Answer:
Step-by-step explanation:
a)
If we implement the combinations recursively without memoization, then the running time would be exponential in n.
Time Complexity:
If we implement this equation literally, as a recursive program, then the running
time of our algorithm without using memoization, T(n), as a function of n, has the following behavior:
T(0) = 1
T(1) = 1
T(n) = T(n − 1) + T(n − 2).
But this implies that
T(n) ≥ 2T(n − 2) = 2^(n/2).
b)
But if we store the combinations in an array, C[][], then we can instead calculate the combinations, C(n,k), iteratively, as follows:
C[0,0] = 0
C[1,1] = 1
for i = 2 to n do
C[n,k] = C[n-1, i−1] + C[n-1,k]
This algorithm clearly runs in O(n) time, and it illustrates the way memoization
can lead to improved performance when subproblems overlap and we use table
lookups to avoid repeating recursive calls.
In parallelogram DEFG, DH = x + 2, HF = 2y, GH = 4x – 3, and HE = 5y + 1. Find the values of x and y.
Answer: x = 6, y = 4
Step-by-step explanation:
Given the following :
In parallelogram DEFG:
DH = x + 2, HF = 2y, GH = 4x – 3, and HE = 5y + 1
According to the diagram,
The diagonals of the parallelogram buscect each other
The diagonal GE:
GH = HE
4x - 3 = 5y + 1 - - - - (1)
The Diagonal DF:
DH = HF
x + 2 = 2y
x = 2y - 2 - - - - - (2)
Replace x = 2y - 2 in equation (1)
4(2y - 2) - 3 = 5y + 1
8y - 8 - 3 = 5y + 1
8y - 5y = 1 + 8 + 3
3y = 12
y = 4
Substityte y = 4 in equation (2)
x = 2(4) - 2
x = 8 - 2
x = 6
x = 6, y = 4
Square root of 8.8 up to two decimal step by step explanation
Answer:
2.97
Step-by-step explanation:
8.8 = 4 *2.2 = 4 * 220/100
220 = 4 *55
8.8 = (4 *4*55)/100 = 16 *55/100
[tex]\sqrt{8.8} =\sqrt{(16 * 55)}/\sqrt{100\\}[/tex]
[tex]\sqrt{8.8}= \frac{4}{10}*\sqrt{55}[/tex]
≈[tex]\sqrt{8.8} = 0.4 * 7.416 = 2.9664 \\2.97[/tex]
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Formula for the area of a quarter circle: A = (pi x r^2) / 4
A = (pi x 2^2) / 4
A = (pi x 4) / 4
A = 4pi / 4
A = 1pi = 3.14 square miles
Hope this helps! :)
A boat travels upstream for 96 miles in 4 hours and returns in 3 hours traveling downstream in a river. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Speed of boat in still water = 28 miles/hr
Speed of current = 4 miles/hr
Step-by-step explanation:
Speed upstream, u = 96/4 = 24 miles/hr
Speed downstream, v = 96/3 = 32 miles/hr
Speed of boat in still water = ½(v+u)
= ½ (24 + 32) = 28 miles/hr
Speed of the current = ½ ( v - u)
= ½ (32 - 24) = 4 miles/hr
Area between two shapes circles ixl
Can someone help me with this question
Answer:
b
Step-by-step explanation:
3 + 4x < 2(1 + 2x)
3 + 4x < 2 + 4x
Answer: the second answer
Step-by-step explanation:
If we want to find an inequality with no solution, that means we can expect no x and an unbalanced inequality (e.g., 3<0 which is untrue).
The second one is like that because the inequality is
3+4x[tex]\leq[/tex]2(1+2x)
If we solve it out, we get
3+4x[tex]\leq[/tex]2+4x
When you remove the variable from both sides, you now have
3[tex]\leq[/tex]2
This statement is false, since 2 will never be greater than 3.
If we look at the others, we can see that there are answers for all of them.
What is 3x10^7 x 8x10^4 in standard form
Answer:
They are already in standard form.
Step-by-step explanation:
please help me quickly !!
Answer:
A ... [tex]\frac{3}{4} (\frac{4}{3})x=-6 (\frac{4}{3})[/tex]
Step-by-step explanation:
Multiplying 4/3 on both sides gets x by itself
Divide ( 4x2 - 24x + 35 ) / ( 2x - 5 )
Answer:
the closest i got is [tex]\frac{43-24x}{2x-5}[/tex]
Step-by-step explanation:
Which scenario cannot be modeled by a right triangle?
A 13-foot ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the
wall is 12 feet
Wendy leaves school to go home. She walks 60 yards north and then 80 yards west. She is 10 yards from the
school
The dimensions of a triangular-shaped garden are 28 yards, 53 yards, and 45 yards.
A Babylonian writing mentioned a triangle with side lengths 120, 169, and 119.
Answer:
B
Step-by-step explanation:
B. Wendy leaves school to go home. She walks 60 yards north and then 80 yards west. She is 10 yards from the school.
got it right on edge
A circular table top has a radius of 3 feet. Enter the area in square feet or the table top. Round your answer
Answer:
28.26 square feet
Step-by-step explanation:
A=πr²
A=(3.14)(3)²=28.26 square feet
please identify each that are central angles!!
Correct answers are
<BDE
<EDF
What the missing value X^2-20x+—
Answer:
it is -1x2
Step-by-step explanation:
by the ex variable u will get it
Simon took out a zero-interest loan for $3,300 to buy a boat. He must pay $300 per month to pay off the total balance of the boat's purchase price. Simon also has $1,000 in his savings account. He plans to deposit $600 every month in this account. So, Simon would like a system of equations that tells him at what point he will be able to pay off the total balance for the boat with the help of his savings. Write the second equation in the system. Enter the correct answer in the box. Substitute numerical values into the expression for all known variables.
Answer:
After 3 months, Simon will be able to pay off his loan with the money he holds at his savings account.
Step-by-step explanation:
ending loan's principal balance = beginning loan's principal balance - number of months x $300
or we can simplify it: l₁ = l₀ - 300x ⇒ l₁ = 3,300 - 300x
l₁ = ending loan's principal balance
x = number of months
ending savings account balance = beginning savings account balance + number of months x $600
or we can simplify it: s₁ = s₀ + 600x ⇒ s₁ = 1,000 + 600x
s₁ = ending savings account balance
x = number of months
account balances for months
month 1 month 2 month 3 month 4
boat loan $3.000 $2,700 $2,400 $2,100
savings account $1,600 $2,200 $2,800 $3,400
Answer:
y equals 300x plus 3300
Step-by-step explanation:
A child's sandbox is 5 feet wide, 4 feet long, and 3 feet deep. Grace fills the sandbox so that the sand is 2 ½ feet deep. What is the volume of the sand in the box?
Answer:
the volume of sand is [tex]50 ft^{3}[/tex]
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, rectangular prism.
Given data
[tex]Length l= 4 ft Width w= 5ft\\Height h = 3ft[/tex]
if the sandbox is filled with sand of [tex]2\frac{1}{2 } ft[/tex] deep the volume of the sand in the box will be calculated based on the the depth of the sand
converting the depth of sand from mixed fraction to proper fraction we have [tex]2\frac{1}{2} = \frac{5}{2}[/tex]
the expression for the volume of a rectangular prism is
[tex]volume of sand = length * width* height[/tex]
substituting our data into the expression we have
[tex]volume of sand= 5*4 * \frac{5}{2} \\volume of sand = \frac{100}{2} \\volume of sand = 50 ft^{3}[/tex]
Correct answer only please!
Elizabeth deposited $4,530 in a savings account earning 11% interest, compounded annually.
To the nearest cent, how much will she have in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer: Elizabeth earned $7270.91.
Step-by-step explanation:
The formula given to us is the formula for compounded interest.
You can substitute the values given in the first part of the problem into the equation to find B, the final amount:
[tex]B = p*(1+r)^t\\\\B = 4530 * (1 + 0.11)^5[/tex]
Note that 11% interest is expressed as 0.11 because it is a percentage of a whole number.
Now, use a calculator to raise 1.11 to the fifth degree to get this:
[tex]B = 4530 * 1.605058\\B = 7270.912[/tex]
As such, Elizabeth earned $7270.91 in interest after 5 years.
Which Postulate/Theorem below would prove that the triangles shown below are congruent?
a. SSS
b. SAS
c. AAS
d. ASA
Answer:
Correct answer is D. ASA
Step-by-step explanation:
Let us first define ASA congruence rule:
2 triangles are called congruent according to ASA congruence rule if 2 angles of the triangle and the corresponding side between these two angles are equal to each other.
In the question figure, we can figure out following conclusions from Triangles [tex]\triangle SRT\text{ and }\triangle WXY[/tex] respectively:
[tex]\angle TRS = \angle YXW[/tex]Side RS = Side WX[tex]\angle TSR = \angle YWX[/tex]As per the definition of option d) ASA congruence, the triangles are congruent.
Answer:
D. ASAStep-by-step explanation:
the sign has a diameter of 30 inches what is the circumference use 3.14 for pie
Answer:
94.2 inches.
Step-by-step explanation:
First, I just want to clarify that [tex]\pi[/tex] is actually spelled pi, not pie, like the pie you eat.
Finding the circumference is pretty easy. It is just the diameter times pi.
So if the diameter is 30 inches, and we use 3.14 for pi, then the circumference of the sign would be 94.2 inches.
Hope this helps!
PLEASE HELP!! I will mark the brainliest if you can explain your answer!! I think it’s either b or c..... but I’m not sure!!! Pls help!!
(Attached below isn’t the question and the answer choices)
Answer:
A(x) = 6.2 - 0.005x
Step-by-step explanation:
If you think about it, either 0.5/0.005 needs to be equal to 0.5%
0.5 is the same as 1/2 and therefore it is the same as 50%
So it must be 0.005!
Tip: I always just divide by 100 to get the decimal, it is a nice, easy and quick method
how would you solve 4x - 3y = 78 2x + 3y = 48 by elimination
Answer:
x = 21, y = 2
Step-by-step explanation:
4x- 3y = 78....(1)
2x + 3y = 48 ...(2)
Adding eqiautions (1) and (2)
4x- 3y = 78
2x + 3y = 48
-----------------------
6x + 0 = 126....(Here y has been eliminated)
6x = 126
[tex] x= \frac{126}{6}\\\\
\therefore x = 21\\[/tex]
Plugging x = 21 in equation (2) we find:
2 * 21 + 3y = 48
42 + 3y = 48
3y = 48 - 42
3y = 6
[tex] y= \frac{6}{3}\\\\
\therefore y = 2\\[/tex]
Determine the intercepts of the line
Answer:
x-intercept (-7,0)
y-intercept (0,2)
Step-by-step explanation:
Answer:
x-intercept (-7 , 0)
y-intercept (2 , 0)
x intercept is where on the x - aces a point is sitting on on the line
-------------------------- <--- this one is x
y intercept is where on the y- aces a point is sitting on the line
║ <---- this one is y
5. Janet Gilbert is director of labs. She has some extra capacity and has contracted with some small neighboring hospitals to run some of their lab tests. She has recently had a study conducted and has determined that her costs of these contracts are $10,000 of which $7,000 are for supplies and items related to each test. She currently charges an average of $10.00 per lab test. She is thinking of lowering her price by 20 percent in hopes of raising her current volume of 10,000 tests by 15 percent.
Answer:
Check the explanation
Step-by-step explanation:
Present predicted
Revenue - per test 10000 8000
Variable cost - per test 7000 7000
Contribution – per test 3000 1000
Net income (10,000 test – 11,500 tests) 30,000,000 11,500,000
z - 5 = 33
a) twice 5 is 33
b) z increased by 5 is 33
c) 5 less than z is 33
d) 5 times z is 33
Answer:
C) 5 less than z is 33
Step-by-step explanation:
z-5=33
z-5+5=33+5
z=38
38-33=5
Can some one help me plz with step by step
x^2 + x - 42
Answer:
x = 6 or x = -7
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + x - 42 = 0
The left hand side factors into a product with two terms:
(x - 6) (x + 7) = 0
Split into two equations:
x - 6 = 0 or x + 7 = 0
Add 6 to both sides:
x = 6 or x + 7 = 0
Subtract 7 from both sides:
Answer: x = 6 or x = -7
Help with this question asap!!
Answer:
1st option.
[tex]\sum_{k=1}^{6} \frac{1}{2k-1}[/tex]
Step-by-step explanation:
The given sequence is as follows:
[tex]1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}[/tex]
Here, we can see that the denominator is in AP and the sequence is:
1, 3, 7, 9, 11
first term, a = 1
Common difference, d = 2
We know that nth term for an AP:
[tex]a_n = a+(n-1)d[/tex]
where a is the first term and
d is the common difference.
So, nth term for above AP:
[tex]a_n = 1+(n-1)\times 2\\\Rightarrow 2n-1[/tex]
Here, we have 'k' in place of 'n':
[tex]a_k = 2k-1[/tex]
And as per the given sequence in the question, the kth term is simply the reciprocal:
i.e. [tex]\dfrac{1}{2k-1}[/tex]
and sum is to be done up to k = 6 from k = 1.
Hence, the summation notation for the sequence
[tex]1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}[/tex]
is:
[tex]\sum_{k=1}^{6} \frac{1}{2k-1}[/tex]
On a road map, the distance from Portland to Seattle is 8 cm. What is the actual distance between the cities if the map scale is 2 cm = 37.5 miles?
Answer:
150 miles
Step-by-step explanation:
8/2 = 4
4x37.5 = 150
Find the sum of the geometric series 3+12+48+...+12,288
Answer:
I think that you need to add obvoiusly.
12351 Thats what I got. But Im not sure if its correct. I hope his helps
Step-by-step explanation:
Answer:
16383
Step-by-step explanation:
12288+3072+767+192+48+12+3 =
Someone can help me in this question!
Answer:
ACB=61°, BAC=58°, AEF=65°
Step-by-step explanation:
C = 122°, 180-122=58° ACB= 122°÷2=61°
61°+61°+A=180, hence 58°
65 because of opposite angles, they are equal
Please help!
You flip a coin twice.
What is the probability of getting tails and then getting heads?
Write your answer as a percentage.
___%
Your answer would be 25%.
Assuming the coin is not biased, the probability of flipping a heads or tails is 1/2 equally. This remains the same no matter how many times you flip the coin, because the outcome of one flip does not affect the outcome of another.
This means that the probability of getting a tails the first flip is 1/2, and the probability of then getting a heads is also 1/2, so to find the probability of both happening you need to multiply these probabilities together, and 1/2 × 1/2 = 1/4, and 1/4 as a percentage is 25%.
I hope this helps! Let me know if you have any questions :)
Solve the system of equations
-10x+3y=5
x=y-4
x=
y=
Answer:
x=1
y=5
Step-by-step explanation:
Found the answer online at math way
no work and don't report me or delete my answer!!!
I want brainliest