Two angles in a triangle are equal and their sum is equal to the third angle in the triangle. What are the measures of each of the three interior angles?


Answer 1
Answer: A triangle is 180 if two angles equal to eachother and the other angle is these two combines the angels will be 45 45 90

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Find the exact values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [−2, 2]. (Enter your answers as a comma-separated list.)



The answer is "\bold{c= \pm (2)/(√(3))}"

Step-by-step explanation:

If the function is:

\to f'(x) = 3x^2-2 \n\n\to f'(c) = 3c^2-2

points are:

\to  -2 \leq x \leq2

use the mean value theorem:

\to f'(c) = ( f(b)- f(a))/(b-a)

            = ( f(2)- f(-2))/(2-(-2))\n\n= (4-(-4) )/(4)\n\n= (8)/(4)\n\n= 2

\to 3c^2-2=2 \n\n\to 3c^2=4  \n\n\to c^2=(4)/(3) \n\nc= \pm (2)/(√(3))

Final answer:

The Mean Value Theorem states that for a continuous and differentiable function on a closed interval, there exists at least one 'c' within that interval where the average change rate equals the instantaneous rate at 'c'. In the given case of interval [-2,2], to find 'c', first calculate the average slope between the points (f(2)-f(-2))/4. Then equate this average slope to the derivative 'f'(c). The solution(s) to this equation are the c values for this problem.


The subject of this question pertains to the Mean Value Theorem in Calculus. According to this theorem, if a function f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that the average rate of change over the interval equals the instantaneous rate of change at c.

In the given case, we're trying to find the 'c' value for the interval [-2,2]. First, we need to find the average slope between the two points. Assuming f is your function, that would be (f(2)-f(-2))/ (2 - -2). Subtract the function values of the two points and divide by the total interval length. Next, we need to see where this average slope equals the instantaneous slope 'f'(c), this entails solving the equation 'f'(c) = (f(2)-f(-2))/4. The solution to this equation will be the c values that satisfy the Mean value theorem within the provided interval.

Learn more about Mean Value Theorem here:


The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there
would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.



(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

  The given standard deviation = 3.4 minutes

The value of  n sample size = 45


H(t) = 50 - t/h
h(35) =



Step-by-step explanation:


Identify the problem with the following poll.A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.

correlation and causality

loaded questions


self interest


It is Nonresponse. We can infer that the entire population cannot be made.

PLEASE HELP ME ASAPP if can of not then just leave it




Step-by-step explanation:

To make the cone, melted chocolate is pumped onto a huge cold plate at a rate of 2 ft3/sec. Due to the low temperature, the chocolate forms the shape of a cone as it solidifies quickly. If the height is always equal to the diameter as the cone is formed, how fast is the height of the cone changing when it is 5 ft high?



The height of cone is increasing at a rate 0.102 feet per second.

Step-by-step explanation:

We are given the following in the question:

(dV)/(dt) = 2\text{ cubic feet per second}

Instant height = 5 feet

The height of the cone is always equal to the diameter.

Volume of cone =

V = (1)/(3)\pi (d^2)/(4)h\n\n\text{where d is the diameter and h is the height of cone}\n\nV = (1)/(12)\pi h^3

Rate of change of volume =

(dV)/(dt) = (d)/(dt)((1)/(12)\pi h^3)\n\n(dV)/(dt) =(\pi)/(4)h^2(dh)/(dt)

Putting all the values, we get,

2=(\pi)/(4)(5)^2(dh)/(dt)\n\n\Rightarrow (dh)/(dt) = (8)/(25\pi) =0.102

Thus, the height of cone is increasing at a rate 0.102 feet per second.