Find the absolute maximum and minimum, if either exists, for the function on the indicated interval.
f(x) = x⁴ - 4x + 2
(A) (-1, 1)
(B) (0, 4)
(C) (-1,2)
Find the absolute maxima and minima for A, B and C.

Answer:

141−1−14

=126                     I hope this helps

Answer:

n=6

Step-by-step explanation:

56.38 is not a whole number, we can conclude that 3177 is not a perfect square. We can repeat this process with different numbers until we find one that results in a perfect square.

The difference between the larger and smaller four-digit numbers can be found by reversing the order of the digits in the original number and then subtracting it from the original number.

Let's go through an example to illustrate this process.

Let's say the original four-digit number is 5862.

Reversing the order of the digits gives us 2685.

Now, we subtract the smaller number (2685) from the larger number (5862):

5862 - 2685 = 3177

In this case, the resulting number is 3177.

To determine if it is a non-zero square number, we need to check if it is the square of any positive integer.

By finding the square root of 3177, we can determine if it is a perfect square.

However, if the square root is not a whole number, then 3177 is not a perfect square.

√3177 ≈ 56.38

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The mathematics problem involves a four-digit number and its reverse, where you subtract the smaller from the larger. The difference should be a non-zero square number, which is a number that results from squaring another number, i.e., multiplying the number by itself.

The subject of the question is a number problem involving a four-digit number and its reversed equivalent. Let's say the original four-digit number is 'abcd' (where a, b, c, and d are the digits of the number), and the reversed number is 'dcba'. If 'abcd' > 'dcba', we would calculate 'abcd' - 'dcba', and result must be a non-zero square number. Conversely, if 'abcd' < 'dcba', we would do 'dcba' - 'abcd'.

The process of checking whether a number is a square is called squaring, which involves multiplying the number by itself - if a number multiplied by itself gives the original number, that number is square. For example, 5² = 5 x 5 = 25, meaning 25 is a square number.

However, this problem might not have a specific numerical answer without more information, such as a range of digits you can use, but it is a good training for understanding number properties, arithmetic and the concepts of square numbers.

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Answer:

1/18

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Conversion a mixed number 3 3/

4

to a improper fraction: 3 3/4 = 3 3/

4

= 3 · 4 + 3/

4

= 12 + 3/

4

= 15/

4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/

4

= 12/

4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters

Conversion a mixed number 2 2/

5

to a improper fraction: 2 2/5 = 2 2/

5

= 2 · 5 + 2/

5

= 10 + 2/

5

= 12/

5

To find new numerator:

a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/

5

= 10/

5

b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12

c) Write a previous answer (new numerator 12) over the denominator 5.

Two and two fifths is twelve fifths

Multiple: 15/

4

* 12/

5

= 15 · 12/

4 · 5

= 180/

20

= 9 · 20/

1 · 20

= 9

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the next intermediate step , cancel by a common factor of 20 gives 9/

1

.

In words - fifteen quarters multiplied by twelve fifths = nine.

Answer:

9:20 A.M.

Step-by-step explanation:

Let's list out the points at which the 25-minute bell rings:

25 mins, 50 mins, 1 hour 15 mins, 1 hour 40 mins,  2 hours 5 mins, 2 hours 30 mins, 2 hours 55 mins, 3 hours 20 mins

Next let's list out the points at which the 40-minute bell rings:

40 mins, 1 hour 20 mins, 2 hours, 2 hours 40 mins, 3 hours 20 mins

From the lists above we see a common multiple of 3 hours and 20 minutes.

So, to find what time they ring after 6 A.M. add 3 hours and 20 minutes to it.

6 AM + 3 hours and 20 minutes = 9:20 A.M.

Thus, both bells would ring together again at 9:20 A.M.

Hope this helps!!

Answer:

Step-by-step explanation:

To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.

Vertical asymptote:

The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.

x^2 - 20 = 0

x^2 = 20

x = ±√20

The vertical asymptotes are x = √20 and x = -√20.

Horizontal asymptote:

To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is

y = 0.

X-intercepts and y-intercept:

To find the x-intercepts, we need to set the numerator equal to zero.

5x + 20 = 0

x = -4

Therefore, the x-intercept is (-4,0).

To find the y-intercept, we need to set x equal to zero.

f(0) = (5(0) + 20) / (0^2 - 20)

f(0) = -1

Therefore, the y-intercept is (0,-1).

Hole:

We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.

To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:

Vertical asymptotes at x = √20 and x = -√20

Horizontal asymptote at y = 0

X-intercept at (-4,0)

Y-intercept at (0,-1)

Hole at x = -4

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Answer:

A-- 98.9 degrees in the morning

B-- 0.3 degrees above average

Step-by-step explanation:

Answer:

98.9 degrees F, .3 degrees

Step-by-step explanation:

Brainliest Please!!!

The weekly standard deviation of the stock price calculated from this sample is 42.957

Given info,

Bear Stearns' stock price closed at $98, $103, $58, $29, and $4 over five successive weeks,

To find the weekly standard deviation of the stock price calculated from this sample,

We use,

μ = (98 + 103 + 58 + 29 + 4) / 5

μ = 58.4

The mean of this sample is 58.4

The standard deviation is,

σ = \(\sqrt{\frac{(98-58.4)^2+(103-58.4)^2+(58 - 58.4)^2+(29-58.4)^2+(4-58.4)^2}{(5-1)} }\)

σ = √1845.3

σ = 42.957

Hence, the standard deviation is 42.957

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Answer:

-9.6

Step-by-step explanation:

\(2\frac{2}{5} =2.40\\-\frac{1}{4} =-0.25\)

If change them into decimals it looks like that.

Then all you have to do is use standard calculator to find the answer.

\(\frac{2.40 }{-0.25} =-9.6\)

Answer:9 and 3/8  

Step-by-step explanation:

you have to make 2 and 2/5 into an improper fraction then make the -1/4 into a -4/1 then multiply across to make 48/5 then you have to reduce down to 8 and 8/5. but that cant happen so you reduce again and get 9 and 3/8.

a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

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The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

-----------------------

It is an isosceles triangle if two sides are same.

There are two possible triangles with given values.

If the 45° is between the two 8 cm sides, then as the isosceles triangle the other two angles have the measure:

So this is an acute triangle.

If the 45° angle is opposite to 8 cm side, then the other 8 cm side also has same opposite angle measure.

Then the third angle is:

It means it is a right triangle.

The bank must have at least 17 nickels on hand.

Given data;

A bank has three more dimes than nickels and twice as many nickels as quarters. if the value of the coins exceeds $5.

Let x be the number of nickels;

⇒ 25(x/2) + 10(x+3) + 5x = 500 cents

⇒ 25x + 20(x+3) +10x = 1000

⇒ 25x + 20x + 60 + 10x = 1000

⇒ 55x = 940

⇒  x = 17

Hence, the minimum of nickels in the bank is 17.

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d. Dummy coding. Categorical variables need to be converted into numerical variables to be used in regression analysis. Dummy coding involves creating binary variables for each category of the categorical variable.

For example, if the categorical variable is "color" with categories "red," "green," and "blue," dummy coding would involve creating three binary variables: "red" (0 or 1), "green" (0 or 1), and "blue" (0 or 1). These binary variables can then be used in the regression analysis. In conclusion, to use categorical variables in regression analysis, dummy coding is necessary.


In order to use categorical variables in a regression analysis, they must be converted into numerical values. This process is called dummy coding (also known as one-hot encoding). Dummy coding involves creating new binary variables (0 or 1) for each category of the categorical variable. This allows the regression model to incorporate the categorical data while maintaining its numerical nature.

To use categorical variables in a regression analysis, you must apply dummy coding to convert them into numerical values.

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The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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To derive an equation for the time ta it takes for rock a to hit the ground in terms of v0, tb, and physical constants, we can start by considering the equations of motion for both rocks.

For rock b, we can use the equation of motion for vertical free fall:

yb = 1/2 * g * tb^2

where yb is the vertical position of rock b at time tb, g is the acceleration due to gravity, and tb is the time it takes for rock b to hit the ground.

For rock a, we know that it is launched with an initial velocity v0 and undergoes vertical free fall as well. Using the same equation of motion, we have:

ya = v0 * ta - 1/2 * g * ta^2

where ya is the vertical position of rock a at time ta and ta is the time we want to find.

Since both rocks hit the ground, their vertical positions are zero when they land. Therefore, we can set both equations equal to zero:

yb = 1/2 * g * tb^2 = 0

ya = v0 * ta - 1/2 * g * ta^2 = 0

Now we can solve the second equation for ta:

v0 * ta - 1/2 * g * ta^2 = 0

ta * (v0 - 1/2 * g * ta) = 0

Solving for ta, we find two solutions: ta = 0 (which corresponds to the time when rock a is launched) and ta = (2 * v0) / g.

Therefore, the equation for the time ta it takes for rock a to hit the ground in terms of v0, tb, and physical constants is ta = (2 * v0) / g.

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Given the following data set:

[13,13,13,15,15,16,16,17,17]​

Let's determine the median.

Step 1: Arrange the data points from smallest to largest.

The set is already arranged in ascending order.

[13,13,13,15,15,16,16,17,17]​

Step 2:

a.) If the number of data points is odd, the median is the middle data point in the list.

b.) If the number of data points is even, the median is the average of the two middle data points in the list.

There are 9 data in the set, it is odd. The middle data is the 5th data.

[13,13,13,15,15,16,16,17,17]​

The 5th data is 15.

Therefore, the median of the given set of data is 15.

8(2)^2 + 8(2) + 9 = 57

your answer is 57

have a nice semester :)

Answer:

57

Step-by-step explanation:

8(2)^2 + 8(2) + 9

8×4+16+9

32+16+9=57

The boundaries of the class 1.87-3.43 are D) 1.865-3.435. The lower boundary is 1.865 and the upper boundary is 3.435.

The boundaries of the class 1.87-3.43 can be determined by subtracting and adding half of the smallest possible unit of measurement to the given class limits. In this case, since the given class limits are 1.87 and 3.43, we need to find the boundaries by subtracting and adding half of the smallest possible unit of measurement.

Let's assume the smallest possible unit of measurement is 0.01.

To find the lower boundary:

Lower Boundary = Lower Limit - (0.01/2)

Lower Boundary = 1.87 - 0.005

Lower Boundary = 1.865

To find the upper boundary:

Upper Boundary = Upper Limit + (0.01/2)

Upper Boundary = 3.43 + 0.005

Upper Boundary = 3.435

Therefore, the boundaries of the class 1.87-3.43 are:

D) 1.865-3.435

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Answer:

The answer is 40

Step-by-step explanation:

You are counting by 4's

Answer: 88

Step-by-step explanation:

Answer: 88

Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88

Step-by-step explanation:

<2+<3=180° because they are on a staright line.

Mathematically this will be

(5x+9)°+(4x+19)°=180°

9x+28°=180°

9x=180°-28°

9x=152°

\( \frac{9x}{9} = \frac{152}{9} \\ x = \frac{152}{9} \)

We are not done yet we found the value kf x now we can find the value of <2 GIVEN BY 5X+9 BU PLUGGING IN THE VALUE OF X

\( < 2 = 5(\frac{159}{9} ) + 9 \\ < 2 = \frac{841}{9} \\ = 93.44444444\)

Rounded is 93.44

a) The exponential equation that models can be written as: h = h₀ * r^n. b) the multiplier is 0.4, indicating that the height of the ball decreases by a factor of 0.4 with each bounce. c) the ball rose to a height of 32 inches after the second bounce.

Where:

- h is the height of the ball after n bounces,

- h₀ is the initial height from which the ball is dropped,

- r is the multiplier or the ratio of the height of each bounce to the previous bounce (in decimal form), and

- n is the number of bounces.

In this case, the initial height (h₀) is 200 inches, and the ball rises to a height of 12.8 inches after the third bounce. We can use this information to find the value of the multiplier (r).

b. The multiplier (r) in this context represents the ratio between the height of each bounce and the height of the previous bounce. In other words, it determines how much the ball's height decreases or increases with each bounce.

To find the multiplier, we can set up an equation using the given information. After the third bounce, the ball rises to a height of 12.8 inches. Let's assume the ball's height after the second bounce is h₂.

Using the exponential equation, we have:

12.8 = 200 * r^3

To find the value of r, we can rearrange the equation:

r^3 = 12.8 / 200

r^3 = 0.064

Taking the cube root of both sides, we find:

r = 0.4

Therefore, the multiplier is 0.4, indicating that the height of the ball decreases by a factor of 0.4 with each bounce.

c. To find the height the ball rose to after the second bounce, we can substitute the values into the exponential equation. Let's denote the height after the second bounce as h₂:

h₂ = h₀ * r²

Substituting the known values, we have:

h₂ = 200 * 0.4²

h₂ = 200 * 0.16

h₂ = 32

Therefore, the ball rose to a height of 32 inches after the second bounce.

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For this problem, all you need to do is find the three #'s that add up to 156.

So, lets look at the answers and add them up.

A. 50, 52, 54

50 + 52 + 54 = 156

B. 51,52,53

51 + 52 + 53 = 156

C. 49,50,51

49 + 50 + 51 = 150

D. 49,51,53

49 + 51 + 53 = 153

We get the answers (50,52,54) and (51,52,53)

Now, consecutive numbers are numbers that in order, like 1,2,3.

Therefore, the answer is (51,52,53)

The range and domain of the graphs have been determined .

Domain is the value that can be an input to the function and the range is all the value a function can obtain.

From the given graphs ,

For Graph 1

It can be seen that the line extends from x = -5 to +4

where -5 is not included

therefore the domain is given by

D = { x| -5 < x ≤4}

and the range is

R = {y | -3 < y≤4}

For Graph 2

The input value x extends from -∞ to +∞

so the domain is

D = { x| - ∞ ≤ x ≤ +∞ }

and the range is given by

R = {y | - ∞ ≤ y ≤ 3}

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Answer:

hi is this you from omegle?

Step-by-step explanation:

The directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

To get the directional derivative of the function f(x, y) = 3(e^x) sin y at the point (0, π/3) in the direction of the vector v = <-6, 8>, follow these steps:       Compute the gradient of the function:
∇f(x, y) = (df/dx, df/dy) = (3(e^x) sin y, 3(e^x) cos y)
Evaluate the gradient at the given point (0, π/3):
∇f(0, π/3) = (3(e^0) sin(π/3), 3(e^0) cos(π/3)) = (3(1)(√3/2), 3(1)(1/2)) = (3√3/2, 3/2)
Normalize the direction vector v:
||v|| = √((-6)^2 + 8^2) = √(36 + 64) = √100 = 10
u = v/||v|| = (-6/10, 8/10) = (-3/5, 4/5)
Compute the directional derivative D_u f(0, π/3) by taking the dot product of the gradient at the given point and the normalized direction vector:
D_u f(0, π/3) = ∇f(0, π/3) · u = (3√3/2, 3/2) · (-3/5, 4/5) = (-3/5)(3√3/2) + (4/5)(3/2) = (-9√3/10) + (6/5)
So, the directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

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