Answer:

**Answer:**

(E)Nothing can be concluded.

**Step-by-step explanation:**

Given the function

If the derivative is set equal to zero, the function is **undefined.**

Nothing can be concluded since and no such c in (-1,1) exists such that

**THEOREM**

**Rolle's theorem** states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative is zero.

Answer:
### Final answer:

### Explanation:

### Learn more about Rolle's Theorem here:

The function f(x) = 1 - x^2/3 has f(-1) = f(1) = 2/3. The derivative f'(x) = -2x/3 equals zero at x=0, which is in the interval (-1, 1). Therefore, this does not **contradict** Rolle's Theorem.

The function given is f ( x ) = 1 - x ^ 2 /3. To find the values f(-1) and f(1), we simply substitute these values into the function. Therefore, f(-1) = 1 - (-1) ^ 2 /3 = 1 - 1/3 = 2/3 and f(1) = 1 - 1^2/3 = 2/3. As you can see, f(-1) = f(1).

Now, to find the value 'c' such that f'(c) = 0, first we need to determine the derivative of the function, f'(x) = -2x/3. Setting this equal to zero gives the equation 0 = -2x/3, which has the solution x = 0. Therefore, f'(c) = 0 at c = 0, which is within the interval (-1, 1).

Finally, regarding Rolle's Theorem which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f'(c) = 0, our results are consistent with **Rolle's Theorem**, since f is differentiable, f(-1) = f(1), and a 'c' value exists in the interval (-1, 1) such that f'(c) = 0.

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John ordered five large size pizzas for a party. Five kids each ate 1/10 slice, and twelve adults each at 3/10 slices.a) Find the total number of slices consumed.41/10b) Find the leftover pizza if any.

Camden is making accessories for the soccer team. He uses 513.72 inches of fabric on headbands for 34 players and 2 coaches. He also uses 299.54 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

S = the team's scoreg = the number of goals a team has scoredWhich of the variables is independent and which is dependent?

Jenna must run a total of 12 miles on Monday.Jenna ran 3 5/6 miles in morning and 4 1/12 miles in the afternoon.How many miles does Jenna still need to run before the end of the day?•1 9/12•4 1/12•7 11/12•5 5/12

(12pts) Inequalities please help me !?

Camden is making accessories for the soccer team. He uses 513.72 inches of fabric on headbands for 34 players and 2 coaches. He also uses 299.54 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

S = the team's scoreg = the number of goals a team has scoredWhich of the variables is independent and which is dependent?

Jenna must run a total of 12 miles on Monday.Jenna ran 3 5/6 miles in morning and 4 1/12 miles in the afternoon.How many miles does Jenna still need to run before the end of the day?•1 9/12•4 1/12•7 11/12•5 5/12

(12pts) Inequalities please help me !?

Answer:

Step-by-step explanation:

2 3/4 ÷ 4 1/8

23/4×8/41

23×8/4×41

46/41

=1.122

So the answer is 1.122

The **solution **after **divide **2 3/4 by 4 1/8 in fraction form is,

⇒ 2/3

We have to given that,

To **divide **2 3/4 by 4 1/8.

Simplify it as,

2 3/4 ÷ 4 1/8

11/4 ÷ 33/8

11/4 x 8/33

(11 x 8) / (4x33)

2/3

Therefore, The **solution **after **divide **2 3/4 by 4 1/8 in fraction form is,

⇒ 2/3

Learn more about the **divide **visit:

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the mean is found by adding the time it takes Greg each day and then diving by the number of days: 27+25+32=84.

84/3=28 min

it takes Greg 32 min on the third day

84/3=28 min

it takes Greg 32 min on the third day

28x3=84

84-27-25=32

That is my solution.

what were the options

**Answer:**

**Step-by-step explanation:**

a( c + b ) = d

__Divide both sides by a__

That's

Move b to the right side of the equation to make c stand alone

We have the final answer as

Hope this helps you

**Answer:**

c = - b.

**Step-by-step explanation:**

a(c + b) = d

(c + b) = d / a

c + b =

**c = **** - b.**

Hope this helps!

X=1

3*4=12

x*4=4

Or

12/4=3

4/4=1

3*4=12

x*4=4

Or

12/4=3

4/4=1

**Answer:**

x=1

**Step-by-step explanation:**

i did it

**Answer:**

**Mean increase or decrease (same quantity) according to the quantity of the increment or reduction**

**As all elements were equally affected the standard deviation will remain the same**

**Step-by-step explanation:**

**For the original set of salaries: ( In thousands of $ )**

**51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46**

**Mean = μ₀ = 47,92**

**Standard deviation = σ = 9,56**

**If we raise all salaries in the same amount ( 5 000 $ ), the nw set becomes**

**56,58,53,67,39,39,56,58,53,35,67,56,51**

**Mean = μ₀´ = 52,92**

**Standard deviation = σ´ = 9,56**

**And if we reduce salaries in the same quantity ( 2000 $ ) the set is**

**49,51,46,60,32,32,49,51,46,28,60,49,44**

**Mean μ₀´´ = 45,92**

**Standard deviation σ´´ = 9,56**

**What we observe**

**1.-The uniform increase of salaries, increase the mean in the same amount**

**2.-The uniform reduction of salaries, reduce the mean in the same quantity**

**3.-The standard deviation in all the sets remains the same.**

**We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the data spread around the mean will be the same**

**Any uniform change in the data will directly affect the mean value **

**Uniform changes in values in data set will keep standard deviation constant**

The mean salary is affected by each employee's changes in salary, such as raises and pay cuts, but the standard deviation (the spread of salaries) remains the same provided the change is the same for all individuals.

To answer this question, we need to calculate the **sample mean** and **sample standard deviation** in each case. The sample mean is the average of the data, while the sample standard deviation is a measure of the amount of variation or dispersion in the data set.

**(a)**Calculate the sample mean and sample standard deviation of the initial salaries. This involves summing all the salaries and dividing by the total number to get the mean, then calculating the standard deviation using the formula: square root of [sum of (each salary - mean salary)² divided by (total number of salaries - 1)].**(b)**When each employee is given a $5000 raise, the mean will increase by 5, while the standard deviation will remain the same because raises do not affect the dispersion of the team's salaries.**(c)**Similarly, when each employee takes a pay cut of $2000, the mean salary will decrease by 2, but the standard deviation will again remain the same because pay cuts do not affect the dispersion of the team's salaries.**(d)**We can conclude that while the mean is affected by changes in individual salaries (like raises and pay cuts), the standard deviation is not, provided the change is the same for all individuals. Therefore, it shows that while supply changes can affect the central tendency (mean), they do not impact how spread out the salaries are (standard deviation).

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