Algebra 1. 5(x + 6) – 2x = 3(x + 10)

To solve the given third-order linear homogeneous differential equation, we can use the method of finding the characteristic equation and its roots. Let's denote y(x) as the solution to the equation.  Answer :  1,7,-31

The characteristic equation is obtained by substituting y(x) = e^(rx) into the differential equation, where r is an unknown constant. Plugging this into the equation, we get:

r^3 - 3r^2 - r + 3 = 0

To solve this equation, we can use various methods, such as factoring, synthetic division, or numerical methods. By applying these methods, we find that the roots of the characteristic equation are r = -1, r = 1, and r = 3.

Since we have distinct real roots, the general solution for y(x) can be expressed as a linear combination of exponential functions:

y(x) = C1e^(-x) + C2e^x + C3e^(3x)

To find the specific solution for the given initial conditions, we can substitute the values of x = 0, y(0) = 1, y'(0) = 7, and y''(0) = -31 into the equation and solve for the unknown coefficients C1, C2, and C3.

Using the initial condition y(0) = 1, we get:

C1 + C2 + C3 = 1

Using the initial condition y'(0) = 7, we get:

-C1 + C2 + 3C3 = 7

Using the initial condition y''(0) = -31, we get:

C1 + C2 + 9C3 = -31

Solving this system of linear equations, we can find the values of C1, C2, and C3. Substituting these values back into the general solution, we obtain the specific solution for y(x).

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Answer:

A coin toss

Step-by-step explanation:

if you flip one coin repeatedly like 10 to 10000 it can be 0.5

Answer:

69

Step-by-step explanation:

Answer:

1: (B)

2: (C)

3: (D)

4: (D)

5: (A)

Step-by-step explanation:

Question 1:

Answer choice B is the only set of ordered pairs where there is only possible ouput for each input.

Question 2:

The y-intercept represented on the graph is (0, -3) and only answer choice C & D have it. Next, we're going to find the slope by using the rise/run method. From point (0, -3) to point (2, 0), it rises 3 and runs 2, so the slope is 3/2. Answer choice C is the only one with a y-intercept of -3 and a slope of 3/2.

Question 3:

From point (0, 0) to point (1, 3), it rises 3 and runs 1, so the slope is 3/1 or 3.

Question 4:

It is nonlinear because linear functions increase/decrease at the same rate. In the question, it says that the function decreases quickly at first, but then decreases more slowly as time passes. This function is not decreasing at the same rate the entire time.

Question 5:

The $5 fee is the initial fee, or the y-intercept, and the $2.25 per pound is the rate, or slope, so answer choice A is correct.

Hope this helps (●'◡'●)

Answer:

measure of angle 1=180-123=57°[exterior angle is supplementary]

The probability that the passenger waits less than 5 minutes for a bus is approximately 0.45.

The probability that a passenger arriving at a specified stop between 7:00 AM and 7:30 AM waits less than 5 minutes for a bus can be calculated as follows:

There are 31 buses that arrive at the stop between 7:00 AM and 7:30 AM, since they arrive at 15-minute intervals. If a passenger arrives at a random time within this 30-minute period, then there is a uniform distribution of possible arrival times.

If we assume that the passenger's arrival time is uniformly distributed over this period, then the probability that the passenger waits less than 5 minutes for a bus is equal to the proportion of the 30-minute interval during which a bus arrives within 5 minutes of the passenger's arrival time.

Since each bus arrives at 15-minute intervals, the probability that a bus arrives within 5 minutes of the passenger's arrival time is the same for each of the 31 buses.

Therefore, the probability that the passenger waits less than 5 minutes for a bus is equal to the proportion of the 30-minute interval that is covered by the 31 buses arriving within 5 minutes of the passenger's arrival time.

To calculate this probability, we can consider the total time covered by the 31 buses that arrive within the 30-minute interval, and then subtract the time during which these buses arrive more than 5 minutes before or after the passenger's arrival time.

There are 2 buses that arrive before the passenger's arrival time, and 2 buses that arrive more than 5 minutes after the passenger's arrival time, so we need to subtract the time covered by these 4 buses.

The time covered by the 31 buses that arrive within the 30-minute interval is 31 × 15 = 465 minutes. The time covered by the 4 buses that arrive before or after the passenger's arrival time is 4 × 15 = 60 minutes. Therefore, the time covered by the 31 buses that arrive within 5 minutes of the passenger's arrival time is 465 - 60 = 405 minutes.

The probability that a bus arrives within 5 minutes of the passenger's arrival time is therefore 405/30 = 13.5/1 or approximately 0.45.

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Answer:

?

Step-by-step explanation:

I can't read that. Please write it neater and bigger, I'm sure I can help you then.

Answer:

x2 + x + 1

Step-by-step explanation:

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial . Example 1: x2+x+1. (:

Answer:

50%

Step-by-step explanation:

each section of the plot represents 25% and from 38 to 46 that is two 25% sections which would make it 50%.

To find the limit of the given expression, we can use the FOIL method to expand the numerator and then simplify it by combining like terms. After simplification, we notice that the resulting numerator has a common factor of h, which needs to be removed from the denominator before taking the limit.

Let's begin by expanding the numerator using the FOIL method:

6(x + 5)² - 6x² = 6(x² + 10x + 25) - 6x² = 6x² + 60x + 150 - 6x²

Next, we simplify the numerator by combining like terms:

= 60x + 150

Now, let's rewrite the expression with the simplified numerator:

lim (60x + 150) / h

Since the numerator contains a common factor of h, we can factor it out:

= lim (h(60x + 150)) / h

We can cancel out the common factor of h from the numerator and the denominator:

= lim (60x + 150)

Now, we can take the limit as h approaches 0, which simplifies to:

= 60x + 150

Therefore, the limit of the given expression as h approaches 0 is 60x + 150.

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The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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Answer:

46.8

Step-by-step explanation:

0.45*104=46.8

The results of the Monte Carlo simulation study provided insights into the influence of within-case variability on the accuracy of the tau-u indices and the hierarchical linear modeling approach for multiple-baseline design data.

The impact of within-case variability on tau-u indices and the hierarchical linear modeling approach for multiple-baseline design data was investigated in a Monte Carlo simulation study.
To understand the impact of within-case variability on tau-u indices, researchers conducted a Monte Carlo simulation study using a hierarchical linear modeling approach for multiple-baseline design data.
The study aimed to assess how within-case variability affects the tau-u indices, which are measures used to estimate the treatment effect in single-case research designs.
During the simulation study, various scenarios were created to examine the impact of different levels of within-case variability on the tau-u indices.
By manipulating the within-case variability and running multiple simulations, the researchers were able to observe how the tau-u indices varied under different conditions.
The results of the Monte Carlo simulation study provided insights into the influence of within-case variability on the accuracy of the tau-u indices and the hierarchical linear modeling approach for multiple-baseline design data.

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With a constant work rate, Shanice will take 1 1/2 more hours to finish planting the 2 garden beds by herself.

Rate is defined as the relationship between two quantities of different units.

If Shanice can plant one garden bed in 8 hours. her mother can plant 2 in this time and her father can plant 1 1/3 garden beds in that time, then their rates are:

Shanice : rate = 1 garden bed/8 hours = 1/8 garden bed/h

Shanice's mother : rate = 2 garden bed/8 hours = 1/4 garden bed/h

Shanice's father : rate = 1 1/3 garden bed/8 hours = 1/6 garden bed/h

If the three began planting together until Shanice's father left for work after 3 hours, then the amount of work done for 3 hours is:

(1/8 + 1/4 + 1/6) garden bed/h (3 hours) = 13/8 garden bed

If her mother and Shanice work for another half an hour before she left for work, then the amount of work done for half an hour is:

(1/8 + 1/4) garden bed/h (1/5 hour) = 3/16 garden bed

Subtracting the two amounts of work done from 2 garden beds, and dividing it by Shanice's rate, then the time it will took her to finish the garden beds are:

2 - (13/8 + 3/16) garden bed / 1/8 garden bed/h

= (2 - 29/16) garden bed / 1/8 garden bed/h

= 3/16 garden bed / 1/8 garden bed/h

= 3/2 hours

= 1 1/2 hours

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Step-by-step explanation:

y = kx, where k is a real constant.

When x = 12, y = 60.

=> (60) = (12)k, k = 5.

Therefore when x = 20,

y = kx = (5)(20) = 100.

The probability that Diesel will win her 6th game on the 18th game is approximately 0.000568, or 0.0568%.

The probability that Diesel will win her 6th game on the 18th game is calculated using the binomial distribution formula.

Let's define the following terms:
- n = number of trials (games played) = 18
- k = number of successes (games won by Diesel) = 6
- p = probability of success (Diesel winning a game) = 1/4
- q = probability of failure (Daisy winning a game) = 1 - p = 3/4

The formula for the probability of exactly k successes in n trials is:

P(k) = (n choose k) * p^k * q^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials. It can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(6) = (18 choose 6) * (1/4)^6 * (3/4)^12
= 18! / (6! * 12!) * (1/4)^6 * (3/4)^12
= 18564 * 0.00000244 * 0.0122
= 0.000568

Therefore, the probability that Diesel will win her 6th game on the 18th game is approximately 0.000568, or 0.0568%.

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Answer:

\(y=\frac{1}{4} +x\)

Step-by-step explanation:

use desmos graphing calculator

Since triangles RST and XYZ are congruent, the statement that must be true is:

B. ∠R ≅ ∠X

When two triangles are congruent, then every corresponding sides and corresponding angles of both triangles would also be congruent.

Since ΔRST and ΔXYZ are said to be congruent, then all its corresponding parts would also be congruent to each other. Angles R and X are corresponding angles. Therefore, the statement that must be true is:

B. ∠R ≅ ∠X

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Answer:
1. X=4.85

2. X=5.09

Step-by-step explanation:

1.
a. 20.85-7= 13.85
b. 13.85÷2.97
=4.85...

2.
a. 25.63-7=18.63
b. 18.63÷3.66
=5.09...

Answer:

Bueno, sí y no. Si está multiplicando dos términos como (x - 2) y (x - 2), usaría el método FOIL: primero, adentro, afuera, último. Vea el diagrama adjunto. Los dos signos negativos se cancelarían entre sí solo al multiplicar los últimos valores. Avísame si necesitas más explicaciones.

-cjhunter.26

Answer:

PS = 82.8 ; XT = 46.1

Step-by-step explanation:

PZ = \(\sqrt{TP^2 - TZ^2}\) = √(82.8² - 76.5²) = √1003.59

TZ = SZ = 76.5

PS = \(\sqrt{PZ^2 +SZ^2}\) = √(1003.59 + 5852.25) = 82.8 units

XT = RX = 46.1 units

The answer is c) the diagram does not a function.

Explanation:

A x-value can not have more than one y-value:

The graph will be a asymptote, because is a vertical line and it does not represent a function.

Answer:

Step-by-step explanation:

It's the third option:

-3 maps to 0 1 and 2 so is a one-to-many relation which is not a function.

The required program which can solve the given problem is as follows

class TestCode {

  public static void main(String args[]) {

      Scanner scanner = new Scanner(System.in);  // to take input from the user

      int n = scanner.nextInt();  // data type is integer

      int arr[] = new int[n];    // initialization of array

      int min = Integer.MAX_VALUE;

      for(int i = 0;i<n;i++){   // using for loop to assign values to the array

          arr[i] = scanner.nextInt();

          if(min > arr[i]){

              min = arr[i];

          }

      }

for(int i = 0;i<n;i++){

         System.out.print((arr[i]-min) + " ");  // printing the output of for loop   }

}

}

The program is written in java , deducts the least from a list of user given integers and prints the output.

Java is a object oriented programming language.

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If the cost of advertising was $100,000 and the reach or circulation was 10,000,000 people, then the CPM is $10.

Cost per thousand (CPM), which is also called cost per mille, is a marketing word used to denote the price of 1,000 advertisement prints on one web page. If a publisher of a website charges $2.00 CPM, that means an advertiser must pay $2.00 for every 1,000 prints of its ad.

The CPM is calculated by dividing the cost of the advertisement by the number of people reached and then multiplying by 1000.

Given that the cost of advertising was $100,000 and the reach was 10,000,000 people, the CPM can be calculated as follows:

CPM = ($100,000 / 10,000,000) × 1000 = $10.

So, the CPM is $10.

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Answer:

Step-by-step explanation:

Imsureeeeeeee123

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

(a) PR = 55.2 cm

(b) RT = 19.7 cm

(c) <RPT = \(20.8^{o}\)

Step-by-step explanation:

(a) to determine the value of PR, apply the Pythagoras theorem to PQR.

PQ = 45, and SP = QR = 32. So that;

\(/hyp/^{2}\) = \(/Adj 1/^{2}\) + \(/Adj 2/^{2}\)

\(/PR/^{2}\) = \(45^{2}\) + \(32^{2}\)

          = 2025 + 1024

          = 3049

PR = \(\sqrt{3049}\)

     = 55.218

PR = 55.2 cm

(b) To determine RT, apply the appropriate trigonometric function to QRT.

Let RT be represented by x, so that;

Sin \(38^{o}\) = \(\frac{x}{32}\)

x = 32 * Sin \(38^{o}\)

  = 32 * 0.6157

x = 19.7024

RT = 19.7 cm

(c) To determine <RPT, let the angle be represented by θ.

Sin θ = \(\frac{opposite}{hypotenuse}\)

        = \(\frac{RT}{PR}\)

Sin θ = \(\frac{19.7024}{55.218}\)

         = 0.3568

θ = \(Sin^{-1}\) 0.35568

  = \(20.84^{o}\)

Thus, <RPT = \(20.8^{o}\)

Answer:

Step-by-step explanation:

150 - 15w

where w is the number of weeks he payed his mother the $15

Answer:

11, 096, 858, 082

Step-by-step explanation:

Firstly, add 10,009 and 274,628 together which is equal to 284, 637

then you're going to multiply 284,637 and 38,986

which is equal to 11,096,858, 082

The probability of having 63 or more successes in the sample is approximately 0.0266, or 2.66%.

To use the normal approximation to find the probability P(X ≥ 63) for a sample size of n = 90 and population proportion of successes p = 0.6, follow these steps:

Step 1: Calculate the mean (μ) and standard deviation (σ) for the binomial distribution.
\(μ = n * p\) = 90 * 0.6 = 54
\(σ = \sqrt{(n * p * (1 - p))} = \sqrt{(90 * 0.6 * 0.4) }\)= √21.6 ≈ 4.65

Step 2: Use the normal approximation.
To find P(X ≥ 63), first convert X to a z-score:
z = \((X - μ) / σ\) = (63 - 54) / 4.65 ≈ 1.93

Step 3: Find the probability using a z-table or calculator.
Using a z-table or calculator, find the probability of a z-score less than 1.93 (since we want P(X ≥ 63), we need to find the area to the right of the z-score):
P(Z ≤ 1.93) ≈ 0.9734

Step 4: Calculate the complement probability.
Since we want P(X ≥ 63), we need to find the complement probability (1 - P(Z ≤ 1.93)):
P(X ≥ 63) = 1 - 0.9734 = 0.0266

So, the probability of having 63 or more successes in the sample is approximately 0.0266, or 2.66%.

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