The solution of the differential equation y apostrophe minus y over x equals y squared is a. y equals fraction numerator 1 over denominator open parentheses c over x minus x over 2 space close parentheses end fraction b. y equals 1 plus c e to the power of x c. y equals c x minus x ln x d. y equals c over x minus x over 2 e. y equals fraction numerator 1 over denominator c x minus x ln x end fraction
The solution of the differential equation is
a. b. c. d. e.

Answer:

4 is the maximum number of ride tickets she can buy

Step-by-step explanation:

Here, r represents the number of ride tickets and f represents number of food tickets.

The system of inequalities is given as:

r+f\geq 16                         ....[1]

4r+2f\leq 40                    .....[2]

To solve Mathematically:

Multiply equation [1] by -2 we have;

-2r-2f \leq -32               .....[3]

Add equation [2] and [3] we have;

2r \leq 8

Divide both sides by 2 we have;

r \leq 4

Since r must be less than or equal to 4.

You can also see the graph of the given system of inequalities as shown below.

The intersection point is, (4, 12)

Therefore, the maximum number of ride tickets she can buy is, 4

Answer:

A. 4

Step-by-step explanation:

edg2021 hope this helps :>

The solution for x in the compound inequality is 18 < x ≤ 3

The compound inequality is given as

6x − 10 ≤ 8 or 1/3x + 6 > 12

Add or subtract the constant to both sides of the compound inequality

So, we have

6x ≤ 18 or 1/3x > 6

Divide both sides of the compound inequality by the coefficient of x

So, we have

x ≤ 3 or x > 18

Rewrite as

x > 18 or x ≤ 3

Combine both inequalities

18 < x ≤ 3

Hence, the solution for x in the compound inequality is 18 < x ≤ 3

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

6 x 4

Step-by-step explanation:

Multiples of 24:

12 x 2 (12 + 2 = 14)

8 x 3 (8 + 3 = 11)

6 x 4 (6 + 4 = 10)

Answer:

the median is 38 and the mean is 31

Step-by-step explanation:

Answer:

Mean: 31, Median: 38

Step-by-step explanation:

Mean: 48 + 50 + 38 + 4 + 8 + 46 + 23 = 217 divided by 7 (the amount of numbers) = 31

Median: 4, 8, 23, 38, 46, 48, 50 (The middle number of the numbers in order from least to greatest)

(Please correct me if I'm wrong)

The answer to the following algebra is;

b² at b = 4 is 16

y /5 at y = 15 is 3

27/s at s = 9 is 3

q/3 + 4 at q = 3 is 5

Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

Given the following:

b² at b = 4

substitute b = 4

= 4²

= 4 × 4

= 16

y /5 at y = 15

substitute y = 15

= 15/5

= 3

27/s at s = 9

substitute s = 9

= 27/9

= 3

q/3 + 4 at q = 3

substitute q = 3

= 3/3 + 4

= 1 + 4

= 5

In conclusion, the algebraic expression is solved by substituting the value of the variables.

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The joint probability that a randomly selected customer chose Movie A and did not enjoy it is 0.2262 or approximately 0.23.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To solve this problem, we can use a probability tree to visualize the information given:

We can see that the joint probability of a customer choosing Movie A and not enjoying it is the product of the probabilities along the "Did not enjoy" branch of the Movie A path:

```

P(Choose Movie A and Did Not Enjoy) = P(Movie A) x P(Did not enjoy | Movie A)

                                   = 0.58 x 0.39

                                   = 0.2262

```

Therefore, the joint probability that a randomly selected customer chose Movie A and did not enjoy it is 0.2262 or approximately 0.23.

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Answer:

-2 I think hopefully that is right

Answer:

-2 and 3

Step-by-step explanation:

edge2020

The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

What is population variance?

Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.

Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

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(b-2)x = 8

In the given equation, b is a constant. If the equation

has no solution, what is the value of b ?

Step 1

identify

b is a constant, so (b-2) is a constant too.

If the equation has no solution, it is, there is not a value of x to satisfy (b-2)x=8

Step 2

solve for x

This value becomes indeterminate when the denominator takes the value of zero,it is

so , the value of b=2 makes the equation has no solution.

Answer

A) 2

Answer:

2 For the most part this is all I have at the moment hope this helps

Step-by-step explanation:

Answer: x=9

Step-by-step explanation: 2(x+5+)=3x+1 or 2x+10=3x+1

Answer:

x =  9

Step-by-step explanation:

2(x + 5) = 3x + 1  Distribute the 2

2x + 10 = 3x + 1  Subtract 2x from both sides

10 = x + 1  Subtract from both sides

9 = x

Check:

2(x + 5) = 3x + 1

2(9 + 5) = 3(9)+1

2(14) = 27 + 1

28 = 28

Answer: look at the picture

Step-by-step explanation: Hope this help :D

The differential equation is: r(1 - r ln r) y'' + (1 + x² ln x) y' - (1 + r) y = (1 - x ln x)² e². To find the particular solution, let's assume a particular solution of the form: yp(x) = A e^(r + ln x - x ln x)

Differentiating yp(x), we have:yp'(x) = A e^(r + ln x - x ln x) * (r/x - ln x - 1)

yp''(x) = A e^(r + ln x - x ln x) * [(r/x - ln x - 1)^2 - 1/x]. Substituting these into the differential equation, we have:r(1 - r ln r) [A e^(r + ln x - x ln x) * [(r/x - ln x - 1)^2 - 1/x]] + (1 + x² ln x) [A e^(r + ln x - x ln x) * (r/x - ln x - 1)] - (1 + r) [A e^(r + ln x - x ln x)] = (1 - x ln x)² e². Simplifying and collecting like terms, we get: A e^(r + ln x - x ln x) [(r/x - ln x - 1)^2 - 1/x + (1 + x² ln x)(r/x - ln x - 1) - (1 + r)] = (1 - x ln x)² e². Expanding and simplifying, we have:A e^(r + ln x - x ln x) [r²/x - 2r ln x + (1 - x²) ln x] = (1 - x ln x)² e². For this equation to hold for all x, the coefficients of the terms on both sides must be equal. Therefore, we have:r²/x - 2r ln x + (1 - x²) ln x = (1 - x ln x)² e².  Simplifying and rearranging, we get:r²/x - 2r ln x + ln x - x² ln x + x ln x = (1 - x ln x)² e²

Further simplifying, we have: r²/x - x² ln x = (1 - x ln x)² e²

Unfortunately, we cannot obtain a specific value for r that satisfies this equation. Hence, we are unable to determine a particular solution using the given form. However, the general solution y(x) = C₁e + C₂ ln x + yp(x) is still valid, where C₁ and C₂ are arbitrary constants, and yp(x) represents the particular solution that we were unable to determine explicitly.

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Answer:

A. 16 seconds.

Step-by-step explanation:

Well, it would take him 4 seconds to get 4/16 of the way, or 1/4. So just multply that by 4 and boom, 16 seconds. (yes ik my technique is weird)

Answer:

Answer is v=182

Step-by-step explanation:

v=volume of the glass

v/2+65=6v/7

Multiply by 14

7V+910=12V

910=5V

V=182

I hope it's helpful!

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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Roads that are well-maintained, dry, and free from hazards are generally less likely to result in traction loss.

The likelihood of losing traction depends on various factors such as road conditions, weather, vehicle type, and driver behavior. However, in general, roads that are well-maintained, dry, and free from debris or hazards are less likely to result in traction loss. Additionally, roads with good grip surfaces, such as asphalt or concrete, tend to provide better traction compared to unpaved or slippery surfaces. It's important to drive cautiously and adapt to the specific conditions of the road to minimize the risk of losing traction.

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In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.

Let the plane P be represented by the equation:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane.

Since the line d is parallel to P and passes through the origin, it can be represented by the equation:

lx + my + nz = 0

where (l, m, n) is a vector parallel to the plane P.

To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:

(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2

Expanding this equation and collecting terms, we get:

(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0

Since the line d passes through the origin, we have:

l(0 - a) + m(0 - b) + n(0 - c) = 0

which simplifies to:

al + bm + cn = 0

Therefore, the quadratic equation reduces to:

(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0

This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:

t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)

t2 = -t1

The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:

A = lt1, B = mt1, C = nt1

and

D = lt2, E = mt2, F = nt2

To find the distance between A and B, we can use the distance formula:

AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)

To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:

d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0

This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.

Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.

Answer: I think its $58.4

Answer:

5 miles per hour

Step-by-step explanation:

Let the speed of Kelly is \(v_1\) miles per hour and speed of Raul is v₂ miles per hour.

Since, speed = \(\frac{\text{Distance}}{\text{Time}}\)

Kelly took 135 minutes to cover 90 miles from New York to Philadelphia.

∵ 1 minute = \(\frac{1}{60}\) hours

∴ 135 minutes = \(\frac{135}{60}\) = \(\frac{9}{4}\) hours

v₁ = \(\frac{90}{\frac{9}{4}}\)

   = \(90\times \frac{4}{9}\)

   = 40 miles per hour

Raul took 153 minutes to cover the same distance as Kelly,

∵ 1 minute = \(\frac{1}{60}\) hours

∴ 153 minutes = \(\frac{153}{60}\) = \(\frac{51}{20}\) hours

v₂ = \(\frac{90}{\frac{51}{20}}\)

    \(=90\times \frac{20}{51}\)                        

    = 35.29

    ≈ 35.3 miles per hours

v₁ - v₂ = 40 - 35.3

         = 4.7

         ≈ 5.0 miles per hours

Therefore, Kelly is 5 miles per hours faster than Raul.     

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

y = 23

x = 28

Step-by-step explanation:

Find y first.

3y + 5y - 4 = 180                     The two angles are supplementary if the all the lines are parallel.  Combine the left side.

8y - 4 = 180                              Add 4 to both sides

8y - 4 + 4 = 180 + 4

8y = 184                                   Divide both sides by 8

y = 23

====================================

Now if the lines are parallel, then 3y = 2x + 13

But we already know y

3*23 = 2x + 13                         Do the multiplication

69 = 2x + 13                             Subtract 13

56 = 2x                                    Divide by 2

x = 56/2

x = 28

Answer:

y = 23

x = 28

Step-by-step explanation:

Shoooooot i am so late with this answer, so so sorry haha-

and i'm no gonna do the explanation because the guy above me did a fairly well explanation of how i solve them too.

uhm, have a good day!

The answer will be 180 .

Given,

15% × 1200.

Firstly convert 15% to fraction form.

Percentage to fraction;

15% = 15/100

Now,

15/100 × 1200

15 × 12

180.

Thus the value of 15% of 1200 is 180.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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Each guest receive 352 gm veal roast.

The pound is a unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weights.

We know that,

1 pound = 453.592 gm

12.4 pound = ? gm

12.4 pound = 12.4×453.592

                   = 5624.541 gm

Total number of guest = 16

Then,

Each guest receive veal roast = \(\frac{5624.541 gm}{16}\)

                                                 = 352 gm

Hence, Each guest receive veal roast is 352 gm.

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The probability that the Watson family eats dinner together at least six times during a 7-day period can be calculated using the binomial distribution. The probability is approximately 0.0332 or 3.32%.

Let's define success as the event that the Watson family eats dinner together on a particular day, with a probability of success being 2/5. Since the events of eating dinner together on different days are independent, we can use the binomial distribution to calculate the probability.  

To find the probability of having at least six successful events (eating dinner together) in a 7-day period, we need to sum the probabilities of having exactly 6, 7 successful events, and so on, up to 7.

Using the binomial probability formula, P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (7 in this case), k is the number of successful events (6 or 7), and p is the probability of success (2/5), we can calculate the probabilities for each k and sum them.

P(X≥6) = P(X=6) + P(X=7) ≈ 0.0332 or 3.32%

Therefore, there is approximately a 3.32% chance that the Watson family will eat dinner together at least six times during any 7-day period.

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