the measure of an angle is 156°. what is the measure of its supplementary angle​

2 1/7 x 4.3 (repeating the three) as a mixed number in simplest form is 9 2/7.

First, we can simplify the mixed number 4.3 (repeating the three) as follows:

Let x = 4.3 (repeating the three)

Then 10x = 43.33333...

Subtracting x from 10x, we get:

10x - x = 43.33333... - 4.33333...

9x = 39

x = 4.33333... / 9

x = 4 1/3

Now, we can multiply 2 1/7 by 4 1/3:

2 1/7 x 4 1/3 = (15/7) x (13/3)

= (15 x 13) / (7 x 3)

= 195 / 21

To write this as a mixed number in simplest form, we can divide 195 by 21 and write the quotient as a mixed number:

195 ÷ 21 = 9 with a remainder of 6

So, 195 / 21 = 9 6/21, which can be simplified to 9 2/7.

Therefore, 2 1/7 x 4.3 (repeating the three) as a mixed number in simplest form is 9 2/7.

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Assuming that the trail is a total of "x" miles, we can set up the following equation to solve for "x":

816 = 0.48x

To solve for "x", we can divide both sides by 0.48:

x = 1700

Therefore, the total length of the trail is 1700 miles.

To get the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2, we'll first need to use the product rule and then simplify the expression. The product rule states that if you have a function g(x)h(x), its derivative is g'(x)h(x) + g(x)h'(x).

Let g(x) = 5x - 5 and h(x) = √x + 3.
Step 1: the derivatives of g(x) and h(x).
g'(x) = 5 (derivative of 5x - 5)
h'(x) = 1/(2√x) (derivative of √x + 3)
Step 2: Apply the product rule.
f'(x) = g'(x)h(x) + g(x)h'(x)
f'(x) = 5(√x + 3) + (5x - 5)(1/(2√x))
Step 3: Simplify the expression.
f'(x) = 5√x + 15 + (5x - 5)/(2√x)
This is the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2. Note that none of the given answer choices match this result, so there might be a mistake in the provided options.

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The y intercept based on the information will be (0,29)

We want to find the value of the y-intercept for the given function.

The y-intercept is (0,29)

First, we define the y-intercept as the value of the function when evaluated in x = 0.

Here the given function is:

h(x) = 29*(5.2)ˣ

It should be noted that too get the y-intercept we just need to evaluate this at x = 0, then we get:

h(0) = 29*(5.2)⁰ = 29

The y-intercept is (0 29)

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Answer:
-Reflection across line p followed by 240 clockwise rotation about point T.

-Reflection across line r.

-120 counterclockwise rotation about point T.

Step-by-step explanation:

All these transformations map the triangle onto itself.

The type of study the sales director is conducting is an experiment to compare the number of orders secured by those who attended the training program and those who didn't attend.

The sales director conducted an experimented

The experiment is to do a test to see if something works or to try to improve it

Here the objective of the experiment was to see the effectiveness of the training by providing a one-month training program for employees. After that, the sales director collects the sales data for the first month. The sales director compared the number of orders secured by those who attended the training program and those who didn't attend. This experiment will help the company to determine the effectiveness of the training. If the experiment is effective or not.

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Answer:

Ryan spent $72 on his shopping trip.

Step-by-step explanation:

To find out how much money Ryan spent, we need to add up the cost of the shirts and the sneakers.

First, we know that Ryan purchased two shirts for $16 each. So we can find the total cost of the shirts by multiplying the cost per shirt by the number of shirts:

So the total cost of the shirts is $32.

Next, we know that Ryan purchased a pair of sneakers that cost 2 1/2 times as much as a shirt. We can use this information to find the cost of the sneakers.

If the cost of a shirt is $16, then we can find the cost of the sneakers by multiplying $16 by 2 1/2:

So the cost of the sneakers is $40.

Finally, we can find the total cost of Ryan's shopping trip by adding up the cost of the shirts and the sneakers:

Therefore, Ryan spent $72 on his shopping trip.

Answer:

Method 1 (Using Slope-Intercept Form):

First, we need to find the equation of the line that passes through the given points.

Slope (m) = (Change in y) / (Change in x) = (45 - 25) / (4 - 0) = 20 / 4 = 5

Using the slope and one point (0, 25), we can find the y-intercept:

y - y1 = m(x - x1)

y - 25 = 5(x - 0)

y = 5x + 25

Therefore, when the input is 200, the output would be:

y = 5(200) + 25

y = 1025

Method 2 (Using Linear Interpolation):

We can use the formula for linear interpolation:

y = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1)

where:

x1 = 0, y1 = 25

x2 = 4, y2 = 45

x = 200

Substituting the values, we get:

y = 25 + ((200 - 0) / (4 - 0)) * (45 - 25)

y = 25 + (200 / 4) * 20

y = 25 + 500

y = 525

Therefore, when the input is 200, the output would be approximately 525.

This is a linear equation in slope-intercept form, where the slope (m) is 50 and the y-intercept (b) is 62.

Since the milepost increases by a fixed amount of 50 for every hour that they drive, the most appropriate type of equation to describe this relationship is a linear equation.

A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is 50, since the milepost increases by 50 for every hour of driving, and the y-intercept is 62, since they start at milepost 62.

Therefore, the equation that represents Abby's relationship between the milepost they pass, y, and the number of hours they drive, x, is:

y = 50x + 62

This is a linear equation in slope-intercept form, where the slope (m) is 50 and the y-intercept (b) is 62.

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The sequence (n){(1-2)/(3^n+1) + 3} is bounded and decreasing. The GLB is 3 and the LUB is 1.

To determine the boundedness and monotonicity of the sequence, we can look at the limit as n approaches infinity.

Taking the limit of the sequence, we have:

lim(n→∞) [(1-2)/(3^n+1) + 3] = 3

This means that the sequence approaches a finite value as n gets larger, so the sequence is bounded.

Next, to check the monotonicity of the sequence, we can take the first derivative of the sequence with respect to n:

d/dn [(1-2)/(3^n+1) + 3] = [(2-1)(-ln3)(3^n+1)]/[(3^n+1)^2]

Simplifying, we get:

d/dn [(1-2)/(3^n+1) + 3] = (-ln3)/(3^n+1)^2

Since the derivative is negative for all n, the sequence is decreasing.

To find the GLB and LUB, we can use the fact that the sequence is decreasing and bounded. Since the sequence approaches 3 as n approaches infinity, 3 is the lower bound.

To find the upper bound, we can use the fact that the sequence is decreasing and start with the second term, which is 2. Therefore, the upper bound is 2. Since 1 < 2, we can conclude that the LUB is 1.

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the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.

We're given the position vector and time and asked to find the velocity vector, speed, and acceleration vector of the object. Let's solve this step-by-step.

1. Differentiate the position vector with respect to time (t) to find the velocity vector:
Position vector: r(t) = 3ti + tj + (1/4)t^2k

Velocity vector: v(t) = dr(t)/dt = d(3ti)/dt + d(tj)/dt + d((1/4)t^2k)/dt

v(t) = 3di/dt + dj/dt + (1/2)tk

v(t) = 3i + j + (1/2)tk

2. Plug in the given time (t = 2) into the velocity vector to find the velocity at that time:
v(2) = 3i + j + (1/2)(2)k

v(2) = 3i + j + k

3. Find the speed by calculating the magnitude of the velocity vector:
Speed = |v(2)| = sqrt((3^2) + (1^2) + (1^2))

Speed = sqrt(9 + 1 + 1)

Speed = sqrt(11)

4. Differentiate the velocity vector with respect to time (t) to find the acceleration vector:
Acceleration vector: a(t) = dv(t)/dt = d(3i)/dt + d(j)/dt + d((1/2)tk)/dt

a(t) = 0i + 0j + (1/2)k

So, the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.

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The variables of interest are both non-parametric and measured on an ordinal scale, a suitable analysis for determining the relationship between them would be the Spearman rank correlation coefficient.

The Spearman rank correlation coefficient is a non-parametric measure of the strength and direction of association between two variables.

It is based on the rank order of observations for each variable, rather than their actual numerical values.

The coefficient can range from -1 perfect negative correlation to +1 perfect positive correlation.

And with a value of 0 indicating no correlation.

Use the Spearman rank correlation coefficient to determine the strength and direction of the relationship between CI and student satisfaction.

The coefficient would tell us if there is a significant correlation between the two variables, and whether the correlation is positive or negative.

Perform the analysis, first rank the observations for both variables and calculate the difference in ranks between each pair of observations.

Calculate the Spearman rank correlation coefficient using the formula,

ρ = 1 - (6Σd² / n(n² - 1))

where ρ is the Spearman rank correlation coefficient,

d is the difference in ranks for each pair of observations,

n is the sample size,

and n² is the sum of the squares of the ranks.

A value of ρ close to +1 would indicate a strong positive correlation between the two variables.

A value close to -1 would indicate a strong negative correlation.

A value close to 0 would indicate no significant correlation between the two variables.

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The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:

Find the length of vector v:

|v| = sqrt(3^2 + (-4)^2) = 5

Divide vector v by 2 to get a vector with half its length:

v/2 = (3/2, -2)

To get a vector that is oppositely directed to v, we can reverse the direction of v/2:

-(3/2, -2) = (-3/2, 2)

Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:

|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)

u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)

Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

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C. The constant of proportionality between the diameter and circumference of a circle is pi.

The constant pi comes from the relationship between the diameter and circumference of a circle.

Constant of Proportionality

A constant of proportionality is a number that describes the ratio between 2 values. No matter the measurements of a circle, the constant of proportionality between a circumference and diameter is always the same. This means that the circumference divided by the diameter ≈ 3.14.

Pi

Pi is an irrational number that can be estimated but never completely solved. The value of pi can be used to complete many different calculations such as the area of a circle, and it is used in many different functions like sin. For this reason, pi is one of the most important constants in math.

The missing dimension of the triangle is the height, which is 19 cm.

To find the missing dimension of the triangle, we can use the formula for the area of a triangle:

Area = (1/2) x base x height

We know that the area is 256.5 cm^2 and the base is 27 cm. Therefore, we can plug in these values into the formula and solve for the height:

256.5 = (1/2) x 27 x height

256.5 = 13.5 x height

height = 256.5 / 13.5

height = 19

Therefore, the missing dimension of the triangle is the height, which is 19 cm.

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The number does MOVED represent 1110.

Since GOD=605, we know that D=5. We can now substitute this value of D into the addition problem to get:

GOD+ DOG = MOVED

605+ 506 = 1111

Since M cannot be 0 (otherwise it wouldn't be a 4-digit number), we know that M=1.

We can now subtract 1 from both sides of the equation to get:

604+ 506 = 1110

Now we can see that E+4=10, so E=6. We can also see that O+0=0, so O=0. Finally, we can see that G+D=1, so G=6 and D=5.

Therefore, MOVED = 1110.

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Answer:  B.
Given expression: (-9x) / (x^2 - 9)
Simplify the rational expression by factoring the denominator:
(x^2 - 9) = (x + 3)(x - 3)
= (-9x) / [(x + 3)(x - 3)]

Now, we can evaluate the limit as x approaches 3:
lim (x -> 3) [(-9x) / ((x + 3)(x - 3))]

Since the expression is defined and continuous at x = 3, we can directly substitute the value of x:
((-9 * 3) / ((3 + 3)(3 - 3))) = (-27) / (6 * 0)

The denominator becomes zero, which means the limit does not exist, and is neither ∞ nor -∞. So, the correct choice is B. The limit does not exist and is neither ∞ nor -∞.

The value of the calculated percent markup of the cookie is 100%

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

The percent markup of the cookie is then calculated as

Percentage = (Selling price - cost price)/cost price

substitute the known values in the above equation, so, we have the following representation

Percentage = (3 - 1.5)/1.5

Evaluate

Percentage = 100%

Hence, the percent markup of the cookie is 100%

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Answer:

24

Step-by-step explanation:

add all of them up

The task requires estimating the rate of change of atmospheric pressure with respect to altitude using the given data.

First, a table needs to be created to estimate the rate of change of pressure with respect to altitude. The rate of change will be the difference in pressure divided by the difference in altitude between two consecutive data points.

Second, two plots should be created: one illustrating the pressure depending on altitude, and another illustrating the estimated rate of change depending on altitude.

Third, a function should be constructed to model the pressure-altitude data. The function should be selected based on how well it fits the data points.

Fourth, the model function should be used to estimate the rate of change of atmospheric pressure with respect to altitude at different heights over the range from sea level to 10,000 ft.

Fifth, a comparison should be made between the rate of change information computed from the model function and the rate of change information estimated directly from the data. This comparison will be used to assess the accuracy of the model function.

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Answer:

A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)

Step-by-step explanation:

in the described situation you only need to multiply the coordinates by the scale factor (in our case the given 5/8)

A (-4, 6) turns into

A' (-4×5/8, 6×5/8) = A' (-2.4, 3.75)

and therefore we know already here that all the other answer options are wrong.

The parabola with a focus of (-4, 5) and a directrix of y = -9 is vertically oriented, opens upward, has a vertex at (-4, -2), and its equation is (x + 4)^2 = 28(y + 2).

1. The parabola is vertically oriented since the directrix is a horizontal line.
2. The vertex of the parabola is equidistant from the focus and the directrix. To find the vertex, we can calculate the midpoint between the focus and a point on the directrix with the same x-coordinate: (-4, -9 + (5 - (-9))/2) = (-4, -9 + 7) = (-4, -2).
3. The parabola opens upward because the focus is above the directrix.
4. The equation of the parabola can be found using the vertex form: (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix. In this case, (h, k) = (-4, -2), and p = (5 - (-2)) = 7. The equation is therefore (x + 4)^2 = 28(y + 2).

In summary, the parabola with a focus of (-4, 5) and a directrix of y = -9 is vertically oriented, opens upward, has a vertex at (-4, -2), and its equation is (x + 4)^2 = 28(y + 2).

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The scope of both functions is all real numbers.

To compute the values of (f+g)(x) and (f-g)(x), we apply the addition and subtraction of two distinct functions, respectively:

(f+g)(x) = f(x) + g(x) = [tex](-2x + 4) + (3x^2) = 3x^2 - 2x + 4[/tex]

(f-g)(x) = f(x) - g(x) = [tex](-2x + 4) - (3x^2) = -3x^2 - 2x + 4[/tex]

The scope of both functions is all real numbers.

Subsequently, we evaluate the expressions for x = -3:

(f+g)(-3) = [tex]3(-3)^2 - 2(-3) + 4[/tex] = 3(9) + 6 + 4 = 27 +6 +4 = 37

(f-g)(-3) = [tex]-3(-3)^2 - 2(-3) + 4[/tex]= -3(9) + 6 + 4 = -27 + 6 + 4 = -17

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The most common distance in miles would be = 1,200 miles.

To determine the distance that is most travelled the following is considered;

The total number of road trips = 7

On day 3 the distance travelled = 600 and 1,200 miles

On day 4 the distance travelled = 1,000,1,100 and 1,200 miles

On day 5 the distance travelled = 800 miles.

On day 6 the distance travelled = 1,300 miles

Therefore the most travelled distance = 1,200 miles.

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A telephone pole has a wire attached to its top that is anchored to the ground then conclude the height of the pole is approximately 51.53 feet.

Let h be the height of the pole. The equation h = (h - 69) + 6 represents the given information. Solving it gives h = 75.

Let's denote the height of the pole as "h". Then, according to the problem, the distance from the bottom of the pole to the anchor point is 69 feet less than the height of the pole, which means it is h - 69. Additionally, the wire is to be 6 feet longer than the height of the pole, so its length is h + 6.

Now we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the wire) is equal to the sum of the squares of the lengths of the other two sides (in this case, the height of the pole and the distance from the bottom of the pole to the anchor point). So we have:

(h - 69)^2 + h^2 = (h + 6)^2

h^2 - 138h + 4761 + h^2 = h^2 + 12h + 36

h^2 - 75h - 1602 = 0

h = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -75, and c = -1602.

h = (75 ± sqrt(75^2 - 4(1)(-1602))) / 2(1)

h ≈ 51.53 or h ≈ -31.53

Since the height of the pole cannot be negative, we can ignore the negative solution and conclude that the height of the pole is approximately 51.53 feet.

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If the events are exclusive, use the Rule of Sum. If the events are independent, use the Fundamental Counting Principle.

The Rule of Sum and the Fundamental Counting Principle are two common methods used in probability to calculate the total number of possible outcomes. Knowing which method to use depends on the nature of the problem and the type of events involved.

The Rule of Sum is used when we have two or more exclusive events. This means that only one of the events can happen at a time. For example, when rolling a die, the events of rolling a 2 or a 4 are exclusive because you cannot roll both at the same time.

The rule of sum states that the total number of possible outcomes is the sum of the number of outcomes for each event.

On the other hand, the Fundamental Counting Principle is used when we have a sequence of events that are independent of each other. This means that the outcome of one event does not affect the outcome of the next event.

For example, when flipping a coin, the outcome of the first flip does not affect the outcome of the second flip. The fundamental counting principle states that the total number of possible outcomes is the product of the number of outcomes for each event.

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Answer:

Step-by-step explanation:

The English language is an art that I am using to convey this message to you. Without this form of communication, we would be unable to talk or write without using another language. We think everyday with this awesome language, and don't think much about the language we think in. English is an amazing language, and I am proud to be able to verbalize it to you today.

Of course! Please let me know what you need help with and I'll do my best to assist you within the given time frame.

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Answer:

5.09

Step-by-step explanation:

You eliminate the decimal by multiplying both sides by 10:

10(.25x+0.5)=10(0.61+0.14x)

Then you get your new equation and combine like terms:

25x+5=61+14x

-14x           -14x

11x+5=61

11x+5=61

    -5  -5

11x=61

Then finally you do 61/11 which gets you around 5.09 if you round to 2 decimal places.

After formula for the volume of a cylinder, the increase in water level results in approximately 260 more cubic feet of water in the tank.

The current water level is 10 feet, which is 120 inches. When the water level increases by 2 inches, the new water level will be 122 inches.

The radius of the tank is half of the diameter, which is 30 feet or 360 inches.

The current volume of water in the tank can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height of the water level.

V = π(360²)(120) ≈ 15,465,920 cubic inches

When the water level increases by 2 inches, the new height of the water level is 122 inches.

The new volume of water in the tank can be calculated using the same formula:

V = π(360²)(122) ≈ 15,914,693 cubic inches

The difference in volume between the two levels is:

15,914,693 - 15,465,920 = 448,773 cubic inches

To convert cubic inches to cubic feet, we divide by 1728:

448,773 ÷ 1728 ≈ 259.6 cubic feet

Rounding to the nearest cubic foot, we get:

260 cubic feet

Therefore, the increase in water level results in approximately 260 more cubic feet of water in the tank.

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