Answers
Answer:
7/6561
Step-by-step explanation:
nth term = a1 r^(n-1) so
9th term = 7* (1/3)^(9-1)
= 7*(1/3)^8
= 7/6561
Related Questions
A home owner wants to purchase two different chairs for the living room, one for in front of the fire place and one for in front of the bay window. An interior decorator arrives at the home with photos of several different chairs, and shows the owner all 72 possible arrangements. Photos of how many different chairs were shown to the home owner?
Answers
Using the combination formula, it is found that photos of 9 different chairs were shown to the home owner.
The order in which the chairs are chosen is important, hence, the permutation formula is used to solve this question.
What is the permutation formula?\(P_{n,x}\) is the number of different permutations of x objects from a set of n elements, given by:
\(P_{n,x} = \frac{n!}{(n-x)!}\)
In this problem, two chairs are chosen from a set of n, and there are 72 different outcomes, hence:
\(P_{n,x} = 72, x = 2\)
\(P_{n,x} = \frac{n!}{(n-x)!}\)
\(72 = \frac{n!}{(n-2)!}\)
\(72 = \frac{n(n - 1)(n - 2)!}{(n-2)!}\)
\(n^2 - n = 72\)
\(n^2 - n - 72 = 0\)
Which is a quadratic function with coefficients \(a = 1, b = -1, c = -72\), hence:
\(\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-72) = 289\)
Taking the positive root:
\(x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{289}}{2} = 9\)
Photos of 9 different chairs were shown to the home owner.
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Multiply the following:
(-4x^5) (2x^6)
Answers
Answer:
-8x^11
Step-by-step explanation:
How much must be invested today at 10 %, compounded continuously, to be worth $271,000 in 10 years? Pick the closest answer. [Use e = 2.71]
a. $250,000
b. $130,000
c. $1,000
d. $10,000
e. No amount will be enough
Answers
The amount should be around $130,000 must be invested today at 10 % to be worth $271,000 in 10 years. A = $271,000k = 0.1t = 10 years P = Ae^{-kt}P = $271,000e^{-0.1*10}P ≈ $108,347.39 The closest answer is b. $130,000.
The question is to find out how much must be invested today at 10 %, compounded continuously, to be worth $271,000 in 10 years. Using the formula for continuously compounded interest: A = Pe^{rt}, where A is the amount at the end of the investment period, P is the principal, e is the exponential function, r is the annual interest rate, and t is the number of years.
A = Pekt, where k = 0.10 is the annual interest rate and e is a constant equal to 2.71, is a more straightforward version of the formula.P = Ae-kt, where A = PektWe are informed that the sum will be $271,000 in total. So, A = $271,000,000 = 0.1 trillion = 10 years. P = Ae-kt; P = $271,00e-0.1*10; P $108,347.39;The closest response is b, which is $130,000.
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Consider these preferences defined overstudent submitted image, transcription available below2+ by (x1' , x2 ')student submitted image, transcription available below(x1'' , x2 '') if x1'+x2' < x1''+x2 '' , in which x1 is the total number of hours worked and x2 is the quantity of particle pollution inhaled.
(a) Are those preferences monotonic? Explain.
(b) Suppose the consumer has exogenous income m > 0 and has strictly positive prices p1 and p2. Which of these bundles would be taken by the consumer? Is the budget constraint binding? Explain why it cannot be that prices are strictly positive if all consumers similar preferences.
(c) Assume that prices are strictly negative. To simplify the interpretation we will denote p1 = −ω and p2 = −e, where ω > 0, e > 0. Furthermore, assume that the consumer has no exogenous income but an initial endowment of good 2, P > 0. Represent graphically the budget set of the consumer and give an economic interpretation: particularly, provide an interpretation of the initial endowment P. (Hint: when interpreting the budget constraint, try to isolate what corresponds to expenditures by the consumer and what corresponds to money earned by the consumer)
(d) Characterize the optimal selection of the consumer depending on whether ω > e or e > ω. You can solve the problem with a graph by drawing indifference curves alongside the budget set. Provide an interpretation of these choices.
Answers
a) Given preferences are not monotonic.
b) The budget constraint is binding and the consumer cannot afford that bundle.
c) The interpretation of these choices is that the consumer maximizes their utility.
(a) These preferences are not monotonic. Monotonicity means that if one bundle is preferred to another, any bundle with more of both goods should also be preferred. In this case, if x1'+x2' < x1''+x2'', it does not necessarily mean that x1'+x2' < x1''+x2'' for all bundles with more of both goods.
(b) To determine which bundle would be chosen by the consumer, we need to compare the total expenditure on each bundle to the consumer's income. If the total expenditure on a bundle is less than or equal to the consumer's income, then that bundle would be chosen.
If the total expenditure exceeds the consumer's income, then the budget constraint is binding and the consumer cannot afford that bundle.
(c) When prices are strictly negative (p1 = -ω, p2 = -e), the budget set can be represented graphically as a set of bundles that the consumer can afford.
The initial endowment P represents the amount of good 2 that the consumer already possesses without having to spend any money. It is a starting point for the consumer's choices.
(d) To characterize the optimal selection of the consumer, we need to consider whether ω > e or e > ω.
If ω > e, the consumer's optimal choice would lie on the highest attainable indifference curve that is tangent to the budget set.
If e > ω, the optimal choice would lie on the indifference curve that is tangent to the budget set at a point where the consumer exhausts their initial endowment P.
The interpretation of these choices is that the consumer maximizes their utility by selecting the bundle that provides the most satisfaction given their budget constraints and initial endowment.
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Maddy had a piece of ribbon that was 3 yards long. She used this riboon to make
bows. Each bow was made from a piece of ribbon that was yard long. The situation
can be represented by the equation 34 47 4 = 42. Which statement best describes
what the quotient 4 2/3 represents?
Answers
The statement that best describes what the quotient represents in the situation above is: "Maddy made 4 bows from the piece of ribbon and had 2/3 yards of a yard left." (Option C)
What is the rationale for the above answer?Note that the length of the piece of ribbon Maddy used is 31/2 yards or 7/2 yards.
We also know that the length of the ribbon required to make a bow is 3/4.
Hence the number of bows made is:
7/2 ÷ 3/4
= 7/2 * 4/3
= 28/6
= 14/3
= 4 2/3
Thus it is correct to state that Maddy made 4 bows from the piece of ribbon and had 2/3 of a yard remaining.
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Full Question:
Maddy had a piece of ribbon that was 31/2 yards long. She used this ribbon to make bows. Each bow was made from a piece of ribbon that was 3/4 yard long. This situation can be represented by the equation 31/2 ÷ 3/4 - 42/3. Which statement best describes what the quotient represents in the situation above?
A Maddy had bows that were each 42/3 yards long.
B Maddy had 42/3 yards of ribbon left after making the bows.
C Maddy made 4 bows from the piece of ribbon and had 2/3 yards of a yard left.
D Maddy made 4 bows from the piece of ribbon and had enough left for 2/3 of a bow.
3. Of the students in Liliana's homeroom, of
them have brown hair, 1/2— have black hair,
and 1/3 have red hair. How many times more
10
students have brown hair than black or red?
(Example 2)
Answers
Therefore, students in Liliana's homeroom have remaining students 0.192 times more students with brown hair than black or red.
To find out how many times more students have brown hair than black or red, we need to compare the number of students with brown hair to the combined number of students with black and red hair.
Let's assume that there are a total of 100 students in Liliana's homeroom for simplicity.
Of these 100 students, 1/2 of them have black hair, which is
1/2 * 100 = 50 students.
Similarly, 1/3 of the students have red hair, which is
1/3 * 100 = 33.33 students
(rounded to the nearest whole number).
The number of students with brown hair is 100 - (50 + 33.33) = 16.67 students (rounded to the nearest whole number).
Therefore, there are 16 students with brown hair.
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Students with brown hair are approximately 0.36 times more than students with black or red hair.
In Liliana's homeroom, some students have brown hair, some have black hair, and some have red hair. The question asks how many times more students have brown hair than black or red hair.
To solve this problem, we need to find the number of students with each hair color. Let's say there are 30 students in total.
To find the number of students with brown hair, we multiply the fraction of students with brown hair (3/10) by the total number of students (30). 3/10 * 30 = 9 students with brown hair.
To find the number of students with black hair, we multiply the fraction of students with black hair (1/2) by the total number of students (30). 1/2 * 30 = 15 students with black hair.
To find the number of students with red hair, we multiply the fraction of students with red hair (1/3) by the total number of students (30). 1/3 * 30 = 10 students with red hair.
Now, we compare the number of students with brown hair to the combined number of students with black and red hair. The combined number is 15 (black hair) + 10 (red hair) = 25 students.
The question asks how many times more students have brown hair than black or red hair. To find this, we divide the number of students with brown hair (9) by the combined number of students with black and red hair (25).
9 / 25 = 0.36
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Find the cube of (x-1/3x)
Answers
Answer:
2/3x
Step-by-step explanation
Answer:
(x³-3x²-3x-1) / (27x³)
Step-by-step explanation:
((x-1) / (3x))³
= (x-1)³ / /3x)³
(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1
then:
(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)
What does, 0.201 L x 1000 mL, equal?
Answers
Answer:
2.01 × 10-7 m6
Step-by-step explanation:
THANKS
PA MARK
3 ÷ 4 on number line
Answers
Take a look at the picture below to see how 3/4 looks when represented on a number line.
This is further explained below.
What is a number line?Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers.
It is generally accepted that a real number may be assigned to each point on a number line and that each real number can be assigned to a point.
In conclusion, consider the image below for the number line representation of 3/4
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on a number line, 1.38 would be located. choose all answers that make a true statement
A. to the right of 1.29
B. to the left of 1.36
C. between 1 and 2
D.between 0 and 1
Answers
Awnser: C, A.
Reasoning: On a number line, the bigger number is to the right tthe lower number. for A. For C, it is between 1 and 2 because the number is 1.38.
compute eight rows and columns in the romberg array
Answers
The Romberg array is a table of values that is used to estimate the value of a definite integral. To compute the Romberg array, we use the Richardson extrapolation method, which is a process of successive approximation.
To compute the eight rows and columns of the Romberg array, we begin by splitting the integration interval into two equal-length subintervals. The trapezoidal method is then applied to each subinterval to produce two estimates of the integral. The Richardson extrapolation method is then used to get a better estimate of the integral based on these two estimations. This operation is continued, splitting the subintervals into smaller and smaller subintervals, until the Romberg array has the necessary number of rows and columns.
The Romberg array's general formula is as follows:
R(m,n) = (4^n R(m,n-1) - R(m-1,n-1)) / (4^n - 1)
where R(m,n) is the value of the integral estimate at row m and column n in the Romberg array.
The first column of the Romberg array contains the estimates obtained by the trapezoidal rule, while the subsequent columns are obtained by applying the Richardson extrapolation method using the values in the previous column.
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Two roots of a 3-degree polynomial equation are 5 and -5. Which of the following cannot be the third root of the equation ?
0
-5i
-5
5i
5
Answers
Answer:
- 5i and 5i
Step-by-step explanation:
The Fundamental theorem of Algebra states that a polynomial of degree 3 has 3 roots, real and/ or complex.
Complex roots occur in conjugate pairs.
Given 2 real roots x = 5, x = - 5
There cannot be complex roots as they occur in pairs which would result in the polynomial having 4 roots instead of 3.
Which set of coordinates is NOT a function?
O {(5,5), (3, 9), (2, -1), (5, 8)}
O {(2,5),(3,9),(4, -1), (5,9)}
O {(-2,-5).(-3,5),(4,-5), (5,5)}
Answers
Answer:
O {(-2,-5).(-3,5),(4,-5), (5,5)}
Step-by-step explanation:
brainest plz
Put the following numbers in order from greatest to least. -3, -6, 2, 0, -1 4/5
Answers
The first step to solve this exercise is to write the Mixed number as a decimal number. You can do it by dividing the numerator by the denominator of the fractional part and adding the quotient to the Whole number part, as follows:
\(1+\frac{4}{5}=1+\text{0}.8=1.8\)So:
\(-1\frac{4}{5}=-1.8\)Knowing that Positive numbers are greater than zero and knowing that Negatives numbers are less than zero, we can order the given numbers from greatest to least, as you can see below:
\(undefined\)A sports camp places it's participants on teams. Each team will have 8 members. There are 3208 people registered to participate.
Answers
The number of teams that can be formed is 401
Finding the number of teams:
To determine the number of teams that can be formed with the given number of participants, we need to divide the total number of participants by the number of members per team.
Here we have
Number people registered = 3208
Number of members each team will have is 8 members
The number of teams that can be formed is equal to 3208 ÷ 8
Number of teams = 3208/8 = 401
Therefore,
The number of teams that can be formed is 401
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in (figure 1) take the half-cylinder's radius and length to be 3.4 cm and 15 cm, respectively.
Answers
The flux through the half cylinder will be -75.48 Nm² / C
How to illustrate the cylinder?It should be noted that the projected surface will be the rectangular surface that is formed by the diameter of the half cylinder.
Therefore, A = 2r × L.
where r = 3.4cm = 0.034cm.
L = 15cm = 0.15m
A = 2 × 0.034 × 0.15
A = 0.0102m²
It should be noted that area vector is towards the negatives m x direction and electric field is towards positive direction. This will be illustrated as:
= 7.4 × 10³ × 0.0102 × (-1) Nm² / C
= -75.48 Nm² / C
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Complete question
take the half-cylinder's radius and length to be 3.4 cm and 15 cm, respectively. Calculate the flux through the half cylinder
AABC ~ AQRS
Find the missing side length, m.
R
3
A
B
2
C
10
m = [?]
4
S
![AABC ~ AQRSFind the missing side length, m.R3AB2C10m = [?]4S](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/QZHtTDEkpno6Twntzac6mmQSaUsrOzEH.png)
Answers
Answer: 5
Step-by-step explanation:
these two triangles are a dilation of each other. triangle QRS is a dilation of triangle ABC times two
pythagorean theorem calc: find a, b=12, c=37
Answers
Answer:
a = 35
Step-by-step explanation:
\(a^2+b^2=c^2\\a^2+12^2=37^2\\a^2+144=1369\\a^2=1225\\a=35\)
Mary Sweet works in a pizza store where busiest days fall on the weekend.
She receives time -and-a-half pay on Saturday and double time on
Sundays. She is paid $10.75 per hour and work 30 hours regular. This
weekend she worked 3 1/2 hours on Saturday and 5 hours on Sunday. What
is her total pay?
Answers
Answer:
$10.75 x 3 1/2 = $37.625 (rounded to the nearest cent: $37.63). $10.75 x 5 = $53.75. $37.625 + $53.75 = $91.375. (rounded to the nearest cent: $91.38) hope this helps
Step-by-step explanation:
- Zombie
Helppppp what is the answerrrr????
Answers
just multiply all the digits
which type of drive is typically installed in a 5.25 inch (13.34 cm) bay?
Answers
An optical drive, like a DVD or Blu-ray drive, or a front panel with various sorts of connectors, like USB or audio, are commonly installed in a 5.25 inch (13.34 cm) bay.
What is a drive?
A disc drive is a computer component that saves and retrieves data, information, files, applications, and other things from discs. The drive is frequently identified by its letter (your drive letter may differ). The "C: drive" is the standard designation for a hard disc drive (also known as a fixed disc).
An optical drive, like a DVD or Blu-ray drive, or a front panel with various sorts of connectors, like USB or audio, are commonly installed in a 5.25 inch (13.34 cm) bay. Floppy disc drives were also utilized for it in the past, although they are now less typical.
Hence, An optical drive, like a DVD or Blu-ray drive, or a front panel with various sorts of connectors, like USB or audio, are commonly installed in a 5.25 inch (13.34 cm) bay.
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The 5.25-inch bay in computers is typically used to install optical drives, such as CD-ROM, DVD, or Blu-ray drives.
Explanation:The type of drive typically installed in a 5.25 inch (13.34 cm) bay is the optical drive, such as a CD-ROM, DVD, or Blu-ray drive. These drives are designed to fit into this larger bay size, which was originally intended for floppy disk drives in older computer models. It's worth noting that modern computers now predominantly use smaller bays (such as the 3.5-inch bay for hard drives) as disk-based data storage has become smaller and more efficient.
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when will i know when to add or when to subract
Answers
Answer:
Look below:
Step-by-step explanation:
adding is when u see 6 + 10. the plus sign ( the cross ) means to add. Subtract is using the minus sign: 6 - 10.
Answer:
You will know when to add or subtract because of keywords and symbols.
Step-by-step explanation:
Most addition and subtraction problems have keywords that tell you what operation to use. For example, so keywords that tell you that you have to add are altogether, sum, together, and a few other words. Some examples of subtraction problems are less than, and a bunch of other words.
Hope This Helps :)
I need help on this one. it says solve for w. and it says w-8=32. will someone help plz thx.
Answers
Answer:
w= -4
Step-by-step explanation:
First we know 8 x 4 is 32 so then we make the 8 negative
and divide -8 by 32 which is -4
You can check it by doing -4 x -8 which is 32!
Remember-
1. When you multiply two negatives it equals a positive.
2. You can check by plugging -4 where w is then solving.
3. If there is a subtraction next to a number (w-8) then whichever number the subtraction sign is in front of is negative.
4. If a variable is next to a number it means to multiply the variable by the number.
PLEASE HELP ME I NEED HELP FAST PLEASEE
Answers
Answer:
20cm
Step-by-step explanation:
1. First find the area of the triangle
a = 1/2 × base × h
a = 1/2 × 10 × 11
a = 55cm²
2. Then times the area of the triangle by 8 to find the area of the rectangle
55 × 8 = 440cm²
3. Find the width of the rectangle:
The area of a rectangle is = l × w
22 × width = 440cm²
width = 440 ÷ 22
width = 20cm
Answer: Width = 20
Step-by-step explanation:
Give the area of triangle = x
So the area of rectangle = 8x
the area of triangle = (11 × 10) ÷ 2 = 55
So the area of rectangle = 8(55) = 440
The area of rectangle = W × L
So 440 = W × 22
W = 20
please give me a brainliest answer
Given θ is in the third quadrant and φ is in the second quadrant, sin θ=-5/13 and tanφ=-8/15 evaluate cos(θ-φ)1) 140/2212) 220/2213) -220/221
Answers
we know that
\(\cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\cos \varphi\)Now, we have to find every value in the formula using the identities.
Now, substitute the values in the formula:
\(\begin{gathered} \cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\sin \varphi \\ =\frac{-12}{13}\times\frac{-15}{17}+\frac{-5}{13}\times\frac{8}{17} \\ =\frac{180}{221}-\frac{40}{221} \\ =\frac{140}{221} \end{gathered}\)Thus, the correct answer is 140/221.
2x + y = -4
-3y = 2x + 12
Answers
Answer:
x = 0 and y = -4
Step-by-step explanation:
2x + y = -4...................................(i)
-3y = 2x + 12................................(ii)
from (i)
2x+y=-4
=> y=-4-2x
again from (ii)
-3y=2x+12
=> -3(-4-2x)=2x+12
=> 12+6x=2x+12
=> 6x-2x=12-12
=> 4x=0
=> x= 0
now,
y=-4-2(0)
=> y=-4-0
=> y=-4
What is the answer of the question
Answers
probably the one cut off
Answer:
n - 8 = 20
Step-by-step explanation:
convert the number into a scientific notation
Answers
how to solve:
Show all work to identify the asymptotes and state the end behavior of the function
Answers
The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.
As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.
ascending asymptotes
There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.
horizontal asymptotes:
When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.
Given the function is f(x) = 6x/x-36
limx→±∞ 6x/x-36
= limx→±∞ 6/1-36/x
= 6 ⇒ horizontal asymptote: y = 6
Consider denominator = 0 ↔ x-36 = 0 ↔ x=36
limx→₊₂₅ 6x/x-36
= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36
End behavior of f(x):
As x → -∞ or x → ∞, f(x) → 6.
Hence we get the asymptote and the end behavior of the function.
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Reuben made $247 for 13 ours of work.
At the same rate, how many hours would he have to work to make $171 ?
pls help!!!
Answers
Answer:
9 hours
Step-by-step explanation:
We can use a ratio to solve
247 dollars 171 dollars
---------------- = -------------
13 hours x hours
Using cross products
247* x = 13*171
247x =2223
Divide each side by 247
247x/247 =2223/247
x=9