In a geometric sequence, a2=108 and as 256. Write the explicit formula for this sequence.
Answers
Answer:
C. 81[-4/3]^n-1
Step-by-step explanation:
The explicit formula for a geometric sequence is given by a_n = a * r^(n-1). Using the provided values of a2 = 108 and a5 = 256, we can establish two equations to solve for 'a' and 'r'. This results in two possible explicit formulas for the sequence.
Explanation:In a geometric sequence, each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. If we denote the first term of the sequence by 'a' and the common ratio by 'r', then the explicit formula of the sequence is: a_n = a * r^(n-1). Given that a2 = 108 (the second term is 108) and a5 = 256 (the fifth term is 256), we have two equations: a*r = 108 and a*r^4 = 256. Dividing the second equation by the square of the first equation, we get r^2 = 256/108^2 = 0.022. So, r is about +- 0.148. Substituting r into the first equation, we can solve for a. This gives us two possible explicit formulas for the sequence depending on whether we take the positive or negative value of r.
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Related Questions
How many solutions does this system have!
y = 3x + 5
y = -x + 4
a. one
b. two
c. infinite number
d. no solution
Answers
Answer:x=-14y=174
y=3x+5,y=-x+4
3x+5=-x+4
There are infinite number of solutions!
Move all terms containing
x
x to the left side of the equation.
Tap for more steps...
4
x
+
5
=
4
4x+5=4
y
=
−
x
+
4
y=-x+4
Move all terms not containing
x
x to the right side of the equation.
Tap for more steps...
4
x
=
−
1
4x=-1
y
=
−
x
+
4
y=-x+4
Divide each term by
4
4 and simplify.
Tap for more steps...
x
=
−
1
4
x=-14
y
=
−
x
+
4
y=-x+4
Replace all occurrences of
x
x with the solution found by solving the last equation for
x
x. In this case, the value substituted is
−
1
4
-14.
x
=
−
1
4
x=-14
y
=
−
(
−
1
4
)
+
4
y=-(-14)+4
Simplify the right side.
Tap for more steps...
x
=
−
1
4
x=-14
y
=
17
4
y=174
The solution can be shown in both point and equation forms.
Point Form:
(
−
1
4
,
17
4
)
(-14,174)
Equation Form:
x
=
−
1
4
y
=
17
4
x=-14y=174
The linear inequality y ≤ 3/2x + 3/2
is graphed. Determine a solution for the inequality.
A) (0, 2)
B) (1, 3)
C) (-2, 0)
D) (-3, 1)
Answers
Answer:
it's (B)
Step-by-step explanation:
To find a solution for the linear inequality y ≤ (3/2)x + (3/2), we need to graph it and find the region that satisfies the inequality. The correct solution for the inequality is (-2, 0).
Explanation:To determine a solution for the linear inequality, y ≤ (3/2)x + (3/2), we need to graph it and find the region that satisfies the inequality. This inequality represents a line with a slope of 3/2 and a y-intercept of 3/2. Starting from the y-intercept, we can draw a line that goes up 3 units vertically and 2 units horizontally, and another line that goes down 3 units vertically and 2 units horizontally. Shade the region below the line to include the points that satisfy the inequality. The correct solution for the inequality is (C) (-2, 0).
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There are 1,200 students at roosevelt middle school. There are 700 boys at the school. What percentage of the students at roosevelt are boys( to the nearest tenth of a percent)?
Answers
Answer:
x=175/3
Step-by-step explanation:
700/1200=x/100
Simplify to 7/12
7/12=x/100
Multiply both sides by 100
7/12×100=x
Simplify 7/12 ×100 to 700/12
700/12=x
Simplify 700/12 to 175/3
175/3=x
Switch Sides x=175/3
hope that helps you
To determine the percentage of boys in Roosevelt Middle School, divide the number of boys by the total number of students and multiply by 100. The result is about 58.3% when rounded to the nearest tenth.
Explanation:In order to find the percentage of boys in Roosevelt Middle School, you'll need to take the number of boys and divide it by the total number of students, and then multiply by 100 to get the percentage. So the calculation is as follows:
Number of Boys ÷ Total number of Students × 100 = Percentage of Boys
Substituting the given values:
700 ÷ 1200 × 100 = 58.33
Rounding to the nearest tenth of a percent, we get 58.3%.
Therefore, the percentage of boys at Roosevelt Middle School is approximately 58.3%.
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find the radius of the circle if the center is at 1, 2 and the point -5, 6 lies on the circle
Answers
Answer:
The answer is 7.21
Answer:
That’s the answerStep-by-step explanation:
4. Find the length of AB if A is located (-2,0) and B is located at (5,0)
5. If EF=9x+14, FG=56, and EG=250, find the value of x. The drawing is not to scale.
Answers
Answer: 4. 7 unit
5. 20 unit
Step-by-step explanation:
4. Since, A≡ (-7,0) and B≡ (5,0)
Thus, By the distance formula,
[tex]AB = \sqrt{(5-(-2))^2+ (0-0)^2}[/tex]
⇒ [tex]AB = \sqrt{(5+2)^2+ (0)^2}[/tex]
⇒ [tex]AB = \sqrt{(7)^2+ (0)^2}[/tex]
⇒ [tex]AB = \sqrt{49+0}[/tex]
⇒ [tex]AB = \sqrt{49}[/tex]
⇒ AB = 7 unit
5. Here EF = 9x + 14, FG = 56 and EG= 250
But, According to the given diagram,
EF + FG = EG ( because G divides the line EG )
⇒ 9x + 14 + 56 = 250
⇒ 9x + 70 = 250
⇒ 9x = 250 - 70 ( By subtracting both sides by 70)
⇒ 9x = 180
⇒ x = 20 ( by dividing both sides by 9 )
Thus, the value of x is 20.
Dan’s ice cream comes in cartons of two sizes.The large carton holds4 1/2 pounds.the small carton holds 1 3/4 pounds less .how much ice cream does the small carton hold?
Answers
Answer:
2 and 3/4 lbs
Step-by-step explanation:
4 and 1/2 is equal to 9/2. If you multiply 4 by 2 and then add 1, you get 9, and put it over 2 because that is the denominator in the mixed number. Using the same method, we can find that 1 and 3/4 is equal to 7/4. However, the denominators are different, so we need to change that so they will be common. We can change 9/2 to 18/4 by multiplying both the numerator and the denominator by 2. This is technically the same as multiplying by 2/2, which is equal to 1, so the fraction will be equivalent, since anything multiplied by 1 is itself. Now we have 18/4 for the large carton and 7/4 for the small carton. Since the denominators are the same, they do not change. Just subtract the numerators to get 11, and then put it over 4 to get 11/4. In mixed number form, this is 2 and 3/4 lbs because 4 goes into 11 twice (8) and then you will have 3 left over. 8+3 = 11
Answer:
23/4pounds.
Step-by-step explanation:
41/2 take away 1 3/4 = 2 3/4.
An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t, by the equation d=0.15t. How fast is the airplane flying? Be sure to include the units. 60 mph How far will it travel in 30 seconds? How long will it take to go 12.75 miles?
Answers
A. Upon substituting t=1 in our equation we will get,
We can see that our plane is travelling at rate of 0.15 miles per second.
Therefore, plane is flying at the rate of 0.15 miles per second.
B. To find distance traveled by airplane in 30 seconds we will substitute t=30 in our given equation.
Therefore, plane will travel 4.5 miles in 30 seconds.
C. To find time it will take to travel 12.75 miles we will substitute d=12.75 in our given equation.
Therefore, plane will take 85 seconds to travel 12.75 miles.
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For a 30 second flight, the airplane will travel 4.5 miles. To cover a distance of 12.75 miles, it will take 85 seconds.
The relationship between the distance an airplane travels and the time it takes is given by the equation [tex]d=0.15t[/tex].
Here, d stands for distance in miles and t for time in seconds. The coefficient 0.15 in this equation represents the speed of the airplane in miles per second.
To find how fast the airplane is flying, we must convert this speed to a more familiar unit, such as miles per hour.
Since there are 3600 seconds in one hour, the airplane's speed in miles per hour (mph) is
[tex]0.15 miles/second \times 3600 seconds/hour = 540 mph[/tex]
Now, to determine how far the airplane will travel in 30 seconds, we substitute t with 30 in the original equation:
[tex]d = 0.15 \times 30[/tex], yielding a distance of 4.5 miles.
To calculate how long it will take the airplane to go 12.75 miles, we use the original equation but solve for t:
[tex]t = \frac{d}{0.15} t = \frac{12.75}{0.15}[/tex]
which simplifies to 85 seconds.
Write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Answers
Answer:
3/4(6,-1)
Step-by-step explanation:
(6,6)*-(-6,1)
/by answer
Answer:
[tex]y = \frac{5}{12}x + \frac{21}{6}[/tex]
Step-by-step explanation:
We are given the following information in the question.
The line passes through the point (6,6) and (-6,1).
We have to find the point slope form of the equation.
The point slope form of equation is given by:
[tex]y-y_1 = m(x-x_1)\\\text{where}\\m = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\\text{Putting}\\(6,6) = (x_1,y_1), (-6,1) = (x_2,y_2)\\\\y - 6 = \frac{1-6}{-6-6}(x - 6)\\\\y-6 = \frac{-5}{-12}(x-6)\\\\12(y-6) = 5(x-6)\\12y - 72 = 5x - 30\\12y = 5x -30 + 72\\12y = 5x +42\\\\y = \frac{5}{12}x + \frac{42}{12}\\\\y = \frac{5}{12}x + \frac{21}{6}[/tex]
The above equation is the required slope intercept form of equation passing through the given points.
Please help ASAP!!!
A six-sided number cube is rolled. What is the probability of getting a 3 and then a 4, given that the first number rolled was a 3?
1. 1/3
2. 1/6
3. 1/36
4. 1/2
Answers
The probability of getting a 3 and then a 4, given that the first number rolled was a 3 on a six-sided number cube is 1/36.
The probability of getting a 3 and then a 4, given that the first number rolled was a 3 on a six-sided number cube:
Probability of rolling a 3 on the first roll: 1/6
Since each roll is independent, the probability of rolling a 4 after rolling a 3: 1/6
Therefore, the overall probability of getting a 3 and then a 4: 1/6 × 1/6 = 1/36
7.3 homework help me
Answers
Answer:
1. Yes
∆RST ~ ∆WSX
by SAS
2. Yes
∆ABC ~ ∆PQR
by SSS
3. Yes
∆STU ~ ∆JPM
by SAS
4. Yes
∆DJK ~ ∆PZR
by SAS
5. Yes
∆RTU ~ ∆STL
by SAS
5. Yes
∆JKL ~ ∆XYW
by SAS
6. No
7. Yes
∆BEF ~ ∆NML
by SAS
8. Yes
∆GHI ~ ∆QRS
by SSS
9. x=22
10. x=12
Step-by-step explanation:
1. RS/WS=ST/SX and m<RST=m<WSX
2. AB/PQ=8/6=4/3
BC/QR=AC/PR=12/9=4/3
AB/PQ=BC/QR=AC/PR
3. ST/JP=10/15=2/3
SU/JM=14/21=2/3
ST/JP=2/3=SU/JM
and m<TSU=70°=m<PJM
4. DK/PR=8/4=2
JK/ZR=18/9=2
DK/PR=2=JK/ZR
and m<DKJ=65°=m<PRZ
5. RT/ST=UT/LT
and m<RTU=m<STL
6. KL/YW=20/18=10/9
JL/XW=36/24=3/2
KL/YW=10/9≠3/2=JL/XW
7. BF/NL=24/16=3/2
BE/NM=39/26=3/2
BF/NL=3/2=BE/NM
and m<EBF=m<MNL
8. GH/QR=32/20=8/5
HI/RS=40/25=8/5
GI/QS=24/15=8/5
GH/QR=HI/RS=GI/QS=8/5
9. x/33=18/27
Simplifying the fraction on the right side of the equation:
x/33=2/3
Solving for x: Multiplying both sides of the equation by 33:
33(x/33)=33(2/3)
x=11(2)
x=22
10. x/16=9/12
Simplifying the fraction on the right side of the equation:
x/16=3/4
Solving for x: Multiplying both sides of the equation by 16:
16(x/16)=16(3/4)
x=4(3)
x=12
Which point is on the graph of f(x)=5^x?
Answers
Answer:
B. (0 , 0)
Step-by-step explanation:
Plug in the coordinate into the equation given.
Note that:
x = x
f(x) = y
Also note that in B, x = 0, y = 0
Plug in the corresponding number with the corresponding variable
0 = 5^(0)
Simplify
5^0 = 0
0 = 0 (True)
B. (0 , 0) is your answer
~
Answer:
(1,5)
Step-by-step explanation:
This is the correct answer.
felix bought 5/6 pound of peanuts. He ate 3/4 pounds of peanuts. How much did felix hace left
Answers
Joshua receives a $70 gift card to use at a clothing store. he buys a pair of jeans for $36 and 8 pair of socks. he does not use the entire amount of the gift card. Write and solve an inequality to find s, the price of each pair of socks?
Answers
Molly took an exam that had 25 questions. She got 75% on the test, how many questions did she get wrong
Answers
A water yank holds 18,000 gallons. How long will it take for the water level to reach 6,000 gallons if the water is used at an average rate of 450 gallons per day?
Answers
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
18,000 - 6000 = 12,000
12,000 ÷ 450 = 26.66 = 26 days 16 hours
The GCF of 12 and 15 is _____.
Answers
Answer:
3.
Step-by-step explanation:
To find the GCF of two numbers:
List the prime factors of each number.
Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.
Hope This Helps!
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- Innverted
Answer:
3
Step-by-step explanation:
HELP PLS 15+ POINTS
Write an equation of the line that has:
a. no slope and passes through the point (4,-5)
b. a slope of 0 and passes tgrough the point (-4,-1)
Answers
For b, the slope is zero meaning there is no slope. so like a, there will be no x. this line will also be a horizontal line. this line crosses at -1 on the y axis so the answer will be y = -1
to mail a cardboard box, you measure its size and mass. It is 55cm long , 25cm wide and 20 cm high. The mass of the box is 4kg. What is the density of the boxes in grams over cm squared
Answers
Answer:
Density is usually expressed as grams per cubic centimeter.
Volume = 55 * 25 * 20 = 27,500 cc
Density = Mass / Volume = 4,000 grams / 27,500 cc
= 0.1454545455 grams/cc
which is an extremely low density
Step-by-step explanation:
The density of the box is found by dividing its mass (4000 grams) by its volume (27500 cubic centimeters), resulting in a density of approximately 0.1455 grams per cubic centimeter.
Explanation:To calculate the density of the box, you must find the mass per unit volume. The mass given is 4 kg, which is equivalent to 4000 grams since 1 kg = 1000 grams. To find the volume, multiply the length by the width by the height of the box:
Volume = Length × Width × Height = 55 cm × 25 cm × 20 cm = 27500 cm³
Now, divide the mass of the box by the volume to get the density:
Density = Mass / Volume = 4000 g / 27500 cm³ ≈ 0.1455 g/cm³
Therefore, the density of the box is approximately 0.1455 grams per cubic centimeter (g/cm³).
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What is 6.39 / 0.09
Answers
The answer is 71 when simplified
Answer:
71
Step-by-step explanation:
One way of doing this problem is to remove the fractions. If we move both decimal points two places to the right, we get 639/9.
Routine division results in a quotient of 71.
20 POINTS!!!
PLEASE HELP!
Which statement is true about the graphs shown? A) Only graph A represents a proportional relationship. B) Only graph B represents a proportional relationship. C) Graph A and graph B both represent a proportional relationship. D) Graph A and graph B both represent a non-proportional relationship.
Answers
Answer:
Option A) Only graph A represents a proportional relationship
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
therefore
Graph A represent a proportional relationship, because the line passes through the origin
Answer: GRAPH B
Step-by-step explanation: i got it right
plz help
x-2 1/4=1/18
Answers
Answer: x = 2 11/36
Step-by-step explanation:
x-2 1/4 = 1/18
Isolate x: x - 2 1/4 + 2 1/4 = 1/18 + 2 1/4
x = 4/72 + 2 18/72
x = 2 22/72
x = 2 11/36
Check:
2 11/36 - 2 1/4 = 1/18
2 11/36 - 2 9/36 = 1/18
2/36 = 1/18
1/18 = 1/18
Isolate the variable which in this case is x. To do this you mast do what ever you do to both sides. You add 2 1/4 to negative 2 1/4 and you do that also to 1/18.
Second
You now have x = -79/36 which also can be x = 2 7/36
X = 2 7/36
Which number is a solution of the inequality? Choose one:
-3x(10-x)>4
a. 2
b. -3
c. 1
d. 0
Answers
Answer:
b
Step-by-step explanation:
to determine which value gives a solution, substitute the given values into the left side of the inequality and check the validity
a
- 6(10 - 2) = - 6 × 8 = - 48 < 4 → 2 is not a solution
b
9(10 + 3) = 9 × 13 = 117 > 4 → - 3 is a solution
c
- 3(10 - 1) = - 3 × 9 = - 27 < 4 → 1 is not a solution
d
0(10 - 0) = 0 × 10 = 0 < 4 → 0 is not a solution
Which of the following is a correct interpretation of the expression 6-13?
Answers
Answer:
The answer is C
Step-by-step explanation:
Subtraction goes left on the number line
You always start with the first number on the number line
Find the absolute value of |-15|
Answers
Answer:
15 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Absolute value is always positive.
Answer:
Step-by-step explanation: Absolute value of -15 is 15. Absolute value is the distance of a number on the number line from 0. Even though it is a negative, it is a positive because it is a number of units from number line. Hope it helps!!☺☻ Please give Brainliest!
eleanor purchased $2568 worth of stock and paid her broker a 0.5% fee. She sold the stock when the stock price increased to 3928 using an online broker that charged $7 per trade. What are her net proceeds?
Answers
Answer:
Eleanor's net proceeds would be $1340.16.
Step-by-step explanation:
If Eleanor purchased $2568 worth of stock and paid a 0.5% broker fee, she would have to pay $12.84 for the service, which is what we get when we multiply her initial purchase by the percentage (0.005). When Eleanor sold the stock at $3928, she had to pay a flat fee of $7 for the trade, decreasing her overall profit by $7, or $3921. Subtracting her initial investment from the overall profit gives Eleanor a net proceed of $1340.16.
Eleanor's net proceeds from her stock sale, after accounting for both the original broker's fee and the online trading fee, are $3908.16.
Explanation:To calculate Eleanor's net proceeds, we first need to calculate the fee she paid to her first broker. At 0.5% of $2568, that comes to $2568 * 0.005 = $12.84.
Next, she sold her stocks for $3928 using an online broker that charges a flat rate of $7 per trade. So, she paid another $7 in fees.
Therefore, the total fees she paid are $12.84 (first broker) + $7 (second broker) = $19.84.
Finally, to find her net proceeds, we subtract the total fees from the amount she sold her stocks for: $3928 - $19.84 = $3908.16.
So, Eleanor's net proceeds from selling her stocks are $3908.16.
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What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?
10, 5, 0, -5, -10, ...
A) -5n
B) -5n + 15
C) -3n + 15
D) 5n
Answers
Answer:
B
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
where d is the common difference and [tex]a_{1}[/tex] the first term
here d = - 10 - (- 5) = - 5 - 0 = 0 - 5 = - 5 and [tex]a_{1}[/tex] = 10, hence
[tex]a_{n}[/tex] = 10 - 5(n - 1) = 10 - 5n + 5 = 15 - 5n → B
What is the quotient of 3 ÷ 2 1/3, reduced to lowest terms?\
Answers
Final answer:
To find the quotient of 3 ÷ 2 1/3, convert the mixed number to an improper fraction (7/3), find the reciprocal (3/7), and multiply it by 3 to get 9/7, which is the answer in lowest terms.
Explanation:
The quotient of 3 ÷ 2 1/3 can be found by first converting the mixed number 2 1/3 to an improper fraction. The mixed number 2 1/3 is equal to ⅔, which when summed (2 * 3 + 1), gives us 7/3. To divide by a fraction, you multiply by its reciprocal. Thus, we have 3 × ⅓ (which is 3/7). Multiplying these we get 9/7, which cannot be further simplified. Therefore, the quotient in lowest terms is 9/7.
The quotient of 3 ÷ 2 1/3 is found by converting 2 1/3 to an improper fraction (7/3), taking the reciprocal (3/7), and multiplying it with 3. The result is the fraction 9/7, which is already in lowest terms.
Explanation:To find the quotient of 3 ÷ 2 1/3, we first convert the mixed number to an improper fraction. The mixed number 2 1/3 is equivalent to 7/3 (because 2 × 3 + 1 = 7). To divide by a fraction, we multiply by its reciprocal. Therefore, we need to multiply 3 by the reciprocal of 7/3, which is 3/7.
The multiplication is straightforward: 3 × 3/7. We multiply the numerators (3 × 3) to get 9, and the denominators (1 × 7) to get 7, so we have 9/7. Since 9 and 7 have no common factors other than 1, 9/7 is already in its lowest terms. Thus, the quotient is 9/7 or 1 2/7 when expressed as a mixed number.
Simplify the expression. −9(z + 3) − 5(2z + 10)
A. −19z − 77
B. −19z + 13
C. −19z − 13
D. −11z + 77
Answers
Answer:
A. −19z − 77
Step-by-step explanation:
−9(z + 3) − 5(2z + 10)
The first step is to distribute
-9*z -9*3 -5*2z -5*10
-9z-27 -10z-50
-19z -77
Answer
The correct answer is A
Step-by-step explana
Sade found that 75% of 60 is the same as 30% of another number,n.What is the value of n?
Answers
Patty needs a total of 80$ to buy a bicycle .she has already saved 35$. If she saves 10$ a week. From her earnings ,what is the best number of weeks she must work to have enought money to but a bicycle?
A) 3
B)4
C)5
D)8
Answers
Answer:
C) 5 weeks
Step-by-step explanation:
Given :- Cost of bicycle = $80,
Current Savings = $35 and
Saves $10 per week
Additional money that is required to buy the bicycle = $80 - $35
= $45
If she saves $10 per week then the best number of weeks to save $45 is 5 weeks
(Savings in 5 weeks = $10 × 5 = $50)