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What is the slope of the line that contains these points? x 5 6 7 8 y -5 -6 -7 -8

In this case we must apply the properties of supplementary angles and opposite angles.

1 .

opposite angles

∠ 1 = 120 °

supplementary angles

∠ 1 + ∠ 2 = 180

120 + ∠ 2 = 180

∠ 2 = 180 - 120

∠ 2 = 60 °

The same properties can be applied in the other exercises to solve them.

The solution is:

∠ 1 = 120 °

∠ 2 = 60 °

The composition fog represents the composition of functions f and g, while \(f^{-1}\) denotes the inverse of the function f.

1) To find fog, we need to compute the composition of functions f and g. The composition fog is denoted as f(g(x)), where x is an element of A.

First, we apply g to the elements of A, and obtain the corresponding elements in B. Applying g to the elements of A gives us:

g(a) = 2, g(b) = 1, g(c) = 3, g(d) = 2.

Next, we apply f to the elements of B obtained from g. Applying f to the elements of B gives us:

f(g(a)) = f(2) = 3,

f(g(b)) = f(1) = 8,

f(g(c)) = f(3) = 2,

f(g(d)) = f(2) = 3.

Therefore, the composition fog is given by:

fog = {(a, 3), (b, 8), (c, 2), (d, 3)}.

2) To find \(f^{-1}\), we need to determine the inverse of the function f. The inverse of a function reverses the mapping, swapping the input and output values.

Examining the function f = {(1, 8), (2, 3), (3, 2)}, we can observe that no two elements have the same output value. This property allows us to find the inverse of f by swapping the input and output values.

Therefore, the inverse function \(f^{-1}\) is given by:

\(f^{-1}\) = {(8, 1), (3, 2), (2, 3)}.

Note that f^(-1) is a valid function since it maps each output value of f to a unique input value, satisfying the definition of a function.

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(i) To solve this problem, we need to use De Moivre's Theorem. It is a formula that helps us raise complex numbers to integer powers quickly and efficiently.

De Moivre's Theorem states that (cosθ + i sinθ)ⁿ = cosnθ + i sinnθ, where n is any integer and θ is the argument of the complex number.

Now let's find the answer to the given complex number:  (a+bi) 4n+2 +(b−ai) 4n+2   = a(4n+2) + bi(4n+2) + b(4n+2) - ai(4n+2)   = a(4n) (2) + bi(4n) (2) + b(4n) (2) - ai(4n) (2)   = 16n(a + bi) + 16n(b - ai)   = 16n(a + bi + b - ai)   = 16n[(a + b) + (b - a)i]   = 16n(2bi)   = 32nbi  

Therefore, the complex number evaluated will be 32nbi.

(ii) The cube roots of i are given by i, (-1 + i√3)/2, and (-1 - i√3)/2.

We can use these values to solve for w³ = i. w = i¹/³, so w can take any of these three values: w₁ = i, w₂ = (-1 + i√3)/2, and w₃ = (-1 - i√3)/2.

Let's use w₂ as our value for w.

If we let z = a + bi, then we can write the equation as z³ = i(z - 1)³.

We can then plug in w₂ for i and solve for z. z³ = i(z - 1)³ ⇒ z³ = (-1 + i√3)/2 (z - 1)³ ⇒ z³ = (-1 + i√3)/2 (z - 1) (z - 1) (z - 1) ⇒ z³ = (-1 + i√3)/2 (z - 1) (z - 1) (z² - 2z + 1) ⇒ z³ = (-1 + i√3)/2 (z - 1) (z² - 2z + 1) (z - 1) ⇒ z³ = (-1 + i√3)/2 (z - 1)² (z² - 2z + 1) ⇒ z³ = (-1 + i√3)/2 (z - 1)² (z - 1) (z - 1)

 Now we can substitute w₂ for i and solve for z. z³ = w₂(z - 1)² (z - 1) (z - 1)   z³ = (-1 + i√3)/2 (z - 1)² (z - 1)   ⇒ z³ = (-1 + i√3)/2 (z - 1)³   ⇒ z³ = w²   ⇒ z = w₁², w₂², or w₃²  

Now we can plug in each value of w and solve for z. If w = i, then z = i² = -1. If w = (-1 + i√3)/2, then z = (-1 + i√3)/2. If w = (-1 - i√3)/2, then z = (-1 - i√3)/2.

Therefore, there are three possible values of z: -1, (-1 + i√3)/2, and (-1 - i√3)/2.

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The length of the median of the trapezoid is 12 units.

What is trapezoid?

Let the parallel sides be  x and x+4

The area of a trapezium is  the average or the parallel sides multiplied by the height

Area = [(x + x+ 4)/2 ] *h

= [ (2x+4)/2] * 5

= [2(x+2)/2] * 5

Area = 5(x+2)

60 = 5(x+2)

60/5 = x+2

12 = x+2

x = 12 - 2

x = 10

The parallel sides are 10 and 14 units.

Now the median length is the average of the parallel side lengths

Length of median = (10+14)/2

Length of median = 12 units

Hence, the length of the median of the trapezoid is 12 units.

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To solve the given problem, let's break it down into two parts:

(a) At what time did the man arrive back in Ibadan?

We can calculate the time taken for the initial journey from Ibadan to Lagos using the formula:

Time = Distance / Speed

Time = 142 km / 60 km/h

Time = 2.37 hours

The motorist then spent an additional 5/2 hours in Lagos.

To calculate the total time taken for the return journey from Lagos to Ibadan, we use the formula:

Time = Distance / Speed

Time = 142 km / 80 km/h

Time = 1.775 hours

Adding the time spent in Lagos to the return journey time:

Total time = 2.37 hours + 5/2 hours + 1.775 hours

Total time = 6.145 hours

Therefore, the man arrived back in Ibadan approximately 6.145 hours after he left.

(b) To find the average speed for the total journey, we use the formula:

Average Speed = Total Distance / Total Time

The total distance covered in the round trip is 2 times the distance between Ibadan and Lagos, which is:

Total Distance = 2 x 142 km

Total Distance = 284 km

Average Speed = 284 km / 6.145 hours

Average Speed = 46.22 km/h

Therefore, the average speed for the total journey is approximately 46.22 km/h.

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Answer:

A, -11

Step-by-step explanation:

f(x)=-3x(-2)+1

=-3(4)+1

=-12+1

=-11

Step-by-step explanation:

f(x)=3x²+1

f(-2)=3(-2)²+1

= -12+1

=-13 ans

By using the concept of counting and arrangement, it can be calculated that

Sir Fluffles could ascent a flight of 6 stairs in 13 ways.

What is counting and arrangement?

Counting is the process of adding one by one to find the total number of objects present.

The act of putting a number of objects in order is called arrangement.

This is a problem on counting and arrangement

Let S represents single step and D represents double steps

Sir Fluffles is capable of hopping up either one step or two at a time.

Number of steps to be climbed

Possibilities are

SSSSSS, SSSSD, SSSDS, SSDSS, SDSSS, DSSSS, DDSS, SDSD, DSDS, SSDD, SDDS, DSSD, DDD

Total number of possibilities is 13

Sir Fluffles could ascent a flight of 6 stairs in 13 ways.

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Answer:

The missing angle is 55°.

Step-by-step explanation:

==========================================

The three interior angles of a triangle add up to 180°.

This means that:

\(x\textdegree + 75\textdegree+50\textdegree=180\textdegree\\\rule{150}{0.5}\\x - \text{unknown angle}\)

==========================================

Using the equation above, we would solve for x.

\(x\textdegree + 75\textdegree+50\textdegree=180\textdegree\\\rule{150}{0.5}\\x\textdegree + 75\textdegree+50\textdegree=180\textdegree\\\\x\textdegree + 125\textdegree=180\textdegree\\\\x\textdegree + 125\textdegree-125\textdegree=180\textdegree - 125\textdegree\\\\\boxed{x = 55\textdegree}\)

The missing angle should be 55°.

==========================================

Hope this helps.

Answer:

25

Step-by-step explanation:

75 - 25 is 50

50 - 25 is 25

So the answer is 25

Hope this helps!

Answer:

Soybeans: 205, Corn: 95

Step-by-step explanation:

let x rep acre of soybeans

let y rep acre of corn

Equation one: 110 + y = x

Equation two: 300 = x + y or 300 - y = x

Substitute

300 - y = 110 + y

190 = 2y

y = 95

Find x

110 + y = x

110 + (95) = x

x = 205

The element that orients readers by previewing the structure of the report is "Organization."

Organizing a report effectively helps readers understand the flow of information and the logical structure of the content. By providing an overview of the organization, readers can anticipate the main sections, their sequence, and the connections between them.

The organization element typically includes headings, subheadings, and a clear hierarchy of information. It outlines the main sections and subsections of the report, indicating how they are related and how they contribute to the overall message or argument.

In addition to the organization element, the other options listed—Definitions of key terms and Sources and methods—also play important roles in a report. Definitions of key terms clarify terminology and provide a common understanding, while Sources and methods explain the sources of information and the methods used in the report's research or analysis. However, in the context of previewing the structure, the Organization element specifically serves this purpose.

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The MCAT scores variable can predict some of the variation in the response variable.

The logistic regression model is a type of regression analysis that is widely used in various fields. A logistic model can be fitted using the glm() function in R. Now fit a logistic model with a single explanatory variable, MCAT scores.In logistic regression, the null deviance is the deviance for a model that has only the intercept. The null deviance will always be equal to the residual deviance if the model has only the intercept.The null deviance is calculated based on the difference between the saturated and null models' likelihoods. It is the amount of variation in the response variable that cannot be explained by the model when no predictor variables are used. When the single predictor variable MCAT scores is added to the null model, it reduces the null deviance by 11.59. This is significant because it indicates that the MCAT scores variable can predict some of the variation in the response variable.

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Answer:

\(t_7 =\frac{5}{729} \)

Step-by-step explanation:

We are given that:

First term (a) = 5

common ratio (r) =\(\frac{1}{3}\)

The nth term of a geometric sequence is given as:

\(t_n =ar^{n-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{7-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \frac{1}{729}\\\\\huge\red{\boxed{\therefore t_7 =\frac{5}{729} }}\)

Answer:

Step-by-step explanation:

200

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.

Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.

Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.

Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.

The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.

Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.

This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.

Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.

Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.

Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).

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Answer:

I think you mean significant figures

Step-by-step explanation:

Answer:

\(2.\overline {24}\) = 2\(\frac {8} {33}\) or D.

Step-by-step explanation:

2  is a whole number, so its \(\frac {2} {1}\) and \(0.\overline {24}\) is a repeating decimal, so that means we try to simplify it: \(\frac {24} {100}\)÷\(\frac {3} {1}\)=\(\frac {24} {100}\)·\(\frac {1} {3}\)=\(\frac {8} {33}\)

Answer:

Yes

Step-by-step explanation:

An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.

Answer:

yes

Step-by-step explanation:

Answer:

2 ft 4 inches

Step-by-step explanation:

12 inches = 1 ft

28/12=2.4

To calculate the ocean freight charges in Canadian dollars, we need to determine the volume of each cargo and convert the volume to cubic meters (m³) since the ocean freight rate is given in USD per m³.

Calculate the volume of each cargo: Skid of Apple: Volume = length x width x height = 100 cm x 100 cm x 150 cm = 1,500,000 cm³. Box of Orange: Volume = length x width x height = 35" x 25" x 30" = 26,250 in³. Convert the volumes to cubic meters: Skid of Apple: 1,500,000 cm³ ÷ (100 cm/m)³ = 1.5 m³. Box of Orange: 26,250 in³ ÷ (61.0237 in/m)³ ≈ 0.43 m³. Calculate the total volume of both cargos: Total Volume = (2 skids of Apple) + (3 boxes of Orange) = 1.5 m³ + 0.43 m³ = 1.93 m³. Convert the ocean freight rate from USD to CAD:  Ocean Freight Rate in CAD = $250 USD/m³ × (1.25 CAD/USD) = $312.50 CAD/m³.

Calculate the ocean freight charges in Canadian dollars: Ocean Freight Charges = Total Volume × Ocean Freight Rate = 1.93 m³ × $312.50 CAD/m³. Therefore, the ocean freight charges for the given shipment in Canadian dollars will be the calculated value obtained in step 5.

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A geodesic is the shortest path between two points on a curved surface, such as a sphere. To find a geodesic, an integral is set up to determine the length of a path on the surface.

This integral is similar to the one used for flat surfaces but may be more complex and involve different coordinates depending on the nature of the curved surface. In the case of a sphere, spherical polar coordinates are commonly used.

The length of a path on a curved surface can be expressed using an integral similar to Equation (6.2) for flat surfaces. However, when dealing with a sphere, the integral may involve different coordinates, specifically spherical polar coordinates. Spherical polar coordinates consist of three components: radius (r), polar angle (θ), and azimuthal angle (φ). By expressing the path in terms of these coordinates, the integral can be set up to calculate the length of the geodesic.

To illustrate this, let's consider the example of finding the geodesic on the surface of a sphere. The integral would involve integrating the square root of the sum of squared differentials of the three spherical polar coordinates, weighted by the appropriate metric coefficients. The specific form of the integral would depend on the metric tensor associated with the spherical polar coordinate system. By minimizing this integral, the geodesic between two points on the sphere can be determined. In summary, finding the geodesic, or shortest path, between two points on a curved surface involves setting up an integral to calculate the path length. The integral is similar to the one used for flat surfaces but may be more complex and use different coordinates, such as spherical polar coordinates for a sphere. By minimizing the integral, the geodesic on the curved surface can be found.

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The probability that less than a third of the entry forms will include an order is 0.3760.

To solve this problem, we need to use the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials. In this case, we want to find the probability that less than a third of the 15 entries will include an order, given that the probability of receiving an order with an entry form is 0.5.

Let X be the random variable that represents the number of entries with an order out of the 15 total entries. Then X follows a binomial distribution with parameters n=15 and p=0.5. The probability of less than a third of the entries having an order is equivalent to the probability of X being less than or equal to 5, since 5 is one third of 15.

Using a binomial probability table or calculator, we can find that the probability of X being less than or equal to 5 is 0.3760, rounded to four decimal places.

In summary, we used the binomial distribution to model the number of entries with an order, and found the probability that less than a third of the entries will include an order. We obtained a probability of 0.3760, which represents the likelihood of observing 5 or fewer entries with an order out of the 15 total entries.

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Answer:

Height 15 feet

Base 12 Feet

Step-by-step explanation:

The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.

A=(.5) x 12 x 15

A=(.5) x 180

A= 90

Answer:

Slope= -1/3

Step-by-step explanation:

The slope is found using (y₂ - y₁) / (x₂ - x₁)

(y₂ - y₁)

So let's do the numerator first with the y. -52-(-32). The two negative signs  make 32 positive so -52 + 32= -20

(x₂ - x₁)

Now the denominator, x. -10-(-70). Same thing here, the two negative signs  make 70 positive so -10 + 70 = 60

(y₂ - y₁) / (x₂ - x₁)

Now put them together so -20/60 which equals -1/3 which the slope

Answer:

This equation is a difference of squares factorization. It states that the difference between the square of x and 7x plus some constant c is equal to the square of (x+a). To solve for a and c, we can expand both sides of the equation:

X^(2) - 7x + c = x^(2) + 2ax + a^(2)

And we can set them equal to each other and solve for a and c:

x^(2) - 7x + c = x^(2) + 2ax + a^(2)

-2ax - a^(2) = -7x + c

a = (7x - c) / 2x

c = x^(2) - 7x + a^(2)

Note that this is valid as long as x is not equal to 0.

Answer:

Step-by-step explanation:

sin50=w/10

w=10sin50

w=7.66

sinx=w/11

x=arcsin(w/11)

x=arcsin(10sin50/11)

x=44.14 degrees

Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840