The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
4, 3 2/3, 3 1/3, 3....
In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term
Take for instance
2nd = 4 - 1/3 = 3 2/3
3rd = 3 2/3 - 1/3 = 3 1/3
4th = 3 1/3 - 1/3 = 3
And so on
This means that
First term, a = 4Common difference, d = -1/3So, the explicit rule is
f(n) = a + (n - 1)d
This gives
f(n) = 4 - 1/3(n - 1)
Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)
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Complete question
Consider the sequence 4,3 2/3,3 1/3, 3....
What is the explicit rule for this sequence
Find the surface area of the cube.
You should have atleast 2 steps shown in your work.
(Need help!!!)
Step-by-step explanation:
Each of the six sides is 7 mm x 7 mm = 49 mm^2
times six sides : 6 * 49 mm^2 = 294 mm^2
Answer:Area = Side2 = a2
Therefore, the total surface area of a cube = 6 × (area of each side)
= 6 × a2 = 6a2 Square Unit
soooooooooo
Mrs hanger is painting the following picture of a h to hang in the entryway of her home she has made the following scale as her model the scale is used on the drawing is 1:6 on the scale drawing h is centered on the page and 5/6 inches from the top bottom and sides of the drawing as you can see the h is to be painted red in the center of a rectangular beige background what is the actual width of the painting what is the actual height of the painting what is the actual height of the h actual width of the h through the center actual distance from the left edge of the painting to the left edge of the h
Part E
Isaiah wants to compute his total earnings after picking 10 baskets of each fruit.
Complete the equations and find Isaiah's total earnings. Enter your answers in the boxes.
Apples: 10 x ____ = ____
24+ ___ = a
Peaches: 10 x ____ =
18+____= p
Total: a+p=$ ___
Isaiah's total earnings after picking 10 baskets of apples and peaches each is: $117
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
We are told that Isaiah as already earned $24 picking apples and $18 picking peaches.
Amount for each basket of apple = $3 each
Amount for each basket of Peach = $4.5 each
Thus, for 10 baskets each:
Apples = 10 * 3 = $30
a = 24 + 30
a = $54
Peaches = 10 * 4.5 = $45
p = 18 + 45
p = $63
Total earnings = a + p
= $54 + $63
= $117
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Complete question is:
Isaiah picks fruit at a local orchard. He has already earned $24 picking apples and $18 picking peaches. He earns $3 for each basket of apples and $4.50 for each basket of peaches picked.
Isaiah wants to compute his total earnings after picking 10 baskets of each fruit.
Complete the equations and find Isaiah's total earnings. Enter your answers in the boxes.
Apples: 10 x ____ = ____
24+ ___ = a
Peaches: 10 x ____ =
18+____= p
Total: a+p=$ ___
HELP PLEASEE!! The aquarium has 6 fewer yellow fish than green fish. 40% of the fish are yellow. How many green fish are in the aquarium? Show your work. Show all steps please.
12 Kittens to 15 puppies ratio in
Answer:
4:5 or 4/5 or .8 or 80%
Step-by-step explanation:
divide both by 3. then convert to percent or decimal
What meaning of the statement this: subgroups partition groups into subsets of equal size?
Answer:
This statement means that subgroups divide a larger group into smaller groups, and each of these smaller groups has the same number of things in it. For example, if there are 12 people in a group, and they form subgroups of 3 people each in a group, there will be 4 groups total, and each individual subgroup will have 3 people in it.
A box falls off a window ledge on a tall building. The height of the box above the ground can be found using the function h(t)=-16t^2+150, where r stands for the number of seconds since the box fell.
a). Find the height of the window ledge.
Answer:
The height of the window ledge is the height of the box when t = 0. So, we need to find h(0).
```
h(0) = -16(0)^2 + 150
h(0) = 150
```
Therefore, the height of the window ledge is 150 feet.
Step-by-step explanation:
A student transformed the system of
equations shown below by multiplying
the second equation by a constant and
then adding the resulting equation to the
first equation.
x + 4y = 12
3x - y = 10
Answer:
The answer to your problem is, 3x+6y=9 then -2x-4y=4
Step-by-step explanation:
So first we are going to multiply the first equation by 2 and second equation by 3 and add it.
If there is both x and y terms gets cancelled then we can say there were no solutions at all.
Shown;
A) -2x+4y=4
-3x+6y=6
Which then becomes;
-4x + 8y = 8
-9x + 18y = 18
For, -13x + 26y = 26
B) 3x+y=12-
3x+6y=6
Which we then multiply first equation by 2 and second equation by 3
6x + 2y = 24
-9x + 18x = 18
For, -3x + 20y = 42
C)3x+6y=9
-2x-4y=4
Again multiply first equation by 2 and second equation by 3
6x + 12y = 18
-6x - 12y = 12
Which can equal to:
30
Which both x and y terms becomes 0.
Thus the anwer to your problem is, 3x+6y=9 then -2x-4y=4
Suppose that a random variable X is a discrete variable with the following distribution law P(X=k)=c/2^k, k= 0, 1, 2, . . . , Find the value of the constant c. (Using the normalization property of the distribution law)
Answer:
The normalization property of the distribution law states that the sum of probabilities of all possible outcomes must equal 1. In this case, we have:
P(X=k) = c/2^k, for k = 0, 1, 2, ...
To find the value of the constant c, we need to use the normalization property:
∑ P(X=k) = ∑ c/2^k = c/2^0 + c/2^1 + c/2^2 + ... = 1
To simplify this expression, we can use the formula for the sum of an infinite geometric series:
∑ a*r^n = a/(1-r), where a is the first term, r is the common ratio, and n goes from 0 to infinity.
In this case, a = c, r = 1/2, and n goes from 0 to infinity. So we have:
∑ P(X=k) = ∑ c/2^k = c/2^0 + c/2^1 + c/2^2 + ... = c/(1-1/2) = 2c
Setting this expression equal to 1, we get:
2c = 1
c = 1/2
Therefore, the value of the constant c is 1/2.
Step-by-step explanation:
determine the value of x (asap)
The values of the missing terms are 1) 24 and 2) 1.6.
Given are two similar figures, we need to find the value of x,
According to the definition of similar figures, the ratios of the corresponding sides are equal,
So,
1) GE / EF = RS / TR
5/6 = 20/x
5x = 120
x = 24
2) JH / LK = WX / ZY
3.84 / 2.04 = 3.2 / x
3.84x = 2.04 × 3.2
3.84x = 6.528
x = 1.7
Hence, the values of the missing terms are 1) 24 and 2) 1.6.
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26=-9w-2w-18?????????????????
Answer:
w = -4
Step-by-step explanation:
Hope this helps
if a baseball team has lost 50 matches out of the 120 matches played in total find out their winning percentage
Answer:
58.3%
Step-by-step explanation:
120-50=70 (wins)
120 is 100% wins
70. ??
We multiply 70 by 100% then divide by 120.
11. If the revaluation of the asset is higher than the carrying value, the following entries will be made via the revaluation account; Debit Asset account and Credit Capital account of each partner. True/False?
Answer:
False. If the revaluation of the asset is higher than the carrying value, the following entries will be made: Debit Asset account and Credit Revaluation reserve account. The revaluation reserve account is a balance sheet account and does not affect the capital accounts of the partners directly. However, the revaluation reserve may indirectly affect the capital accounts of the partners if the revaluation reserve is distributed to the partners or used to offset losses in the future. It is worth noting that the specific accounting treatment may vary depending on the accounting standards being used by the company.
Step-by-step explanation:
select the correct answer. which expression is equivalent to this polynomial ? x^2 +12
The expression that is equivalent to this polynomial "x²+12" is option A. (x + 2√3i) (x — 2√3i)
How did we get the value?In mathematics, a polynomial is an expression consisting of variables and coefficients that concern only the operations of addition, subtraction, multiplication, and nonnegative integer exponents.
A. (x + 2√3i) (x — 2√3i)
= (x² + 2√3i)² (i² = -1)
= (x² - 12x (— 1)
= x² + 12
B. (x + 6i) (x - 6i)
= (x² - (6i)²
= x² + 36
C. (x + 2√3)²
= x² + 4√3x + 12
D. (x + 2√3) (x - 2√3)
= x² - (2√3)²
= x² - 12
Therefore, the correct answer is as given above. Option A. (x + 2√3i) (x — 2√3i) is equivalent to the given polynomial.
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The complete question goes thus:
Which expression is equivalent to this polynomial?
x²+12
OA. (x + 2√3i) (x — 2√3i)
B. (x+6)(x-61)
Oc. (x + 2√3)2
OD. (x + 2√3) (x - 2√3)
Claim: The standard deviation of pulse rates of adult males is 12 bpm. For a random sample of 173 adult males, the pulse rates have a standard deviation of 10.6bpm. Find the value of the test statistic.
Based on the standard deviation given and the sample size, the test statistic can be found to be 134.20.
The test statistic can be found by the formula:
= ((Sample size - 1) x Standard deviation of sample²) / Standard deviation of population
Solving gives:
= ((173 - 1) x 10.6²) / 12²
= 19,325.92 / 144
= 134.20
Hence, the test statistic is 134.20.
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Which of the following functions are vertical translations of f(x)=√x?
Select all that apply.
A. K(x)=√√√-5+x
B. n(x) = -7+ √x
C. g(x)=√x -4
D. h(x)=3+√x
E. m(x)=√5x
Answer:
The function f(x) = √x is the square root function.
A vertical translation of a function is a transformation that shifts the graph of the function up or down without changing its shape.
Option (A) is a vertical translation of f(x) because it shifts the graph of f(x) to the right by 5 and then applies three square root operations. However, it is not a vertical translation that shifts the graph up or down.
Option (B) is a vertical translation of f(x) because it shifts the graph of f(x) down by 7 units.
Option (C) is a vertical translation of f(x) because it shifts the graph of f(x) down by 4 units.
Option (D) is a vertical translation of f(x) because it shifts the graph of f(x) up by 3 units.
Option (E) is not a vertical translation of f(x) because it involves multiplying the input of f(x) by a constant factor of 5.
Therefore, the options that are vertical translations of f(x) are (B), (C), and (D).
Step-by-step explanation:
Solve using the elimination method, and also determine whether a system is consistent or inconsistent, and whether the equations are dependent or independent.
Please helppp <3
To solve using the elimination method, we need to eliminate one of the variables.
Multiplying the first equation by 3, we get:
9x = 165 - 21y
Now we can write the system as:
9x = 169 - 22y
9x = 165 - 21y
Subtracting the second equation from the first, we get:
0 = 4 - y
Solving for y, we get:
y = 4
Substituting y = 4 in the first equation, we get:
3x = 55 - 7(4)
3x = 27
x = 9
Therefore, the solution to the system is (x, y) = (9, 4).
The system is consistent and independent, since it has a unique solution.
20 pts
Need help asap!
The probability that the student is a sophomore, given that they are in work, is given as follows:
P(sophomore|work) = 30%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Total outcomes: 3 + 2 + 5 = 10 people at work.Desired outcomes: 3 sophomores at work.Hence the probability is obtained as follows:
P(sophomore|work) = 3/10 = 0.3 = 30%.
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Find the quotient of x+4/x^2 dividend by 2/x
The division of the given algebraic expression is: (x + 4)/2x
How to divide algebraic problems?The division algorithm for polynomials says, if p(x) and g(x) are the two polynomials, where g(x) ≠ 0, we can write the division of polynomials as: p(x) = q(x) × g(x) + r(x).
Where:
p(x) is the dividend.
q(x) is the quotient.
We want to solve:
[(x + 4)/x²] ÷ 2/x
Thus, we can simplify to:
[(x + 4)/x²] * x/2
= (x + 4)/2x
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
The option or function that is NOT an exponential function is (4/7)ˣ.
Why is this so?The function (4/7)ˣ is no exponential because the base (4/7) is smaller or lesser than 1. All exponential functions must have a base that is less than -1 or greater than 1.
The other functions
1) (3/5)ˣ
2) 4ˣ
are both exponential function.
3/5ˣ is a decay function and it's base is less than 1. 4ˣ on the other hand is a growth function. Of course, it's base is greater than 1.
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Kevin is k years old. Ben is 8 years older than Kevin. Hannah is 2 times older than Ben. What is Hannah’s age?
Answer:
2k+16
Step-by-step explanation:
Kevin: k
Ben: 8 years older than k, k+8
Hannah: 2 times Ben's age, 2(k+8)=2k+16
ANSWER PLEASE! It's multiple choice
Answers are: 13FT, 125FT, 313FT, AND 425 FT.
Answer:125
Step-by-step explanation:
the drawing (fountains) was 10 inches apart, but real life was 400. 400/10 = 40. this means that the real life distance is 40x the distance of the drawing.
therefore, multiply 3.125 by 40 as well. you get 125.
Answer: 125 ft
Step-by-step explanation:
Let x be the real remove between the two shows.
At that point, we are able set up the extent:
10 inches / 400 feet = 3.125 inches / x
To illuminate for x, able to cross-multiply and disentangle:
10 inches * x = 400 feet * 3.125 inches
10x = 1250
x = 125 feet
The heights in inches of players on Tracy basketball team are shown. Find the mean of the data:
Player Height. (In.)
58,60,61,59,63
Answers:
56.8in
58.5in
60in
60.2in
Answer:
To find the mean of the data, we add up all the heights and then divide by the number of players:
Mean = (58 + 60 + 61 + 59 + 63) / 5
Mean = 301 / 5
Mean = 60.2 inches
Therefore, the mean height of the players on the Tracy basketball team is 60.2 inches.
The answer is 60.2in.
Step-by-step explanation:
If a company uses standard costs to record its inventory in the general ledger, what would the journal entry be for a purchase of direct materials with a favorable price variance?
The journal entry for the company is Debit - Raw Materials Inventory - Standard Cost, Credit - Accounts Payable - Actual Cost.
When a company uses standard costs to record its inventory in the general ledger, the journal entry for a purchase of direct materials with a favorable price variance would be as follows
Debit - Raw Materials Inventory - Standard Cost
Credit - Accounts Payable - Actual Cost
The debit entry would record the standard cost of the direct materials purchased, and the credit entry would record the actual cost of the direct materials purchased, which is lower than the standard cost due to the favorable price variance.
It's important to note that this journal entry assumes that the company is using a perpetual inventory system, where the inventory account is updated continuously as purchases and sales occur. If the company is using a periodic inventory system, the journal entry would be different and would involve adjusting the cost of goods sold account at the end of the period.
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find the least common denominator
What is the slope of a line that passes through the points (-2, 3) and (4, -12)?Choices -3/2 -5/2 -2/5 -9/2
Answer:
B) - 5/2--------------------------
To find the slope use the slope formula:
[tex]m=\cfrac{y_2-y_1}{x_2-x_1}[/tex], where, [tex]x_1=-2,\ y_1=3,\ x_2=4,\ y_2=-12[/tex]Substitute the coordinates into slope formula to get the slope:
[tex]m=\cfrac{-12-3}{4-(-2)}=\cfrac{-15}{6}=-\cfrac{5}{2}[/tex]The matching choice is B.
Solve for x. Assume that lines which appear to be diameters are actual diameters.
Answer:
x = 9
Step-by-step explanation:
We Know
A circle is 360°
An angle is 85° & one is 130°
Find x
We Take
85° + 130° + 16x + 1 = 360°
216 + 16x = 360°
16x = 144°
x = 9
I've been struggling a lot with interpreting what this problem wants me to find.
The plane departs an airport at 9:00 AM and flies 200 mph southwest. A second plane ldeparts the same airport at 9:30 AM and flies 320 mph northwest. Find the bearing of the second plane from the first one at 10:00 AM.
The reason: I've heard some people say a bearing has to be in one direction (north). I've also heard that a bearing has to be an acute angle and some insist there is an answer to this greater than 90º.
I drew out a diagram with a right triangle, legs of 200 and 160 (320 ÷ 2 for the half hour), separated my right triangle into two triangles with 45º angles, and went from there.
Where the hypotenuse and the 160 side meet, the angle is 51.34º. The 200 side makes a 38.66º angle (both came from arctan). I know for a fact there is an 83.66º angle that can be found.
Trouble is, I'm not sure if that's the actual bearing or not. Everything SEEMS correct there, but I've just heard so many other answers on this that I'm not sure who or what to believe!
Figured I'd see what everyone else thought. It's the "second from the first" that I'm struggling with semantically too. I can do the math just fine here.
Answer:
6.34°
Step-by-step explanation:
You want to know the bearing of a second plane from the first at 10 a.m. when the first leaves at 9 a.m. and flies 200 mph SW, while the second leaves at 9:30 a.m. and flies 320 mph NW.
LocationsThe first plane flies for an hour at 200 mph, so is 200 miles from the airport on a bearing of 180° + 45° west of south, or 225°.
The second plane flies for half an hour at 320 mph, so is 160 miles from the airport on a bearing of 360° -45° west of north, or 315°.
DirectionThe vector in the direction of the second plane from the first is found by subtracting the location of the first plane from the second:
vector of interest = (160∠315°) -(200∠225°)
A suitable calculator can tell you the difference is ...
vector of interest = 256∠6.34°
The second plane is on a bearing of 6.34° from the first.
__
Additional comment
You are correct that an angle of 83.66° is involved. That would be the measure of the direction vector counterclockwise from the +x axis. You want the bearing angle, measured clockwise from the +y axis (North), so the angle you're looking for is 90° -83.66° = 6.34°.
If you work enough of these problems, you will find that it doesn't matter how you measure the angles, as long as you do it consistently. The second attachment shows the arithmetic using distance∠bearing. The effect is to swap the x, and y coordinates so that they are (N, E) coordinates, rather than the usual (E, N) coordinates. This doesn't have to be confusing. A diagram usually helps.
<95141404393>
m/1 = x and m/2 = 2x. Find
the value of 'x'.
Answer:
-m = x is the answer hope it helps
In the data set below, what is the upper quartile?
24 28
28 47 53 55 58 78 79
Submit
Answer:
68
Step-by-step explanation:
the median is the term in the middle (53) the upper quartile is the median of the terms above the median. Since there are an even number of terms, you need to average them (58+78)/2