The substitution that should best be used in solving the recurrence T(n) = 5T(4n/3) + 2 is "n = (4/3)^k".
The idea behind choosing a substitution for a recurrence relation is to simplify the relation and make it easier to solve. In this case, we want to simplify T(4n/3) to something involving T(n). By setting n = (4/3)^k, we can rewrite T(4n/3) as T((4/3)^(k+1)).
This substitution allows us to express T(4n/3) in terms of T(n) and simplify the relation.
T(n) = 5T(4n/3) + 2
becomes
T(n) = 5T((4/3)^(k+1)) + 2
We can then use this substitution to solve the relation using, for example, the Master Theorem.
In conclusion, the substitution "n = (4/3)^k" is the best option because it simplifies the relation and makes it easier to solve.
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i12 + 1 = 1 - i 1 + i 0 2
when the bread doubles its size, how much does the distance between any two raisins will change?
The distance between two raisins will increase by a factor of the square root of 2.
As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.
However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.
This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.
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Which set of numbers could represent the lengths of the sides of a right triangle?
A. 15, 18, 21
B. 7, 24, 25
C. 8, 9, 10
D. 9, 11, 14
Answer: B- 7, 24, 25
Hope this helps :)
Step-by-step explanation:
Use the Pythagorean Theorem
a^2 + b^2 = c^2
49 + 576 = 625
625 = 625
the variables r and s are inversely proportional, and r=7 when s=6. determine s when r=10.
If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .
When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :
⇒ r × s = k, where k is a constant ;
the value of variable "r" = 7 when s = 6,
First , we have to find the value of k:
⇒ k = r × s = 7 × 6 = 42 ;
So, for any value of r and s, the product "rs" will always be equal to 42.
When r = 10, we can use the equation to find s:
⇒ s = k/r = 42/10 = 4.2
Therefore , when r = 10 , the variable "s" is 4.2.
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Please help with this
Answer:
D
Leah spent y
15 times ryan's
ryan spent x
y = 15x
Step-by-step explanation:
A - Leah spent x
15 times more than
Ryan spent y
x = 15 * y
B - Leah spent y
15 more
Ryan spent x
y = x + 15
C- Leah spent x
15 less
Ryan spent y
x = y-15
In the diagram below, ST is parallel to PQ. If SR = 2.4, PQ = 1.8, RQ = 3,
and ST 1.2, find the length of PR. Figures are not necessarily drawn to scale.
PR=
Answer:
PR = 3.6
Step-by-step explanation:
Triangles PQR and STR are similar figures. PQ is the base of triangle PQR just like ST is of triangle STR. PR is parallel to SR and RQ is parallel to RT.
[tex]\frac{Side PQ}{Side ST} =\frac{Side PR}{Side SR}[/tex]
=[tex]\frac{1.8}{1.2} = \frac{PR}{2.4}[/tex]
Cross-multiplying:
=(1.8)(2.4) = (1.2)(PR)
= PR = [tex]\frac{(1.8)(2.4)}{(1.2)}[/tex]
= PR = 3.6
Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept
Answer:
slope = 1/2
y-intercept = -1
Step-by-step explanation:
Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept?
The equation given is: y= 1/2x - 1
y = mx + b
where m = slope and b = y-intercept, so:
slope = 1/2
y-intercept = -1
hussain receives about six telephone calls from friends and family between 6 pm and 8:00 pm. what is the probability that hussain receives more than two calls in the next 30 minutes?
The required probability for the number of phone calls more than two in next 30 minutes is equal to ( 18 / 5)e⁻⁶.
Number of phone calls between 6pm and 8.00 pm 'n' = About 6 calls
Using Poisson's distribution we have,
P ( X = x ) = ( e⁻ⁿ nˣ ) / x!
Probability of receiving more than 2 phone calls in next 30 minutes
= P( X > 2 )
= P ( X = 3 ) + P ( X = 4 ) + P ( X = 5) + P( X = 6)
= ( e⁻⁶ 6³ ) / 3! + ( e⁻⁶ 6⁴ ) / 4! + ( e⁻⁶ 6⁵) / 5! + ( e⁻⁶ 6⁶ ) / 6!
= ( e⁻⁶ 6³ ) / 3! [ 1 + (6 / 4) + (6² / 5× 4 ) + ( 6³ / 6 ×5× 4) ]
= ( e⁻⁶ 6³ ) / 3! [ ( 20 + 30 + 72 ) / 20 ]
= ( 18 / 5)e⁻⁶.
Therefore, the probability of more than two phone calls is ( 18 / 5)e⁻⁶.
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Which measure is equivalent to 3 mi?
1 ft = 12 in.
1 mi = 5,280 ft
Answer: See below
Step-by-step explanation:
First, we will use the conversions that you provided to find how many feet are in 3 miles. Since we know that one mile = 5,280 feet, all we have to do is multiply that number by 3 to find the conversion.
5,280 * 3 = 15,840 feet
Now, we can use the value found above to find how many inches are in 3 miles. We know that 12 inches are in one foot, so we have to multiply 12 by 15,840. This equals 190,080 inches.
I hope this helps, and if you need me to show you the step-by-step work for multiplication, let me know!
19. Becca's birthday is June 10th. Her friend's birthday is November 10th. If Becca's birthday this year is a Wednesday, what day of the week is her friend's birthday this year? (A) Wednesday (B) Friday (C) Saturday (D)Monday (E) Other
A circle has an area of 25m. The radius of the circle is increased by 3. What is the increase in the area of the circle? (A) 24π (B) 64π (C) 39π (D) 36π (E) Other
In a modified ladder toss game, all scores are worth either 4 points or 9 points. Hunter made 100 y more 9 point scores scores when playing that game, and his point total was 755 points. How many than 4 point scores did Hunter made? ) (A) 42 (B)44 (C)41 (D) 43 (E) Other
Answer:
Becca's birthday is June 10th, which is a Wednesday this year. November 10th is exactly 6 months after June 10th, so the friend's birthday is also a Wednesday this year.
The increase in the area of the circle is 64π, not 39π. If the original circle had an area of 25m, then the original radius was 5. The new radius would be 5 + 3 = 8. The new area would be 8^2 * pi = 64 * pi = 64π.
Let X be the number of 4 point scores that Hunter made and Y be the number of 9 point scores. X + Y = total number of scores and 4X + 9Y = 755. Substituting Y = 100 + X, we get 4X + 900 = 755. Solving for X, we get X = 41. Therefore, Hunter made 41 4 point scores.
at the beginning of the week my investment account's balance was 1,459 dollars. if it grows at a constant rate of 4.73/day, what is my account's balance at every point in time during the week? use n to represent the number of days since the week began.
The balance of your investment account at any given point in time during the week can be calculated using the exponential growth formula:
N(t) = N0 * (1 + r)^t, where N0 is the initial balance (1,459 dollars), r is the growth rate per day (4.73/day), and t is the number of days since the week began (n).
For example, if it is the fourth day of the week (n = 4), then the balance of your investment account would be N(4) = 1,459 * (1 + 4.73/day)^4 = 2,719.37 dollars.
The exponential growth formula is a mathematical equation used to calculate the growth of a population over time. It is expressed as N(t) = N0 * (1 + r)^t, where N0 is the initial population size, r is the growth rate, and t is the time in days.
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Frank had 4/7 of a spool of yarn. He used 4/5 of his yarn for a project. What fraction of the spool was used for the project?
Write your answer in the simplest form.
Answer:
f = 4/7 * 4/5 = 16 / 35 Fraction of spool used
4/7 of spool was originally present and Frank used 4/5 of the yarn left on the spool
Jackson is recording the height of his plant in centimeters, every week. The results are in the table below.
Step-by-step explanation:
add it and the answer is 2,453
What is the coefficient of q in the sum of these two expressions?(2/3q−3/4)and(−1/6q−2)
Answer:
the two coefficients are 2/3 and -1/6
the sum of the expressions are = 1 /2 q−r+ −3 /4
hope this helps :)
how many solutions does x^2=7 have in each of the following rings?You need not find the solutions(a) Z/19 (b) Z/21 (c) Z/57
The solution of the expression is Z/57
A ring is a mathematical structure that combines the properties of an additive group with the properties of a multiplicative group.
When we look at solutions to the equation x² = 7 in different rings, we are asking "In what mathematical structures can we find numbers which, when squared, equal 7?"
(a) In the ring Z/19, the solutions are the residue classes modulo 19 that satisfy x² = 7. This means that we only consider the integers 0, 1, 2, ..., 18, and we take their remainders after dividing by 19. In this ring, we use the operations of addition and multiplication modulo 19.
(b) In Z/21, the equation x² = 7 has no solutions. This is because none of the remainders 0, 1, 2, ..., 20 after dividing by 21 can be squared to give 7.
(c) In Z/57, the equation x² = 7 has exactly 2 solutions. This is because there are exactly two residue classes modulo 57 that, when squared, give 7. To find these two solutions, we would need to perform a bit of calculation to determine which residues satisfy x² = 7.
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Which 3-dimensional figure is associated with the volume formula?
Answer:
Prisms
Step-by-step explanation:
The only two associated are rectangles and prisms
NOW
NOW
NOW
NOW
HELP IMMEDIATELY
1) How much would you have to invest in an account earning 8% interest compounded continuously, for it to be worth one million dollars in 30 years?
Answer:
$174,850.10
Step-by-step explanation:
the future value of $7000 at the end of 5 periods at 8% compounded interest is
$10,285.30
so you multiply $10,285.30 x 17 = 174,850.10 that's the amount you have to invest. After thirty years you will have $1,049,100.60
This figure is made from a square and part of a circle. What is the area of the figure, to the nearest whole number square unit?
According to the problem,The area of the figure is approximately 34 square units.
What is the square ?A square is a four-sided plane figure where all sides are equal length and all angles are right angles. It is a two-dimensional shape with four equal-length sides and four equal angles of 90°. Squares are often used in designs and architecture, and are an important part of Euclidean geometry. They are also found in nature, such as in a honeycomb, in a checkerboard pattern, and in tessellations.
To calculate this, we need to calculate the area of the square and the area of the circle's segment. The side of the square is 4 units, so the area of the square is 4 x 4 = 16 square units. The radius of the circle is also 4 units, so the area of the circle's segment is (1/2)πr^2, which is (1/2)π(4^2) = 16π/2 = 16 x 3.14/2 = 24.96 square units.
Therefore, the area of the figure is 16 + 24.96 = 40.96 square units, which is approximately 34 square units to the nearest whole number.
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name and briefly explain at least one alternative method for correcting the external effect that exists between the players. explain how the method would work to achieve a pareto efficient outcome and what effect it would have on the distribution of fish. do not get into the mathematics of the way to correct for the external effect, simply explain it intuitively in no more than 30 words for each alternative method.
One alternative method for correcting the external effect between players is the Coasian bargaining solution. This method allows players to bargain with each other to reach a mutually beneficial outcome that is Pareto efficient.
Another alternative method is a Pigouvian tax. Under this approach, the government taxes each player based on their fishing effort, thus reducing the external effect between them. The revenue generated from the tax is then used to subsidize fishing activities and to finance conservation efforts. This results in a more efficient distribution of fish among the players, as the external effect is reduced.
Finally, another alternative method is the use of tradable fishing permits. Under this approach, a certain number of permits are allocated to each player, and they can trade them with each other in order to achieve a Pareto-efficient outcome. This allows players to internalize the external effect of their decision, as they have to pay for the fishing permits. This results in a more equitable distribution of fish among the players.
Overall, the use of Coasian bargaining, Pigouvian taxes, and tradable fishing permits are all alternative methods for correcting the external effect between players in order to achieve a Pareto-efficient outcome. These methods allow players to adjust their strategies in order to reduce the external effect and to ensure a more equitable distribution of fish among them.
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Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears ,how many pounds of gummy bears did she buy?
Answer:
Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears,how many pounds of gummy bears did she buy?
1/8 pound
Step-by-step explanation:
your bank statement shows a balance of -R500 what does it mean
A bank statement balance of -R500 means that the account holder has an overdraft of R500. This means that the account holder has spent more money than they have in their account and now owe the bank R500. It is a negative balance, which indicates that the account holder needs to deposit funds into their account to bring the balance to zero or above.
A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1 per slice of pizza. Benjamin purchased a membership to this pizza shop. How much would Benjamin have to pay the pizza shop if he bought 7 slices of pizza this month? What would be the monthly cost for
x
x slices of pizza?
Answer:
$27
Cost = 20 + 1x = 20 + x
Step-by-step explanation:
Membership fee is $20 per month. This amount has to be paid whether he buys pizzas or not that month
If x is the number of pizzas, the total cost for 7 pizzas at discounted price of $1 is 20 + 7 x 1 = $27
For x pizzas, the equation is
Cost = 20 + x
Kyle is looking to buy a shirt that normally costs $85. Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items. After the discount, Kyle must pay 6% sales tax on the shirt. How much does Kyle end up spending on this shirt?
Kyle spending on this shirt at end up is, $63.07.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Kyle is looking to buy a shirt that normally costs $85.
Here, Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items.
Hence, The discount price is,
⇒ 30% of 85
⇒ 30/100 × 85
⇒ $25.5
So, The price of shirt after discount = $85 - %25.5
= $59.5
Since, After the discount, Kyle must pay 6% sales tax on the shirt.
Hence, The sales tax is,
⇒ 6% of 59.5
⇒ 6/100 × 59.5
⇒ $3.57
Thus, The amount to pay at endup by Kyle = $59.5 + $3.57
= $63.07
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9) Which inequality represents the solution to the given inequality? State the letter of the correct answer.
-13t≤78
A. t<-6
B. t≤6
C. t>6
D. t>-6
10) For the solution to the inequality in the previous problem, list all integers from -10 through 10 that will make
the inequality a true statement when substituted for "t"? (The integers for -10 through 10 are shown below.)
(-10,-9,-8,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Answer:
see explanation
Step-by-step explanation:
solving the inequality
- 13t ≤ 78
divide both sides by - 13, reversing the symbol as a result of dividing by a negative quantity.
t ≥ - 6
this means that any value of t greater than 6, including 6, is a solution.
listing the solutions from - 10 through to 10 that are solutions when substituted for t
- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6
What is an inequality that can be written in any of the following forms: Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are real numbers and A and B are not both equal to zero?
A. Quadratic Equation
B. Linear Equation
C. Exponentional Equation
D. Linear Inequality
Maya has 7 yards of ribbon. She uses 4 yards to make bows and 1 yard 2 feet for
a wreath. How many feet of ribbon does Maya have left?
Answer:
1 yard and 1 foot
Step-by-step explanation:
7-4=3
3-1 yd and 2 feet
there are three feet in a yard. you can subtract the yard first, leaving you with two yards, then subtract two feet. you will be left with 1 yard and 1 foot.
Solving systems by elimination -4x-5y=8,7x+5y=16
Answer:
(8, -8)
x = 8
y = -8
Step-by-step explanation:
-4x - 5y = 8
7x + 5y = 16
-----------------------
3x = 24
÷3 ÷3
----------------
x = 8
7x + 5y = 16
7(8) + 5y = 16
56 + 5y = 16
-56 -56
----------------------
5y = -40
÷5 ÷5
------------------
y = -8
(8, -8)
I hope this helps!
evaluate the iterated integral. 1 0 s7 cos(s8) dt ds
The value of the evaluated iterated integral is = 0.002
As per the given data the iterated integral is, = integral. 1 0 s7 cos(s8) dt ds
Here we have to evaluate the given iterated integral.
The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,
= f(b) - f(a)
Where,
a = Lower limit
b = Upper limit
f(x) = Integrand
dx = Integrating agent
Thus, ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.
Indefinite integrals are implemented when the boundaries of the integrand are not specified.
= integral. 1 0 s7 cos(s8) dt ds
Integrate the given iterated integral.
We get:
= integral. 1 0 s7 cos(s8) dt ds
= t when s = 0
= 6 t = 0
= ds when s = 1..... t = 1
Replace the assumed terms.
Then we get:
= cos(t)
= cos(t) dt
= [sin(t)]
= [ sin(1) - sin(0) ]
= 0.002
Therefore,
The value of the evaluated iterated integral is = 0.002
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In rectangle QRST QS= 4x 2 and RT = 5x - 1 find the length of the diagonal of QRST
The lengths of the diagonals of QRST is 14units.
In a rectangle, the diagonals are equal in length and bisect each other at 90 degrees. This means that the diagonals divide the rectangle into four congruent right triangles.
Since the diagonals of a rectangle are of equal length. then
QS = RT
4x + 2 = 5x - 1
Simplify and solve for the value of x.
4x + 2 = 5x - 1
x = 3
Substitute the value of x in any of the expression for the length of the diagonal.
QS = 4x + 2
length of diagonal = 4(3) + 2 = 14
Hence, the length of the diagonals QS and RT is 14 units.
The problem seems unreadable, it must have been...
"In rectangle QRST, QS = 4x + 2 and RT = 5x - 1. Find the lengths of the diagonals of QRST."
Attached is the full question together with the diagram that shows the rectangle.
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Help me please I would appreciate it thanks
Using the properties of triangle, the value of x = 10.5 and y = 8.75.
A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.
The sum of the angles of the triangle is 180 degrees.
A triangle's exterior angles add up to 360 degrees.
The shortest side of a triangle is always on the opposite side of its smallest angle.
From the given figure,
If we consider the line measuring 4, divides the triangle into 2 equal halves,
The sides of triangle will be in equal ratio,
⇒ [tex]\frac{5}{y} = \frac{6}{x} = \frac{4}{7}[/tex]
⇒ x = 10.5
⇒ y = 8.75
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