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A polynomial multiple by a polynomial is always a polynomial. The given statement is true.

What are polynomials?

Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

When two polynomials are multiplied by each other, then each term of the first polynomial is multiplied by each term of the second polynomial.

The result is always a polynomial, regardless of what the coefficients might be of any of the terms, including the leading coefficients.

Thus, A polynomial multiples by a polynomial is always a polynomial.

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Answer:

Variance: 322.4479999999996

Standard Deviation: 17.956837137981722

Final answer:

To calculate the variance and standard deviation for the given sample set of data, find the sample mean, calculate the squared differences, and then find the sample variance and standard deviation.

Explanation:

To calculate the variance and standard deviation for the given sample set of data (83.6, 92.3, 56.5, 43.8, 77.1, 66.7), follow these steps:

1. Calculate the sample mean by adding all the values together and dividing by the total number of values: (83.6 + 92.3 + 56.5 + 43.8 + 77.1 + 66.7) / 6 = 69.8.
2. Calculate the squared differences between each value and the sample mean: (83.6 - 69.8)^2, (92.3 - 69.8)^2, (56.5 - 69.8)^2, (43.8 - 69.8)^2, (77.1 - 69.8)^2, (66.7 - 69.8)^2.
3. Calculate the sample variance by summing up the squared differences and dividing by (n-1), where n is the total number of values: (83.6 - 69.8)^2 + (92.3 - 69.8)^2 + (56.5 - 69.8)^2 + (43.8 - 69.8)^2 + (77.1 - 69.8)^2 + (66.7 - 69.8)^2 = 300.46. Sample variance = 300.46 / 5 = 60.1.
4. Calculate the sample standard deviation by taking the square root of the sample variance: √60.1 = 7.79. Rounded to the nearest tenth, the sample standard deviation = 7.8.

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Answer:

ironically the units are Always squared and area is the distance around the circle

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

The cost of the dryer is $475 and the cost of the washer is $382.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a washer and a dryer cost $857 combined.

Let the cost of dryer be x.

The washer costs $93 less than the dryer.

Then, the cost of washer will be x-93

So, x+x-93=857

2x=857+93

2x=950

x=$475

x-93=475-93

= $382

Hence, the cost of the dryer is $475.

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Answer:

Dryer cost $475;  Washer cost $382

Step-by-step explanation:

For this problem, we will simply set up a system of equations to find the value of each the washer (variable x) and the dryer (variable y).

We are given the washer and dryer cost $857 together.

x + y = 857

We are also given that the washer cost $93 less than the dryer.

x = y - 93

So to find the cost of the dryer, we simply need to find the value of y.

x + y = 857

x = y - 93

( y - 93 ) + y = 857

2y - 93 = 857

2y = 950

y = 475

So now we have the value of the dry to be $475.  We can check this by simply plugging in the value and see if it makes sense.

x + y = 857

x + 475 = 857

x = 382

And check this value:

x = y - 93

382 ?= 475 - 93

382 == 382

Therefore, we have found the values of both the washer and the dryer.

Cheers.

Answer:

D is the answer to your question