Use the trapezoidal rule to approximate the value of
∫ ^4√xdx for n = 4

Events that have no outcomes in common  are said to be disjoint or mutually exclusive.

Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.

If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.

Set A = {2, 4, 6, 8, 10, 12, 14, 16}

Set B = {1, 3, 5, 7, 9, 11, 13, 15}

A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.

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Given the marginal willingness to pay for oil, the constant marginal cost of extraction, and a discount rate of 1%, the oil reserve will last for approximately 10.8 periods.



To determine how long the oil reserve will last, we need to find the point at which the marginal cost of extraction equals the marginal willingness to pay for oil. In this case, the marginal cost is constant at $4 per unit. The marginal willingness to pay is given by the equation P = 7 - 0.40q, where q represents the quantity of oil extracted.

Setting the marginal cost equal to the marginal willingness to pay, we have:4 = 7 - 0.40q

Simplifying the equation, we get:0.40q = 3

q = 3 / 0.40

q ≈ 7.5So, at q ≈ 7.5, the marginal cost and marginal willingness to pay are equal. We can interpret this as the point at which the country would extract the oil until the quantity reaches 7.5 units. To determine how long this would last, we need to divide the total oil reserve (5 units) by the extraction rate (7.5 units per period):5 / 7.5 ≈ 0.67

Since the extraction rate is less than 1 unit per period, it means that the oil reserve will last for approximately 0.67 periods. However, the discount rate of 1% needs to be taken into account. To calculate the present value of the oil reserve, we discount each period's value. Using the formula for present value, we find that the oil reserve will last for approximately 10.8 periods.

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the temperature will be 2.5 degrees per second.

We are given the data:

Seconds       Temperature (°F)

0                            75

10                          100

20                         125

30                         150

We need to find the temperature in degrees per second.

So, we get that:

Seconds       Temperature (°F)                    degrees / sec

0                            75                                            Nil

10                          100                           (100 - 75) / (10 - 0) = 2.5

20                         125                         (125 - 100) / (20 - 10) = 2.5      

30                         150                         (150 - 125) / (30 - 20) = 2.5            

Therefore, the temperature will be 2.5 degrees per second.

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Shiloh has done 80 squats during her first week.

Shiloh was recommended by the trainer to increase the number of squads she does by 35% every week, so she does 108 squats in the second week. We have to find how many squats she did during her first week.

This is the percentage increase in value that something obtains that is greater than 100.

Let the number of squats in the first week be x.

After increasing by 35% she does 108 squats.

x+35/100*x=108

x+0.35*x=108

1.35x=108

x=108/1.35

x=80 squats.

Therefore, the number of squats she did in first week is 80 squats before increasing the squats by 35 percentage.

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The equation of the line through (−1,−2) which is perpendicular to y = 2x - 9 is y = -(1/2)x - 5/2

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

The standard form of a linear function is:

y = mx + b

where m is the rate of change (slope) and b is the y intercept

Two lines are perpendicular if the product of their slope is -1.

Given the line y = 2x - 9. The line perpendicular to y = 2x - 9 would have a slope of -1/2.

The line  perpendicular to y = 2x - 9 that includes the point (-1, -2), is:

y - y₁ = m(x - x₁)

substituting:

y - (-2) = (-1/2)(x - (-1))

y = -(1/2)x - 5/2

The equation of the line is y = -(1/2)x - 5/2

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7) Required value of HG is 13 ft.

8) The measure of x in the triangle below is 13 ft.

What is value of cosine formula ?

let say there is AABC,and opposite side of ZA is a, opposite side of <B is b, opposite side of C is c.

then cos(A) = (b² × c² - a²)/(2bc)

given that AFGH . FH = 8ft , FG = 13ft ,and m angle F = 72 deg

by law of cosines to find the HG, since

we know the lengths of FH and FG and

the measure of angle F.

Let's say length of HG be "x".

Then by law of cosines:

x² = 8² + 13²- 2(8)(13) × cos(72°)

x²= 64 + 169 - 208cos(72°)

cos(72°) , which is approximately 0.309., we get:

x²= 233 - 208(0.309)

x² = 169.072

x² = 64+169-208cos(72°)

cos(72°), which is approximately 0.309., we get:

x² = 233-208(0.309)

x²= 169.072

Taking the square root of both sides, we get:

x = 13 (approx)

So the length of HG is approximately 13 feet.

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Answer:

-2 3/5

Step-by-step explanation:

that is the answer yep

Answer: Bruce can predict the value of his investment account to be $49,800 after 3 decades

Step-by-step explanation:

If the value of the investment account doubles every decade, then after one decade (10 years), it will be worth $6,225 x 2 = $12,450.

After two decades (20 years) it will be worth $12,450 x 2 = $24,900.

Finally, after three decades (30 years), it will be worth $24,900 x 2 = $49,800.

Therefore, Bruce can predict the value of his investment account to be $49,800 after 3 decades if he makes no other deposits or withdrawals.

Answer:

It will be 53

Step-by-step explanation:

add all of them up together

The complement of 45° is the angle that when added to 45° forms a right angle (90° ).

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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Answer:

246.5

Step-by-step explanation:

86275÷35

= 246.5

approximately 247

Answer:

15

Step-by-step explanation:

3 x 3=9

2 x 2=4

1x1=1

-1x-1=1

9+4+1+1=15

Answer:

15

Step-by-step explanation:

The square of 3 is 3 times 3, so 9.

2 times 2 is 4.

1 times 1 is 1.

-1 times -1 is 1, because the negative cancels out.

So, it's 9 plus 4 plus 1 plus 1, so the answer is 15.

Answer:

pretty sure its 16 but im not sure.

Step-by-step explanation:

Answer:

c¹⁵

Step-by-step explanation:

When there are parenthesis like that you multiply the exponents.

Answer:

8 meters

Step-by-step explanation:

This is a question that deals with Proportion

Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke

Length of the shadow of Luke = x

= 12/24 = 4/x

We cross Multiply

12 × x = 24 × 4

x = 24 × 4/12

x = 8 meters

Hence, the length of the shadow of Luke = 8 meters

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

ok so the probabilty of getting something on a six sided die is \(\frac{1}{6}\), since there was 6 possible outcomes. so the probabolity of getting 1 would be 1 out of 6

i hope this helps :)

Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.

Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable.

Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers.

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Answer:

16

Step-by-step explanation:

2 times 1 is 2

The given sequence is defined as a_n = 10 + (-1/9)^n. By applying the limit laws and theorems, we can determine the limit of the sequence or show that it diverges.

The sequence a_n = 10 + (-1/9)^n does not converge to a specific limit. The term \((-1/9)^n\) oscillates between positive and negative values as n approaches infinity.

As n increases, the exponent n alternates between even and odd values, causing the term (-1/9)^n to alternate between positive and negative. Consequently, the sequence does not approach a single value, indicating that it diverges.

To further understand this, let's analyze the terms of the sequence. When n is even, the term (-1/9)^n becomes positive, and as n increases, its value approaches zero.

Conversely, when n is odd, the term (-1/9)^n becomes negative, and as n increases, its absolute value also approaches zero. Therefore, the sequence oscillates indefinitely between values close to 10 and values close to 9.

Since there is no ultimate value approached by the sequence, we can conclude that it diverges.

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If the area of the inner square to be 25% of the total area of the rug,  the side length of the inner square is 3 ft.

The first step to solve this problem is to find the area of the entire rug. Since one side of the rug is given as 6 ft, the area of the entire rug is:

Area of rug = (side length)² = 6² = 36 ft²

Next, we need to find the area of the inner square, which is 25% of the total area of the rug. We can write this as:

Area of inner square = 0.25 * Area of rug

Substituting the value of the area of the rug, we get:

Area of inner square = 0.25 * 36 = 9 ft²

The formula for the area of a square is A = side², so we can solve for the side length of the inner square as follows:

9 = x²

x = √(9)

x = 3 ft

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Complete question is:

The design of a square rug for your living room has one side of the rug is 6 ft. you want the area of the inner square to be 25% of the total area of the rug. find the side length x of the inner square.

Burger Quick, because it has a larger median.

Burger Quick typically has more wait time because it has a larger range (30-2=28) compared to Super Fast Food (27-3=24) and also has a larger interquartile range (IQR) (24-9.5=14.5) compared to Super Fast Food (15.5-8.5=7), indicating more variability in the wait times. The fact that Burger Quick's median (15.5) is larger than Super Fast Food's median (12) reinforces this conclusion.

Therefore, the correct answer is: Burger Quick, because it has a larger median.

Answer 2: The appropriate measure of center for this data is the median, which is represented by the line in the box at 19. This is because the data is skewed, with a longer tail to the right, and the median is less sensitive to extreme values compared to the mean. Therefore, the correct answer is: The median is the best measure of center, and it equals 19.

Answer 3: The measure of variability that the charity should use to accurately represent the data is the IQR (Interquartile Range), which is the range of the middle 50% of the data. The reason for this is that the data is skewed to the right, with many values concentrated in the upper range of the data, and the IQR is less sensitive to outliers compared to the range.

The IQR for this data is 20-10=10, which represents the spread of the middle 50% of the data. Therefore, the correct answer is: The IQR of 20 is the most accurate to use, since the data is skewed.

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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The gambler's payoff has a standard deviation of $1. The gambler can expect to win or lose $1 on average for each coin flip, and there is a high degree of variability in the possible outcomes of the game.

The standard deviation of the gambler's payoff can be calculated using the following formula:

σ = √(Σ(xi - μ)^2 * P(xi))

where σ is the standard deviation, xi is the possible outcome of the game, μ is the expected value of the game, and P(xi) is the probability of each outcome.

In this case, there are two possible outcomes: winning $1 with probability 1/2 and losing $1 with probability 1/2. The expected value of the game is:

μ = (1/2 * $1) + (1/2 * -$1) = $0

To calculate the standard deviation, we need to determine the variance first. The variance can be calculated as:

σ^2 = Σ(xi - μ)^2 * P(xi)

= (1 - 0)^2 * 1/2 + (-1 - 0)^2 * 1/2

= 1

Therefore, the standard deviation is:

σ = √1 = 1

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Answer:

im pretty sure its a,e and i,d

Step-by-step explanation:

Answer:

Amedia =  30 m

Top of the Lighthouse = +45 m

Boat = 0

Fish = - 10 m
The distance between Amelia and the fish  is 40 meter

Step-by-step explanation:

Amelia  = 30 m ( height of the cliff) since Amelia is standing on it's edge

-Top of lighthouse =  lighthouse is located on top of the cliff ;
mean height of cliff + height of light house = (30 + 15) = 45 m

-The boat = 0 (on the surface of water) ; this is the sea level surface or point

-The fish = - 10 m (10 meters below the water surface).

Distance between Amelia  and fish :

30 m - ( - 10 m) = 30 m + 10 m = 40 m

The product is given as 6y²√10 +12√5y. Option A

It is important to know that algebraic expressions are defined as expressions that are made up of terms, variables, constants and factors.

From the information given, we have that;

3√10 (y²√4 + √8y)

Substitute the value√4 with 2

3√10(y²×2 +√8y)

Substitute √8y with 2√2y

3√10(2y²+2√2y)

Expand the bracket, we get;

3×2y²√10 + 3×2×√10×√2y

Multiply the value, we get;

6y²√10 + 6√20y

simplify √20y to 2√5y

6y²√10 + 6 × 2√5y

Multiply the values, then add the product of the separate expressions, we get;

6y²√10 +12√5y

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The complete question:

What is the following product? Assume y greater-than-or-equal-to 0

3 StartRoot 10 EndRoot (y squared StartRoot 4 EndRoot + StartRoot 8 y EndRoot)

A. 6 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot

B. 6 StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot

C. 6 y squared StartRoot 10 EndRoot + 4 StartRoot 5 y EndRoot

D. 3 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot

Answer:

Step-by-step explanation:

We know the diagonals of a parallelogram bisect each other.

If O is the point of intersection of diagonals, AC is split into AO and OC.

Since AO = OC, the length of AC is: