Find the Unit Rate: Twenty emails in 5 minutes.

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

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Answer:

  A The line segments are parallel, and the image is twice the length of the given line segment.

Step-by-step explanation:

Dilation by a factor of 2 means any measure of the image is 2 times the corresponding measure of the original.

Dilation does not change any orientations, so the image will have the same orientation with respect to the origin, axes, or any other line segments. That means the dilated segment is parallel to the original. (If the center of dilation is on the original line segment, the dilated segment will overlay the original segment. That is specifically not the case here.)

Answer:

The probability that the sample mean will be within 0.5 of the population mean is 0.3328.

Step-by-step explanation:

It is provided that a random variable X has mean, μ = 50 andstandard deviation, σ = 7.

A  random sample of size, n = 36 is selected.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

And the standard deviation of the distribution of sample mean is given by,

So, the distribution of the sample mean of X is N (50, 1.167²).

Compute the probability that the sample mean will be within 0.5 of the population mean as follows:

Thus, the probability that the sample mean will be within 0.5 of the population mean is 0.3328.

Final answer:

To approximate the probability that the sample mean will be within 0.5 of the population mean, we can use the Central Limit Theorem. This theorem states that the sampling distribution of the sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. To calculate the probability, we need to find the standard error of the mean (SE), calculate the z-score for the upper bound of 0.5 deviations above the mean, and then find the cumulative probability corresponding to that z-score using a z-table or calculator.

Explanation:

To find the approximate probability that the sample mean will be within 0.5 of the population mean, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).

1. Calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation of the population and n is the sample size. In this case, σ = 7 and n = 36, so SE = 7/√36 = 7/6 = 1.1667.
2. Next, calculate the z-score corresponding to the upper bound of 0.5 deviations from the mean by using the formula z = (X - μ)/SE, where X is the value 0.5 deviations above the mean (50 + 0.5 = 50.5 in this case), μ is the mean of the population, and SE is the standard error of the mean. The z-score for 0.5 deviations above the mean can be calculated as z = (50.5 - 50)/1.1667 ≈ 0.4292.
3. Finally, use a z-table or a calculator to find the probability corresponding to the z-score found in the previous step. The probability can be determined by subtracting the cumulative probability of the lower bound (z = -0.4292) from the cumulative probability of the upper bound (z = 0.4292). This can be expressed as p = P(Z < 0.4292) - P(Z < -0.4292).

Using a standard normal distribution table or a calculator, the approximate probability that the sample mean will be within 0.5 of the population mean is the difference between the cumulative probabilities of the upper and lower bounds found in step 3.

Learn more about Central Limit Theorem here:

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Answer: Please see explanation column for answers. Also check number 6, its question is incomplete.  i used an assumed function, incase its not the same function with the one omitted, just follow steps

Step-by-step explanation: Questions 1-5 do not need any step by step explanation, its purely straight forward but Question 6 involves step by step explanation but  is not a complete question, though i used an assumed function.

FALSE   ---> 1. THE ABSOLUTE MAXIMUM OF A FUNCTION ALWAYS OCCURS WHERE THE DERIVATIVE HAS A CRITICAL FUNCTION. ___TRUE_____-->__ 2. IMPLICIT DIFFERENTIATION CAN BE USED TO FIND dy/dx WHEN x IS DEFINED IN TERMS OF y .

TRUE__--->3. IN A RELATED RATES PROBLEM, THERE CAN BE MORE THAN TWO QUANTITIES THAT VARY WITH TIME.

_FALSE  ---> 4. A CONTINUOUS FUNCTION ON AN OPEN INTERVAL DOES NOT HAVE AN ABSOLUTE MAXIMUM OR MINIMUM.

____TRUE__--->____ 5. IN A RELATED RATES PROBLEM, ALL DERIVATIVES ARE WITH RESPECT TO TIME.

6. FIND THE MAXIMUM ABSOLUTE EXTREMUM AS WELL AS ALL VALUES OF x WHERE IT OCCURS ON THE SPECIFIED DOMAIN

----Incomplete question Please.

But assuming the function---- f(x)= x³ -3x+1

 for (E)=(0,3)

step 1= let us use the power rule to find derivative of   f(x)= x^3 -3x+1

we will have f¹ (x) = 3x² -3

The critical values occurs when  3x² -3 = 0

which makes x=⁺₋1

As can be seen 3x² -3 = 0

                         3x²=3

                          x²=3/3=1

                       x= ⁺₋1

step 2=Now x= -1 cannot be considered because it is not in the interval  of the critical values (0,3)

therefore we consider x=1

step 3=The absolute extremes occurs at x=0, x=1, x=3 forf(x)= x³ -3x+1

when x=0,  f(0)= 0³-3(0)+ 1= 1

         x=1    f(1)=1³-3(1) +1=  -1

         x=3    f(3)= 3³ -3(3)+1= 19

Absolute minimum at x=1 has absolute value of-1

Absolute maximum of x=3 has absolute value of 19

Answer:

speed=200 m/s

Step-by-step explanation:

Answer:

the measurement of angle 6 is 60