Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodicall

Answer:

Yes, Bill surpassed his target by £2,200.

Step-by-step explanation:

The cost for the laptops totals = 50 x 400

= 20,000

He sold 40 laptops with a profit margin of 30%

Calculating that gives (40 x 400) x 1.30

= 20,800

He sold 10 laptops with a profit of 15%

Calculating that gives (15 x 400) x 1.15

= 6900

Thus, the overall sales revenue totals

= 20800 + 6900 = 27,700

Answer:

u(t)  = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

Step-by-step explanation:

The characteristic equation is k² + 1 = 0, which leads to k² = -1, resulting in k = ±i.

The roots are k = i or -i.

The general solution takes the form  u(x)=C₁cosx+C₂sinx.

Applying the method of undetermined coefficients, we have

Uc(t) = Pcos wt  + Qsin wt

Calculating the derivatives gives us Uc’(t) = -Pwsin wt  + Qwcos wt

And differentiating again yields Uc’’(t) = -Pw^2cos wt  - Qw^2sin wt

With the equation U’’ + u = 8cos wt, we substitute:

-Pw^2cos wt  - Qw^2sin wt + Pcos wt  + Qsin wt = 8cos wt.

This simplifies to (-Pw^2 + P) cos wt   + (-Qw^2 + Q) sin wt = 8cos wt.

From -Pw^2 + P = 8, we find P= 8  /(1- w^2).

From -Qw^2 + Q = 8, we can conclude Q = 0.

Thus, Uc(t) = Pcos wt  + Qsin wt = 8 cos wt /(1- w^2).

Combining gives us U(t) = uh(t ) + Uc(t)

     = C1cos t + c2 sin t + 8 cos wt /(1- w^2).

Initial conditions yield:

U(0) = C1cos(0) + c2 sin (0) + 8 cos (0) /(1- w^2)

Which leads us to C1 + 8 /(1- w^2) = 5

So C1 = 5 - 8 /(1- w^2) = -(3 + w^2 ) /(1- w^2).

Next, taking the derivative:

U’(t) = -C1 sin t + c2 cos t - 8 w sin wt /(1- w^2).

Evaluating at t = 0 gives us:

U’(0) = -C1 sin (0) + c2 cos (0) - 8 w sin (0) /(1- w^2) = 7.

Thus, c2 = 7.

  u(t)  = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

   

Thus, the most suitable answer is b..42.Step-by-step reasoning:Prior concepts include an explanation of Analysis of variance (ANOVA), which is employed to assess variances among group averages within a sample. The sum of squares constitutes the total squared variation where variation is defined as the disparity between each value and the grand mean. The correlation coefficient evaluates the strength of the correlation between two variable movements, noted as r, with values bounded between -1 and 1. In conducting multiple regression analysis, we seek to ascertain the relationship among multiple independent (predictor) variables and a dependent (criterion) variable.Solution:Assuming the presence of independent variables and individuals, we can articulate various formulas of variation: We also possess a characteristic identified as . The model's degrees of freedom in this circumstance is represented by , with k =2 indicative of the variable count. The error's degrees of freedom is articulated by . The coefficient of determination in multiple regression is illustrated as: thus, the answer is b..42.

She ought to select the monthly plan for unlimited movies instead of paying $2.99 per film. This choice is advisable because if she continues paying this amount for each individual movie, her total monthly costs will rise significantly. For example, if she has 8 days off in a month (on Saturdays and Sundays) and pays for each film on those days, the total expense would exceed that of the unlimited monthly plan priced at $7.99. And that doesn't include other potential viewing days or any public holidays that could allow her to watch more movies.

Answer: d. AB = CD and BC = AD

Step-by-step explanation:

A parallelogram is defined as a four-sided figure with the following characteristics:-

1. Opposite sides are equal (AB = CD and BC = AD ).
2. Opposite angles are equal (∠A=∠C and ∠D=∠B).
3. Consecutive angles are supplementary (∠A + ∠D = 180°).
4. The diagonals bisect one another.
5. If one angle is a right angle, then all angles are right angles.