A state began an effort to increase the deer population. In year 2 of the effort, the deer population in a state forest was 1,200. In year 4, the population was 1,728.
The explicit rule for the geometric sequence is:
Answers
Answer:
nth term = 1000×1.2ⁿ⁻¹
Step-by-step explanation:
The explicit rule for the given geometric sequence is aₙ = a₁rⁿ⁻¹ = 1000 x 1.2ⁿ⁻¹
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.
Given that, in two years the deer population in a state forest was 1,200. In year 4, the population was 1,728,
Therefore,
a₄ = 1728 and a₂ = 1200
We have two terms of the GP, therefore, finding r,
r² = 1728 / 1200 = 1.44
r = 1.2
Therefore,
a₁ = a₂r¹⁻²
= 1200r⁻¹ = 1200/r
= 1200 / 1.2 = 1000
Therefore, the formula will be = aₙ = a₁rⁿ⁻¹ = 1000 x 1.2ⁿ⁻¹
Hence, the explicit rule for the given geometric sequence is aₙ = a₁rⁿ⁻¹ = 1000 x 1.2ⁿ⁻¹
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Related Questions
Two girls divided $1.60 in the ratio 5 : 3. How much more does one girl get than the other?
Answers
let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly
\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)
Parents of children with developmental disorders can apply for federal funding, to help pay for psychosocial rehabilitation. A sociologist working for the annual Current Population Survey wants to know the percentage of applicants for this funding who are in poverty. She needs a sample of applicants from across the U.S., so she groups all of the applications by state and randomly selects applicants from each state. What sampling scheme did she use
Answers
Answer:
Stratified sampling
Step-by-step explanation:
key word "groups"
The sampling scheme did she used is stratified sampling.
What is stratified sampling?It is a method of sampling where the division of the population should be split into the smaller subgroup called a strata. The strata should be created depending upon on the members shared like the income etc. Here the sample should be needed for applicants for across the US also it randomly selects the applicants for each state.
So, The sampling scheme did she used is stratified sampling.
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A rectangular yard is enclosed by 100 meters of fencing. The table shows some possible values for the length and width of the yard. Replace all variables (letters) with numerical values. length (meters) width (meters) area (square meters) 10 40 400 20 30 600 25 25 625 35 15 525 40 10 1600
Answers
10, 40, 400.
20, 30, 600.
25, 25, 525.
40, 60, 2400.
I think.
An urn contains 3 white balls and 7 red balls. A second urn contains 7 white balls and 3 red balls. An urn is selected, and the probability of selecting the first urn is 0.3. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
Answers
Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
Step-by-step explanation:
Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.
First, let's find P(A):
P(A) = 0.3
Next, let's find P(B|A):
P(B|A) = (3/10) * (3/10) = 9/100
Finally, let's find P(A and B):
P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027
So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
On a long hike, Tammy drank 5 pints of water. How much did she drink in quarts?
Answers
Answer:
1 1/4
Step-by-step explanation:
if he drank 5 pints and 4 pints is 1 quart that means 1 pint will be left(1/4) and there will be 1 quart (1) so in total 1 1/4
What is the slope of the line that contains the points (8, 4) and (−4, 8)?
3
−3
one third
negative one third
Answers
Answer: negative one third
Answer:
-1/3
Explanation:
There's a formula that I'll use to find the slope - it's called the slope formula.
\(\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)
Plug in the data:
\(\sf{m=\dfrac{8-4}{-4-8}}\\\\\sf{m=\dfrac{4}{-12}\)
Simplify:
\(\sf{m=-\dfrac{4}{12}}\)
\(\sf{m=-\dfrac{1}{3}}\)
Hence, the slope is negative one-third.
PLEASE HELP 10 FREE BRAINLY POINTS IF YOU ANSWER THIS
Find each probability and then order from least probable to most probable.
Answers
Answer:
The probabilities are:
1. 1/6
2. 1/2
3. 9/14
4. 0
5. 1
So ordering from least to most probable:
4. 7 on a 6 sided die
1. 4 on a 6 sided die
2. heads with a coin
3. red or green marble
5. <7 on a 6 sided die.
Step-by-step explanation:
1. The probability of rolling 4 on a 6-sided die is 1/6, as each side is equally probable.
2. The probability of flipping a coin onto heads is 1/2, as there are 2 equally probable outcomes.
3. The probability of drawing red or green out of 6 red, 5 blue, 3 green is 9/14 (9 positive outcomes out of 14).
4. The probability of rolling a 7 with a 6 sided die is 0, as there is no such number on the die.
5. The probability of rolling a number less than 7 on a 6 sided die is 100%, or 1, because any outcome is positive (we can only roll numbers smaller than 7).
The probabilities are:
1. 1/6
2. 1/2
3. 9/14
4. 0
5. 1
So ordering from least to most probable:
4. 7 on a 6 sided die
1. 4 on a 6 sided die
2. heads with a coin
3. red or green marble
5. <7 on a 6 sided die.
Answer:
Step-by-step explanation:
all creds to person above
identify the segments that are parallel
Answers
============================================================
Explanation:
Let's go through the answer choices one by one
A) I'll come back to this later.B) There is no segment AE, since points A and E are not connected with a single straight line, so we can cross choice B off the list.C) Segments AD and CB do look parallel, but unfortunately we don't have the right info to say if they are or not. Angles EDA and HCB are same side exterior angles. If we knew they were supplementary, then we'd know that AD is parallel to CB. Unfortunately we don't have the info about the angles being supplementary or not. Choice C is crossed off the list.D) Segments AC and CD are never parallel. They share point C in common. In other words, AC and CD intersect at point C. Recall that parallel lines never intersect. Choice D is crossed off the list.We've eliminated choices B, C and D from the list. Only choice A remains. Luckily the answer "none of these" is a perfect fit since we've eliminated everything else.
Answer:
Using the process of elimination you can tell the answer is A.
B and D dont make sense, it may be C but I dont think so, so it is A.
Using the graph below, what would the y-value (range) be for an x-value (domain) of -3?
Answers
By looking at the graph of the linear equation, we conclude that the y-value for x = -3, is y = -9
what would the y-value be for an x-value of -3?Here we have the graph of a linear equation. What the graph tells us is "what is the value of y for each value of x".
So, if we want to find the value of y when we have x = -3, then:
We need to find the value x = -3 on the horizontal axis.Then we move vertically upwards (or downwards, depending on the case) until we reach the graphed equation.Once we reached the graphed equation, we move horizontally until we meet the vertical axis.The value at which we meet the horizontal axis gives the value in the range related to the value in the domain from which we started.Following these steps, you should be able to see that, when x = -3, the value of y is -9
So we conclude that the y-value for x = -3, is y = -9
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Express the given quantity as a single logarithm. (Enter your answer using function notation - use In(x) instead of In x.) In(a + b) + In(a - b) – 4 Inc Differentiate the function. (Enter your answer using function notation - use In(x) instead of In x.) f(x) = 5.2 In(4x) - 52 Differentiate the function. (Enter your answer using function notation - use In(x) f(t) = sin(3 In x) Differentiate the function. (Enter your answer using function notation - use In(x) f(x) = ln(4 sin’z)
Answers
The given quantity as a single logarithm are as follows:
1. 20.8In(4x)
2. 3cos(3Inx)Inx
3. 4cos'zln'z
What is function?Function ve process of state of instruction that text input papa mississippi start x and output function ladki company it's a programming language allow me the code to create the complex command with simple instruction for example function in the used to it to numbers together a generator and i'm number from san also be combined to create more public sequence are instruction.
Express the given quantity as a single logarithm: In(a + b) + In(a - b) - 4Inx = In[(a+b)(a-b)] - 4Inx
Differentiate the function f(x) = 5.2In(4x) - 52: f'(x) = 20.8In(4x)
Differentiate the function f(t) = sin(3Inx): f'(t) = 3cos(3Inx)Inx
Differentiate the function f(x) = ln(4sin'z): f'(x) = 4cos'zln'z
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A music streaming service charges $7 per month for the first user, and $4 more per month for each additional user. Which function represents the monthly bill y in terms of the number of additional users x ?
Answers
The function for the monthly bill can be written as y = 7 + 4x.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a music streaming service charges $7 per month for the first user and $4 more per month for each additional user.
The equation can be written as,
y = 4x + 7
Here, y is the monthly charge and x is the number of months.
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CAN SOMEONE HELP ME WITH THIS
Answers
Point: (2,7)
Reflected across y-axis: (-2,7)
Reflected across x-axis: ????
My options for the answer is
(-7,-2)
(-2,7)
(2,-7) which answer is it I have already tried the first one and it said it was wrong.
Answers
Answer:
(2,-7)
Step-by-step explanation:
Reflection rule for across the x-axis: \((x,y)\rightarrow (x,-y)\)
Using the rule and point (2,7):
\((2,7)\rightarrow(2,-7)\)
(2,-7) should be the correct answer.
Brainilest Appreciated.
write 100 in exponential notation
Answers
Answer:
10^2 AKA ten squared
Step-by-step explanation:
A number squared is that number times its self to 10 times 10 is 100
Answer:
\(1.00\) × \(10^{2}\)
I hope this helps!
1. 50 x 36 =
2. 36/20 =
3. 1,089 - 203 =
4. 1,094 + 2,999 =
Answers
Answer:
1. 1,800
2. 1.8
3. 886
4.4,093
Write the expression: the product of 2 and a number, divided by the difference of 9 and another number
Answers
Answer:
2n ÷ 9 - x
Step-by-step explanation:
The product of 2 and a number, I used "n" to replace the number. Putting a number next to a variable means multiplying.
So we have 2n and divide by the difference (subtracting) of 9 and ANOTHER number, that means we need a different variable for this I used "x".
And that's how I got 2n ÷ 9 - x as my answer.
Hope that helps and have a great day!
A summary of the two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metropolis, Ltd MTP 17.95 18.25 18.28
Suburbia, Inc SBR 5.63 4.98 5.25
Suppose you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks and by how much?
Day 2 is the best by $13.00.
Day 3 is the best by $13.00.
Day 2 is the best by $2.45.
Day 3 is the best by $2.45.
Answers
The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.
Given are the closing prices of two stocks in three days.
If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,
Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25
If the stock is sold in day 2,
Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25
Profit = $1435.25 - $1448.25 = -$13
If the stock is sold in day 3,
Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7
Profit = $1450.7 - $1448.25 = $2.45
The profit is more for day 3 than day 2.
Hence it is best to sell on day 3 by $2.45.
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PLEASE HURRY TAKING A TEST RN
Type the correct answer in each box.
An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure.
The value of x is
degrees, and the value of y is
degrees.
Answers
The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.
What is the value of angle x and angle y?The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;
The value of angle adjacent x = 102⁰
The value of angle x is calculated as;
x = 180 - 102 ( sum of angles on a straight line)
x = 78⁰
The value of angle y is calculated as follows;
y = 115⁰ (corresponding angles are equal)
Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.
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what is the measure of ∠p
Answers
Answer:
63.2
Step-by-step explanation:
The triangles are similar so corresponding angles are congruent. Angle K corresponds to angle P so the answer is 63.2 degrees.
∠p = 180 - 90 - 26.8
∠p = 63.2
What is the value of b?
25-15
3b +25
Answers
Answer:
B=34
Step-by-step explanation:
2b-15+3b+25=180
5b+10=180
5b=170
b=34
An individual borrowed $78,000 at an APR of 6%, which will be paid off with monthly payments of $503 for 25 years.
Answers
Based on the amount that the individual is paying monthly, the total amount that will be paid over the full term of the loan is $150,900
How much will be paid in total?The amount that the individual will pay in total over the loan's full term can be found to be:
= Amount paid per month x Number of years x number of months per year
Solving gives:
= 503 x 25 x 12
= 503 x 300
= $150,900
In conclusion the total amount paid is $150,900.
The rest of the question is:
What is the total amount paid over the full term of the loan?
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in need of help solving this
Answers
Answer:
b is the answer .
Step-by-step explanation:
a + b -b = a
Answer:
a + b - b =a
Step-by-step explanation:
a+b-b = a
because
As a normal step,
b-b =0
a + 0 =a
I AM NOT THAT GOOD AT EXPLAINING, SORRY BUT IF YOU NEED MORE EXPLANATION, I'D BE READY TO HELP.
Aliyyah
Expand ; 3(1-x/2)^2
Answers
Answer:
\(3 {( \frac{1 - x}{2}) }^{2} = 3 \times {(1 - x)}^{2} \div {2}^{2} \\ =3 \times (1 - 2 \times 1 \times x + {x}^{2}) \div 4 \\ = 3 \times (1 - 2x + {x}^{2} ) \div 4 \\ = \frac{3}{4} (1 - 2x + {x}^{2})\)
\( \bold \pink{ \underline{hope \: it \: helps}}\)
HELP PLEASE!!! (FOR 10 POINTS)
The sales tax in town is 8 %. So, the total cost of an item can be written as c+0.008c. What is the total cost of an item that sells for $12?
Answers
The total cost of an item that sells for $12 is $1500.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the sales tax = 8%.
Total cost of an item = $12.
The equation for the total cost of an item = c+0.008c.
Now , 12 = c+0.008c
=> 12=1.008c
=> c = 12/1.008
=> c= $1500.
Hence the total cost of an item that sells for $12 is $1500.
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Order from least to greatest -5, -3, -2.6, 3, 0,-15 , sorry for my english
Answers
Answer:
-15, -5, -3, -2.6, 0, 3
Step-by-step explanation:
Answer:
-15,-5,-2.6,0,3
Step-by-step explanation:
negative goes before positive numbers.
Plant Parts
Add labels to the flower.
(Please help meeeeeee)
Answers
Answer:
1. Can't tell where it's pointing on the picture
2. Anther
3. Filament
4. Pedicel
5. Petal
Step-by-step explanation:
The three angles inside of a triangle add up to HOW MANY degrees?
180
90
360
120
Answers
Answer:
180
Step-by-step explanation:
This is 180 because the specific angles in a triangle will unless an irregularly shaped triangle will equal up to 180.
Please help and thank you
Answers
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
3x+(8x-16) simplest form
Answers
Step-by-step explanation:
3x × 8x- 3x×16
24x -48x
-24x
The volume of a cylinder is 637 cm³. If the radius is 3 cm, what is the height
of the cylinder?
Answers
If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:
637 = π(3²)h
Simplifying:
637 = 9πh
h = 637 / (9π)
h ≈ 7.06
Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.
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