Enter the equation of the circle described below. Center (-1, 4), radius = √3

The values of the two supplementary angles are 89 and 1.

To arrive at this, we set the angles as A and B.

We understand that A=B+88 and A+B=90 degrees. Solving this gives A as 89 and B as 1.

Respuesta:

B. Generalmente, el tamaño del zapato de un estudiante no influye en la cantidad de libros recolectados.

Explicación paso a paso:

Answer:

a)

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

b)

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

c)

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

Where and

We seek the probability:

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

By applying this formula, we can find the probability:

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

Part b

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

Part c

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

Response:

a

    f'(t) is negative

b

 The unit is degC/min

c

At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.

Detailed explanation:

According to the question, we are informed that

   The temperature of a cup of coffee on a counter is represented by the equation

         

where t indicates the time in minutes since the coffee was set on the counter.

In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee

As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.

The temperature is measured in degrees Celsius while time is expressed in minutes.

Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).

The question states that

       

which means the rate of temperature change after 35 minutes is 1.5.

And

         

indicating that the coffee's temperature after 35 minutes is 67 degrees Celsius.

Subsequently, after another t= 30 seconds = the rate at which the coffee's temperature changes is

         

=>        

=>            

Thus

At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.

     

The cubic equation formed is L^3 - 52L +144 = 0. Dimensions: Length = 4 inches, Width = 2 inches, Height = 3 inches. To determine this, let L be the length, W the width, and H the height. The box volume is 24 cubic inches, and its total surface area is 52 sq. inches. Setting W = L/2 leads to Volume = L * W * H, thus substituting W gives us the equation 0.5L^2 * H = 24 resulting in H = 48/L^2. The surface area equation simplifies to (L*W) + (L+H) + (W+H) = 26. Introducing W = 0.5L yields 0.5L^2 + 1.5LH = 26. Substituting H into this gives 0.5L^2 + 72/L = 26. Multiplying throughout by L to eliminate denominators yields 0.5L^3 - 26L + 72 = 0. After multiplying through by 2: L^3 - 52L +144 = 0. Testing L=4 confirms a factor, thus Length (L) = 4 inches, and subsequently, W and H calculate to 2 inches and 3 inches respectively.