Answer:
Step-by-step explanation:
We know that there is no rational number which when multiplied with 0, gives 1. Therefore, the rational number 0 has no reciprocal.find a recurrence relation for the number of bit strings of length n that contain three consecutive 0s. b) what are the initial conditions? c) how many bit strings of length seven contain three consecutive 0s?
a) A recurrence relation for the number of bit strings of length n that contain three consecutive 0s :
a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3) for n ≥ 3
b) The initial conditions are:
a_0 = a_1 = a_2 = 0 and a_3 = 1
c) There are 47 bit strings of length seven contain three consecutive 0s
Let s_n be a string of length n that does not have 3 consecutive 0's, and a_n be the number of strings that contain three consecutive 0's
Consider a string of length n -1 that does not have 3 consecutive 0's, s_(n-1)
If we add 1 to this string, then we get a string s_n.
Consider a string s_(n-2)
If we add 10 at the end, then we get a string s_n
Now consider a string s_(n-3)
If we add 100 at the end we get a string s_n.
Now we got all possible strings s_n: that end in 1 (i.e. the last 3 digits could be 001, 011, 101 and 111),
Those strings that end in 10 (i.e. the last 3 digits could be 010 and 110)
and those strings that end in 100. There are no other possibilities without having 3 consecutive zeros.
In the third case, there are a_(n-3) possibilities. And, in the fourth case, there are 2^(n-3) possibilities.
Hence the recurrence relation is
So, a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3) for n ≥ 3
The initial conditions are a_0 = a_1 = a_2 = 0 and a_3 = 1
The recurrence gives the sequence of positive integers 0, 0, 0, 1, 3, 8, 20, 47, 107, 238, 520, 1121, 2391, . . . .
Hence there are a_7 = 47 bit strings of length seven that contain
three consecutive 0's.
Therefore, a) the recurrence relation:
a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3) for n ≥ 3
b) Initial conditions: a_0 = a_1 = a_2 = 0 and a_3 = 1
c) there are 47 bit strings of length seven
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What i 464 divided by 60 with a remainder?
(trying to figure out how many hour i 464 minute)
When we divide the 464 by 60 we get the following remainder in our answer that is 44.
What do math remainders mean?The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.
Briefing :7.733333333333333
=7 44/60 ⇔ 7 R 44
464 divided by 60
=7 with a remainder of 44
Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:
464 divide by 60 yields a quotient and residual of 7 R 44.
464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.
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PLEASE HELP MEE I DONT UNDERSTAND
A supervisor keeps record about her team she worked out the value of sales each salesperson made this morning
The total value of the sales today is £1581 and the total value of the sales for each salesperson today is:
Mo = £330 + £247 = £577,
Daz = £180 + £259 = £439,
Colin = £300 + £265 = £565,
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
The value of sales each salesperson made this morning from the bar chart:
Mo = £330, Daz = £180, Colin = £300,
The value of sales each salesperson made this afternoon from the table given:
Mo = £247, Daz = £259, Colin = £265,
so, the total value of the sales today is :
= £330 + £180 + £300 + £247 + £259 + £265
= £1581.
also the total value of the sales for each salesperson today is:
Mo = £330 + £247 = £577,
Daz = £180 + £259 = £439,
Colin = £300 + £265 = £565,
Hence, the total value of the sales today is £1581 and the total value of the sales for each salesperson today is:
Mo = £330 + £247 = £577,
Daz = £180 + £259 = £439,
Colin = £300 + £265 = £565,
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The first barn contained 3 times more hay than the second one. After 20 tons of hay
were removed from the first barn and 20 tons were added to the second barn, the
amount of hay in the second barn was -
of the amount remaining in the first barn.
How many tons of hay were there in each barn?
Answer:
find the size of unknown angle in the following figure
Step-by-step explanation:
angle PQR=115°angle POR=xref. angle POR =2pQRthe solve by putting the given valu
work: solve the system of equations.
2) Xochitl is going to a carnival that has games and rides. Each game costs $2.50 and each ride
costs $5. Xochitl spent $30 altogether on 9 games and rides Graphically solve a system of
equations in order to determine the number of games Xochitl played and the number of
rides Xochitl went on, y.
6 games are played by Xochitl and 3 rides went on by Xochitl
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Xochitl is going to a carnival that has games and rides
The cost of each game is $2.50 and cost of each ride is $5.
Xochitl spent $30 altogether on 9 games
Let x represents the number of games and y represents the number of rides.
By the given information we form two equations.
x+y=9...(1)
2.5x+5y=30...(2)
From equation (1)
x=9-y
Now plug in x value in (2)
2.5(9-y)+5y=30
22.5-2.5y=30
Subtract 22.5 on both sides
-2.5y=30-22.5
-2.5y=7.5
Divide both sides by 2.5
y=3
x+y=9
x+3=9
x=6
Hence, the number of games Xochitl played is 6 and the number of rides Xochitl went on is 3.
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Customers of a certain credit card earn points for using the card. The table below shows the number of points earned for the amount spent.
Answer:
Step-by-step explanation:
18/2 = 9
36/4 = 9
72 / 8 = 9
each dollar spent appears to earn the same number of points
points / dollars = 9
points = 9 · dollars
dollars = points / 9
dollars = 81/9
dollars = 9
The rectangular floor of a classroom is 30 feet in length and 35 feet in width. A scale drawing of the floor has a length of 6 inches. What is the perimeter, in inches, of the floor in the scale drawing?
HURRY PLEASE!!!!!!!!!!!!!!!!!!
Answer:
7 feet
Step-by-step explanation:
Because they divided the length by 5 to get the scaled length so you would do the same for the width.
Answer:
26 inches squared
Step-by-step explanation:
If the real length is 30 feet and the scale drawing is 6 inches its 5:1
So if the actual width is 35 feet the scale drawing will be 7 inches
The perimeter is the sum of all sides of the rectangle, 2 sides have 6 inches and the other 2 sides are 7 inches
6+6+7+7= 26
The bank
agrees to give you a loan of
$45,000 with 2% simple interest over 5 years.
How much will your monthly payments be?
The monthly payment will be $84.375 to the bank.
What is simple interest?
The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.S.I = Pnr / 100
where P = prinicipal
n= number of years
r = rate of interest
= 45000 * 2 * 8 / 100
= 810000 /100
= $8100
where, the divide by number of months
Balance= 8100 / 96
= $84.375
Hence, the monthly payment will be $84.375 to the bank.
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The following scores represent students’ test grades in Mr. Preisser's fashion class.
Test Scores
798883937988839379888393798883937988
What is the median score for Mr. Preisser's fashion class?
Answer:
Median: 85.5
Step-by-step explanation:
Knowledge Needed
Median is the middlemost value of the data set.
For example, we have a data set:
1, 7, 5
Line up in least to greatest.
1, 5, 7
Median is 5.
If there is an even amount of terms, the value of the median is the average of the 2 middlemost terms. For example:
1, 7, 16, 8
Line up in least to greatest.
1, 7, 8 , 16
(7 + 8)/2, average: 7.5
Median is 7.5
Question
Test Scores:
79 88 83 93 79 88 83 93 79 88 83 93 79 88 83 93 79 88
Line them up in least to greatest.
79 79 79 79 79 83 83 83 83 88 88 88 88 88 93 93 93 93
Middle of the set: 83 & 88 (Because there is an even amount of terms).
83 + 88 = 171
171/ 2= 85.5
Median: 85.5
explain how regression toward the mean can describe two friends who have a fight then later go to the movies together.
Given the circumstances of the question, it is feasible that the two friends would feel that they overreacted during the argument, and as a result, they decide to see a movie together to make up for it.
Regression toward the mean is a statistical condition that involves events that the outcomes produce based solely on chance rather than on real facts. Therefore, it is impossible to forecast with precision what will happen in a regression towards the mean.
Example
Two military units are brought back, one with 20% casualties and the other with 50%. He compliments the first while criticizing the second. The two units return with the opposite outcomes the following time. He "learns" from this experience that praise reduces performance and berating strengthens it.
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0. 5*
Zach and Naomi are studying geometric transformations. Zach is able to
move the triangle A to A' using the following sequence of basic
transformations:
1. Reflection across the x-axis
2. Reflection across the y-axis
3. Translation two units to the right
864
y
A
2
ON 4
-8-6-4-20 24 68
-2-
Jö
6
-8-
A
X
Naomi claims that the same three transformations, done in any order will
always produce the same result. Zach disagrees. Who is correct?
Answer:
Zach is correct
Step-by-step explanation:
You want to know if reflection across the two axes and translation right will achieve the same effect if the transformations are done in any order.
TransformationsTranslation right adds a value to the x-coordinate.
Reflection over the y-axis changes the sign of the x-coordinate.
If the order of these two transformations is changed, the result will change.
Example
Consider point (0,0) and the translation right 1 unit.
Reflection, then translation: (0, 0) ⇒ (0, 0) ⇒ (1, 0)
Translation, then reflection: (0, 0) ⇒ (1, 0) ⇒ (-1, 0)
Zach is correct that the transformations ...
Reflection over the x-axisReflection over the y-axisTranslation 2 units rightcannot be done in any order.
Answer:
Zach
Step-by-step explanation:
17. Louis is offered an interest rate of 6.35%
for an investment with continuous
compounding. What is his equivalent rate
of interest with simple compounding?
[A] 1.23 or 12.3%
[B] 0.0593 or 5.93%
[C] 0.423 or 42.3%
[D] 0.0656 or 6.56%
[E] 0.0615 or 6.15%
The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Louis is offered an interest rate of 6.35% for an investment with continuous compounding,
Here, P will be the same, the amount will be the same and the time period will be the same then,
The amount in simple compounding = The amount in continuous compounding
[tex]P(1 + r)^t = Pe^{Rt}[/tex]
Here, r is the rate of interest for simple compounding,
[tex]1 + r = e^{0.0635}[/tex]
r = 1.0656 - 1
r = 0.06556
r = 0.0656
r = 6.56%
Thus, the rate of interest for simple compounding is 6.56%.
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{(a^2-16)÷(a^2-25)}÷{(a^2-2a-8)÷(a^2+10a+25)}
The answer is -[tex]\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}[/tex]
Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.
In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.
The equation is :
[tex]\frac{a^{2} - 16 }{ a^{2} - 25 }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
=[tex]\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
= [tex]\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}[/tex] ÷ [tex]\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}[/tex] ( by applying middle term factor method)
(using [tex]a^{2} - b^{2}[/tex] formula )
= [tex]\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}[/tex] ÷ [tex]\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}[/tex] ( by applying middle term factor method)
=[tex]\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}[/tex] ÷ [tex]\frac{(a + 2) ( a -4)}{( a +5) (a+5)}[/tex]
= [tex]\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}[/tex] * [tex]\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}[/tex]
=[tex]\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}[/tex]
so, the answer is - [tex]\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}[/tex]
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Using the net below, find the surface area
of the triangular prism.
20 cm
9 cm
8cm
6 cm
9 cm
20 cm
Surface Area = [?] cm²
Answer:
Get math teacher
Step-by-step explanation:
go talk to them.
what would be the coefficient of determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03?
The coefficient of determination if the total sum of squares is 23.29 and the sum of squares due to regression is 10.03 is 0.43
How to calculate regression?
The standard formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
Here we need to find the coefficient determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03.
Here we know that the value of the following are given,
Sum of square = 23.29
Sum of regression = 10.03
Then the coefficient determination is calculated as,
The coefficient of determination r2 = SSR/SST.
When we apply the value, then we get,
=> 10.03/23.29
=> 0.43
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At a restaurant, the bill comes to $70. If you decide to leave a 11% tip, how much is the tip? Give dollars and cents (like 1.23)
For the first 30 km, the bicyclist rode with a speed of v km/hour. For the remaining 17 km he rode with a speed which was 2 km/hour greater than his original speed. How much time did the bicyclist spend on the entire trip? Let t be the time (in hours), and find t in terms of v if v=15 and if v=18.
Answer:
t= 2.52 hours
Step-by-step explanation:
it is given that for first 30 km, the speed of bicyclist is v km/hour
time taken to cover first 30 km is given by
( )
for next 17 km the speed of bicyclist is 2 km/hour greater than his original speed
so the speed to cover next 17 km = v+2
time taken to cover next 17 km is given by
now total time t spent by the bicyclist to cover entire trip is given by
now if v=18 , we have
now to add fractions we make the denominator same
Hence we will find the LCM of 18 and 20
LCM of 18 and 20 = 180
now we need to make both the denominator equal to 180
hours (approx)
Hope it helps :) Make me as brainlest!
PLEASE HELP- ALGEBRA 2
PICTURE WILL BE PROVIDED
Graph each system of inequalities. Name the coordinates of the vertices of
the feasible region. Find the maximum and minimum values of the given
function for this region.
Answer:
Step-by-step explanation:
We need to graph all the given constraints(inequalities). The intersection of the of all the graphed system of inequalities gives the vertices of the feasible region.
The first inequality is .
This is very simple to graph. It is the region bounded by the horizontal lines,
and .
The next constraint or inequality is
To graph this inequality, we need to graph the corresponding linear equation .
We plot the intercepts and .
We then draw a solid line through the points.
Next, we test the origin to determine which half plane to shade.
This statement is true so we shade the lower half plane.
We now graph the inequality,
To graph this inequality, we need to graph the corresponding linear equation .
We plot the intercepts and .
We then draw a solid line through the points.
Next, we test the origin to determine which half plane to shade.
This statement is true so we shade the lower half plane.
The feasible region is shown in the above diagram.
The vertices of the feasible region are;
We substitute the vertices into the objective function to obtain;
Therefore the maximum value is and it occurs at .
The minimum value is and it occurs a
ANSWER TO QUESTIONS 14 We need to graph all the - 1
Please help me thank you
Step-by-step explanation:
3.1×10⁵ ÷ 5.4×10⁵
= (3.1/5.4) × 10^5-5
=0.5741 × 10⁰
= 5.7 × 10^-1
Quadrilateral ABCD is rotated 90° clockwise to produce A'B'C'D' Is each statement true?
AB=A'B'
If AC BD, then A'C' B'D'.
m2ABC
Yes No
000
PLEASE HELPP
Rotation of a shape is a type of transformation. The required answers are:
1. AB=A'B' (YES)
2. AC II BD, then A'C' II B'D' (YES)
3. m<ABC < m<A'B'C' (NO)
A quadrilateral is a family of shapes which have four sides. Examples are square, rectangle, rhombus etc.
Transformation is a process which can be used to change the orientation or dimensions of a given figure or shape called an object. Some types of transformation are: rotation, translation, reflection, and dilation.
Rotation implies turning an object at a certain angle in a specific direction. The direction could be either clockwise or counterclockwise.
NB: Rotating an object changes only its orientation, but not the length of its dimensions or angles.
So that the required answers to the questions are:
1. AB=A'B' (YES)
2. AC II BD, then A'C' II B'D' (YES)
3. m<ABC < m<A'B'C' (NO)
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2. Name all angle pairs and what makes
them "special".
8
5
7
6
3
2
Answer:
1 & 3, 2 & 4, 5 & 7, and 6 & 8 are vertically opposite angles
4 & 8, 3 & 7, 1 & 5, and 2 & 6 are corresponding angles
4 & 6 and 3 & 5 are alternate angles
1 & 2, 2 & 3, 3 & 4, 1 & 4, 5 & 6, 6 & 7, 7 & 8, and 5 & 8 are supplementary angles
State if the two triangles are congruent based on the given information. If they are, state
how you know (SSS, SAS, ASA, or HL). (2pts each)
By SAS congruence, the triangles LMO and LNO are concurrent.
What is congruent triangles?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.If two sides and the included angle of one triangle are congruent with two sides and the included angle of another, the two triangles are congruent.Here given,
LM ≅ ON
∠ M ≅ ∠ N
From the figure it is clear that, the side LO is shared by both triangles.
So, in the concurrency SAS, two sides of a triangle are equal, and an angle is equal.
As a result, the triangles LMO and LNO are congruent by SAS congruence if LM ≅ ON, ∠ M ≅ ∠ N .
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I need help with particular type of psat math question . I'm really struggling pls help me.
Answer:
D. 80 trees-------------------------------------
For each tree you need 3 + 12 = 15 feet space.
On one side of the street you can plant:
600/15 = 40 treesSame number is applicable for the opposite side, so the total number is:
40*2 = 80 treesThe matching choice is D.
10. Which expression is equivalent to t+4+3-2.2t?
A 1.2t+7
B-1.2t+7
5.8t
D 10.2t
Answer: B
Step-by-step explanation:t+4+3−2.2t
Add 4 and 3 to get 7.
t+7−2.2t
Combine t and −2.2t to get −1.2t.
−1.2t+7
When $\dfrac{7}{11}$ is written as a decimal, what is the sum of the first $20$ digits after the decimal point?
Writing the fraction 7/11 as a decimal gives a repeating decimal 0.636363 the sum of the first two digits is 90
How to add the first twenty digits of a decimal numberThe fraction 7/11 is written in fraction to give a repeating deicmal
Where decimal with repeats. Recurring decimal, often known as repeating decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals.
The division inform of fraction when converted to decimal gives
0.636363
the sum of the first 20 decimals is 90
this is 6 ten times and 3 ten times
6 * 10 + 3 * 10
60 + 30
90
the sum is 20
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Michael buy a baket of mangoe on ale for \$ 4$4 before tax.
The ale tax i 12%.
What i the total price Michael pay for the baket of mangoe?
Total price paid by Michael for the basket of mangoes is $4.48.
For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -
Total price = 4 + 12%×4
Calculating the percentage of sales tax on Right Hand Side of the equation
Total price = 4 + 12×4/100
Solving the percentage part on Right Hand Side of the equation
Total price = 4 + 0.48
Performing addition on Right Hand Side of the equation
Total price = $4.48
Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.
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Learn more
Here is a number sequence.
31 26 21 16 11 ...
Write down the rule for continuing the sequence.
I don't need explanation, I only need the ANSWER
Answer: 11 16 21 26 31
Step-by-step explanation: the shows the sequence.
I need help on this question for part A and B
Answer:
PART A
x-intercept: (-7,0)
y-intercept: (0,9)
PART B
Answer is A (Top Left One)
Step-by-step explanation:
I left a desmos explanation on my previous answer
Which of these graphs represents a function?
A graph plots an ellipse through the points (negative 5, 3), (negative 5, 2), (0, 1), (1, 1), (2, 1), (5, 3), (2, 4), (0 4) and (negative 2, 4) on the x y coordinate plane.
W. A parabola declines through (negative 5, 2), (negative 3, 0), (negative 2, 0), (0, 1), (1, 2), (2, 3), (3, 5) on the x y coordinate plane.
X.
A curve declines from (0, 6) through (2, 5), (3, 3), (3, 2), (3, 1), (2 points 5, negative 3), (2 points 3, negative 4) and (2 points 2, negative 5) on the x y coordinate plane.
Y. A curve declines from (5, 5), (3, 5), (2, 4 points 9), (negative 1, 4), (negative 2, 4), (negative 3, 3), (negative 2, 2), (0, 1 point 5), (2, 1), (3, 10, (4, 1) and (5, 1) on the x y coordinate plane.
Z.
The graph of the parabola declines through (-5, 2), (-3, 0), (-2, 0), (0, 1), (1, 2), (2, 3), (3, 5) on the x y coordinate plane represents the function.
What is a Function?A function is defined as the relation between the x and y coordinates such that no value of x maps to two values of y.
A vertical line test is a test used to determine whether the graph given is a function or not. This is a test where we draw a vertical line passing through a point x. If the graph is a function, then the vertical line will not intersects the graph at two points.
That is, no x coordinate maps to more than 1 y coordinate.
In the first graph of ellipse, the value -5 maps to two values 3 and 5. So this is not a function.
In the parabola all x values only maps to one y value. So this graph represents a function.
In the third graph, the value 3 maps to three values of y, 3, 2, and 1. So this is also not a function.
In the fourth graph, -2 maps to both 4 and 2, which also indicates that the given graph is not a function.
Hence the second graph of the parabola represents a function.
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Answer: B. X
Step-by-step explanation; I JUST DID IT(;