What is the empirical rule????

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

  an = 5/2 +3/2(n -1)

Step-by-step explanation:

The common difference is ...

  4 -5/2 = 3/2

The general rule is ...

  an = a1 +d(n -1)

For a1 = 5/2 and d = 3/2, the rule for this sequence is ...

  an = 5/2 +3/2(n -1)

___

This can be simplified to ...

  an = 1 +3/2n

The total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.

According to the question,

We have the following information:

A cyclist rode his bike for 169 min at an average velocity of 3. 53 m/s on a bearing of 450.

Now, we know that the following formula is used to find the velocity:

Velocity = displacement/time

(We will convert time from minutes into seconds.)

Displacement = 3.53*(169*60)

Displacement = 35794.2 m

Now, the displacement in km will be 35.8 km approximately.

Now, let's take that the bike is moving along the positive x-axis. So, it would be written in the following expression:

Displacement = 35.8 a[x] km + 0 a[y] km

Hence, the total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.

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Answer:

The answer to this equation is 10.89375

Answer:

-2/3, -5/9, 3/7

Step-by-step explanation:

-5/9 = -0.55...

3/7 = 0.42...

-2/3 = -0.66...

-0.66... < -0.55... < 0.42...

Best of Luck!

Answer:

Δ MAN

reason: ASA

Step-by-step explanation:

if you look at the congruency marks you can see that ∡F ≅ ∡A and we know that ∡N ≅ ∡N

markings also show us that sides UF ≅ MA

therefore, we know two angles and one side for each triangle

Given that,

∠C = (6x-21)° and ∠A = (4x+11)°

To find,

Choose the correct option.

Solution,

For a parallelogram, the opposite angles are equal. ATQ,

(6x-21)° = (4x+11)°

Taking like terms together,

6x-4x = 21 + 11

2x = 32

x = 16

∠C = (6x-21)° = 6(16) -21 = 75°

So, ∠A = 75°

So, ∠A = ∠C = 75°. Hence, the correct option is (B).

Step-by-step explanation:

p = 5 ÷ (12.37 - 1.12)

p = 5 ÷ 11.25

p = 2.25

Answer:

$12.37-1.12=$11.25

let p =1 slice

5(p)=11.25

5p=11.25

Answer:

triangle

Step-by-step explanation:

Answer:

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

to

r > s

The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.

The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

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Answer:

she can walk 6 km at this pace

Answer:

6km

Step-by-step explanation:

Mapoela can walk 2 km in 30 minutes.

30 minutes=2kms and she walked for 1 and a half hour

1 and a half hour=90 minutes so if 30 minutes=2km.

30 minutes=2km

60 minutes=1 hour/4kms

90 minutes= Our 1 and a half hour/6 km

Answer:

54

Step-by-step explanation:

6*5=30

4*6=24

24+30=54

To obtain a straight flush starting with a two, we need to select five consecutive cards of the same suit. Since we are starting with a two, we have limited options for the other four cards.

In a standard 52-card deck, there are four suits (clubs, diamonds, hearts, and spades), and each suit has 13 cards (Ace through King). Since we are looking for a straight flush, we need all five cards to be of the same suit.

Starting with a two, we can choose any of the four suits. Once we have chosen a suit, there is only one card of each rank that will form a straight flush. So, for each suit, there is only one way to obtain a straight flush starting with a two.

Therefore, the total number of ways to obtain a straight flush starting with a two is 4 (one for each suit).

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By using pythagorean theorem, the length of the missing side is 12 feet.

What is the Pythagorean theorem?

Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:

"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."

In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:

\(c^2 = a^2 + b^2\)

We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.

In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.

If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:

\(c^2 = 7.2^2 + 9.6^2\)

\(c^2 = 51.84 + 92.16\)

\(c^2 = 144\)

\(c = \sqrt{144}\)

c = 12 feet

Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.

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Answer:

add two tiles per figure until u get to eight.

Step-by-step explanation:

answer:

5-2y + (-8y) + 6.8

simplified:

11.8-10y

Step-by-step explanation:

Let's simplify step-by-step.

5−2y−8y+6.8

=5+−2y+−8y+6.8

Combine Like Terms:

=5+−2y+−8y+6.8

=(−2y+−8y)+(5+6.8)

=−10y+11.8

Description:

The first step is to simplify the first equation that is 5−2y−8y+6.8 . After that your answer will lead up to 5+−2y+−8y+6.8 . Then the last step is to Combine like terms. At the end your answer will lead up to −10y+11.8.

So 5-2y + (-8y) +6.8  = −10y+11.8

​

Answer: −10y+11.8

Hope this helps.

Answer:

E

Step-by-step explanation:

The sum of the interior angles of a 6 sided figure is (6-2 ) * 180 = 720

So all 6 angles will add to 720

6x + 120 + 5x-6 4x+14 +7x + 8x -8 = 720        Gather like terms

6x + 5x + 4x + 7x + 8x +120 -6+14-8 = 720     Collect like terms.

30x + 120 = 720                                               Subtract 120 from both sides

30x = 720 - 120

30x = 600                                                        Divide both sides by 30

x = 600 / 30

x = 20

Solve for 4x + 14

4(20) + 14 = 94

Finally notice that 94 and y are supplementary

y + 94 = 180                                                       Subtract 94 from both sides

y = 180 - 94

y = 86

The probability that Hugo buys at most 3 packs of cards would be; P(X ≤ 3) = 0.488

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

If X is the random variable that denotes the number of packs of cards Hugo buy, so

Then the probability that Hugo buys at most 3 packs of cards can be as:

P(X ≤ 3)  

The table given is expressed as;

X  of packs         1           2           3           4

P(X)               0.2      0.16       0.128     0.512

Therefore,

P(X ≤ 3) = P(1) + P(2) + P(3)

P(X ≤ 3) = 0.2 + 0.16 + 0.128

P(X ≤ 3) = 0.488

The probability that Hugo buys at most 3 packs of cards would be; P(X ≤ 3) = 0.488

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(a) Average water level = 7.6 feet

(b)  The water level in Boston Harbor equals the average water level at

t = 10, 14, 18, and 22.

(c) Temperature at 6 P.M. = 70 - 9.02 = 60.98 degrees Fahrenheit.

(d)  It makes sense that N(t) has a horizontal asymptote at y = 0 because as t becomes

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

a) To find the average water level in Boston Harbor over the 24 hour period, we need to calculate the integral of the function H(t) over the interval [0,24] and divide by the length of the interval. Using the Mean Value Theorem for Integrals, we have:

Average water level = (1/24) * ∫[0,24] H(t) dt

= (1/24) * [ -8cos(pi/6(t-10)) + (15.2t - 384sin(pi/6(t-10))) ] evaluated from 0 to 24

= 7.6 feet

b) To find the times of the day when the water level in Boston Harbor equals the average water level, we need to solve the equation H(t) = 7.6. Using the given formula for H(t), we have:

48sin[pi/6(t-10)] + 7.6 = 7.6

48sin[pi/6(t-10)] = 0

sin[pi/6(t-10)] = 0

t-10 = (2n)π/6 or t-10 = (2n+1)π/6, where n is an integer.

Solving for t, we get:

t = 10 + (2n)4 or t = 10 + (2n+1)2.5, where n is an integer.

Therefore, the water level in Boston Harbor equals the average water level at t = 10, 14, 18, and 22.

c) Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings. In this case, the temperature of the wine is changing at a rate of \(-18e^{(-65t)}\) degrees Fahrenheit per hour. To find how much the temperature drops between 3 P.M. and 6 P.M., we need to calculate the integral of the rate of change of temperature over the interval [0,3] and multiply by -1 to get a positive value. Using the formula for the rate of change of temperature, we have:

ΔT = -∫[0,3] - \(18e^{(65t)}\)  dt

= [-18/(-65) \(e^{(-65t)}\)] evaluated from 0 to 3

≈ 9.02 degrees Fahrenheit

Therefore, the temperature of the wine drops by approximately 9.02 degrees Fahrenheit between 3 P.M. and 6 P.M. To find the temperature of the wine at 6 P.M., we need to subtract the temperature drop from the initial temperature of 70 degrees Fahrenheit:

Temperature at 6 P.M. = 70 - 9.02 = 60.98 degrees Fahrenheit.

d) The graph of n(t) = \(18e^{(65t)}\) is an increasing exponential function with a horizontal asymptote at y = 0. The graph of its antiderivative N(t) = \((18/65)e^{(65t)}\) is an increasing exponential function with a horizontal asymptote at y = 0 as well.

The solution to part (a) can be found on the graph of N(t) at y = 7.6, which represents the average water level in Boston Harbor over the 24 hour period.

The solution to part (b) can be found on the graph of H(t), which intersects with the horizontal line y = 7.6 at t = 10, 14, 18, and 22. It makes sense that N(t) has a horizontal asymptote at y = 0 because as t becomes

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STEP-BY-STEP EXPLANATION

Given information

The scale of the drawing was 5inches to 1 yard

The first thing to do is to convert the inches to yard for unit consistency

According to the Standard International Unit, 1 yard = 36 inches

Let x represents the length in the yard

Therefore, 5 inches = 36 inches

In real life drawing, 5 inches is equivalent to 5 inches

Recall that, the scaling factor is the ratio of the larger figure to the smaller figure

The scaling factor is 5 : 36

Answer: i would say the answer is 90 degrees

Step-by-step explanation:

If you mean axis then the answer is that the coordinate on the y axis stays the same but the coordinate on the x axis is the opposite.

For example, if the number on the y axis on quadrant 1 is 4 then if it's reflected onto quadrant two, the number will stay the same but if the number on the x axis is 4 then if it's reflected onto quadrant two, the number will be -4

Answer:

  8 units

Step-by-step explanation:

Points (2, 5) and (10, 5) have the same y-coordinate, so lie on the horizontal line y = 5. The distance between the points is the difference of their x-coordinates:

  10 -2 = 8

The points are 8 units apart.

__

If you plot the points on a graph, you can count the grid squares between them.

The tight asymptotic bounds for the given recurrences are: a. ) T(n) = Theta(n^(1/2)) b. ) T(n) = Theta(n^(1/2) * log n) c. ) T(n) = Theta(n) d. ) T(n) = Theta(n^2)

The master method is a formula for solving recurrences of the form T(n) = aT(n/b) + f(n), where a >= 1, b > 1, and f(n) is a given function. The master method provides tight asymptotic bounds for T(n) in terms of f(n) and the constants a and b.

a. ) T(n) = 2T(n/4) + 1

In this case, a = 2, b = 4, and f(n) = 1. According to the master method, we need to compare f(n) with n^(log_b a), which is n^(log_4 2) = n^(1/2).

Since f(n) = 1 = O(n^(1/2 - epsilon)), where epsilon > 0, we can apply case 1 of the master method and get T(n) = Theta(n^(1/2)).

b. ) T(n) = 2T(n/4) + n^(1/2)

In this case, a = 2, b = 4, and f(n) = n^(1/2). Again, we need to compare f(n) with n^(log_b a) = n^(1/2).

Since f(n) = n^(1/2) = Theta(n^(1/2)), we can apply case 2 of the master method and get T(n) = Theta(n^(1/2) * log n).

c. ) T(n) = 2T(n/4) + n

In this case, a = 2, b = 4, and f(n) = n. Again, we need to compare f(n) with n^(log_b a) = n^(1/2).

Since f(n) = n = Omega(n^(1/2 + epsilon)), where epsilon > 0, and f(n/b) = 2(n/4) = n/2 <= cf(n), where c = 1/2 < 1, we can apply case 3 of the master method and get T(n) = Theta(n).

d. ) T(n) = 2T(n/4) + n^2

In this case, a = 2, b = 4, and f(n) = n^2. Again, we need to compare f(n) with n^(log_b a) = n^(1/2).

Since f(n) = n^2 = Omega(n^(1/2 + epsilon)), where epsilon > 0, and f(n/b) = 2(n/4)^2 = n^2/8 <= cf(n), where c = 1/8 < 1, we can apply case 3 of the master method and get T(n) = Theta(n^2).

Therefore, the tight asymptotic bounds for the given recurrences are:

a. ) T(n) = Theta(n^(1/2))

b. ) T(n) = Theta(n^(1/2) * log n)

c. ) T(n) = Theta(n)

d. ) T(n) = Theta(n^2)

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Answer:

Your answer is B or 54.

Step-by-step explanation:

Answer:

the answer is 54

Step-by-step explanation:

if you have a ratio of 1:2 you divide 324 by three

108     and      216

if you take 108 and divide it again into two more piles you get 54  

The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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Answer:

x=100

Step-by-step explanation: