Someone help pls I'll give BRAINLIEST

Answer:

the coefficient of x is 2/3 which is the constant.

The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.

This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:

y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.

Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.

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The complete solution to the initial value problem is: y(t) =\(e^{(-3t)\)(3/5cos(√7t) + C₂sin(√7t)) + (4/5)t - 4/5

To solve the given symbolic initial value problem:

y''' + 6y' + 10y = 8(t - 1), y(0) = 2, y'(0) = 2

We will use the method of undetermined coefficients to find a particular solution for the non-homogeneous equation, and then combine it with the general solution of the homogeneous equation to obtain the complete solution.

Homogeneous Equation:

The characteristic equation for the homogeneous equation is:

r³ + 6r² + 10r = 0

Simplifying the equation:

r(r² + 6r + 10) = 0

Since the roots of the characteristic equation are complex, we can write the general solution for the homogeneous equation as:

y_h(t) = e^(-3t)(C₁cos(√7t) + C₂sin(√7t)) + C₃e^(-3t)

Particular Solution:

To find a particular solution for the non-homogeneous equation, we assume a solution of the form:

y_p(t) = At + B

Taking the derivatives of y_p(t):

\(y_p'(t) = A\\y_p''(t) = 0\\y_p'''(t) = 0\)

Substituting these derivatives into the non-homogeneous equation:

0 + 6(0) + 10(At + B) = 8(t - 1)

Simplifying:

10At + 10B = 8t - 8

Comparing coefficients:

10A = 8, 10B = -8

Solving for A and B:

A = 8/10 = 4/5

B = -8/10 = -4/5

Therefore, the particular solution is:

\(y_p(t) = (4/5)t - 4/5\)

Complete Solution:

The complete solution is the sum of the homogeneous and particular solutions:

\(y(t) = y_h(t) + y_p(t)\)

= e^(-3t)(C₁cos(√7t) + C₂sin(√7t)) + C₃e^(-3t) + (4/5)t - 4/5

Applying the initial conditions:

y(0) = C₁cos(0) + C₂sin(0) + C₃ = 2

y'(0) = -3C₁√7sin(0) + 3C₂√7cos(0) - 3C₃ + 4/5 = 2

From the first initial condition, we get C₁ + C₃ = 2.

From the second initial condition, we get -3C₃ + 4/5 = 2.

Solving these equations, we find C₁ = 3/5, C₃ = 7/5.

Thus, the complete solution to the initial value problem is:

y(t) = \(e^{(-3t)}\)(3/5cos(√7t) + C₂sin(√7t)) + (4/5)t - 4/5

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Step-by-step explanation:

Using the equation \(a^{2} + b^{2} = c^{2}\)

so \(a^{2} = 35\) and \(b^{2} =50\)

\(a^{2} + b^{2} = 85^{2}\)

Answer:

85 units²

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is the side opposite the right angle ( third side ) , then

area = 35 + 50 = 85 units²

A truly random sample would be more likely to be representative of the overall town population is no, because it was not truly random. A

The mayor's sample is not likely to be representative of the overall town population because it suffers from a form of sampling bias known as selection bias.

By only surveying people who were present in the library on a Saturday morning, the sample is likely to over-represent people who are frequent library users and under-represent those who are not.

Selecting every tenth person who walked into the library is not truly random since it does not guarantee equal representation of all segments of the population.

If the library is located in a particular part of the town the sample may over-represent people from that area and under-represent people from other areas.

Due to selection bias, a type of sampling bias, the mayor's sample is unlikely to be representative of the entire town's population.

The sample is likely to overrepresent regular library users and underrepresent occasional library users since it only includes individuals who were at the library on a Saturday morning.

Since it does not ensure equitable representation of all racial, ethnic and socioeconomic groups in the population, choosing every tenth individual who entered the library is not completely random.

If the library is situated in a certain neighbourhood, the sample may overrepresent residents of that neighbourhood and underrepresent residents of other neighbourhoods.

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Answer:

x= 27.4

Step-by-step explanation:

a triangle's angles always equal 180 so

34.6+118+x=180

add 34.6 and 118 to get

152.6+x=180

subtract both sides by 152.6 to get

x=27.4

Answer: 1/2 + 3/4

1/2 + 3/4

---Find a common denominator

2/4 + 3/4

5/4

---Convert improper fraction to a mixed number

5/4 = 1 1/4

Answer: 1 1/4 miles

Hope this helps!

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

The measured signal could have a dynamic error of approximately 21.6% of the true value due to the limitations of the 1st order system with a time constant of 0.7 seconds.

The dynamic error that could result from measuring a 2 Hz periodic waveform using a 1st order system with a time constant of 0.7 seconds can be estimated using the following formula:

Dynamic error = 100% x (1 - exp(-T/τ)),

where T is the period of the input signal, τ is the time constant of the system, and exp(-T/τ) is the system's gain at the input frequency.

Substituting T = 0.5 s (since the period of a 2 Hz waveform is 0.5 seconds) and τ = 0.7 s, we get:

Dynamic error = 100% x (1 - exp(-0.5/0.7)) ≈ 21.6%

This means that the measured signal could have a dynamic error of approximately 21.6% of the true value due to the limitations of the 1st order system with a time constant of 0.7 seconds. This error is due to the fact that the system cannot respond fast enough to the rapid changes in the input signal, leading to an output that lags behind the input. The larger the time constant of the system relative to the period of the input signal, the larger the dynamic error will be.

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After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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Using linear functions, it is found that the two plans cost the same for 5000 minutes of calling.

A linear function is modeled by:

\(y = mx + b\)

In which:

For Plan A, the cost is of $25 plus an additional $0.09 for each minute of calls, hence the y-intercept is \(b = 25\), the slope is of \(a = 0.09\), and the function is:

\(A(x) = 0.09x + 25\)

For Plan B, the cost is of $0.14 for each minute of calls, hence the y-intercept is \(b = 0\), the slope is of \(a = 0.14\), and the function is:

\(B(x) = 0.14x\)

The plans cost the same for x minutes of calling, considering that:

\(B(x) = A(x)\)

\(0.14x = 0.09x + 25\)

\(0.05x = 250\)

\(x = \frac{250}{0.05}\)

\(x = 5000\)

The two plans cost the same for 5000 minutes of calling.

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Answer:

Step-by-step explanation:

Answer:

88.4 centimeters

Step-by-step explanation:

I just finched the quiz 2.03

that was the right answer :)

Answer:

the first one

Step-by-step explanation:

the first one is correct

Answer:

the first one

Step-by-step explanation:

the first one is correct

Answer:

0.60

Step-by-step explanation:

becouse of two probability within added gives the above answer

Answer: 8

Step-by-step explanation: 8 * 5 = 40

The rest don't work.

Would appreciate brainliest <3

Answer:

8

Step-by-step explanation:

You can do 8 *5

Answer:

There are 10 cards in the stack, and 5 of them are odd (1, 3, 5, 7, and 9). There are 3 cards (1, 2, and 3) that are less than 4. Since we are replacing the first card before selecting the second, the outcomes are independent and we can multiply the probabilities of each event.

The probability of selecting an odd card on the first draw is 5/10, or 1/2.

The probability of selecting a card less than 4 on the second draw is 3/10, since there are 3 cards that meet this condition out of a total of 10.

Therefore, the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is:

(1/2) x (3/10) = 3/20

So the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is 3/20.

Step-by-step explanation:

Answer:

3/20.

Step-by-step explanation:

To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is:

5/10 x 3/10 = 15/100

We can simplify this fraction by dividing both the numerator and denominator by 5:

15/100 = 3/20

So, the final answer is 3/20.

Received message. To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is: 5/10 x 3/10 = 15/100 We can simplify this fraction by dividing both the numerator and denominator by 5: 15/100 = 3/20 So, the final answer is 3/20.

Brutus Construction Company pays approximately 0.80% of the outstanding principal in interest each month.

To calculate the percentage of the outstanding principal that Brutus Construction Company pays in interest each month,

Calculate the monthly interest rate.

The Annual Percentage Rate (APR) is 9.60%.

To find the monthly interest rate, we divide the APR by 12: 9.60% / 12 = 0.80% (0.008 in decimal form).

Determine the number of months for the loan.

The loan is for five years, so the number of months is 5 years× 12 months/year = 60 months.

Calculate the monthly payment.

To calculate the monthly payment,

we can use a loan amortization formula or financial calculator.

For the purpose of this calculation,

we'll assume the loan is fully amortizing,

meaning the principal and interest are paid off by the end of the loan term.

In this case, the monthly payment can be calculated by dividing the total loan amount by the number of months:

$1,235,000 / 60 = $20,583.33.

Calculate the interest payment for the first month.

The interest payment for the first month can be calculated by multiplying the outstanding principal (initial loan amount) by the monthly interest rate:

$1,235,000×0.008 = $9,880.

Calculate the percentage of the outstanding principal paid in interest each month.

To find the percentage, we divide the interest payment for the month by the outstanding principal and multiply by 100:

($9,880 / $1,235,000) × 100 ≈ 0.80%.

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Answer:

\(g(51) = \sqrt{2(51) - 1} \\ = \sqrt{102 - 1 } \\ = \sqrt{101} \)

Answer:

-22

Step-by-step explanation:

each mark decreases by three, two marks down from 16 would be 16+3+3; which equals 22, and it has to be negative

hope this helped!

Answer:

x to the power of 67000 to the 5th power.

Step-by-step explanation:

In the east town hatchery, around (d) 95% of the fish will have z-scores between 2 and -2.

A z-score is a measure of how far a specific point is away from the mean in terms of standard deviations. A z-score of 2 means that the point is 2 standard deviations above the mean, while a z-score of -2 means that the point is 2 standard deviations below the mean.

In this case, the mean length of a baby sunfish is 2.2 inches and the standard deviation is 0.6 inches. Therefore, a z-score of 2 means that the fish is 2 * 0.6 = 1.2 inches above the mean, while a z-score of -2 means that the fish is 2 * 0.6 = 1.2 inches below the mean.

The 68-95-99.7 rule tells us that approximately:

68% of the fish will have z-scores between -1 and 1.

95% of the fish will have z-scores between -2 and 2.

99.7% of the fish will have z-scores between -3 and 3.

Therefore, approximately (d) 95% of the fish in the east town hatchery will have z-scores between 2 and -2.

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Answer:

352.05

Step-by-step explanation:

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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Answer:

can u show me a picture of this problem.

Step-by-step explanation:

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

\(\angle B=150^{\circ}\)

Step-by-step explanation:

The diagram is two parallel lines cut by a transversal therefore Angle A and Angle B are alternate interior angles, in this case meaning they are equivalent (because lines are parallel).

We can use this information to set up an equation:

\(8x-10=3x+90\)

Add 10 to both sides:

\(8x=3x+100\)

Subtract 3x from both sides

\(5x=100\)

Divide both sides by 5

\(x=20\)

Then, substitute 20 for x to solve for Angle B:

\(\angle B=3(20)+90\\\angle B=60+90\\\angle B=150\)

Answer:

C Subtraction property of equality

Step-by-step explanation:

You are subtracting 21 from both sides in step 3

Answer:

I would guess C

Step-by-step explanation:

I hope I'm correct, good luck.