Find the first 5 terms of the following sequence. For the first term let a_1=1. Round your answer to the nearest hundredth.a_n= \frac{2^n}{n^2} 1st term = Answer2nd term = Answer3rd term = Answer4th term = Answer5th term = Answer
Answers
1st term
Given:
[tex]a_1=1[/tex]With the formula of the sequence:
[tex]\begin{gathered} a_1=\frac{2^1}{1^2}=\frac{2}{1}=2 \\ \\ a_1=2 \end{gathered}[/tex]________
Second term:
[tex]\begin{gathered} a_2=\frac{2^2}{2^2}=\frac{4}{4}=1 \\ \\ a_2=1 \end{gathered}[/tex]____________
Third term:
[tex]\begin{gathered} a_3=\frac{2^3}{3^2}=\frac{8}{9}\approx0.89 \\ \\ a_3=0.89 \end{gathered}[/tex]_________
Fourth term:
[tex]\begin{gathered} a_4=\frac{2^4}{4^2}=\frac{16}{16}=1 \\ \\ a_4=1 \end{gathered}[/tex]-________________
Fifth term:
[tex]a_5=\frac{2^5}{5^2}=\frac{32}{25}=1.28[/tex]Related Questions
Mental Math Using the slope formula, find the slope of the line through the points (0,0) and (3,6).Use pencil and paper. Explain how you can use mental math to find the slope of the line.
Answers
Given the points (0,0) and (3,6)
slope = y2 - y1 / x2 -x1
x1= 0, y1 = 0 , x2= 3, and y2 = 6
slope = 6 - 0 / 3 - 0
slope = 6 / 3
slope = 2
the answer is 2
what are the correct answers for each blank using the dropbox's provided for each blank?Dropbox 1: Congruent, Similar, Not congruent or similarDropbox 2: Proportional, Not proportional, CongruentDropbox 3: Proportional Not proportional, Congruent
Answers
The pair of triangles shown are similar because the sides are proportional and corresponding angles are congruent.
A random sample of 89 observations produced a mean x = 25.4 and a standard deviation s = 2.4.a. Find a 95% confidence interval for u.b. Find a 90% confidence interval for H.c. Find a 99% confidence interval for u.a. The 95% confidence interval is O.(Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)
Answers
The formula for the confidence interval is;
Where:
[tex]undefined[/tex]Given:
The mean is 25.4, the sample size n is 89, the standard deviation s is 2.4.
a. For the 95% confidence interval, the z-score for a 95% interval is 1.96.
Therefore, the 95% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.96\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.96\frac{2.4}{\sqrt[]{89}} \\ CI=24.90<\operatorname{mean}<25.90 \end{gathered}[/tex]Answer: (24.90, 25.90)
b. For the 90% confidence interval, the z-score for a 90% interval is 1.645.
Therefore, the 90% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.645\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.645\frac{2.4}{\sqrt[]{89}} \\ CI=24.98<\operatorname{mean}<25.82 \end{gathered}[/tex]Answer: (24.98, 25.82)
c. For the 99% confidence interval, the z-score for a 99% interval is 2.576.
Therefore, the 99% confidence interval is;
[tex]\begin{gathered} CI=25.4-2.576\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+2.576\frac{2.4}{\sqrt[]{89}} \\ CI=24.74<\operatorname{mean}<26.06 \end{gathered}[/tex]Answer: (24.74, 26.06)
Ken exercise at a park first he run 3 miles in 30 minutes.Then he rests for 15 minutes.Then he runs 2 miles in 15 minutes.Finally he walks 1 mile in 15 minutes.Assume each running and walking segment was done at a constant rate.skecth a graph to represent ken's exercing at the park.the fisrt segment should begin at (0,0).
Answers
The horizontal axis represents the time in hours, and the vertical axis represents the number of miles ran.
So for the first part we have 3 miles in 30 minutes (0.5 hour), so we can draw a line from point (0, 0) to point (0.5, 3)
For the second part, he rests for 15 minutes (0.25 hour), so the y-value doesn't change, therefore we have a horizontal line from (0.5, 3) to (0.75, 3).
Then, we have 2 miles in 15 minutes, so we have a line from (0.75, 3) to (1, 5).
And finally, 1 mile in 15 minutes, so a line from (1, 5) to (1.25, 6).
Sketching the graph, we have:
Is -7. a rational number
Answers
A rational number can be represented by dividing two integers.
So, it can be represented as a ratio of 2 integers.
-7 = -7/1
-7 is a rational number
rectangle perimeter ; 36 unitswidth; xlength ; 4x - 2solve for x
Answers
Perimeter = 36 units
width = x
length = 4x - 2
Equation of perimeter = 2width + 2length
Substitution
36 = 2(x) + 2(4x - 2)
Expanding
36 = 2x + 8x - 4
36 = 10x - 4
36 + 4 = 10x
40 = 10x
x = 40/10
x = 4
help l need help with this
Answers
Answer:
Step-by-step explanation:
Answer: Y = 3x + 3
Simply plug in points on graph calculator.
Answer:
Step-by-step explanation:
I think it might be y=3/1+6 ??? i might be wrong
A local hamburger shop sold a combined total of 598 hamburgers and cheeseburgers on Wednesday. There were 52 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
Answers
In the local hamburger shop the total number of hamburgers sold on Wednesday , based on the given data is :
325 hamburgers.
Explanation:A General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.here form a equation based on given data ;
let , Hamburgers be = x
let, Cheeseburgers be = y
here , No. of burgers (hamburgers and cheeseburgers )sold = 598
here,
x + y = 598 =>(1)
y = x - 52 => (2)
solving 2 equations ,
x + ( x - 52 ) = 598
x + x - 52 = 598
2x = 598 + 52
x = 650 /2
x = 325
on Wednesday 325 hamburgers were sold.
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There are 6 roses in a vase of 14 flowers. The rest are daisies. What is the ratio of all flowers in the vase to daisies?
Answers
Given:
There are 6 roses in a vase of 14 flowers.
Required:
To find the ratio of all flowers in the vase to daisies.
Explanation:
The total number of daisies in the vase are
[tex]\begin{gathered} =14-6 \\ =8 \end{gathered}[/tex]So the ratio of all flowers in the vase to daisies is,
[tex]14:8[/tex][tex]7:4[/tex]Final Answer:
[tex]7:4[/tex]Hi I have tried calling but I can’t do anything
Answers
For the given functions, we will find the first derivative of each function
Note:
a, and b are constants
y, f, and g are functions
2) y = (a+bf)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]=============================================================
3) y = (x+f)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]==========================================================
4) y = (x+f)³
We will use the exponent rule to find the derivative as follows:
[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]===========================================================
5) y = ax² + bg² + f
so, y' will be as follows:
[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]==========================================================
A car was valued at $41,000 in the year 1994. The value depreciated to $13,000 by the year 2004
Answers
Firstly, we have to write the general depreciation fomula as follows;
[tex]V(t)=I(1-r)^t[/tex]where V(t) represents the value of the commodity after a certain t years
I is the initial value of the item
r is the annual percentage change (rate of depreciation)
t is the number of years
a) Here, we want to calculate the annual rate of change
According to the data given in the question;
V(t) = $13,000
I = $41,000
r = ?
t = 2004-1994 = 10 years
Now, we proceed to substitute these values, to find the find of r as follows;
[tex]\begin{gathered} 13,000=41,000(1-r)^{10} \\ (1-r)^{10\text{ }}\text{ = }\frac{13,000}{41,000} \\ (1-r)^{10\text{ }}=\text{ }\frac{13}{41} \\ \\ (1-r)\text{ = }\sqrt[10]{\frac{13}{41}} \\ \\ 1-r\text{ = 0.8915} \\ r\text{ = 1-0.8915} \\ r\text{ = 0.1085} \end{gathered}[/tex]b) To write r in percentage form, we have to multiply the answer in 'a' above by 100
We have this as ;
[tex]0.1085\times100\text{ = 10.85 \%}[/tex]c) Here, we want to get the car value by year 2009
In that instance;
V(t) = ?
I = $41,000
r = 0.1085
t = 2009-1994 = 15
Substituting these values, we have;
[tex]\begin{gathered} V(15)=41,000(1-0.1085)^{15} \\ V(15)\text{ = \$7,321.56} \end{gathered}[/tex]To the nearest 50 dollars, this is $7,300
write an email as if
you wanted to set up
an interview with
someone
Answers
Answer:Dear Mikey,
I saw your progress on how to serve the best food and we wanted to see if you could help us or join our company if you want.
Call 923-456-2483
Sincerely Johns Bagel Company
Step-by-step explanation:
find the perimeter of ABC with vertices A(-4,4), B(4,-1) and C(-4,-1)
Answers
Answer: A=-16 B=-5 C=-3
Step-by-step explanation:
Molly has 250 trading cards. She gives n trading cards to her friend Carol. Marcus has 430 trading cards. He gives away three times as many cards as Molly does. How many trading cards did Molly give away if Molly and Marcus have the same number of trading cards left?
Answers
Molly gave away 90 trading cards out of 250 trading cards to her friend Carol.
Initially molly had 250 cards.
She gave away n trading cards to her friend.
Now molly has (250 - n) trading cards.
Initially Marcus had 4430 trading cards.
The number of cards that Marcus gave away is is three times of molly.
Cards gave away by Marcus = 3n
Now, Marcus is left out with (430 - 3n) trading cards/
After giving away the cards,
Molly and Marcus had same number of trading cards.
So, we can write,
250-n = 430-3n
Now, we have a linear relation between the number of cards given away and the remaining cards,
Further solving,
2n = 180
n = 90.
So, Molly gave away 90 cards.
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If a Ferrari, with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes, what will its final velocity be (in km/h)?
Answers
The final velocity of the Ferrari will be 84.53 km/h. with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes.
This is a typical question from Newtonian mechanics. To solve this problem we have to convert all the given data into a standard unit like C.G.S.
Now, we will convert 10 km/h and 50 km/h by using the formula. (km/h × 5/18 = m/s )
10 km/h = 10× 5/18 = 2.78 m/s
50 km/h = 50× 5/18 = 13.89 m/sec/min = 0.23 m/s²
3 min = 3 × 60 = 180 sec. ( 1 min = 60 sec )
Now, we have to use the formula from Newton's law of motion,
v = u + at/2 .
Here, u is the initial velocity which is 2.78 m/s.a is the acceleration which is 0.23 m/s²t is the period which is 180 sec. v is the final velocity.Now we can calculate the final velocity,
v = 2.78 + (0.23 × 180)/2 = 2.78 + 20.7 = 23.48 m/s
Now, we have to calculate the velocity in km/h, which is (23.48 × 5 )/8 = 84.53 km/h. as we know (km/h = m/s ×18/5 ).
Therefore, the final velocity will be 23.48 m/s according to the given inputs and criteria.
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Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 16 cookies and 24 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
Answers
The greatest number of plates he can make to share is 6.
What is the greatest number of plates he can make to share?From the information, Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors and he has 16 cookies and 24 brownies to share.
It should be noted that this illustrates that we have to find the highest common factor for 16 and 24.
This will be:
18 = 2, 3, 6, 9 and 18.
24 = 2, 3, 4, 6, 8, 12 and 24
The highest common factor is 6.
Therefore, the number will be 6 plates.
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An aeroplane flies between two cities that are 8100 km apart.
The aeroplane takes 9 hours to complete the journey.
Calculate the average speed of the aeroplane, in km/h.
Answers
Answer:
7,290,000.answer
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 minute
8100 km = 810000 m
9 hour=540 minute
60/540.00 cancel
6/54 will be than cut 6×9=54
SO,multiply 810000×9 = 7,290,000
Answer:
The answer is 7,290,00
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 min
8100 km = 810000 m
9 hour=540 min
60/540.00 cancel
6/54 will be than cut 6×9=54
so ,multiply 810000×9 = 7,290,000
718-119x+719 for x =0
please simplify and find the value
Answers
A store generates Monday through Thursday sales of $150, $125, $75, and $180. What sales on Friday would give a weekday average of $150?
Answers
Answer:
mi cola es grande
Step-by-step explanation:
uhh
2. Multiply the matrices.
Answers
Result of matrix multiplication [tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] = \left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right] [/tex].
What is a matrix?A matrix is a series of numbers forming a square or rectangle arranged in rows and columns enclosed in square brackets [ ] or regular brackets ( ).
Solution:
[tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] [/tex]
[tex] \left[ \begin{array}{cc} - 1 \times 2 + 2 \times 7 + 0 \times 1 & - 1 \times ( - 3) + 2 \times ( - 1) + 0 \times 2 \\3 \times 2 + ( - 2) \times 7 + 4 \times 1&3 \times ( - 3) + ( - 2) \times ( - 1) + 4 \times 2\\ - 5 \times 2 + ( - 1) \times 7 + 6 \times 1&( - 5) \times ( - 3) + ( - 1) \times ( - 1) + 6 \times 2 \end{array}\right ][/tex]
[tex]\left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right ][/tex]
7 is added to 11 divided by a number r write the algebraic expression
Answers
Answer: 7+(11/r)
Step-by-step explanation:
ANSWERS ASAPP
i got a 57 in this class
Answers
Answer:
Y=-1/4x+-6
Step-by-step explanation:
convert the line to slope intercept form
x is the slope and the last thing is the y intercept
Use the Multiplication Property of One to rewrite the statement.8+1=x1) = 0
Answers
We need to isolate on the equation
[tex]8+(z\times1)=0[/tex]since any number multiplied by one is the same, then z times 1 is z, so we can write
[tex]8+z=0[/tex]Now, we can add -8 to both side and get
[tex]8-8+z=-8[/tex]since 8 - 8 is zero, we have
[tex]z=-8[/tex]then, z is equal to -8.
rewrite 13% into equivalent fraction
Answers
The number 13% as an equivalent fraction is 13/100
How to rewrite the percentage into equivalent fraction?From the question, the given parameter is
13%
This above number is a percentage or percentile
So, we have
Percentage = 13%
Next, we multiply the percentage by 1
So, we have
Percentage = 13% x 1
Express 1 as 100/100
So, we have
Percentage = 13% x 100/100
Evaluate the product of 13% and 100
So, we have
Percentage = 13/100
Rewrite as
Fraction = 13/100
The fraction cannot be further simplified
Hence, the equivalent fraction of 13% is 13/100
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Given the replacement set: {−9, −10, −11, −12}.
Which value of x correctly solves this equation?
3.2x−5=−40.2
Enter your answer in the box.
Answers
Answer:
x = -11
Step-by-step explanation:
You want to know the value of x that correctly solves the equation 3.2x -5 = -40.2.
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
3.2x -5 +5 = -40.2 +5 . . . . . . . . . add 5 to both sides
3.2x = -35.2 . . . . . . . . . . . . . simplify
Step 2: isolate the variable
3.2x/3.2 = -35.2/3.2 . . . . . . . . . . divide both sides by the coefficient of x
x = -11 . . . . . . . . . . . . . . . . . . simplify
I'll give brainliest!
Answers
Answer:
The answer is A
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-2, 3); y=-3/4x+4
Answers
Answer:
y=4/3x+17/3
Step-by-step explanation:
Perpendicular lines have reciprocal negative slopes, find the slope of the new line:
-3/4 --> m = 4/3
Write line in point slope form:
y-3 = 4/3(x+2)
Distribute:
y-3=4/3x+8/3
Simplify:
y=4/3x+17/3
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-18)°
40°
110°
Answers
The value of the variable x associated to the triangle is equal to 6.
What is the variable associated to internal angles of a triangle?
Triangles are figures with three sides and three internal angles. According to Euclidean geometry, the sum of the measures of the internal angles is equal to 180° and we must solve the following equation for x:
(8 · x - 18) + 40 + 110 = 180
(8 · x - 18) + 150 = 180
(8 · x - 18) = 30
8 · x = 48
x = 6
The triangle has internal angles of 30°, 40° and 110° and the value of variable x is 6.
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Find the values of the variables so that the figure is aparallelogram.
Answers
Answer:
The image is given below as
From the image above, we can deduce that
[tex]\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}[/tex]From the image also, we will have that
[tex]\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}[/tex]Hence,
The value of x= 64°
The value of y = 116°
Two standard 6-
sided dice are
rolled. How would
you describe the
following events
of having their
sum be EVEN OR
GREATER THAN 9?
Answers
The probability of having an even or a number greater than 9 is 2/3.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.
The sample space of two 6-sided dice would be 36
Of this 36, there would be 18 which would have an even sum.
There would be 6 with a sum greater than 9.
The probability of having an even or a number greater than 9 = (18/36) + (6/36) = 24 / 36 = 2/3
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Answer:
5/9
Step-by-step explanation:
You want the probability that a roll of 2 dice will produce a sum that is even or greater than 9.
EvenHalf the numbers on each die are even. Their sum will be even when the dice show ...
even + even . . . . p = (1/2)(1/2) = 1/4
odd + odd . . . . . . p = (1/2)(1/2) = 1/4
So, the 36 possible outcomes will produce an even sum (1/4) +(1/4) = 1/2 of the time. That is, there are 1/2(36) = 18 outcomes with an even sum.
Greater than 9The sums that are greater than 9 are 10, 11, 12. Of these, 10 and 12 are outcomes that are even, so are already counted.
The sum 11 can be made two ways: 6 +5 or 5 +6.
So, "or greater than 9" adds 2 outcomes to the 18 we have already counted.
Final tallyThe final tally of outcomes of interest is ...
18 + 2 = 20 . . . . of 36 possible outcomes
That is ...
P(even or >9) = 20/36 = 5/9
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