allows more variety and diversity, which makes the sample more accurate.
Find the coefficient of the t4
term in the expansion of
(4t – 375
a
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Answer:
-3840t^4
Step-by-step explanation:
The k-th term, counting from k=0, is ...
C(5, k)·(4t)^(5-k)·(-3)^k
Here, we want k=1, so the term is ...
C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4
__
The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.
parabola
Given that tanθ= [tex]-\frac{9}{4}[/tex] and [tex]\frac{\pi }{2\\}[/tex]<θ<π , find the exact values of the trigonometric functions.
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Answer:
sin(θ) = (9√97)/97cos(θ) = (-4√97)/97csc(θ) = (√97)/9sec(θ) = (-√97)/4cot(θ) = -4/9Step-by-step explanation:
The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.
tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16 ⇒ sec = -(1/4)√97
cot(θ) = 1/tan(θ) = -4/9
csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81 ⇒ csc = (1/9)√97
sin(θ) = 1/csc(θ) = (9√97)/97
cos(θ) = 1/sec(θ) = (-4√97)/97
An American tourist visits South Africa with $3000. The exchange rate when she arrives is
$1 = 12.90. She changes all her dollars into rands and then spends R900 per day for seven
days. She changes the rands she has left back into dollars at a rate of $1 = R12.93. How much
does she get in dollars? show your working.
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Answer:
$2505.80
Step-by-step explanation:
After the first exchange, the tourist has ...
$3000(12.90 R/$) = R38,700
After 7 days, she has ...
R38,700 -7(R900) = R32,400
After the second exchange, she has ...
R32,400 × ($1/R12.93) = $2505.80
She gets $2505.80 at the second exchange.
3384/24 step by step ......I really need help
w= 2hx - 11x Solve for X. Please and Thank you
Answer:
[tex]{ \tt{ w = 2hx - 11x}} \\ \\ { \bf{w = x(2h - 11)}} \\ \\ { \bf{x = \frac{w}{2h - 11} }}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = \frac{w}{(2h - 11)} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]w = 2hx - 11x[/tex]
[tex]✒ \: w = x \: (2h - 11)[/tex]
[tex]✒ \: x = \frac{w}{(2h - 11)} [/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Can someone tell me if its A,B, or C? Thanks besties.
Answer:
... ..... C is the answer
In the last six months, Sonia's family used 529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan. To save money, Sonia's family wants to keep their mean cell phone usage below 600 minutes per month.
By how many minutes did they go over their goal in the last six months?
Answer:
They went over their goal for the last six months by 34 minutes per month.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the size of the data-set.
529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan.
The mean is:
[tex]M = \frac{529+499+651+652+1163+310}{6} = 634[/tex]
By how many minutes did they go over their goal in the last six months?
The mean was of 634 minutes, and they wanted to keep it below 600. So
634 - 600 = 34
They went over their goal for the last six months by 34 minutes per month.
please calculate this limit
please help me
Answer:
We want to find:
[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]
Here we can use Stirling's approximation, which says that for large values of n, we get:
[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}[/tex]
Now we can just simplify this, so we get:
[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]
And we can rewrite it as:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]
Madge has cut out two triangular shapes from a block of wood, as shown below. Are the two shapes similar? Show your calculations.
How is the graph of y = 8x2 − 1 different from the graph of y = 8x2?
It is shifted 1 unit down.
It is shifted 1 unit to the right.
It is shifted 1 unit to the left.
It is shifted 1 unit up.
Answer:
since it's the lhs we are concerned about, i. e., Y axis, so it must be either up or down. now look at the question, it says 8x2 - (1), it means one lower value of y i. e., 1 unit down
Answer:It is shifted 1 unit down.
Step-by-step explanation:
The area of a triangular sign is 6x² + 24x What is the measure of the base? (View attachment)
Answer:
[tex]2x + 8[/tex]
Step-by-step explanation:
Area of triangle equal
[tex] \frac{b \times h}{2} = a[/tex]
where b is the base and h is the height.
Plug in what we know.
[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]
Multiply 2 by both sides.
[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]
Divide 6x by both sides.
[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]
2^5 + 10=?????????????
Answer:
Answer is 42
Step-by-step explanation:
2^5 + 10
2*2*2*2*2 + 10
32 + 10
42
the lengths of two sides of a right triangle are 12 inches and 15 inches.What is the difference between the two possible lengths of the third side of the triangle
Answer:10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
Applying the Pythagoras Theorem
Find the length of the hypotenuse
substitute
Second case
The given lengths are one leg and the hypotenuse
so
Applying the Pythagoras Theorem
Find the length of the other leg
substitute
Find the difference between the two possible lengths of the third side of the triangle
so
Answer:
The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.
Step-by-step explanation:
We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.
And we want to find the difference between the two possible lengths of the third side.
In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+(15)^2=c^2[/tex]
Solve for c:
[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]
In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+b^2=(15)^2[/tex]
Solve for b:
[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]
Therefore, the difference between the two possible lengths for the third side is:
[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]
Use the limit definition of the derivative to find the instantaneous rate of change of
f(x)=5x^2+3x+3 at x=4
[tex]f'(4) = 43[/tex]
Explanation:
Given: [tex]f(x)=5x^2 + 3x + 3[/tex]
[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]
Note that
[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]
[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]
[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]
Substituting the above equation into the expression for f'(x), we can then write f'(x) as
[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]
[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]
[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]
Therefore,
[tex]f'(4) = 10(4) + 3 = 43[/tex]
