Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).
P(x) = −x3 − 2x + 4, D(x) = x + 1
P(x) =

Answer:

the total cost is $86.40

Answer:

Bjorn sends 12 messages.

Step-by-step explanation:

Bjorn sends b messages, while Irina sends six times as many messages as Bjorn, which means that Irina sends 6b messages. We also know that Irina sends 72 messages. Therefore, 6b must be equal to 72. If 6b = 72, b = 72/6, which simplifies to b being equal to 12.

Hope this helps! Comment any questions <3

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

21

Step-by-step explanation:

Can I have brainliest:)

Answer:

7 x 24

8 x 1

=

168/8= 21

The expression that describes the relationship is as follows:

D. The number of sheets of paper is 50 times the number of packages

The number of sheet of paper in x packages is described by the rule y = 50x.

Therefore, the verbal description that describes the relationship can be represented as follows:

y = 50x

where

Therefore, the number of sheets of paper is 50 times the number of packages describes the relationship.

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the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

To determine the best estimate of the half-life by combining the two results, we can use the weighted average method. The weights assigned to each measurement are inversely proportional to the squares of their uncertainties. Here's how to calculate the combined result:

Step 1: Calculate the weights for each measurement.

  w1 = 1/σ1^2

  w2 = 1/σ2^2

  Where σ1 and σ2 are the uncertainties associated with each measurement.

Step 2: Calculate the weighted values.

  w1 * t1 = w1 * (15.5 days)

  w2 * t2 = w2 * (16.2 days)

Step 3: Calculate the sum of the weights.

  W = w1 + w2

Step 4: Calculate the weighted average.

  T = (w1 * t1 + w2 * t2) / W

Step 5: Calculate the combined uncertainty.

  σ = √(1 / W)

The best estimate of the half-life is given by the value of T, and the combined uncertainty is given by the value of σ.

Let's calculate the best estimate using the given values:

For the first measurement:

σ1 = 2.3 days

For the second measurement:

σ2 = 1.5 days

Step 1:

w1 = 1/σ1^2 = 1/(2.3^2) ≈ 0.1949

w2 = 1/σ2^2 = 1/(1.5^2) ≈ 0.4444

Step 2:

w1 * t1 ≈ 0.1949 * 15.5 ≈ 3.0195

w2 * t2 ≈ 0.4444 * 16.2 ≈ 7.1993

Step 3:

W = w1 + w2 ≈ 0.1949 + 0.4444 ≈ 0.6393

Step 4:

T = (w1 * t1 + w2 * t2) / W ≈ (3.0195 + 7.1993) / 0.6393 ≈ 13.7421 days

Step 5:

σ = √(1 / W) ≈ √(1 / 0.6393) ≈ 1.3772 days

Therefore, the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

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Answer:

no

Step-by-step explanation:

half of 250k would be 125k and if you add that to 250k that would be 375k

Answer:

6 (c)

Hope this helps

The probability of observing the sequence r, b, b, r, r in the given scenario is 1/120.

To find the probability of observing the sequence r, b, b, r, r in the given scenario, we can break it down step by step:

Probability of drawing the first ball as red (r):

Since the urn initially contains one red and one black ball, the probability of drawing a red ball is 1/2.

Probability of drawing the second ball as black (b) after the first ball was red:

After drawing the first red ball, it is returned to the urn along with another red ball, so the urn now contains two red balls and one black ball.

The probability of drawing a black ball is 1/3.

Probability of drawing the third ball as black (b) after the previous sequence was r, b:

After drawing the second black ball, it is returned to the urn along with another black ball, so the urn now contains two red balls and two black balls.

The probability of drawing a black ball is now 2/4 = 1/2.

Probability of drawing the fourth ball as red (r) after the previous sequence was r, b, b:

After drawing the third black ball, it is returned to the urn along with another black ball, so the urn still contains two red balls and two black balls.

The probability of drawing a red ball is 2/4 = 1/2.

Probability of drawing the fifth ball as red (r) after the previous sequence was r, b, b, r:

After drawing the fourth red ball, it is returned to the urn along with another red ball, so the urn now contains three red balls and two black balls.

The probability of drawing a red ball is 3/5.

To find the overall probability of observing the sequence r, b, b, r, r, we multiply the probabilities of each individual step:

\(P(r, b, b, r, r) = (1/2) \times (1/3) \times (1/2) \times (1/2) \times (3/5)\)

= 1/120.

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Answer:

62  

Step-by-step explanation:

because the total angle is 180 and SPR is 118, so when you subtract 180 - 118 you get 62

Answer:

-28x-8y+2

Distribute the -4 to the (3x-5) by multiplying. -4(3x-5). -12x+20.

Answer:

60

Step-by-step explanation:

10% = ?

54= ?

100%-10%=90%

54=90%

54/9=6

6=10%

6*100%=60

The distance the cyclist traveled into the country, given that he rides into the country at an average speed of 10 miles per hour is 15 miles

Let the total distance traveled into the country be y.

Now, we shall determine the riding time. Details below:

Riding time = Distance / speed

Riding time = y / 10

Next, we shall obtain the walking time of the cyclist. This is shown below:

Walking time = Distance / speed

Riding time = y / 3

Finally, we shall obtain the total distance traveled. This is illustrated below:

Total time = riding time + walking time

6.5 = y/10 + y/3

6.5 = (3y + 10y) / 30

6.5 = 13y / 30

Cross multiply

13y = 6.5 × 30

13y = 195

Divide both sides by 13

y = 195 / 13

y = 15 miles

Thus, the total distance traveled by the cyclist into the country is 15 miles.

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Answer:

$10.07

Step-by-step explanation:

Well you have to subtract 53.43 from 33.29 which equals 20.14 then you have to divide 20.14 by 2 and you get $10.07.

8lbs hamburger will cost

3.25 • 5 + 2.50 • 3 + 2 • 3 = x

16.25 + 7.50 + 6 = x

29.75 = how much they spent all-together

The slope of the tangent to the curve at the point where x = a is given by m = 8a - 6\(a^{2}\), and the equations of the tangent lines at the points (1,7) and (2,5) are y = 2x + 5 and y = -8x + 21, respectively.

(a) To find the slope m of the tangent to the curve y = 5 + 4\(x^{2}\) - 2\(x^{3}\) at the point where x = a, we need to calculate the derivative of the function y with respect to x and then substitute the value of a into the derivative.

First, find the derivative of y with respect to x:

dy/dx = 8x - 6\(x^{2}\)

Next, substitute x = a into the derivative:

m = dy/dx evaluated at x = a

m = 8a - 6\(a^{2}\)

(b) To find the equations of the tangent lines at the points (1,7) and (2,5), we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

For the point (1,7):

m = 8(1) - 6(\(1^{2}\)) = 8 - 6 = 2

Using the point-slope form, the equation of the tangent line is:

y - 7 = 2(x - 1)

y = 2x + 5

For the point (2,5):

m = 8(2) - 6(\(2^{2}\)) = 16 - 24 = -8

Using the point-slope form, the equation of the tangent line is:

y - 5 = -8(x - 2)

y = -8x + 21

(c) To graph the curve and both tangents on a common screen, a visual representation is required and cannot be provided in a text-based format. I recommend using graphing software or a graphing calculator to plot the curve y = 5 + 4\(x^{2}\) - 2\(x^{3}\) along with the tangent lines y = 2x + 5 and y = -8x + 21. This will allow you to see the curve and the tangents simultaneously.

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Based on the given information, the operating characteristics of Willow Brook National Bank's drive-up teller window can be determined and the probability of customers having to wait for service can be calculated.

The arrival rate for the drive-up teller window is 0.5 customers per minute, while the service rate is 0.75 customers per minute. Since both arrival and service times follow exponential distributions, we can use the formulas for an M/M/1 queue to calculate the operating characteristics.

(a) The probability of having no customers in the system can be found using the formula P0 = 1 - (λ/μ), where λ is the arrival rate and μ is the service rate. Plugging in the values, P0 = 1 - (0.5/0.75) = 0.3333.

(b) The average number of customers waiting can be calculated using the formula Lq = (\(\lambda ^2\)) / (μ(μ - λ)). Plugging in the values,

Lq = (\(0.5^2\)) / (0.75(0.75 - 0.5)) = 0.6667.

(c) The average number of customers in the system is given by L = λ / (μ - λ). Plugging in the values, L = 0.5 / (0.75 - 0.5) = 1.

(d) The average waiting time for a customer can be calculated using the formula Wq = Lq / λ. Plugging in the values, Wq = 0.6667 / 0.5 = 1.3333 minutes.

(e) The average time a customer spends in the system is given by W = Wq + (1 / μ). Plugging in the values, W = 1.3333 + (1 / 0.75) = 2.6667 minutes.

(f) The probability that arriving customers will have to wait for service can be calculated using the formula Pw = λ / μ. Plugging in the values, Pw = 0.5 / 0.75 = 0.6667.

These calculations provide the operating characteristics of the drive-up teller window at Willow Brook National Bank.

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Answer:

65 oranges

Step-by-step explanation:

Unit rate: 5 oranges per container

5 x 13 = 65

i literally cannot read, the last thing i put here was wrong.

the answer is 65, lol. the other person is correct.

Since the distanc function is given by

in order to find the distance at 8 seconds, we need to substitute t=8 into this function, that is,

By taking into account that g=32 ft/sec^2, we have

which gives

Therefore, the answer is 1024 ft, which corresponds to the last option.

Sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.The sine function is defined as the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

It ranges from -1 to 1 and is zero at 0 radians and at every multiple of π radians (π, 2π, 3π, etc.). The inverse sine function or sin-1, also known as arcsine, gives the angle whose sine is equal to a given value.In this case, sin-1(0) represents the angle whose sine is zero. Since the sine function is zero at 0 radians and at every multiple of π radians, sin-1(0) is equivalent to either 0 radians or π radians. These are the only two possible solutions for sin-1(0), as the sine function is positive in the first and second quadrants and negative in the third and fourth quadrants, where it takes on nonzero values. In summary, sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.

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Answer:

Df=9x-15

Step-by-step explanation:

The answer is on the question

Answer:

17) #1 = 5

#2 = 49

18) Median= 50.5

Range = 88

Step-by-step explanation:

17) #1 - There are 5 3’s on the leaf side.

#2 - The number that is shown the most times is 49

18) There are 30 numbers in the stem and leaf plot, so the median falls between numbers 15 and 16.  In this plot, those numbers are 50 and 51.  So the median is 50.5.

The data ranges from 10 to 98.  98-10=88

Answer: Linear

Step-by-step explanation: When determining whether the function table represents a linear or exponential relationship, we are checking to see if the rate of change is constant or increasing. If we look at the table, when x increases by 1, y increases by 3. This means that on that interval, the average rate of change is 3/1 = 3. When we increase x by 1 again, we see that y increases by 3 again. This means that the rate of change is constant for the function, so it must be linear.

Answer:

x=9.84375

Step-by-step explanation:

...

Answer:

16.1=x

Step-by-step explanation:

2.1(0.2x-1.4)=1.3(0.4x-3.5)  Distribute          

0.42x-2.94=0.52x-4.55  Combine like terms

+4.55                     +4.55  

0.42x+1.61=0.52x

-0.42x         -0.42x  

1.61=0.1x

0.1     0.1              

16.1=x

Sales tax is added to the price.

From the question, we have the following parameters that can be used in our computation:

The statement is about sales tax

As a general rule

sales tax are added to the price of the item that is being bought

So, the complete statement is Sales tax is added to the price.

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