Claire’s backyard is in the shape of a rectangle, with dimensions shown in the diagram. To complete some landscaping work, she’d like to know both perimeter and area of her yard. Use special right triangle relationships to complete the statements.

Answer:  b

Step-by-step explanation:

I think

The O(n log n) algorithm for finding A + B can be implemented using polynomial interpolation.

To find A + B, we can utilize polynomial interpolation. First, we construct two polynomials, P(x) and Q(x), where the coefficients of P(x) represent the frequencies of the integers in set A, and the coefficients of Q(x) represent the frequencies of the integers in set B.

We can construct these polynomials in O(n) time by iterating through sets A and B and counting the occurrences of each integer. The coefficients of the polynomials can be stored in arrays of size 10n+1, where the index represents the integer and the value represents the frequency.

Next, we multiply the two polynomials, P(x) and Q(x), using fast Fourier transform (FFT) in O(n log n) time. The resulting polynomial, R(x), represents the frequencies of the sums of all possible pairs of integers from sets A and B.

Finally, we can extract the coefficients of R(x) and construct the set A + B by iterating through the coefficients and adding the corresponding integers to the result set.

By utilizing polynomial interpolation and FFT, we can achieve an O(n log n) time complexity for finding A + B, making it an efficient algorithm for large values of n.

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\(\int\limits^a_b {3tan^{5}(x) } \, dx\), with the appropriate use of absolute values and the constant of integration represented as 'C', is equal to (-3/4) ln|sec²(x)| - (3/2) tan³(x) + C.

To evaluate the integral ∫3 tan⁵(x) dx, we can use integration techniques and trigonometric identities. First, we can rewrite tan⁵(x) as \((tan^{2}(x)) ^{2}\) * tan(x). The integral of tan²(x) can be found by using the identity sec²(x) - 1 = tan²(x). Rearranging this identity, we get tan²(x) = sec²(x) - 1. Substituting this back into the original expression, we have ∫3 [\((sec^{2}(x)-1) ^{2}\)* tan(x)] dx.

Next, we can expand the expression \((sec^{2}(x)-1) ^{2}\)using the binomial theorem, which gives us sec⁴(x) - 2sec²(x) + 1. The integral becomes ∫3 [sec⁴(x) - 2sec²(x) + 1] tan(x) dx. Using the power rule for integration, we can find the integral of each term individually.

The integral of sec⁴(x) tan(x) dx can be evaluated by substituting u = sec(x) and using the fact that du = sec(x) tan(x) dx. This simplifies the integral to ∫3 u⁴ du, which can be easily integrated as (u⁵/5) + C.

Similarly, the integral of sec²(x) tan(x) dx can be evaluated by substituting v = sec(x) and using du = sec(x) tan(x) dx. This simplifies the integral to ∫3 v² dv, which can be integrated as (v³/3) + C.

Lastly, the integral of tan(x) dx is simply ln|sec(x)| + C.

Combining the results, we have (-3/4) ln|sec²(x)| - (3/2) tan³(x) + C as the final answer, where C represents the constant of integration.

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Answer:

23rd term

Step-by-step explanation:

Plz mark as Brainliest!

Answer:

2.2

Step-by-step explanation:

100 is his goal, minus what he already did, which is 12, you get 88. Divide 88 with the number of days remaining and then you get the answer.

Answer:

2 1/5 or 2.2 miles per day

Step-by-step explanation:

(100 - 12) / 40 = 2 1/5 or 2.2 miles per day

Answer:

He should have said that his small brother had 100 small building bricks, but lost 5 in total now.

Answer:

Sebastian will know 440 recipes.

Step-by-step explanation:

Since we can assume that the relationship of the situation is directly proportional, proportional relationships are described as:

Then, if he learned 220 appetizers in 44 weeks, after 88 weeks;

Answer:

2.9 per second

Step-by-step explanation:

Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

Answer:

a

Step-by-step explanation:

the graphic is step by step

Answer:

A

Step-by-step explanation:

Since the first number to the problem is -4, you start at -4 on the number line. The next number is +7.5 so you would move 7.5 spaces to the right on your number line. Finally, where you land would be your answer.

Hope this helps! Please mark Brainliest :)

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

3/4

Step-by-step explanation:

Going from the first point to the second, we see the x-coordinate (the 'run') increasing by 4 and the y-coordinate increasing by 3.  Thus, the slope of the line going through these two points is

m = rise / run = 3/4

Answer

I don’t know

Step-by-step explanation:

Answer:

x+5=19

Step-by-step explanation:

i think that right let me know...:/

Answer:

x= 14

Step-by-step explanation:

a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes

x+5=19

19-5=x

14=x

Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

The implied cash price of the vehicle, considering a 5-year lease with $400 monthly payments and a 1.9% monthly interest rate, is approximately $39,919.35, including the residual value.



To find the implied cash price of the vehicle, we need to calculate the present value of the lease payments and the residual value at the end of the lease.First, we need to calculate the present value of the lease payments. The monthly lease payment is $400, and the lease term is 5 years, so there are a total of 5 * 12 = 60 monthly payments. We'll use the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r,

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods.Using the given values, the monthly interest rate is 1.9% / 100 / 12 = 0.0015833, and the number of periods is 60. Plugging these values into the formula, we find:

PV = 400 * (1 - (1 + 0.0015833)^(-60)) / 0.0015833 ≈ $21,919.35.Next, we need to add the residual value of $18,000 at the end of the lease to the present value of the lease payments:

Implied Cash Price = PV + Residual Value = $21,919.35 + $18,000 = $39,919.35.Therefore, the implied cash price of the vehicle is approximately $39,919.35.

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the sum of the terms of the series 36, 24, 16..., we can use the formula for the sum of an infinite geometric series is  is  -36,The limiting sum of a series is 36. If a = 8, we can find the value of r using the formula for the sum of an infinite geometric series is 7 / 9 and the total distance the ball falls is 16 meters.

Given a=−4 and r=2 in a geometric sequence, we can find the values of T3, T8, and Tn by using the formula for the nth term of a geometric sequence:

\(Tn = a * r^(n-1)\)

To find T3:
T3 = -4 * 2^(3-1)
T3 = -4 * 2^2
T3 = -4 * 4
T3 = -16

To find T8:
T8 = -4 * 2^(8-1)
T8 = -4 * 2^7
T8 = -4 * 128
T8 = -512

To find Tn, we need to know the value of n. Please provide the value of n to calculate Tn.

Now, let's move on to the series -3, 15, -75...

To find the common ratio (r), we can divide any term by its previous term. Let's use the second and first terms:

r = 15 / (-3)
r = -5

To find the first term (a), we can use the second term and the common ratio:

-3 = a * (-5)
a = -3 / (-5)
a = 3/5

Now, let's find the 11th term of the sequence:

T11 = a * r^(11-1)
T11 = (3/5) * (-5)^10
T11 = (3/5) * 9765625
T11 = 5859375/5
T11 = 1171875

Moving on to the next question:

1. To find the sum of the terms of the series 36, 24, 16..., we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Since this is an infinite series and the common ratio (r) is less than 1 in absolute value, the sum is finite. So, we can find the sum using the given values:

Sum = 36 / (1 - 2)
Sum = 36 / (-1)
Sum = -36

2. The limiting sum of a series is 36. If a = 8, we can find the value of r using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Substituting the given values:

36 = 8 / (1 - r)

Solving for r:

36(1 - r) = 8
36 - 36r = 8
36r = 36 - 8
36r = 28
r = 28 / 36
r = 7 / 9

3. A ball is dropped from 4 m and bounces back to 3/4 of its previous height. If it continues to bounce until it comes to rest, we need to find the total distance the ball falls.

The first fall from 4 m is straightforward, so the distance fallen is 4 m. For each subsequent bounce, the ball reaches 3/4 of its previous height, so the distance fallen decreases by a factor of 3/4 each time.

The total distance fallen can be calculated using the formula for the sum of an infinite geometric series:

Distance = a / (1 - r)

Substituting the given values:

Distance = 4 / (1 - 3/4)

Simplifying:

Distance = 4 / (1/4)
Distance = 4 * 4
Distance = 16 m

Therefore, the total distance the ball falls is 16 meters.
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Answer:

t>-3 is the answer. hope this helped!

Step-by-step explanation:

Its simple you add 4 to both sides. t-4+4 > -7+4= t > -3

Answer:

C. 5.8

Step-by-step explanation:

We use the Pythagoras theorem here. which is a²+b²=c².

a and b are the replacements for the 5miles and  3miles here.

They are a and b because a  and b are always on the right angle side.

The longest side of this triangle is called a hypotenuse which is the c in this case.

the other sides (a and b) are called the adjacent and the opposite.

it doesn't matter if you use adjacent or opposite for a and b in this case.

the only important thing is the hypotenuse here.

So it's a²+b²=c², which is 5²+3²=c².

5² is 25 and 3² is 9, so we add them and we get 34.

so c²=34, we don't want the square on c  so we send it to 34 which becomes √34.

√34 gives us 5.8 miles which is up to just only one decimal place.

You might need to use calculators for square roots because they take long to calculate.

Answer:

what you mean

Step-by-step explanation:

Answer:

I believe it would be 25% because 25% of the cards are clubs.

Answer:

See below.

Step-by-step explanation:

1+3x+3x

Combine like terms.

3x+3x+1

6x+1

-hope it helps

Based on the information given, let's find the probability that you will not exceed the $50 reimbursement limit for all three dinners.

1. First, identify the number of restaurants that exceed the $50 limit:
One-third of 18 restaurants is (1/3) * 18 = 6 restaurants.

2. Calculate the probability of selecting a restaurant that does not exceed the $50 limit:
There are 12 restaurants (18 total - 6 expensive ones) that meet the criteria. So, the probability of choosing one of them is 12/18 = 2/3.

3. Determine the probability of choosing three restaurants that do not exceed the $50 limit:
Since you're choosing three restaurants, we'll multiply the individual probabilities: (2/3) * (2/3) * (2/3) = 8/27.

4. Round the answer to four decimal places:
The probability is approximately 0.2963, or 29.63%.

So, if you randomly select three of these restaurants for dinner, there is a 29.63% chance that you will not exceed the $50 reimbursement limit for all three dinners.

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Answer:

158x + 14.12

Step-by-step explanation:

Answer:

the correct answer is: 16

Step-by-step explanation:

Answer:

-12p+p^2+36

Step by step explanation:

(-p+6)^2 is the square of -p+6

we use the formula

(a+b)^2=2ab+a^2+b^2

(-p+6)^2=-12p+p^2+36

the minus of p disappears

I think you meant to say the SQUARE ROOT.

sqrt{-p + 6}

If you meant to SQUARE THE BIMOMIAL, then the set up is:

(-p + 6)^2

(-p + 6)(-p + 6)

p^2 -12p + 36

Answer:2

Step-by-step explanation:

Answer:

it is b i did it on eg 2020

Step-by-step explanation:

Answer:

90 cm²

Step-by-step explanation:

Let the greater side be the length L and the smaller side the width W

Given L : W = 5 : 2

we can rewrite this as a fraction

\(\dfrac{L}{W} = \dfrac{5}{2}\)

Cross-multiplying we get
2L = 5W

The perimeter of a rectangle
= 2(L + W)
= 2L + 2W
and we are told it is 42 cm

Therefore
2L + 2W = 42

Substitute 5W for 2L to get

5W + 2W = 42
7W = 42

or

W = 42/6 = 6

Given 2L + 2W = 42, substitute 6 for W to get

2L + 2(6) = 42

2L + 12 = 42

2L = 42 - 12= 30

L = 30/2 = 15

So length  L = 15

Just to check
L/W = 15/6 = 5/2  by dividing both numerator and denominator by 3

Area of the rectangle
= L x W

= 15 x 6

= 90 cm²

Using the given information of the trigonometric function gives:

sin(2x) =  -(4√6)/25

cos(2x) = 24/25

tan(2x) = -(4√6)/23

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have:

tan(x) = -1/5

Since  cos(x) > 0. Thus, x is in the third quadrant.

Also, tan(x) = opposite /hypotenuse = -1/5

adjacent = √(5² - (-1)²) = 2√6

Thus,

cos (x) = (2√6)/5

tan(x) = -1/(2√6)

Using double angle formulas:

sin(2x) =2sinx·cosx

sin(2x) = 2 * (-1/5) * (2√6)/5  =  -(4√6)/25

cos(2x) = 1−2sin²x

cos(2x) = 1− (-1/5)²  = 24/25

\(tan(2x) = \frac{2tanx}{1-tan^{2}x }\)

\(tan(2x) = \frac{2*\frac{-1}{2\sqrt{6} } }{1-(\frac{-1}{2\sqrt{6} })^{2} }\)

\(tan(2x) = -\frac{4\sqrt{6} }{23}\)

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