The pivot point (P) of the main supporting arm (AP) of a construction crane is 46 metres above the top of a 96 metre tall office building. When the supporting arm is at an angle of 55° to the horizontal, the length of cable dropping from the point A to the ground is 215 metres. Find the length of the main supporting arm (AP), to the nearest centimetre.

Answer: D, 25

Step-by-step explanation:

A parallelogram is 360 degrees, and every angle appears twice, so we can set up an equation to solve for the missing variable.

[tex]360 = 2(65) + 2(5y)[/tex]

Multiplying each angle by two shows that each angle appears twice in the shape, and once we multiply the values, we can simplify the equation to:

[tex]360-130=10y[/tex]

360 - 130 is 230, so divide both sides by 10 and you get 23 as the answer.

By using only the positive exponents , the answer of the expression (2x⁻²y³/3xy⁻⁴) is  (2y⁷)/(3x³)  .

The Exponents, are defined as a shorthand way of representing the repeated multiplication of a base number by itself. The exponent is the small raised number that indicates how many times the base number is multiplied by itself.

For example, in the expression 2⁴, the base number is 2 and the exponent is 4,

We use the law of exponents to simplify the expression :

the expression is : (2x⁻²y³/3xy⁻⁴) ;

by using the rule that : a⁻ⁿ = 1/aⁿ  ;

we get ;

⇒ (2y³y⁴)/(3xx²) ;

On adding the exponents having the same base ,

we get ;

⇒ (2y⁷)/(3x³)  ;

Therefore , the simplified value of (2x⁻²y³/3xy⁻⁴) is (2y⁷)/(3x³) .

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The given question is incomplete , the complete question is

Write answer only using positive exponents , (2x⁻²y³/3xy⁻⁴) .

Answer: D

Step-by-step explanation: I can't really see everything well but I think it is D

To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.

Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial.  The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.

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Answer:

0.238

Step-by-step explanation:

By induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

1. To prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders, we can use the following steps:

2. Base case: For k = 1, we have a single node, and if we remove the root, there is no tree left.

3. Inductive hypothesis: Suppose that the result holds for some k = n, that is, if we remove the root of an n-th order binomial tree, it results in n binomial trees of the smaller orders.

4. Inductive step: We need to prove that the result also holds for k = n + 1. To do this, we consider a (n + 1)-th order binomial tree. According to the definition, this tree is formed by joining two n-th order binomial trees. Let's call them T1 and T2. If we remove the root of this tree, the two subtrees T1 and T2 will become the n binomial trees of the smaller orders. These n binomial trees are all distinct because they correspond to the different possible combinations of nodes in the two subtrees T1 and T2.

Therefore, by induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

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Answer:

(6 x 1.5 + 4.9) x 4 = 55.6

Step-by-step explanation:

The correct answer is C. The Mode.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

This measure of centre is most meaningful when the data is qualitative because it shows the value that appears most frequently in the data set. The mode can be used to identify the most popular item or most commonly occurring outcome. It is the only measure of centre that can be used for qualitative data, as the other measures (mean, median, and range) require numerical data.

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Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the typing rate in characters per minute, we need use arithmetic operation of division.

Divide the number of characters by the number of minutes -

Typing rate = Number of characters / Number of minutes

In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -

Typing rate = 1274 / 7 = 182

Therefore, the typing rate is 182 characters/minute.

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The hourly rate that the batches of cookies were made is given as follows:

4.85 batches per hour.

The hourly rate is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate is obtained dividing the total production by the time in hours.

The parameters for this problem are given as follows:

Hence the rate is given as follows:

40/8.25 = 4.85 batches per hour.

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The inequality represented by the graph is given as follows:

y < 4x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 1, y increases by 4, hence the slope m is given as follows:

m = 4.

The values to the left of the line are shaded, hence the inequality represented by the graph is given as follows:

y < 4x - 2.

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Answer:

10

Step-by-step explanation:

i love how you look like a dinosaur

Answer:it guarantees that people can all read and solve a problem in the same way.

Step-by-step explanation:

The Solution using two methods are 323, .291, the correct option is B`.

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Frank is a champion fish charmer who can charm fish with .62 probability of success

He attempts to charm 100 fish, what's the probability he'll charm

between 60 and 80 inclusive

Now, probability out of 100

=62

This is between 60 and 80

So, 323

Therefore, the probability will be 323 and .291

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Answer:

8(8+7)

Step-by-step explanation:

64+56
8 is the GCF
8(8+7)

a) Sin2θ = 22/20 = 11/10

b) cos 2θ = 2(17/20) = 17/10

c)tan 2θ = 2(11/17) = 22/17

The trigonometric ratios are six functions that relate the angles of a right triangle to the lengths of its sides. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

If sin θ = 11/20

The missing side of the triangle is;

b = √20^ - 11^2

b = 17

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Neglecting friction, a similar ride with 12 passengers aboard would take 6 minutes.

The time it takes for a roller coaster ride is directly proportional to the mass of the passengers. If we assume that each passenger has the same mass, then the time it takes for the ride is proportional to the number of passengers.

Let T1 be the time for the ride with 6 passengers, and T2 be the time for the ride with 12 passengers. Then, we have:

T2 = (12/6) * T1

Simplifying this expression, we get:

T2 = 2 * T1

We are given that T1 = 3 minutes, so we can substitute this value into the equation above to find T2:

T2 = 2 * 3 minutes = 6 minutes

Therefore, a similar roller coaster ride with 12 passengers aboard would take 6 minutes, as opposed to the 3 minutes it takes with 6 passengers aboard. The answer is 6 minutes.

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The statement is true. A confidence interval is a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.

In this case, we are interested in the odds ratio between MI (yes, no) and treatment (placebo, aspirin).

If the 95% confidence interval for the odds ratio between MI and placebo is (1.44, 2.33), this means that we can be 95% confident that the true odds ratio falls between these two values. This implies that the odds of having an MI are between 1.44 and 2.33 times greater for those taking the placebo compared to those taking aspirin.

When we switch the rows so that aspirin is in the first row, we need to take the reciprocal of the upper and lower bounds of the confidence interval to get the new interval. This is because the odds ratio is calculated as the odds of MI for one group divided by the odds of MI for the other group, and switching the groups changes the ratio.

So, if we take the reciprocal of the lower and upper bounds of the original interval, we get:

1/2.33 and 1/1.44

which is the new 95% confidence interval for the odds ratio when aspirin is in the first row. Therefore, the statement is true.

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Answer:

if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price

Step-by-step explanation:

Answer:

11 inches

Step-by-step explanation:

If its cubic inches, we just need to cube root it

Plug it into the calculator and you get a number that rounds up to 11

Reasoning is because it is cubic, so to find the distance which is a normal number, you need to cube root it

The arc length and the sector area are l = 0.25πr and A = (πr²) / 8.

The sector is essentially a section of a circle, and it may be described using the following three criteria:

The area of a disc that is surrounded by two radii and an arc is known as a circular sector.

The circle is divided into the Main Sector and the Minor Sector by a sector.

The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.

The arc length is given as:

l = α/360 (2πr)

The angle is 45 degrees thus,

l = (45/360)(2πr)

l = 0.25πr

The sector area is given as:

A = α/360 (πr²)

A = 45/360 (πr²)

A = (πr²) / 8

Hence, the arc length and the sector area are l = 0.25πr and A = (πr²) / 8.

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Step-by-step explanation:

These points are in (X, Y) form. What you want to do is plug in the X coordinates into the equation and see if it equals the Y coordinate.

Equation: Y = X + 4

Point A: (-1, 3)

(-1) + 4 = 3

Point B: (2, 6)

(2) + 4 = 6

Point C: (-2, -2)

(-2) + 4 = 2

Point D: (2, 4)

(2) + 4 = 6

Only point A and point B equal their Y coordinate, making A and B the only correct answers.

The relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value. Hence, option 2 is the correct answer.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that a function is a relationship between inputs where each input is related to exactly one output.

In the given graph (2,2) and (3,2) have the same y value that is two inputs have same output.

Hence, the relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value and option 2 is the correct answer.

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If the sum of three successive integers even numbers is 6000, then their values must be 1998, 2000, and 2002.

In addition tangere is the root of the Latin word integer, which meaning "whole" and "untouched." The word "entire" is derived from the French word entier, which also means entire and integer. The expression was once used to describe a multiple of 1 or the whole part of a mixed number. The definition of the term was given as the collection of all positive integers, which is the same as the collection of all natural numbers. The concept of integer was expanded to include negative integers as the significance of those numbers came to be realized through time. For instance, in his 1765 book Elements of Algebra, Leonhard Euler stated that integers might contain both positive and negative values. Up until about the middle of the 20th century, most European mathematicians ignored negative numbers.

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Answer:

one fifth would be espressos so 3

Step-by-step explanation:

The volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

The volume of a right circular cylinder can be calculated using the formula:

V = π * r² * h

Where r is the radius and h is the height of the cylinder.

Plugging in the values for r and h, we get:

V = π * 7² * 1.5

V = π * 49 * 1.5

V = 73.5 * 1.5

Therefore, V = 110.25

So the volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

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There were 297 children and 185 adults who swam that day. Let x be the number of children and y be the number of adults who swam that day.

According to the problem, we know that:

x + y = 482 ---(1) (total number of people who swam)
1.5x + 2y = 815.5 ---(2) (total revenue generated)

To solve for x and y, we can use any method of solving a system of linear equations, such as substitution or elimination. Here's how to solve using the substitution method:

From equation (1), we can write:

x = 482 - y

Substituting this into equation (2), we get:

1.5(482 - y) + 2y = 815.5

Simplifying and solving for y, we find:

723 - 1.5y + 2y = 815.5

0.5y = 92.5

y = 185

Substituting this value of y back into equation (1), we find:

x + 185 = 482

x = 297

Therefore, there were 297 children and 185 adults who swam that day.

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the first choice is the right answer

please check my working for guidance

The area of a four-sided regular pyramid, given the base edge and the side edge is 340 cm ² .

The area of a four-sided regular pyramid can be found by the formula :

= Area of base + 1 / 2 x perimeter of base x side edge

Area of base :

= 10 x 10

= 100 cm ²

Perimeter of base ;

= 10 + 10 + 10 + 10

= 40 cm

The area of the four-sided regular pyramid is;

= 100 + ( 1 / 2 x 40 x 12 )

= 340 cm ²

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The constant of proportionality for this relationship is the circumference of the wheel.

A proportional relationship between two variables means that the ratio of the two variables is constant. In other words, if the independent variable (time in this case) increases, the dependent variable (the amount of money Steven charges) will increase proportionally.

The distance a wheel can travel is proportional to its radius.

wheel radius(in.)      distance in 4 revolutions (in.)

4                                    32π

3.5                                 28π

0.25                               2π

The distance a wheel can travel in one revolution is equal to the circumference of the wheel. So, if we know the radius of the wheel, we can calculate its circumference using the formula:

circumference = 2π × radius

Then, we can use the circumference to find the distance the wheel can travel in a given number of revolutions by multiplying the circumference by the number of revolutions. In the table provided, we can see that for each wheel radius, the distance traveled in 4 revolutions is a multiple of the circumference of the wheel, which confirms that the constant of proportionality is the circumference.

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