(10 points) Let G(x) = e' - 3x on the interval (-1,3). Find the absolute maximum and absolute minimum value of G on the given interval.

Answer:

Four percent

Step-by-step explanation:

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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Answer:

40%

Step-by-step explanation:

Flips 600 times, that's the total flips. ###/600

Heads flipped 240 times, and that's what you're looking for. 240/600

240/600 simplified is 2/5 (0.4)

You're looking for a frequency/percentage so you're looking at the decimal

Decimal number = Percentage

So it'll be 40%

Answer:

C. 1,120 cubic inches

Explanation:

To find the total volume, we will divide the solid as follows:

The edge with a length equal to 10 in was calculated as:

18 in - 8 in = 10 in

Because 18 in is the length of the largest height of the figure and 8 in is the length of the smaller height.

Now, the volume of a rectangular prism can be calculated as:

Volume = Length x Width x Height

So, the volume of solid 1 is equal to:

V₁ = 12 in x 4 in x 10 in

V₁ = 480 in³

In the same way, the volume of solid 2 is equal to:

V₂ = 20 in x 4 in x 8 in

V₂ = 640 in³

Therefore, the total volume of the solid is the sum of both parts. Then:

V₁ + V₂ = 480 in³ + 640 in³

V₁ + V₂ = 1120 in³

So, the answer is C. 1,120 cubic inches

Step 1

Simplify the expression.

Step 2

Find a trigonometric identity that can be used to simplify the expression in step 1

Step 3

Get the final answer after substitution.

Hence the right answer is option B

The weights in a weighted moving average are selected by: Trial and error, Fitting to a regression line, Guessing, Experience.

The methods for selecting weights in weighted moving averages are trial and error, fitting to a regression line, and experience.

When selecting weights for weighted moving averages, the following methods can be used:
Trial and error:

Testing different weight combinations to find the best fit for the data.
Fitting to a regression line:

Analyzing the relationship between the data points and assigning weights accordingly.
Experience:

Using prior knowledge and understanding of the data or similar situations to determine appropriate weights.

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 Trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

With weighted moving averages, the weights can be selected using various methods. Here are the applicable methods from your given options:

1. Trial and error fitting: Weights can be selected by testing different combinations of weights and observing their impact on the accuracy of the model.

2. Fitting to a regression line: Weights can be determined by fitting a regression line to the data and using the coefficients of the regression line as the weights.

3. Experience: Domain knowledge or past experience with similar data can help in selecting appropriate weights.

In summary, trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

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Answer:

.6

Step-by-step explanation:

First find < ABC

Since this is a right triangle, we can use trig functions

tan < ABC = opp / adj

tan < ABC = 2/4

Take the inverse tan of each side

tan ^-1 tan < ABC =  tan ^-1 2/4

< ABC = 26.56505118

Multiply by 2

53.13010235

Take the cos

cos (53.13010235)

.6

Answer:

Step-by-step explanation:

Given,

No. of nails the factory makes = 600

Time taken by the factory to make 600 nails = 3 minutes

So,

Time taken by the factory to make 1 nail = \(\frac{3}{600}\) minutes

∴ Time taken by the factory to make 27000 nails

= ( \(\frac{3}{600}\) × \(27000\) ) minutes

= ( \(\frac{1}{2}\) × \(270\) ) minutes

= 135 minutes

Or,

As we know ,  [ 1 minute =  \(\frac{1}{60}\) hour]

So, 135 minutes = \(\frac{135}{60}\) hours

= 2.25 hours

Now, [1 hour = 60 minutes]

0.25 hours = \(\frac{1}{4}\) hours

= \(\frac{1}{4}\) × 60 minutes

= 15 minutes

Hence,

The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)

Answer:

2.25 hours or 2 hours 15 minutes

Step-by-step explanation:

600 nails / 3 minutes = 200 nails / minute

27,000 nails / 200 nails/minute = 135 minutes

1 hour = 60 minutes

135 minutes × 1 hour / 60 minutes = 2.25 hours

2.25 hours = 2 hours  + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes

Answer: 2.25 hours or 2 hours 15 minutes

If we shuffle a deck of cards ,turn over first card, then

(a) "Sample-Space" of this experiment is set of all 52 cards.

(b) Number of outcomes in event that the first card is a heart is 13 .

Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.

In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).

So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".

Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.

In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).

Therefore, there are 13 outcomes in the event .

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The given question is incomplete, the complete question is

Shuffle a deck of cards and turn over the first card.

(a) What is the sample space of this experiment?

(b) How many outcomes are in the event that the first card is a heart?

The values of the expressions are P 9, 3 = 504, C 9, 3 = 84, P 8, 8 = 40320 and C 9, 9 = 1

From the question, we have the following parameters that can be used in our computation:

(A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.

The above expressions are permutation and combination expressions

Using the above as a guide, we have

Expression (A) P9, 3

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 9, 3 = 9!/6!

Evaluate

P 9, 3 = 504

Expression (B) C 9, 3

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 3 = 9!/(6! * 3!)

Evaluate

C 9, 3 = 84

Expression (C) P8, 8

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 8, 8 = 8!/0!

Evaluate

P 8, 8 = 40320

Expression (D) C 9, 9

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 9 = 9!/(9! * 0!)

Evaluate

C 9, 9 = 1

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Answer:

Should be 3.9

Step-by-step explanation:

prove me wrong

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

11 years old

Step-by-step explanation:

Create an equation. Let x = the age of Carlos.

2x + x = 33

3x = 33

x = 11

Answer:

ye Carlos us 11 years old

To make a geometric shape with 100 points, there are many options depending on the desired shape.

There are many possible geometric shapes you can make with 100 points, depending on the specific constraints and requirements you have. Few examples are,

Circle: One way to create a circle with 100 points is to evenly distribute the points around the circumference of a circle with a given radius.

Square: Another option is to create a square with 100 points. To do this, you can divide the sides of the square into 25 segments, and then place 4 points at each segment endpoint.

Regular polygon: You can create a regular polygon with 100 sides by following a similar method to the circle.

Spiral: You can create a spiral shape with 100 points by placing the points along a logarithmic spiral.

Fractal: Finally, you can create a fractal shape with 100 points by applying a recursive algorithm to divide and subdivide segments of an initial shape.

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it is given that the expression is,

y = 5x + 23

here , y = number of people

x = number of flyers,

so, the given expression is representing that,

for every extra Flyer used in advertising, the attending increases by 5 people ​

thus, the correct answer is option D

We can prove that the product of three consecutive positive integers is divisible by 6 using mathematical induction, without assuming that one of the integers must be divisible by 3.

Base case: Let the first positive integer be 1. Then the product of the three consecutive positive integers is 1 x 2 x 3 = 6, which is divisible by 6.

Inductive step: Assume that the product of three consecutive positive integers, n(n+1)(n+2), is divisible by 6 for some positive integer n.

We need to prove that the product of the next three consecutive positive integers, (n+1)(n+2)(n+3), is also divisible by 6.

Expanding the product, we get:

(n+1)(n+2)(n+3) = (n(n+1)(n+2)) + 3(n+1)(n+2)

By the inductive hypothesis, n(n+1)(n+2) is divisible by 6. Since 3(n+1)(n+2) is the product of two consecutive integers, it is divisible by 2. Thus, the sum of the two terms is divisible by 6 + 2 = 8.

Since 6 and 8 are relatively prime, their least common multiple is 24. Therefore, the sum of the two terms is divisible by 24. Thus, (n+1)(n+2)(n+3) is divisible by 24, which means it is also divisible by 6.

By the principle of mathematical induction, the statement is true for all positive integers.

Therefore, we have shown that the product of three consecutive positive integers is always divisible by 6, even if we do not assume that one of the integers must be divisible by 3.

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Answer:

Do you mean solve for t?

If you do, the answer is 9.

Step-by-step explanation:

If we expand the equation out, we get:

-t = 9t - 90

If we move the -90 over to the left side and the -t to the right side, we get:

90 = 10t

Dividing both sides by 9, we get:

t = 9

The partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned.

The given water wave function is graphed as z = 1 + sin(x - y) using Mathematica. The crests and troughs of the wave are aligned in the direction of zero change in the height function, which can be determined by analyzing the partial derivatives. The steepest descent from a crest to a trough corresponds to the direction perpendicular to the alignment of crests and troughs. These conclusions are consistent with the graph of the wave.

The water wave function z = 1 + sin(x - y) represents a snapshot of a frozen water wave. To graph this function using Mathematica, the x and y coordinates are assigned appropriate ranges, and the resulting z-values are plotted.

To determine the alignment of the crests and troughs, we examine the rate of change of the height function. Taking the partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned. Setting dz/dx = 0 gives cos(x - y) = 0, which implies x - y = (2n + 1)π/2, where n is an integer. This equation represents lines in the xy-plane along which the crests and troughs are aligned.  

For the steepest descent from a crest to a trough, we need to find the direction of maximum decrease in the height function. This direction corresponds to the negative gradient of the height function, which can be obtained by taking the partial derivatives dz/dx and dz/dy and forming the vector (-dz/dx, -dz/dy). Simplifying this vector, we get (-cos(x - y), cos(x - y)), which represents the direction perpendicular to the alignment of crests and troughs.    

Upon examining the graph of the wave, we can observe that the lines of alignment for the crests and troughs match the lines where the height function has zero change, confirming our conclusion from part (b). Similarly, the direction of steepest descent from a crest to a trough, indicated by the negative gradient, aligns with the steepest downward slopes on the graph.

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An element with a mass of 780 grams decays by 16.3% per minute. To find the amount of the element remaining after 16 minutes, we can use the following formula: `A = P(1 - r)ⁿ`, where `A` is the amount remaining, `P` is the initial amount, `r` is the rate of decay, and `n` is the number of minutes.

Using this formula, we can plug in the given values and solve for `A`:

```
P = 780 grams
r = 0.163 (since the element decays by 16.3% per minute)
n = 16 minutes

A = P(1 - r)ⁿ
A = 780(1 - 0.163)¹⁶
A ≈ 115.3 grams (rounded to the nearest 10th of a gram)
```

Therefore, after 16 minutes, approximately 115.3 grams of the element are remaining.

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Answer:

Equation = 3x11 + 7

Answer = 40

Step-by-step explanation:

Seven more than three times eleven

More = add

Times = Multiply

So 7 added with 3 x 11 is what?

3 x 11 = 33

33 + 7 = 40

"Seven more than three times eleven" simplifies to the number 40.

Given is phrasal expression "seven more than three times eleven", we need to simplify.

The phrase "Seven more than three times eleven" describes a mathematical expression that involves operations and numbers.

Let's break it down step by step:

Three times eleven: Multiply the number 11 by 3.

3 times 11 = 33

Seven more than three times eleven: Add 7 to the result from step 1.

33 + 7 = 40

So, "Seven more than three times eleven" simplifies to the number 40.

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The above question was not properly written.

Complete Question

Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5,-5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle.

Answer:

Quadrilateral EFGH is a rectangle.l because:

EF = GH and FG = EH

Step-by-step explanation:

The formula for coordinate geometry is given as :

√(x2 - x1)² + (y2 - y1)² when we have coordinates: (x1, y1) and (x2 , y2)

For the quadrilateral EFGH with given coordinates above to be a rectangle,

EF = GH

FG = EH

Hence:

For side EF

E(-4,8), F(8,4)

= √(8 - (-4))² + (4 - 8)²

= √12² + -4²

= √144 + 16

= √160 units

For side FG

F(8,4), G(5,-5)

=√(5 - 8)² + (-5 - 4)²

= √-3² + -9²

= √9 + 81

= √90 units

For Side GH

G(5,-5) , H(-7,-1)

= √(-7 - 5)² + (-1 - (-5))²

= √-12² + 4²

= √144 + 16

= √160 units

For side EH

E(-4,8), H(-7,-1)

= √(-7 -(-4))² +(-1 - 8)²

= √-3² + -9²

= √9 + 81

= √90 units

From the above calculation, we can see that truly,

EF = GH

FG = EH

Therefore, quadrilateral EFGH is a rectangle.

Answer:

90

Step-by-step explanation:

To determine whether the two statement forms are equivalent, we need to create a truth table for each statement form and compare the results.

First, let's create a truth table for the statement form (p∧q)∨∼(p∨q):


 
   p
   q
   p∧q
   p∨q
   ∼(p∨q)
   (p∧q)∨∼(p∨q)
 
 
   T
   T
   T
   T
   F
   T
 
 
   T
   F
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   F
 
 
   F
   F
   F
   F
   T
   T
 

Next, let's create a truth table for the statement form (p∨∼q)∧(∼p∨q):


 
   p
   q
   ∼q
   ∼p
   p∨∼q
   ∼p∨q
   (p∨∼q)∧(∼p∨q)
 
 
   T
   T
   F
   F
   T
   T
   T
 
 
   T
   F
   T
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   T
   F
 
 
   F
   F
   T
   T
   T
   T
   T
 

Comparing the results of the two truth tables, we can see that the two statement forms are not equivalent. The statement form (p∧q)∨∼(p∨q) is true when both p and q are true or when both p and q are false. The statement form (p∨∼q)∧(∼p∨q) is true when both p and q are true or when both p and q are false, but it is also true when p is false and q is true. Therefore, the two statement forms are not equivalent.

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Answer:

not sure but can use Calculator

Answer:

13.39285714285714

Step-by-step explanation:

Using the order of operations (P.E.M/D.A/S), we work from left to right starting with multiplication and division.

Start with the multiplication

2 x 123 = 246

Then the adjacent division

246/56 = 4.392857142857143

Last, we work any addition or subtraction

4.392857142857143 + 9 = 13.39285714285714

Hope this helps.

Answer:

3

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Add all the numbers together, to get 31. Then add 9. That leaves you with 40. Divide that by 5, or the number of terms. You get 8.

Hope that this helps!

Answer:4¹⁵/110

Step-by-step explanation:

Take x to be the number

X=4.13636363

Since the repeating numbers are 2 you multiply the number by 100

100x =413.636363

When we minus 413.6363 and 4.136363 we will get a decimal

We multiply the value for x by 1000 we get 4136.3636

And when we minus 4136.3636 by the values of 1x and 100x we will still get a decimal

We multiply the value of x by 10000 we will get 41363.6363 when we divide it by the values of 1x we will get a decimal but when we divide it by the value of 100x we will not get a decimal

Then we minus them

10000×-100×=9900x

41363.6363-413.6363=40950

9900x=40950

Divide both sides by 9900

9900x÷9900=40950÷9900

X=4¹⁵/110

Answer:

B. 14 and 15

hope this helps

have a good day :)

Step-by-step explanation:

the square root of 200 is 14.14213562 so it has to be between 14 and 15