Which of the following is true of (1, 4) and (1, −7)?

More information is needed to determine the relationship between the two points.

The points lie on a diagonal line.

The points lie on a vertical line.

The points lie on a horizontal line.

​

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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, the correct answers are:

Orientation (North Arrow)

Scale

Legend

Neatline Border

The four primary cartographic elements are:

Orientation (North Arrow): This element indicates the orientation or direction of the map, typically pointing towards the north. It helps users understand the map's alignment and relation to the real world.

Scale: The scale provides a ratio or representative fraction that shows the relationship between distances on the map and corresponding distances on the Earth's surface. It helps users determine the actual size or distance of features on the map.

Legend: The legend, also known as a key, explains the symbols, colors, and other graphic elements used on the map. It helps users understand the meaning or representation of various features or data.

Neatline Border: The neatline border defines the outer boundary of the map. It is a solid line that encloses the map area and separates it from the surrounding space or background.

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\(\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x\)

Answer:

Elena's calculator is not broken.

Step-by-step explanation:

0.06 x 0.5

You can also do this by ignoring the decimals and multiplying normally.

6 x 5 = 30

Then you you count the decimal places and start at the end of your product and move the number of decimal places to the left.

0.030 or 0.03

Answer:

1,962.5

Step-by-step explanation:

r=d/2

50 / 2 = 25

25 = r

A= πr²

3.14 x 25²=1,962.5

\(Hope\)  \(this\)  \(helps!\)

The second derivative of y with respect to x is 0 in terms of t.

To find the second derivative of y with respect to x, we need to use the chain rule and differentiate both x and y with respect to t, and then divide dy/dt by dx/dt.

First, we need to find dx/dt and dy/dt:
dx/dt = d/dt(e^-3t) = -3e^-3t
dy/dt = d/dt(e^3t) = 3e^3t

Now, we can find dy/dx:
dy/dx = (dy/dt)/(dx/dt) = (3e^3t)/(-3e^-3t) = -e^6t

Finally, we can find the second derivative of y with respect to x:
d^2y/dx^2 = d/dx(dy/dx) = d/dx(-e^6t) = 0

Therefore, the second derivative of y with respect to x is 0 in terms of t.

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Answer:

x = -8

Step-by-step explanation:

\(3(x-2)=4x+2\\3x-6=4x+2\\-6=x+2\\-8=x\)

By subtracting 2 on both sides, we isolate x, and make the solution to the equation x=-8.

Answer:

Step-by-step explanation:

3(x-2)=4x+2

3x-6=4x+2

-6-2=4x-3x

-8=x

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

Answer:

x=1

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  − 2 + 2 y = 5 .

Answer:

C

Step-by-step explanation:

The radius should give you what is inside the x and y parentheses and use the Pythagorean theorem to find the radius, but do not square root the result.

The common ratio r = 1010 is greater than 1, so the series diverges

The given geometric series is 1 + 1011 + 100121 + .....There are infinite terms in the given geometric series.

Let's find the common ratio first.Now, we will use the formula for the sum of an infinite geometric series, where a is the first term, r is the common ratio, and |r| < 1:S = a / (1 - r)

Now, the first term a = 1 and the common

ratio r = 1010.Thus, S = 1 / (1 - 1010)

Let's simplify:1 / (1 - 1010)

= 1 / (1 - 1 / 10¹⁰)

=(10¹⁰/ (10¹⁰ - 1)Hence, the sum of the given infinite geometric series is 10¹⁰ / (10¹⁰ - 1).

A geometric series is a sequence of numbers in which the ratio of any two consecutive terms is constant. It is given by the formula: a + ar + ar² + ar³ + ...Here a is the first term and r is the common ratio. If |r| < 1,

then the series converges, and its sum is given by the formula S = a / (1 - r).

Otherwise, the series diverges. In the given problem, we have an infinite geometric series whose first term is 1 and common ratio is 1010.

The common ratio r = 1010 is greater than 1, so the series diverges. Hence, it has no sum.

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The answer is C. 13 seconds.

A graph is a visual representation of data, typically using points, lines, or bars to show relationships or trends

Interpolation is the process of estimating values within a set of known data points. It involves using a mathematical algorithm to predict intermediate values based on the given set of data.

According to the given information:T

We can use interpolation to estimate when the skydiver's height above the ground will be approximately 1600 meters. From the given data, we can see that the height of the skydiver is decreasing with time.

We can plot the given data points on a graph with time on the x-axis and height on the y-axis. Then, we can draw a line or curve through the points to estimate the height at any given time.

Using a graphing calculator or software, we can plot the given data points and draw a curve through them. The resulting curve will be a smooth, continuous function that passes through the given data points.

Using this curve, we can estimate the time at which the skydiver's height will be approximately 1600 meters. From the graph, we can see that the skydiver's height will be approximately 1600 meters at around 13 seconds.

Therefore, the answer is C. 13 seconds.

To know more about The answer is C. 13 seconds.

What is graph?

A graph is a visual representation of data, typically using points, lines, or bars to show relationships or trends

What is interpolation?

Interpolation is the process of estimating values within a set of known data points. It involves using a mathematical algorithm to predict intermediate values based on the given set of data.

According to the given information:T

We can use interpolation to estimate when the skydiver's height above the ground will be approximately 1600 meters. From the given data, we can see that the height of the skydiver is decreasing with time.

We can plot the given data points on a graph with time on the x-axis and height on the y-axis. Then, we can draw a line or curve through the points to estimate the height at any given time.

Using a graphing calculator or software, we can plot the given data points and draw a curve through them. The resulting curve will be a smooth, continuous function that passes through the given data points.

Using this curve, we can estimate the time at which the skydiver's height will be approximately 1600 meters. From the graph, we can see that the skydiver's height will be approximately 1600 meters at around 13 seconds.

Therefore, the answer is C. 13 seconds.

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

12*4=48

Answer:

Step-by-step explanation:

To find the least cost allocation of tasks between four people, we need to determine the assignment that results in the minimum total cost. From the given information, we can allocate tasks by assigning a number to each person for each task.

Let's denote the people as A, B, C, and D, and the tasks as 1, 2, 3, and 4. The costs for each assignment are given in the table below:

Task 1 Task 2 Task 3 Task 4

Person A 4 3 5 2

Person B 2 4 3 1

Person C 3 1 2 5

Person D 1 2 4 3

To find the least cost allocation, we need to select one task for each person such that the sum of the costs is minimized.

Based on the table, the least cost allocation would be as follows:

Person A - Task 2 (cost: 3)

Person B - Task 4 (cost: 1)

Person C - Task 3 (cost: 2)

Person D - Task 1 (cost: 1)

The total cost for this allocation is 3 + 1 + 2 + 1 = 7.

Therefore, the least cost allocation of tasks between the four people would be:

a. Person A - Task 2

b. Person B - Task 4

c. Person C - Task 3

d. Person D - Task 1

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Answer: x < -46/17

Step-by-step explanation:

To solve the inequality:

1/3x - 1/4(x + 2) > 3x - 4/3

First, we simplify the left-hand side by finding a common denominator:

4(1/3x) - 3/4(x + 2) > 3x - 4/3

4/3x - 3/4x - 9/2 > 3x - 4/3

Next, we simplify the equation:

7/12x - 9/2 > 3x - 4/3

To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:

7/12x - 3x > 9/2 - 4/3

-17/12x > 23/6

Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:

x < (23/6) ÷ (-17/12)

x < -46/17

Therefore, the solution to the inequality is:

x < -46/17

The surface area is 9pi, thus, the correct option is B.

To find the area of the surface, we need to find the length of the chord:

x = √(25 - y²)

between y = 0 and y = 5/2

Then if L is that length, the surface area will be:

A = 2π( L + x(0) + x(5/2))

Now notice that:

x(0) = 5

x(5/2) = √12.5

Now let's find L.

The function x = √(25 - y²) describes half a circle.

To find the length of the chord, we can find the length of an arc on a circle of radius 5.

The angle between the x-axis and the ray that crosses trhough (0, 0), and (√4.3, 5/2)

is:

θ = Atan(√4.3/(5/2))

θ = 39.7

Then the angle between that ray and the y-axis is:

α = 90° -  39.7° = 50.3°

Then the length of the chord is:

L = (50.3°/360°)*2*3.14*5 = 4.4

Then the surface area is:

S = 2*pi*4.4 = 8.8pi

The closest option (by rounding up) is 9pi, so B is the correct option.

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(a) To show that 〈Ax, ty} =〈x, A^T y〉, let's compute both sides:

Left side: 〈Ax, y〉 = (Ax)^T y = x^T A^T y

Right side: 〈x, A^T y〉 = x^T (A^T y)

As you can see, both the left and right sides are equal (x^T A^T y), so the statement is true.

(b) To show that 〈A^T A x, x〉 = ‖A x‖^2, let's compute both sides:

Left side: 〈A^T A x, x〉 = (A^T A x)^T x = x^T A^T A x

Right side: ‖A x‖^2 = (A x)^T (A x) = x^T A^T A x

Again, both the left and right sides are equal (x^T A^T A x), so the statement is true.

To show (a), we start with the definition of the inner product:
<ax,y〉 = (ax)ᵀy

Then we use the properties of matrix multiplication to rewrite this as:〈ax,y〉 = xᵀaᵀy

Now we can take the transpose of both sides and use the fact that aᵀ = a to get:
(〈ax,y〉)ᵀ = (xᵀaᵀy)ᵀ
〈y,ax〉 = yᵀa x

Finally, we can swap the order of x and y on the right-hand side and use the definition of the inner product again:
〈ax,y〉 = 〈x,aty〉

To show (b), we start with the left-hand side:
〈atax,x〉 = (atax)ᵀx

Using the properties of matrix multiplication, we can rewrite this as:
〈atax,x〉 = xᵀ(aᵀa)x

Now we can use the fact that (aᵀa)ᵀ = aᵀa and the definition of the norm to get:
〈atax,x〉 = xᵀ(aᵀa)x = ‖ax‖²


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The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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To graph the equation \(y=5+((\sqrt(9x+54)/16)),\) we can follow these steps:

Step 1: Determine the Domain of the Function

The square root expression under the fraction bar must be greater than or equal to zero to ensure the function is defined for all values of x. Therefore, we must have:

9x + 54 ≥ 0

Solving for x, we get x ≥ -6.

So, the domain of the function is x ≥ -6.

Step 2: Find the y-Intercept

To find the y-intercept, we set x = 0 in the equation:

y = 5 + (sqrt(9(0) + 54)/16) = 5 + (sqrt(54)/16) = 5 + (3sqrt(6)/8) ≈ 5.55

So, the y-intercept is approximately 5.55.

Step 3: Find the x-Intercept

To find the x-intercept, we set y = 0 in the equation and solve for x:

0 = 5 + (sqrt(9x + 54)/16)

-5 = sqrt(9x + 54)/16

Square both sides of the equation and simplify:

25 = 9x + 54

9x = -29

x = -29/9

So, the x-intercept is approximately -3.22.

Step 4: Find Additional Points

We can find additional points by choosing some values of x and evaluating the function. Let's choose some values of x between -6 and 0 and between 0 and 6.

We can then use a calculator to find the corresponding values of y.

For example, when x = -4, we have:

y = 5 + (sqrt(9(-4) + 54)/16) = 5 + (sqrt(18)/16) ≈ 5.31

So, the point (-4, 5.31) is on the graph of the function.

When x = 2, we have:

y = 5 + (sqrt(9(2) + 54)/16) = 5 + (3sqrt(2)/8) ≈ 5.88

So, the point (2, 5.88) is on the graph of the function.

Step 5: Plot the Points and Draw the Graph

We can plot the points we found in Step 4 and draw a smooth curve that passes through them to get the graph of the function.

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The correct answer of a) the range of controller gain that will yield a stable closed-loop system is 0 ≤ Kp ≤ 1.6.

a. Using a P-controller, the range of the controller gain that will yield a stable closed-loop system is determined. A proportional controller (P-controller) is a feedback controller that performs a proportional action to the error signal (the deviation between the process variable and its set point). The closed-loop transfer function (CLTF) can be found by multiplying the plant transfer function and the controller transfer function. The feedback equation for a proportional controller is as follows: u(t) = Kp [e(t)] where u(t) is the control signal, Kp is the proportional gain, and e(t) is the error signal. The closed-loop transfer function (CLTF) for the system can be expressed as Gcl(s) = Gp(s) / (1 + Kp Gp(s))

Hence, the range of controller gain that will yield a stable closed-loop system is 0 ≤ Kp ≤ 1.6.

b. The process can be simulated with the P-controller to confirm the stability range determined in part (a). Simulink can be used for simulation purposes. The following is the Simulink model for the P-controller: Simulink model for P-controller. In this model, the “step” block is used to generate a step input signal. The “Gain” block is used to set the gain value for the controller. The “Transfer function” block represents the plant transfer function. The “Sum” block is used, to sum up the error signal and the control signal. The “Scope” block is used to view the output signal. By changing the gain value, the response can be observed, and the range of stability can be verified.

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Answer:

138 Degrees

Step-by-step explanation:

Because it is adjacent to the 42 degrees, just subtract 42 from 180 to get 138 degrees.

Answer:

D+42*=180*

D=180-42

138

Step-by-step explanation:

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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the probability of experiencing neither side effect is 0.37 or 37%.let's denote the probability of experiencing nausea by P(n) and the probability of experiencing decreased sexual drive by P(d). We know that:

P(n) = 0.23
P(d) = 0.52
P(n ∩ d) = 0.12

We want to find the probability of experiencing neither side effect, which can be denoted by P(~n ∩ ~d), where ~n and ~d represent the complements of nausea and decreased sexual drive, respectively.

We can use the formula for the probability of the union of two events to find P(~n ∪ ~d):

P(~n ∪ ~d) = 1 - P(n ∪ d)

We know that P(n ∪ d) = P(n) + P(d) - P(n ∩ d), so we can substitute the given values to get:

P(n ∪ d) = 0.23 + 0.52 - 0.12 = 0.63

Therefore,

P(~n ∪ ~d) = 1 - 0.63 = 0.37

So the probability of experiencing neither side effect is 0.37 or 37%.

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Step-by-step explanation:

1. Let the number be a

2 + 3a = (-10)

3a = -10 - 2

3a = -12

a = -12/3 = -4.

2. Let the number be x

3x + 20 = 11

3a = 11 - 20

3a = -9

a = -9/3 = -3

3. Let the number be n

7x/10 = 5.6

x = 5.6 × 10/7

x = 56/7

x = 8

the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

In 1891 the population would be 6250 x  ( 1+ 0.0275)

In 1832 the population would be [ 6250 x ( 1+0.0275 ) ] x (1+0.0275)

in 1893 the population would be [6250 x ( 1+0.0275) ] x ( 1+0.0275) x (1+0.0275)

p= 6250(1.0275)^t

where t= number of years till 1890

t=25

p= 6250(1.0275) ²⁵

= 6250 x 1.9704

= 12314.8

t=50

p= 6250(1.0275) ⁵⁰

= 6250 x 3.8823

=24264.5

To reach 50,000

50000= 6250(1.0275)^t

(1.0275)^t = 50000 /6250

(1.0275)^t =8

Take log on both sides

log (1.0275)^t = log 8

t= log8/ log (1.0275)

t=76.6%

Hence

the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

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Answer:

f = 13\(\sqrt{2}\)

Step-by-step explanation:

Given that f and e are congruent then e = f

Using Pythagoras' identity in the right triangle

f² + e² = 26² , that is

f² + f² = 676

2f² = 676 ( divide both sides by 2 )

f² = 338 ( take the square root of both sides )

f = \(\sqrt{338}\) = \(\sqrt{169(2)}\) = 13\(\sqrt{2}\) ≈ 18.4 ( to 1 dec. place )

Answer:

f = 25.85751233

Step-by-step explanation:

f^2+E^2=26^2