IF YOU ANSWER THIS RIGHT NOW ILL GIVE YOU 64 POINTS

it would be the last one bc it makes a little sense i guess

a) The slope, m, of the tangent to the curve y = 2 x at the point where x = 16

b) The equations of the tangent lines at the following points is y = 2x - 24

c) The graph of the curve and the tangents is illustrated below.

Let's start with point (25, 10). We already know the slope of the tangent line at x = 25, which is 2 (as we found earlier). Therefore, the equation of the tangent line can be written as

=> y - 10 = 2(x - 25).

We can simplify this equation by distributing the 2, which gives us

=> y - 10 = 2x - 50.

Finally, we can rearrange the terms to get the slope-intercept form, which is

=> y = 2x - 40.

Now, let's move on to point (16, 8). We need to find the slope of the tangent line at x = 16.

To do this, we first need to find the derivative of the curve y = 2x. The derivative of y = 2x is again simply 2.

Therefore, the slope of the tangent line at x = 16 is m = 2.

Now that we have the slope and a point on the line (16, 8), we can use the point-slope form of a line to find the equation of the tangent line.

The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Plugging in our values, we get

=> y - 8 = 2(x - 16).

Simplifying this equation, we get

=> y - 8 = 2x - 32,

and rearranging the terms, we get y = 2x - 24. This is the equation of the tangent line at the point (16, 8).

Finally, part (c) asks us to graph the curve and both tangent lines on a common screen. To do this, we can plot the curve y = 2x using any graphing software or calculator.

Then, we can plot the two points (25, 10) and (16, 8) and draw their respective tangent lines using the equations we found earlier. The resulting graph should show the curve and both tangent lines on the same coordinate plane.

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The total area of the given composite figure is 276 square feet.

By dissecting the given composite figure into smaller shapes and adding their individual areas, we can determine the overall area of the given composite figure.

Two rectangles and a triangle make up the figure:

The largest rectangle is 22 feet by 6 feet in size.

Area = length x breadth x height = 22 feet x 6 feet = 132 feet 2

The smaller rectangle is 16 feet by 6 feet in size.

Area = length * width * height = 16 * 6 * height = 96 ft2

The triangle measures 6 feet in height and 16 feet in base:

Area equals (16 ft. x 6 ft.) divided by two equals 48 ft2.

The total area of the figure can now be calculated by adding the areas of the three shapes:

Total Area is equal to the sum of the areas of the two rectangles.

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The volume of the three-dimensional object (cone) formed is equal to 32π cubic units.

In this scenario, the effect of rotating the right triangle around line segment AB would form a three-dimensional object known as a cone, with the following dimensions:

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Substituting the given parameters into the formula, we have;

V = 1/3 × π × 4² × 6

V = π × 16 × 2

V = 32π cubic units.

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Complete Question:

In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AB?

(1) 32π

(2) 48π

(3) 96π

(4) 144π

Louis total distance of 8/5 km. Louis rose his bicycle a total distance of 8/5 km.

Louis rose his bicycle a total distance of 1/2 km + 3/4 km + 7/10 km.

To find the total distance, we need to find a common denominator for the fractions: 2, 4, and 10.

The least common denominator is 20.

So, 1/2 km can be written as 10/20 km, 3/4 km can be written as 15/20 km, and 7/10 km remains the same.

Adding these fractions together, we have:

10/20 km + 15/20 km + 7/10 km = 32/20 km

Simplifying this fraction, we get:

32/20 km = 8/5 km

Therefore, Louis rose a total distance of 8/5 km.

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Louis rode a total distance of 8/5 km or 1 and 3/5 km

Louis rode his bicycle a total of 1/2 km to school, 3/4 km to a ball field, and 7/10 km back home. To find the total distance Louis traveled, we need to add up these three distances.

First, let's add 1/2 km and 3/4 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 4 is 4.

Converting 1/2 to have a denominator of 4, we get 2/4. Now we can add 2/4 + 3/4, which equals 5/4.

Next, we need to add 5/4 km and 7/10 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Converting 5/4 to have a denominator of 20, we get 25/20. Now we can add 25/20 + 7/10, which equals 32/20.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 32/4 and 20/4, we get 8/5.

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if I did it right then it's $32.38.

Answer: To find the absolute value of an imaginary equation, you need to calculate the modulus (also known as the magnitude or absolute value) of the complex number.

The modulus of a complex number a + bi is defined as:

|a + bi| = sqrt(a^2 + b^2)

where sqrt() denotes the square root function.

So, to find the absolute value of an imaginary equation, you can follow these steps:

Step 1: Identify the imaginary part of the complex number.

An imaginary equation is of the form bi, where b is a real number and i is the imaginary unit (i.e., i^2 = -1). For example, if you have the equation 2i, the imaginary part is 2i.

Step 2: Find the real part of the complex number.

In the case of an imaginary equation, the real part is 0.

Step 3: Write the complex number in the form a + bi.

Since the real part of an imaginary equation is 0, you can write the complex number as bi.

Step 4: Calculate the modulus of the complex number.

The modulus of the complex number bi is |bi| = sqrt(0^2 + b^2) = sqrt(b^2) = |b|.

Therefore, the absolute value of an imaginary equation bi is simply the absolute value of the real coefficient b, which is |b|.

Step-by-step explanation:

Answer:

answer 1 is 30

answer 2 is 130.8

answer 3 is 5.85

answer 4 is 36%

answer 5 is 82.55

Answer: For number 8 it is 2  For number 9 it is confusing

Step-by-step explanation:

Thus, the current takes roughly 3.3 time constants to drop to 1/e of its starting value.

An RC circuit's time constant is the length of time it takes for the current to drop to 1/e (or around 0.368) of its starting value. Option E, "1/e," is the correct response, therefore.

The equation: gives the time constant () of an RC circuit.

τ = RC

where C is the capacitance in farads and R is the resistance measured in ohms. A crucial factor in deciding how the circuit will behave is the time constant, which measures the rate at which the capacitor charges or discharges through the resistor.

The voltage across the capacitor will be approximately 63.2% of its final value after one time constant, and the current will be roughly 36.8% of its original value. Thus, the current takes roughly 3.3 time constants to drop to 1/e of its starting value.

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The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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1. The official lines of authority. 2. The formal lines of communication. 3. The base level of the organization.

Organizational structure box-and-lines diagrams show at least three things:

1. The official lines of authority: These diagrams illustrate the formal hierarchy within an organization, indicating the chain of command and reporting relationships. The lines represent the flow of authority and communication, highlighting who reports to whom. For example, a manager may have multiple employees reporting to them, and those employees may further have their own subordinates.

2. The formal lines of communication: These diagrams also depict the formal channels through which information flows within the organization. They show how information is passed between different levels and departments. For instance, a diagram may show that information flows vertically from top management to lower-level employees or horizontally between departments.

3. The base level of the organization: These diagrams display the entry-level positions within the organizational structure. This helps to understand the foundational roles that exist and how they fit into the larger structure. For instance, the diagram may indicate positions such as interns, junior associates, or entry-level staff.

In summary, organizational structure box-and-lines diagrams provide a visual representation of the official lines of authority, the formal lines of communication, and the base level of the organization. These diagrams help individuals understand the hierarchy, communication flow, and entry-level positions within an organization.

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Answer:

20

Step-by-step explanation:

pq + 4

Given:

p = 4

q = 4

We plug the numbers in:

pq + 4

4(4) + 4

16 + 4

20

The answer you are looking for is 20.

Since p=4 and q=4,

Therefore,

pq+4

Substitute each of the given values of the variables,

(4)(4)+4

16+4

20

The interquartile range (IQR) of the data is 70 and the third and the first quartile of the data is (90, 20).

The second and third quartiles, or the middle half of your data collection, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data collection.

The given plot shows the number of days on the market for single-family homes in the city.

The figure shows the first quartile = 20 and the third quartile 90

Therefore the interquartile range of the data is equal to the difference between the third quartile and the first quartile i.

The interquartile range = Q3 - Q1

                                       = 90 - 20

                                       = 70

The third and first quartiles of the data are (90, 20).

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Answer:

69

Step-by-step explanation:

let the first term be n

second term = 2 + n

third term = 3 + second term so we can conclude that the other term will be:

forth term = 4 + third term

fifth term = 5 + forth term etc.

eleventh term will be 11 + 10 term

based on observations the tenth term is 58 so

eleventh term= 11 + 58

= 69

In order to solve the system of equations, let's equate both values of y and solve for x using the quadratic formula:

Now, let's calculate the values of y for each value of x:

Therefore the solutions are (1, 7) and (5/2, 10).

Correct option: second one.

The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)

To find a data set with 5 values for which the standard deviation is zero,

⇒ (4, 4, 4, 4, 4)

For the above dataset;

Mean μ = 4

Number of samples n = 5

Standard deviation σ = \(\sqrt{\frac{sumof(xi - x)^2}{n} }\)

                                   = \(\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }\)

                                   = 0

Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).

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Answer:

AB = √(4^2 + 1^2) = √(16 + 1) = √17

GH = √(4^2 + 4^2) = √(16 + 16) = √32

= 4√2

The notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

What is end behavior of polynomial?

The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.

From the graph we know that the vertex of this parabola is V(0, 8).

This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.

Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.

In a mathematical language this is:

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

Hence, the notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

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line k and second line h are not parallel lines because the have different slopes.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate

y₁ - y coordinate

m - slope

A line k passes through the points ​(−5​,−5​) and ​(1,37​).

Then Slope m = 37 + 5/ 1 + 5

m = 7

Now Write the equation as;

y + 5 = 7(x + 5)

y = 7x + 30

A second line h passes through the points ​(−3​,−33​) and ​(3​,9​).

Then Slope m = 9 + 3/ 3 + 33

m = 0.33

Now Write the equation as;

y + 33 = 0.33(x + 3)

Hence, line k and second line h are not parallel lines because the have different slopes.

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Answer: He run 7 high-speed intervals and 8 low-speed intervals.

Step-by-step explanation:

Let x = Number of high-speed intervals.

y= Number of low-speed intervals .

He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.

4 min 56 sec = (4(60)+56) sec = 296  sec   [ 1 minute = 60 seconds]

According to the question , we have the following linear equations :

\(x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)\)

Multiply (i)by 16 , we get

\(16x+16y=240\ ...(iii)\)

Subtract (iii) from (ii)

\(7y=56\\\\\Rightarrow\ y=8\)

Put value of y in (i) , we get

\(x+8=15\Rightarrow\ x=7\)

Hence, he run 7 high-speed intervals and 8 low-speed intervals.

Answer:

about 18 (17.7)

Step-by-step explanation:

Answer:

About 17 inches

Step-by-step explanation:

Answer:

9.5_<w<9.25

Step-by-step explanation:

Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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Answer:

3 , 6

Step-by-step explanation:

Answer: (2,-3), (2, -3)

Step-by-step explanation: Substitute 2 into each equation. See Attachment and don’t forget to check the work just in case ;)

Step-by-step explanation:

davis is right.

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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