Answer:
[tex]\huge\boxed{a_n=12\cdot3^{n-1}=4\cdot3^n}[/tex]
Step-by-step explanation:
[tex]a_1=12\\\\a_2=36=3\cdot12=3a_1\\\\a_3=108=3\cdot36=3a_2=3\cdot3a_1=3^2a_1\\\\a_4=324=3\cdot108=3a_3=3\cdot3^2a_1=3^3a_1\\\\a_5=972=3\cdot342=3a_4=3\cdot3^3a_1=3^4a_1\\\vdots\\a_n=3^{n-1}a_1=3^{n-1}\cdot12\\\\3^{n-1}\cdot12=3^{n-1}\cdot3\cdot4=3^{n-1+1}\cdot4=4\cdot3^n[/tex]
[tex]\text{Used}\\\\a^n\cdot a^m=a^{n+m}[/tex]
6% pay increases 62,900 thanks i look forward to the additional _ per month
Answer:
Step-by-step explanation:
$314.50
X/5-y = m-1 resolver para y
Okay, let's solve this step-by-step:
X/5-y = m-1
Add y to both sides:
X/5 = m
Multiply both sides by 5:
X = 5m
So in this equation, X = 5m.
To find y, we subtract m-1 from both sides of the original equation:
X/5 = 5m
X/5 - (m-1) = 5m - (m-1)
X/5 - m + 1 = 4m
(X - 5m) / 5 = m - 1
X - 5m = 5(m - 1)
X = 20m - 5
So if we let m = any value, we can calculate y. For example:
If m = 3, then:
X = 20*3 - 5
= 55 - 5 = 50
50/X = 5(m - 1) = 5*2 = 10
y = 10
Does this make sense? Let me know if you have any other questions!
Troys toy box is 4 ft x 3ft x 5 ft. What is the Volume of his toy box?
Answer:
60 ft^2
Step-by-step explanation:
To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.
4 x 3 x 5 = 15x 4 = 60
Answer:
60 ft³
Step-by-step explanation:
V = 4 ft × 3 ft × 5 ft
V = 12 ft² × 5 ft
V = 60 ft³
#CMIIWplease help fast i don’t feel like typing
Answer:
he should have subtracted 17 from both sides of the equation
Step-by-step explanation:
x+ 17 = 22
subtract 17 from both sides
X + 17 = 22
-17 -17
x = 5
The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
> Next Question
Answer:
Step-by-step explanation:
$6.80 x 19 pounds = $129.2
$4.70 x 18 pounds = $84.6
+___________________
37 pounds = $213.8
$213.8 divided by 37 pounds = 5.77837......
= $5.78 per pound
i need the answer for this asap Please!
The system of inequalities for the graph is
a) y < 3x - 4
b) y = x + 3
Given data ,
Let the inequality equations be represented as A and B
where
Let the first point be P ( 0 , 3 )
Let the second point be Q ( -3 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 3 - 0 ) / ( 0 + 3 )
m = 1
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 0 = 1 ( x + 3 )
y = x + 3
And , the second equation is
Let the first point be R ( 0 , -4 )
Let the second point be S ( 2 , 2 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -4 - 2 ) / ( 0 - 2 )
m = -6/-2
m = 3
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 2 = 3 ( x - 2 )
Adding 2 on both sides , we get
y = 3x - 4
Since , it is a dotted line ,
y < 3x - 4
And , the solution to the inequality is point of intersection
where A ( 3.5 , 6.5 ) is the solution
Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
Help My Daughter we not understanding?
Representation of a number in three different ways:
133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]
678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]
877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]
543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]
453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]
341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]
555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]
485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]
789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]
864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]
652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]
Here given an example to write a particular number in different representations.
13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.
14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.
1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.
So three representations are of number 142.
Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.
Representations for some numbers:
133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]
678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]
877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]
543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]
453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]
341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]
555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]
485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]
789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]
864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]
652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]
To know more about numbers here
https://brainly.com/question/30284303
#SPJ1
If ARSU-AVST, then the triangles are
similar by:
Answer:
AA sim post
Step-by-step explanation:
They DO have equal (similar) angles.....but they do not have equal sides
There are 5,144 blocks to be placed
evenly into 8 storage containers. How
many blocks are in each storage
container?
Divide the total number of blocks by the total number of storage containers.
5144/8 = 643 blocks in each storage container.
A natural food company produces and sells organic almond milk for $9.00 per gallon. This company
estimates its fixed costs to be 1121 dollars per month and the variable cost to produce each gallon of
almond milk is $7.50.
What is the margin of profit if 1494 gallons of almond milk are produced and sold each month?
A Select an answer of $
Okay, here are the steps to solve this problem:
Fixed costs per month: $1121
Variable cost per gallon: $7.50
Selling price per gallon: $9.00
Monthly sales (gallons): 1494
Cost of goods sold = Variable cost per gallon * Monthly sales
= $7.50 * 1494 gallons
= $11,105
Gross margin = Revenue - Cost of goods sold
= $9 * 1494 gallons
= $13,446
- $11,105 (Cost of goods sold)
= $2,341
Margin of profit = Gross margin - Fixed costs
= $2,341 - $1121
= $1,220
So the margin of profit if 1494 gallons are produced and sold each month is $1,220.
The answer is:
B $1,220
Need help asap, please and thank you
If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.
In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;
where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;
Substituting the values,
We get;
⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;
Simplifying this expression,
We get;
⇒ P = (111.3 million) × (1.0078)³⁷;
⇒ P ≈ 148.37 million;
Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.
Learn more about Growth Rate here
https://brainly.com/question/29203229
#SPJ1
Tommy and Ruth are cycling to meet each other. Tommy cycles twice as fast as Ruth and they both set off at the same time. At which coordinate will they meet?
Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point.
In this problem, Tommy and Ruth are cycling towards each other. We are given that Tommy cycles twice as fast as Ruth and they both start cycling at the same time. Our goal is to determine at which coordinate they will meet.
To solve this problem, we need to use the concept of distance, speed, and time. Let's assume that Ruth cycles at a speed of "x" km/hr. Since Tommy cycles twice as fast as Ruth, his speed will be "2x" km/hr.
Let's say that Tommy and Ruth meet at a distance of "d" km from Ruth's starting point. Now, let's calculate the time taken by both Tommy and Ruth to reach this point.
Time taken by Ruth = Distance/Speed = d/x
Time taken by Tommy = Distance/Speed = d/2x
Since they both start cycling at the same time, we can set these two equations equal to each other:
d/x = d/2x
We can then simplify this equation by multiplying both sides by 2x:
2d/x = d
Now we can solve for "d" by multiplying both sides by "x":
2d = dx
d = 0.5x
This means that Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point. To determine the exact coordinates, we need to know where Ruth started cycling from and in which direction they are cycling. If we assume that Ruth started cycling from the origin (0,0) and they are cycling towards each other on a straight path, then they will meet at the coordinate (0.5x, 0).
To know more about Coordinate here
https://brainly.com/question/27749090
#SPJ1
Find surface area without mistaking the lateral height.
The total "surface-area" of cone having "slant-height" as 10, and base-radius as 6, is 301.44 square units.
The total surface area of a cone can be calculated by adding the area of the base to the lateral surface area.
Let us first calculate the lateral surface area of the cone:
Lateral surface area = πrl; where r is radius , and 'l" = slant-height,
The radius of base = 6 units and slant height is = 10 units.
So, we have:
Lateral surface area = π × 6 × 10
Lateral surface area = 60π square units
Next, Area of the base = πr²;
Area of the base = π × 6²,
Area of the base = 36π square units,
Total surface area = Lateral surface area + Area of the base
Total surface area = 60π + 36π
Total surface area = 96×3.14 = 301.44 square units.
Therefore, the total surface area of cone is 301.44 square units.
Learn more about Surface Area here
https://brainly.com/question/29147652
#SPJ1
A student has scores of 63, 65, and 73 on his first three tests. He needs an average of at least 70 to earn a grade of C in the class.
What is the minimum score that the student needs on the fourth test to ensure a C?
Answer: 79
Step-by-step explanation:
63+65+73+×/4=79
multiply by 4 on both sides
201+x=280
subtract 201 from both sides
x= 79
Need help on please
Answer:
12
Step-by-step explanation:
The figure is a right triangle with hypotenuse = QS
The base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)
The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)
Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides
QS² = 3² + 4² = 9 + 16 = 25
QS, the hypotenuse = √25 = 5
The perimeter = sum of the sides = 3 + 4 + 5 = 12 units
An object in the shape of a rectangular prism has a length of 9 inches, a width of 5 inches, and a height of 4 inches. The object's density is 11.1 grams per cubic centimeter. Find the mass of the object to the nearest gram.
Answer:
32.741 kg---------------------------
Mass is the product of the volume and density and the volume of the rectangular prism is the product of its three dimensions.
Find the volume first:
V = 9*5*4 = 180 in³Convert volume to cm³, taking 2.54 cm per in:
180*(2.54)³ = 2949.67152 cm³Find the mass:
Mass = 11.1*2949.67152 = 32741.353872 g ≈ 32.741 kg (rounded)Mario was given the following enlargement.
A figure with top measurement A and side measurement 6 centimeters. Side A corresponds to a side with length 24 centimeters. A side with length 6 centimeters corresponds with a side with length 12 centimeters.
Figures not drawn to scale.
What is the length of side A, in centimeters?
12
15
24
33
The length of side A, in centimeters is 12. Option A
How to determine the valueTo determine the value, we need to know that;
When two sides of a figure are equal in length, that is in (measure).
For example in a square all sides are equal in length so they're all corresponding measurements.
From the information given, we have that;
Side A corresponds to 24 cm
Length 6 cm corresponds to Length 12 cm
The given parameters can be represented mathematically as;
A/24 = 6/12
cross multiply the values, we have;
12A = 6(24)
Multiply the values
12A = 144
Divide by the coefficient, we have;
A = 12 centimeters
Learn more about measurements at: https://brainly.com/question/27233632
#SPJ1
The correct answer is, A (aka 12)
what do you add to get the pattern 1, 8, 15, 22, 29 36, 43
Answer:
7
Step-by-step explanation:
Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?
if gender would not have mattered, what would have been the number of males that would have survived, given the data for the number of females who survived (296/402) and the total number of passengers on the ship (1207).
If gender did not matter then the number of males who would have survived would be 593 males
How to find the number who would have survived ?If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.
First, calculate the survival rate of the females:
Survival rate = Number of females who survived / Total number of females
= 296 / 402
= 0.737
Expected number of male survivors = Number of males * Female survival rate
= 805 x 0.737
= 593 males
Find out more on survival rates at https://brainly.com/question/30894892
#SPJ1
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
To know more about speed:
https://brainly.com/question/31756299
#SPJ1
Real World Scenario: Sara and Kim are both three years old. Both have recently talked to their parents about doing chores around the house to earn some money. Both Sara and Kim's parents have agreed to start giving them a constant allowance every week. Sara currently has $1 in her piggy bank. Her parents have agreed to give her $.60 per week for doing her chores. Kim currently has $2.20 in her piggy bank. Her parents have greed to give her $.20 per week for doing her chores.
What equation and graph help support scenario?
The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.
The equation that represents the amount of money in Sara's piggy bank over time can be written as
Y = 0.6x + 1
Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.
Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as
Y = 0.2x + 2.2
Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.
To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.
Here is a graph that represents the scenario
In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.
To Know more about Equations here
https://brainly.com/question/10413253
#SPJ1
Can someone pls explain
163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units
164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.
165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.
166. Missing side = 29 ft.
What is the Pythagorean Theorem?The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.
163. The distance between A(-5, 6) and B(5, -5):
AB = √[(5−(−5))² + (−5−6)²]
AB = √221
AB ≈ 14.9 units
164. Apply the Pythagorean theorem to find the diagonal:
Diagonal = √(15² + 15²) ≈ 21.2 ft.
165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:
c = √676 = 26 units.
166. Missing side = √(20² + 21²) = 29 ft.
Learn more about the Pythagorean theorem on:
https://brainly.com/question/27997683
#SPJ1
someone please answer this its confusing me
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
Find out more on domain here: https://brainly.com/question/26098895
#SPJ1
Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.
This can be written as S = 400+35v , where v is the number of vacuums sold.
If Carlos earns $1590 for a week's work, how many vacuums did he sell?
Answer:
34
Step-by-step explanation:
1. Plug in the week's salary into the formula
S=400+35v
1590=400+35v
2. Solve for v.
1590=400+35v
Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.
1190=35v
Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.
34=v
A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 13.2 inches and standard deviation of 2.3 inches. If a sample of 37 items are chosen at random, what is the probability the sample's mean length is greater than 12.1 inches? Round answer to four decimal places.
The probability that the sample's mean length is greater than 6.3 inches is0.8446.
Here, we have,
Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event.
It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
Learn more about probability at
brainly.com/question/24756209
#SPJ1
ABCD is a rectangle. If AC is 20 inches, what is DE?
B
Al
E
C
D
The measurement of DE is 10 inches.
If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.
Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.
Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:
BD = √(L^2 + W^2)
Since we know that the diagonals of a rectangle are equal, we have:
AC = BD
BD = 20
Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.
Learn more about rectangles here:
https://brainly.com/question/29147156
#SPJ1
Question 1b Identify the amount in this statement. 6 is 30% of 20. The amount = The solution is
The amount in this statement, 6 is 30% of 20 is 6.
The amount in the statement "6 is 30% of 20" is 6.
This statement means that if we take 30% of 20, we get 6.
In other words, the amount 6 is 30% of 20.
We can also verify this by calculating 30% of 20:
30% of 20
= (30/100) × 20
= 0.3 × 20
= 6
Hence, the amount in this statement is 6.
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ1
A bag contains 40 marbles. 12 of the marbles are red. What is the percent of red marbles in the bag?
Answer:
the percentage of red marbles in the bag is 30%.
Step-by-step explanation:
To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:
Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100
Number of red marbles = 12
Total number of marbles = 40
Percentage of red marbles = (12/40) x 100
= 0.3 x 100
= 30%
Therefore, the percentage of red marbles in the bag is 30%.
Find the 15th term of the geometric sequence 2,6,18,...
Answer:
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).
In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:
r = 6 / 2 = 3
Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:
aₙ = a₁ * r^(n-1)
Substituting the values, we have:
a₁ = 2
r = 3
n = 15
a₁₅ = 2 * 3^(15-1)
Calculating the exponent first:
3^(15-1) = 3^14 = 4782969
Now, substituting this value back into the formula:
a₁₅ = 2 * 4782969
a₁₅ = 9565938
Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.
Step-by-step explanation: