An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 represents the height of the object above the ground, in feet, xx seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.

The correct choice for the interval in set-builder notation is C. There is no solution.

The given interval is [−5,5).The set builder notation for the given interval is:{ x ∈ ℜ: -5 ≤ x < 5 }Here, ℜ is the set of all real numbers. Hence, the answer is option A. The graph of the interval on a number line can be represented as shown below:Graph of the given interval.

The interval [-5, 5) can be expressed in set-builder notation as:

{x | -5 ≤ x < 5}

In this notation, {x} represents the set of all values of x that satisfy the given condition. The condition here is that x is greater than or equal to -5 but less than 5.

Graphically, the interval [-5, 5) on a number line would be represented as a closed circle at -5 and an open circle at 5, with a solid line connecting them. The solid line indicates that the endpoint -5 is included in the interval, while the open circle indicates that the endpoint 5 is not included.

Based on the options provided, the correct choice for the interval in set-builder notation is C. There is no solution.

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Answer:

6a + 12b + 18c = 3a + 6 + 9c

Step-by-step explanation:

a) balance factor

The balance factor of a node in a binary tree is defined as the height of its right subtree minus the height of its left subtree. It is commonly used in balance algorithms for maintaining balanced binary trees, such as AVL trees.

What is balance factor?

The balance factor is a keyword that represents the measure of the height difference between the left and right subtrees of a node in a binary tree. It is calculated by subtracting the height of the left subtree from the height of the right subtree

Certainly! In a binary tree, the balance factor of a node is a measure of the difference in height between its right subtree and left subtree. It is calculated by subtracting the height of the left subtree from the height of the right subtree.

The balance factor helps in determining the balance or imbalance of a node in a binary tree. It is used as a criterion for tree balancing algorithms, such as the AVL tree. By checking the balance factor of each node, these algorithms ensure that the tree remains balanced and avoids degeneration into a skewed or unbalanced structure.

A balance factor of 0 indicates that the heights of the left and right subtrees are equal, meaning the node is balanced. A positive balance factor means the right subtree is taller than the left subtree, indicating a right-heavy or right-skewed tree. Conversely, a negative balance factor implies the left subtree is taller, indicating a left-heavy or left-skewed tree.

By maintaining balanced trees using the balance factor, efficient search and retrieval operations can be achieved, ensuring optimal performance in various tree-based data structures.

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

an=20.5+2 5n

correct me if I'm wrong

Answer:

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

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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Answer:

D

Step-by-step explanation:

D is the answer as RS is parallel to XY

Answer:

geometric

common ratio 2/3

Step-by-step explanation:

We know that the sequence is not arithmetic

3-2 =1

2-4/3 = 6/3 -4/3 = 2/3

The common difference is not the same

Now check geometric

The common ratio:

Take the second term over the first term

2/3

Now take the third term over the second term

4/3 ÷ 2

4/3 * 1/2 = 2/3

The common ratio is the same so the sequence is geometric with a common ratio of 2/3

a. To calculate velocity, we need to take the derivative of the position function, r(t). So, the formula for velocity is v(t) = r'(t) = [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a.

b. To calculate acceleration, we need to take the second derivative of the position function, r(t). So, the formula for acceleration is a(t) = r''(t) = [sqrt(2)(e^t + e^-t) + sqrt(2)t(e^t - e^-t) + 2sqrt(2)t(e^t + e^-t)]a.

c. To calculate distance, we need to integrate the velocity function, v(t), over a certain time interval. So, the formula for distance is d(t1, t2) = ∫[t1, t2] v(t) dt = ∫[t1, t2] [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a dt.

d. To calculate position, we need to integrate the acceleration function, a(t), twice over a certain time interval. So, the formula for position is r(t1, t2) = ∫[t1, t2] ∫[t1, t] a(s) ds dt + r(t1), where r(t1) is the initial position at time t1.


a. Velocity (v) can be calculated using the derivative of the position function r(t). In this case, v(t) = dr(t)/dt.

b. Acceleration (a) can be calculated using the derivative of the velocity function v(t). So, a(t) = dv(t)/dt.

c. Distance (d) can be calculated by finding the definite integral of the velocity function v(t) with respect to time over a specific interval. In other words, d = ∫|v(t)|dt, where the integration limits correspond to the interval of time you're interested in.

d. Position (r) is given by the function r(t) = sqrt(2)t * e^t * e^(-t), which represents the position of the object at any given time t.

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The rational number between the square root of 7 and the square root of 8 is 27/10

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The features of the rational number are given as

Value = between the square root of 7 and the square root of 8

Rewrite the value properly

So, we have

Value = between √7 and √8

Evaluate the values of √7 and √8

So, we have

√7 = 2.65

√8 = 2.83

This means that the rational number is between 2.65 and 2.83

A number between 2.65 and 2.83 is 2.7

Express as fraction

value = 27/10

Hence, the rational number between the square root of 7 and the square root of 8 is 27/10

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Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

-128

Step-by-step explanation:

Given, f(x)=2x

3

−21x

2

+36x−20

∴f

′

(x)=6x

2

−42x+36

When f(x) is a maximum or a minimum, f

′

(x)=0

Hence, 6x

2

−42x+36=0

x

2

−7x+6=0

x

2

−6x−x+6=0

x(x−6)−1(x−6)=0

(x−6)(x−1)=0

x=1,6

Again f

′′

(x)=12x−42

=6(2x−7)

Now, when x=1,f

′′

(x)=−30 ....[negative]

And when x=6,f

′′

(x)=30 ....[positive]

Hence, f(x) is maximum for x=1 and minimum for x=6.

The maximum and minimum values of f(x) are

f(1)=2(1)

3

−21(1)

2

+36(1)−20

=2−21+36−20=−3

f(6)=2(6)

2

−21(6)

2

+36(6)−20

=432−756+216−20=−128

Answer:

19.5

Step-by-step explanation:

2 x 19.5 = 39 - 29 = 10 :D

If after hip surgery, your physical therapist tells you to slowly return to walking. The number of  weeks it will be before you are up to 45 minutes of walking per day is: c. 9.

Since the therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter.

Hence,

You will  tend to need 9 weeks to reach 45 minutes of walking per day which are:

Week 1: 5 minutes

Week 2: 10 minutes

Week 3: 15 minutes

Week 4: 20 minutes

Week 5: 25 minutes

Week 6: 30 minutes

Week 7: 35 minutes

Week 8: 40 minutes

Week 9: 45 minutes

The total number of weeks are 9 weeks.

Therefore the correct option is C.

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Answer:

answers below

Step-by-step explanation:

(a) When the sample is less than 30. (b) When we are estimating the population standard deviation with the sample standard deviation

Answer:

Frame 1 to Frame 2:

Translation (x,y) to (x,-y)

Frame 2 to Frame 3:

Rotation R₉₀

Frame 3 to Frame 4:

Translation (x,-y) to (x,y)

Step-by-step explanation:

I know this very well :)

Answer: (C) 25 lawns

Step-by-step explanation: he has 15 cars so his you follow the line from the graph it will end at 25 lawns

sorry this is a bad explanation but C is correct-

Answer:

ok Let’s calculate the money Sam makes per week, not including sales (or Assuming $0 in sales):

Money per week =$6.45/hour×37.5 hours/week= $241.88/week  

The money he Gains from sales must make up the difference, So

money from sales = $400−$241.88 = $158.12  

This Money is only 6% or 0.06 of the total sales though, so

Total sales = $158.120.06 = $2635.33  

of course, this is Assuming that the money per week is rounded up from $241.875 to $241.88 instead of down to $241.87, in which case Sam would Have to make $2635.50 in sales (about 17 cents more).

Step-by-step explanation:

have a nice day.

Answer:

the answer is 40c

Step-by-step explanation:

\(\\ \sf\longmapsto \dfrac{8}{12}=\dfrac{x}{9}\)

\(\\ \sf\longmapsto 12x=8(9)\)

\(\\ \sf\longmapsto 12x=72\)

\(\\ \sf\longmapsto x=\dfrac{72}{12}\)

\(\\ \sf\longmapsto x=6\)

The standard deviation of the speeds of cars travelling on California freeways is approximately 13.96 miles per hour.

Given that the speeds of cars travelling on California freeways are normally distributed with a mean of 57 miles /hour and the highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles /hour.

The records show that exactly 5% of the speeds exceed this limit.

To find the standard deviation of the speeds of cars travelling on California freeways, we need to use the following formula:

z = (x - μ) / σ

Where

z is the z-score,

x is the value of the observation,

μ is the population mean, and

σ is the standard deviation.

To find the z-score for the speed limit of 80 miles per hour, we use the formula.

z = (x - μ) / σ

  = (80 - 57) / σ

  = 23 / σ

The z-score that corresponds to 5% is -1.645.

Therefore, -1.645 = (x - 57) / σ

Now, we need to solve for σ,σ = (x - 57) / (-1.645)

Substituting 80 for x,

σ = (80 - 57) / (-1.645)

σ = 13.96 miles per hour (rounded to two decimal places)

Therefore, the standard deviation of the speeds of cars travelling on California freeways is approximately 13.96 miles per hour.

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Answer:

a=1

Step-by-step explanation:

-20=-8(a+4)-5(1-5a)

Distribute

-20 = -8a -32 -5 +25a

Combine like terms

-20 =17a -37

Add 37 to each side

-20+37 = 17a-37+37

17 = 17a

Divide by 17

17/17 = 17a/17

1= a

The salary of the teacher who is 45 year old according to the best fit line is $50000.

A straight line that minimizes the gap between it and some data is called a line of best fit.

In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

It is a result of regression analysis and a tool for forecasting indicators and price changes.

The line of best fit is a tool used in finance to find patterns or correlations in market returns across assets or across time.

From the graph the two coordinates of the best fit line are:

(30, 40000) and (70, 70000)

The equation of the line is given as:

y = mx + c

The slope of the equation is given as:

m = (y2 - y1) / (x2 - x1)

m = (70000 - 40000)/ 70 - 30

m = 30000/4

m = 750

Substituting the value of slope and coordinate in the point slope form we have:

y - y1 = m (x - x1)

y - 40000 = 750 (x- 30)

y = 750x + 17500

Here, x is the age and y is the salary.

Substituting x = 45 we have:

y = 750(45) + 17500

y = 50000

Hence, the salary of the teacher who is 45 year old according to the best fit line is $50000.

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The correct question is:

The given expression can be expressed in terms of a and b as a + 3/2 b.

Using the laws of logarithms, we can express the given expression in terms of a and b. We have:

log_m (28) + 1/2 log_m (49/4)

= log_m (4*7) + 1/2 log_m (7^2/2^2)

= log_m (4) + log_m (7) + 1/2 (2 log_m (7) - 2 log_m (2))

= log_m (4) + 3/2 log_m (7) - log_m (2)

= 2 log_m (2) + 3/2 log_m (7) - log_m (2) (since log_m (4) = 2 log_m (2))

= log_m (2) + 3/2 log_m (7)

= a + 3/2 b

Therefore, the given expression can be expressed in terms of a and b as a + 3/2 b.

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The area of the supplied trapezium is 20 \(cm^{2}\).

                   The four sides of a trapezium, a geometric shape, consist of a single pair of parallel sides, commonly referred to as the "bases". An additional set of sides, which may or may not be parallel, are referred to as the "legs" of a trapezium. The term "area" refers to the entire space a trapezium takes up on a two-dimensional plane.

                 The area of a trapezium is determined by \(\frac{1}{2} (a+b)h\).  where h is the distance between the two parallel side lengths, a and b. By counting the shaded squares in this graph, one can determine the length of parallel sides.

Here, an is 3 cm and b is 7 cm. The trapezium is 4 cm tall.

Applying the calculation above,

Area= = \(\frac{1}{2} (3+7) 4\)

\(=\frac{1}{2}(10)4\)

\(=\frac{40}{2}\)

=20 \(cm^{2}\)

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