Answers
for any value of n, the nth term of the equation will be:
Aₙ = -3* 2ⁿ⁻¹
What is the geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ-1
Given a geometric sequence:
-3, -6, -12, 24,.....
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ⁻¹
in our case
a₁ = -3
ratio(r) = -6/-3 = 2
Thus for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
For instance,
8th term of the given sequence:
A₈ = -3* 2⁸⁻¹
A₈ = -3* 2⁷
A₈ = -384
Therefore, for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
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Related Questions
Brad's mother says she was tested for HCG during her last two doctor visits. On March 21, her
HCG level was 200 mlU/ml (milli-international units per milliliter). Two days later, her HCG
level was 392 mIU/ml.
a. Assuming that the model for HCG levels is of the form y = ab', write an equation that
models the growth of HCG for Brad's mother's pregnancy.
Answers
The required function is 200 (1.4)ˣ = 5, where the value of x is calculated to be -11.
The given function is y = a bˣ
x₁ = 0, y₁ = 200
x₂ = 2, y₂ = 392
Let us determine a, b.
a b⁰ = 200
a b² = 392
a = 200
200 b² = 392
b² = 392/200 = 49/25 = 7/5 = 1.4
So, the function is y = 200 (1.4)ˣ
Now, let us determine x for y = 5,
200 (1.4)ˣ = 5
(1.4)ˣ = 0.25
Taking log on both sides,
log (1.4)ˣ = log 0.025
x log 1.4 = log 0.025
x = log 0.025/log 1.4
x ≈ -11
This means the embryo was implanted on March 10th and she visited the doctor 11 days later.
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Suppose Randy has 1/4 of a round cake and 1/4 of a square cake. Are the wholes the same? Does the sum 1/4 + 1/4= 2/4 make sense in this situation? Explain
Answers
Randy's cake situation will be better solved in the following manner:
a) If the area of a round cake and a square cake are different then the quarter portion will be different.
b) Though as a concept 1/4 + 1/4 = 2/4, it is not actually true in this case. If the area of different cakes are different then the quarters will also be different.
Measuring a particular region or patch of a figure is its area. Area is significant in contemporary mathematics. Area is crucial in geometry and calculus, but it also plays a role in the definition of determinants in linear algebra and is a fundamental characteristic of surfaces in differential geometry.
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What is the name of the relationship between Angle 1 and Angle 4?
Answers
Answer: alternate exterior angles
Step-by-step explanation:
They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 4 are alternate exterior angles. Angles that are on opposite sides of the transversal of two other lines.
A 6-kg bowling ball sits on top of a building that is 120 meters tall.
Answers
The potential energy of the ball will be 7200 Joules.
What is potential energy?The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.For small height changes, gravitational potential energy can be computed using - E = mgh.Given is a 6-kg bowling ball sits on top of a building that is 120 meters tall.
We can write the potential energy of the ball as -
E = mgh
E = 6 x 10 x 120
E = 60 x 120
E = 7200 Joules
Therefore, the potential energy of the ball will be 7200 Joules.
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an airline has six flights from new york to california and seven flights from california to hawaii per day. if the flights are to be made on separate days, how many different flight arrangements can the airline offer from new york to hawaii?
Answers
The total number of different flight arrangements the airline can offer from New York to Hawaii is 42.
The Flight ArrangementsThe airline has 6 flights from New York to California and 7 flights from California to Hawaii per day. Therefore, the total number of different flight arrangements the airline can offer from New York to Hawaii is 6 x 7 = 42.
The airline has the capability to offer 42 different flight arrangements for travel from New York to Hawaii by combining the number of flights available per day from New York to California (6) with the number of flights available per day from California to Hawaii (7). This calculation is done by multiplying the number of flights from New York to California by the number of flights from California to Hawaii.
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We placed a 2 kg textbook and a 4kg textbook at least 2cm away from each other. After a while we moved the two textbooks so now they are 8 cm away from each other. Explain which textbook has a larger gravitational pull and how do the different distances affect it?
Answers
Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
What is Meant by Gravitational Force?In Physics, the gravitational force is one of the types of forces. It is a force that attracts any two objects with mass. The gravitational force is also known as the attractive force, as it always pulls the masses of two objects together. Newton’s gravitational law states that every object in the universe is pulled by other objects. The other types of forces are electromagnetic force, strong force, weak force, and so on. The formula to calculate the gravitational force is given by Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)².
Given here:
Book 1 has 2 kg textbook and Book 2 weighs 4 kg.
In the first case The gravitational pull when they were 2 cm apart is
F₁= Gm₁m₂ / 2cm
=0.00000133486 N
While if the two books are 8 cm apart we have
F₂= Gm₁m₂ / 8
=0.0000000834288 N
clearly the gravitational pull decreases with the increase in distance.
And owing to Book 2's higher weight it has the superior gravitational pull.
Hence, Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
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Simplify the radical expression completely:
Square root of 48x^2y^5z
Answers
The radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
Now, According to the question:
Factor 48 into its prime factors
48 = 24 × 3
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
16 = [tex]2^4[/tex]
Factors which will remain inside the root are :
3 = 3
To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
4 = [tex]2^2[/tex]
At the end of this step the partly simplified SQRT looks like this:
4 × sqrt[tex](3x^2y^5)[/tex]z
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt[tex](x^8)=x^4[/tex]
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or < (-2) , examples:
(4.1)[tex]sqrt(x^5)=x^2sqrt(x)[/tex]
(4.2) sqrt(x-7)=x-3sqrt(x-1)
Applying these rules to our case we find out that
SQRT[tex](x^2y^5) = xy^2[/tex]SQRT(y)
Simplified root:
4[tex]xy^2[/tex] × sqrt(3y)
Hence, the radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
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amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend. if the postage is $1.77, how many of each stamp did amy use?
Answers
If Amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend worth of $1.77 , then the number of 41 cent stamp used is 3 and the number of 6 cent stamps used is 9 .
Let the number of 41 cents stamps used in postage is = x ;
let the number of 6 cents stamps used in postage is = y ;
the amount 41 cents in dollars is = $0.41 ;
and amount 6 cents in dollars is = $0.06 ;
Amy used 41-cent stamps , 6-cent stamps to pay $1.77 in postage
it is represented in equation form as ⇒ 0.41x + 0.06y = 1.77
Multiplying on both sides by 100 , we get
⇒ 41x + 6y = 177 ;
⇒ y = (177 - 41x)/6 ;
We will test for corresponding values of x and y to satisfies this equation and the number of stamps must be whole numbers.
If x = 1 , then y = 26.66
If x = 2 , then y = 15.83
If x = 3 , then y = 9
If x = 4 , then y = 2.16 .
the only values that shows a whole number is : If x = 3 , then y = 9 .
Therefore , Amy used "3" 41-cents stamps and "9" 6-cent stamps .
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A rectangular garden has a walkway around it. The area of the garden is 2(5.5x + 3.5). The combined area of the garden and the walkway is 2.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
Answers
The total of the two terms that represent the length of the garden's walkway: 26x + 28
Explain the features of term rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.A walkway around a rectangular garden.
The garden's size is 4(4.5 x + 1.5) square meters.The garden's and the walkway's combined area is 5.5(8 x + 4).Simplifying each equation.
Area of the garden : 4(4.5 x + 1.5) = 18x + 6
Combined area: 5.5(8 x + 4) = 44x + 22
Thus,
Area of walkway = Combined area - Area of the garden
= 44x + 22 - 18x + 6
= 26x + 28
Thus, the total of the two terms that represent the length of the garden's walkway: 26x + 28
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what term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? what is wrong with this type of sampling method
Answers
Part A: The respondents in the population are a voluntary response sample.
Part B: The responses may not reflect the opinions of the general population
The total number of internet users in those is 1072 people.
The percentage of the total number of people that chose to respond is 38%
We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.
Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.
In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.
The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.
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HELP!! ASAP! 60 POINTS
This diagram shows right triangular prism UVWXYZ.
What is the volume of UVWXYZ? If necessary, round your answer to the nearest tenth.
Answers
In the diagram which shows right triangular prism UVWXYZ, the volume of UVWXYZ can be expressed in nearest tenth as 750 cm^3.
How can the the volume of UVWXYZbe calculated?The concept that will be used here is volume. In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3
√ (12.5^2 -7.5^2) =10 cm
The volume can be calculated as : (1/2 * 7.5 * 10 *20
=750 cm^3
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Help me solve this Simultaneous equation assignment
Answers
Answer:
Case 1 : x = - 2, y = 3
Case 2 : x = 5. y = 2
Step-by-step explanation:
Case 1
5y + x = 13 --------> Eq 1
y - x = 5 ---------> Eq 2
Add both Eq 1 and y,
5y + x = 13
y - x = 5
________
6y + 0 = 18
6y = 18
y = 18/6
y = 3
Substitute y = 3 in Eq 2,
3 - x = 5
3 - 5 = x
- 2 = x
x = - 2
Hence,
x = - 2
y = 3
Case 2
2x + y = 12 ---------> Eq 1
6x + 5y = 40 -----------> Eq 2
Multiply Eq 1 with 3,
3(2x + y = 12)
6x + 3y = 36 --------> Eq 3
Eq 2 - Eq 3,
6x + 5y = 40
- 6x - 3y = - 36
_____________
0 + 2y = 4
2y = 4
y = 4/2
y = 2
Substitute y = 2 in equation 1,
2x + 2 = 12
2x = 12 - 2
2x = 10
x = 10/2
x = 5
Hence,
x = 5
y = 2
A pizza company charges $60 for 12 pizzas.
v) Create a table from 60=12m
Answers
The required table would be:
Quantity (x) Price (y)
12 $60
What is the slope-intercept form?
The slope-intercept form of a linear equation is y = mx + b, where x and y are variables, m is the slope of the line (also known as the "rate of change" or "rise over run"), and b is the y-intercept (the point where the line crosses the y-axis). The slope-intercept form is so called because it gives the slope of the line and the y-intercept in one equation
Here is the table you requested:
Quantity (x) Price (y)
12 $60
This table shows the relationship between the quantity of pizzas ordered (x) and the price (y) for a pizza company that charges $60 for 12 pizzas. The equation y = mx + b can be used to represent the relationship, where m is the unit price and b is the y-intercept. In this case, m = 5 and b = 0.
Hence, the required table would be:
Quantity (x) Price (y)
12 $60
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assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is
Answers
The possible outcomes are the sample space of the game
The number of possible outcomes in the game is 3
Now, According to the question:
In the domain of Statistics, the number of possible outcomes for a given event help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.
How to determine the possible outcomes
The number of games is given as:
n = 2 i.e. 2 games to finish the season
In each game, the soccer team can either win, lose or tie.
So, we have the outcome of each game to be:
Outcome = {Win, Lose, Tie}
Count the outcomes
Count = 3
Hence, the number of possible outcomes in the game is 3.
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The given question is incomplete , complete question is:
Assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is in the game ____
PLEASE ANSWER QUICK,
Answers
Answer:
C=5Q
Step-by-step explanation:
James has 20$ to pay for a movie ticket and candy. Each box of candy cost 2$, the movie ticket cost 12$. Write and equation that can be used to determine how many boxes of candy, c, James can buy
Answers
Answer:
4 candy boxes
Step-by-step explanation:
2$ one candy box
then 20-12=8 then
left 8$ now,2$=1 candy box 8$=8÷2
Ans will be 4
Answer:
2c + 12 = 20. Simplified to 2c = 8
Step-by-step explanation:
We can start with a Template
Y = Xc + C
Y being the total
X being candy price
c bring candy boxes, as stated
C being ticket price
Plugging those in we get
20 = 2c + 12
Since you bought the ticket with your $20, we can subtract the ticket price from both sides, giving you
8 = 2c or 2c = 8
A rectangle has an area of 15 square millimeters. The width of the rectangle is 3 millimeters.
Answers
Answer:
5 millimeters
Step-by-step explanation:
15 = 3x
5 = x
g) 25+ [14 - {8+ (13-4)}]
Answers
Answer: 22
Step-by-step explanation:
25+ [14 - {8+ (13-4)}]
= 25 + [14 - {8 + 9 }]
= 25 + [14 - 17]
= 25 - 3
= 22
Could someone help me on this problem please thank you if you do!
Answers
Answer:
the third graph
Step-by-step explanation:
1. increase - then you know the line has to go upwards. so only first &3rd lines are potentially correct answer
2. look at the Y axis markings, first one goes from 5 to 11, it increased by 6. so it's not right.
answer is the 3rd one.
the garden clud at central middle school is planting a flower bed. a scale drawing of the flower is shown. the scale 1 in. :2 ft
Answers
If the plant is n inches then,
the actual plant = 2n feet.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
The garden club at central middle school is planting a flower bed.
A scale drawing of the flower is shown.
The scale 1 in:2 ft
The scale factor,
the model = 1 inch
Then the actual plant = 2 feet.
If the plant is n inches then,
the actual plant = 2n feet.
Therefore, If the plant is n inches then, the actual plant = 2n feet.
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a 5 ft tall girl stands on level ground the sun is 25 degrees above the horizon how long is her shadow
Answers
The girl has a shadow of 10.72 ft if she has a 5 ft tall and the sun is 25 degrees.
CALCULATION THE GIRL SHADOWBased on the given conditions, formulate:5 ÷ tan (25°)
Find angles from the level ground of the sun5 ÷ tan (25°)
Calculate5 ÷ 0.466308
Calculate10.722527
TANGENT RATIOWhen measuring the area of a right shadow, the ratio of the opposite side to the adjacent side is known as the tangent ratio. Right angle can have their angles and sides determined using tangent ratios, just as sine and cosine ratios.
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One bank account pays 6% interest and another pays 12%. If $6,000 was invested for a year and the interest earned was $540, how much was invested at 6%?
Answers
Answer:
360
Step-by-step explanation:
0.06x6000=360 also that 6% equal 6/100 wich is 0.06
Solve for x. Write the equation and show ALL STEPS to solve.
(3x - 3)"
AP
(2x+13)"
Answers
Answer:
x = 16
Step-by-step explanation:
(2x+13)° = (3x-3)° [vertically opposite angles]
2x + 13 = 3x - 3
2x - 3x = -3 - 13
-x = -16
∴ x = 16
A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answers
Answer:
I also need help
Step-by-step explanation:
A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answer:
20 miles
Step-by-step explanation:
would you rather go 99 miles or 20 miles
you can answer any 12 questions from a total of 14 questions on an exam. in how many different ways can you select the question?
Answers
In 420 ways different ways can you select the question.
you can answer any 12 questions from a total of 14 questions on an exam
At least 8 questions, including 3 from the last section, must be attempted out of the 5 questions in part and the 7 questions in part 2.
There are three choices.
&% from part 2; (1)3 from part 1
= ⁵C 3 × ⁷ C 5
= 3!(5−3)!/5! × 5!(7−5)!/7!
= 2/5×4 ×= 2/7×6
=5×2×7×3
=210 ways
(2)4 from part 1 & 4 from part 2
= ⁵C 3 × ⁷ C 5
=4!(5−4)!/5!
×= 4!(7−4)!/7!
=5×= 3×2×1/7×6×5
=5×7×5
=175 ways
(3)5 from part 1 & 3 from part 2
= ⁵C 3 × ⁷ C 5
= 5! 0!/5!
×= 3!(7−3)!/7!
=1×= 3×2/7×6×5
=35 ways
Total number of ways =210+175+35
420 ways
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a bowl contains 7 blue chips and 3 white chips. two chips are to be drawn successively at random and without replacement. what is the probability of the first chip is white and the second chip is blue?
Answers
The probability of drawing a white chip first and a blue chip second is 1/5.
To find the probability of drawing a white chip first and a blue chip second, we can use the formula for conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. It is represented by the notation P(A|B), where A is the event of interest and B is the event that has already occurred.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
This formula expresses the probability of event A occurring given that event B has occurred, as a ratio of the probability of the two events occurring together and the probability of event B occurring alone.
Where A is the event of drawing a white chip first and B is the event of drawing a blue chip second.
We know that the probability of drawing a white chip first is 3/10 (since there are 3 white chips out of a total of 10 chips in the bowl), so P(A) = 3/10.
Once a white chip has been drawn, there are 9 chips left in the bowl, with 6 of them being blue. This means that the probability of drawing a blue chip second given that a white chip has already been drawn is 6/9, so P(B|A) = 6/9.
By multiplying these two probabilities together, we get:
P(A and B) = (3/10) * (6/9) = (3/10) * (2/3) = 6/30 = 1/5
Therefore, the probability of drawing a white chip first and a blue chip second is 1/5.
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HELP PLEASE!!!!
What happens if you graph y=f(f^-1(x))? Explain.
Answers
These questions seem hard and mysterious, but they really make sense. Good luck!
Into easier words just incase that brings confusion
y = f(x)
y = x
y = b
x = a
Inverse means that you switch places with x and y. Therefore, you have
x = y
Your point is (b,a).
what number is an integer
Answers
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.
which set represents a Pythagorean triple
A. 1,2,3
B.9,12,16
C. 30,40,50
D.38,44,49
Answers
The set that represents a Pythagorean Triple is given as follows:
C. 30,40,50
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For item c, we have that:
30² + 40² = 50²
900 + 1600 = 2500
2500 = 2500.
Which is a true statement, hence item c represents the Pythagorean Triple in the context of this problem.
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Long division ? ?????
Answers
Answer: 37.5
Step-by-step explanation: To find this, we must move the decimal place one spot over. It would now look like this:
300. ÷ 8
Now for the division look at the attachment. In the end, you've should've got 37.5. To check if that's right, you'd multiply 0.8 and 37.5. Then again, you should get 30. I hope this helped!