Determine whether each pair of triangles are similar. Justify your answer.

Step-by-step explanation:

Let's start by using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume of the cylinder, r is the radius of the cylinder, h is the height of the cylinder, and π is a mathematical constant (approximately equal to 3.14).

Since we are dealing with a drain pipe, we can assume that the height of the cylinder is fixed and does not change. Therefore, we can rewrite the formula as:

V = πr^2h = Ah

where A is the cross-sectional area of the cylinder.

Now, let's use the given information that the drain pipe can carry 36 litres per second. We know that the volume of water that passes through the pipe in one second is equal to 36 litres. We can therefore write:

36 = Ahv

where v is the velocity of the water flowing through the pipe. Since we are assuming that the height of the cylinder is fixed, we can simplify this equation to:

36 = Av

Now we need to determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second. Let's call the new diameter d2 and the old diameter d1. We can set up a proportion to solve for d2:

A1/A2 = d1^2/d2^2

We know that A1 and A2 are proportional to the volumes of water the pipe can carry, so we can write:

A1/A2 = 36/60

Simplifying this equation, we get:

A1/A2 = 3/5

Substituting in the formula for the cross-sectional area of a cylinder, we get:

πd1^2/4 / πd2^2/4 = 3/5

Simplifying further, we get:

d1^2/d2^2 = 3/5

Taking the square root of both sides, we get:

d1/d2 = sqrt(3/5)

Now we can solve for d2:

d2 = d1 / sqrt(3/5)

We want to know the percentage increase in the diameter, which we can find using the formula:

% Increase = (New Value - Old Value) / Old Value x 100%

Substituting in our values, we get:

% Increase = (d1 / sqrt(3/5) - d1) / d1 x 100%

Simplifying, we get:

% Increase = (1 / sqrt(3/5) - 1) x 100%

Using a calculator, we get:

% Increase ≈ 34.64%

Therefore, the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is approximately 34.64%.

Line AB is congruent to line CD , proved.

The proof that line AB is congruent to line CD is determined as follows;

If line AB ≅ CD, then will have the following to be true;

Let angle A = x

The value of angle C will be equal to x (alternate angles are equal)

Let angle B = y

The value of angle D will be equal to y (alternate angles are equal)

Let angle m∠AEB = z

The value of m∠DEC will be equal to z (vertical opposite angles are equal).

So line AB is congruent to line CD , proved.

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Answer: D) 5217

Step 1: Start by finding the three numbers that Julian got from cutting the sheet of paper.

Step 2: We can split the number into three sections: 502, 197, and 2970.

Step 3: Add the three numbers: 502 + 197 + 2970 = 3669

Step 4: The smallest sum Julian can get is 3669 and the answer is D) 5217.

The shortest tour from A to B to C and back to A is 50 km.

We have,

A to Zoo and Port and back to A: 10 km

B to Park and Zoo and back to B: 12 km

C to Port and Park and back to C: 13 km

Zoo to Park and Port and back to Zoo: 15 km

To calculate the shortest tour from A to B to C and back to A, we can add up the distances between each pair of stations:

A to Zoo and Port and back to A (10 km)

Zoo to Park and Port and back to Zoo (15 km)

B to Park and Zoo and back to B (12 km)

C to Port and Park and back to C (13 km)

So, Total distance: 10 + 15 + 12 + 13 = 50 km

Therefore, the shortest tour from A to B to C and back to A is 50 km.

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A. A table of values and graph of the function is shown below.

B. The object would hit the ground at approximately 8.963 seconds.

Based on the information provided, we can logically deduce that the height (s) in meters, of this object above the​ ground is related to time by the following quadratic function:

s(t) = -4.9t² +39.2t + 42.3

When t = 0, s(t) is given by;

s(0) = -4.9(0)² +39.2(0) + 42.3

s(0) = 42.3

When t = 1, s(t) is given by;

s(1) = -4.9(1)² +39.2(1) + 42.3

s(1) = 76.6

When t = 2, s(t) is given by;

s(2) = -4.9(2)² +39.2(2) + 42.3

s(2) = 101.1

Therefore, the table can be created as follows;

Time (t)     Height s(t)

0                  43.3

1                   76.6

2                  101.1

3                  115.8

4                  120.7

5                  115.8

Part B.

Generally speaking, the height of this object would be equal to zero (0) when it hits the ground. By critically observing the graph (see attachment), we can logically deduce that the object would hit the ground at approximately 8.963 seconds.

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Hello!

Answer:

No

Explanation:

A statistical question is answered by collecting data that exhibits variability

[tex]\Huge \fbox{Answer = No}[/tex]

Statistical questions are open ended questions that are created to gather information or data about a population or a sample. Depending on the population or sample being investigated, they often involve variability and can have a variety of possible responses.

Because it is a straightforward factual question that can be answered with a single value, the question being asked is not a statistical one.

There are 1,760 yards in a mile, hence the answer to this question is an exact number. There is no variability or data gathering involved with this response. As a result, the question is not a statistical question.

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The smallest subset containing 7.83 among the common subsets is Q.

We are given that;

The number 7.83

Now,

Subset of a given set is a set whose all elements are in the original set of which it is subset.

So if B is subset of A, then all elements of B are in A but it is not necessary that all elements of A are in B.

If B is subset of A, then A is superset of B.

The smallest subset containing the value 7.83 is the set of rational numbers. A rational number is a number that can be written as a fraction of two integers, such as 7.83 = 783/100. The set of rational numbers is denoted by Q and it is a subset of the set of real numbers R.

Therefore, by subsets the answer will be Q.

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The value of x in the proportion is -9.

To solve the proportion [(3/4) is to -6] is to [(3/4) is to 3] is to x = [(3/4) is to -9], we can cross-multiply and solve for x.

Starting with the left side of the proportion:

[(3/4) is to -6] is to [(3/4) is to 3]

Cross-multiplying:

(3/4) * 3 = (3/4) * (-6)

Simplifying:

9/4 = -18/4

Now, moving to the right side of the proportion:

[(3/4) is to -9]

Cross-multiplying:

x * (3/4) = (3/4) * (-9)

Simplifying:

(3/4) * x = -27/4

To solve for x, we can multiply both sides of the equation by the reciprocal of (3/4), which is 4/3:

(4/3) * [(3/4) * x] = (4/3) * (-27/4)

Simplifying:

x = -9

Therefore, the value of x in the proportion is -9.

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The correct statement is that "Line p must be drawn in plane B."

If a new line, p, is drawn parallel to line /, the statement that is true is "Line p must be drawn in plane B."

To understand this, let's analyze the given information:

Planes A and B are shown.

Line m is shown in plane A.

Line n is shown in plane B.

Line / is the line that connects planes A and B.

When a new line, p, is drawn parallel to line /, it means that line p will also connect planes A and B. However, since line / itself is connecting planes A and B, line p must also lie in plane B to maintain its parallel relationship with line /. This is because parallel lines lie in the same plane.

This ensures that line p remains parallel to line / and maintains its connection between planes A and B.

It is important to note that line p being drawn in plane B does not necessarily imply that it intersects with line n. It simply means that line p lies within plane B and remains parallel to line /.

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Answer:

B: 2/9

Step-by-step explanation:

There are a total of 9 bills in Scott's pocket, and he has 2 five dollar bills.

This means that the probability of pulling out a 5 dollar bill is 2/9.

From the graph, we can calculate that 6 seconds after the ball is thrown, it will be 20 meters from the ground again.

The equation is as follows:

d = d0 + v0 * t - (1/2) * g * t²

d =  distance from the ground

d0 = the initial height

v0 =  initial velocity

g  =  acceleration due to gravity = 9.8 m/s²

t=  time

20 = 20 + 15 * t - (1/2) * 9.8 * t^2

We simplify as follows:

0 = -4.9 * t² + 15 * t

We then go ahead to solve  this quadratic equation to find the values of t when the ball is 20 meters from the ground again.

t * (-4.9t + 15) = 0

t = 0 or

-4.9t + 15 = 0.

-4.9t + 15 = 0

-4.9t = -15

t = 3.06 seconds

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Answer:

[tex]q=4, x=-1[/tex]

Step-by-step explanation:

The given equation is:

[tex]2(3+x)=3q-3+5x---(1)[/tex]

Since [tex]x=q-5[/tex] is a solution of the equation above, so substitute x=q-5 into (1) as follows:

[tex]2(3+q-5)=3q-3+5(q-5)\\2(q-2)=3q-3+5q-25\\2(q-2)=8q-28\\q-2=4q-14\\4q-q=-2+14\\3q=12\\q=4[/tex]

Then, it follows:

[tex]x=q-5\\\therefore x=4-5=-1[/tex]

The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

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

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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[tex]x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z[/tex]

Therefore, it's [tex]2z^5-7z[/tex].

10-10=69.420!!!!!!!!!!

If the events A and B are mutually exclusive, meaning they cannot occur simultaneously, then the probability of both events occurring together is zero. In this case, the formula simplifies to P(A or B) = P(A) + P(B).

The probability that either event A or event B will occur can be calculated using the addition rule of probability. According to this rule, the probability of either event A or event B occurring is equal to the sum of the individual probabilities of each event minus the probability of both events occurring together.

In other words, P(A or B) = P(A) + P(B) - P(A and B)



However, if the events A and B are not mutually exclusive, then the probability of both events occurring together needs to be subtracted from the sum of their individual probabilities to avoid double-counting.

So, the final answer to the question "What is the probability that either event will occur?" depends on the specific probabilities of events A and B and whether they are mutually exclusive or not.

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The value of all the expression which have x = 5 asymptotes are,

⇒ g (x) = 3 log (x - 5)

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ f (x) = (3x + 20) / (x - 5)

We have to given that,

All the expressions are,

⇒ g (x) = 3 log (x - 5)

⇒ f (x) = √(x - 5) + 2

⇒ h (x)= eˣ⁻⁵

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ h (x) = - ∛(x - 5) + 1

⇒ f (x) = (3x + 20) / (x - 5)

Now, We can check all the expressions for which have x = 5 asymptotes.

Hence, We can substitute x = 5 in each expression and check all expression as which are not defined at x = 5,

⇒ g (x) = 3 log (x - 5)

Substitute x = 5;

⇒ g (x) = 3 log (5 - 5)

⇒ g (x) = 3 log (0)

Which is undefined.

⇒ f (x) = √(x - 5) + 2

Substitute x = 5;

⇒ f (x) = √(5 - 5) + 2

⇒ f (x) = 2

Which is defined.

⇒ h (x)= eˣ⁻⁵

Substitute x = 5;

⇒ h (x)= e⁻⁵

Which is defined.

⇒ g (x) = log₁₀ (- x + 5) -  4

Substitute x = 5;

⇒ g (x) = log₁₀ (- 5 + 5) -  4

⇒ g (x) = log₁₀ (0) -  4

Which is undefined.

⇒ h (x) = - ∛(x - 5) + 1

Substitute x = 5;

⇒ h (x) = - ∛(5 - 5) + 1

⇒ h (x) =  1

Which is defined.

⇒ f (x) = (3x + 20) / (x - 5)

Substitute x = 5;

⇒ f (x) = (3x + 20) / (5 - 5)

⇒ f (x) = (15 + 20) / (0)

Which is undefined.

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The equation of the graph is,

⇒ y = 6x + 2

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

For each by sitting job. Adam charges a fee for his bus fare plus an hourly rate.

And, The graph shows how he calculates the cost of a babysitting job.

Now, By graph;

Two points on the line are (1, 8) and (2, 14).

Now,

Since, The equation of line passes through the points (1, 8) and (2, 14).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 8)) / (2 - 1)

m = 6 / 1

m = 6

Thus, The equation of line with slope 6 is,

⇒ y - 8 = 6 (x - 1)

⇒ y - 8 = 6x - 6

⇒ y = 6x + 2

Therefore, The equation of line will be;

⇒ y = 6x + 2

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The measure of BC is 48x - 168.

In the given diagram of triangle BCD, we are told that E is the midpoint of BD and F is the midpoint of CD. Let's denote the measure of BC as y.

Since E is the midpoint of BD, we can say that BE = ED. Similarly, F is the midpoint of CD, so CF = FD.

Using the information given, we can write the equation EF = -9x + 82. Since F is the midpoint of CD, we can substitute FD for EF, so FD = -9x + 82.

Also, we know that BC = 80 - 6x.

In triangle BCD, we can write the equation BC = BE + EF + FD.

Substituting the given values, we have:

80 - 6x = (BE) + (-9x + 82) + (-9x + 82).

Simplifying the equation:

80 - 6x = BE - 9x + 82 - 9x + 82.

Combining like terms:

80 - 6x = BE - 18x + 164.

Moving the variables to one side and constants to the other side:

6x - BE + 18x = 164 - 80.

Combining like terms:

24x - BE = 84.

Rearranging the equation:

BE = 24x - 84.

Since E is the midpoint of BD, we can write:

BE = BD/2.

Substituting the value of BE:

BD/2 = 24x - 84.

Simplifying the equation:

BD = 48x - 168.

We are required to find the measure of BC, which is y. From the equation BC = BD, we have:

y = 48x - 168.

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Answer:

9:30

Step-by-step explanation:

Then you can state that angle DEF is congruent to angle GHJ.

The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.

This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.

In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and

you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.

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Based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

To compare the volume of Kibo, Destiny, and Columbus, we need to calculate the volumes of each module.

The volume of a chamber can be determined utilizing the equation V = πr^2h, where r is the span and h is the level (or length for this situation) of the chamber.

For Kibo:

Radius (r) = 2.2 meters

Length (h) = 11.2 meters

V_kibo = π * (2.2^2) * 11.2

      = 4.84 * 11.2

      ≈ 54.01 cubic meters

For Destiny and Columbus, we would need their respective dimensions to calculate their volumes using the same formula.

Destiny is a U.S. laboratory module on the International Space Station. It is a multi-sided module, so we would need the measurements of each side to calculate its volume.

Columbus is a European laboratory module, which is also multi-sided.

Without the specific dimensions of Destiny and Columbus, we cannot accurately compare their volumes to Kibo. However, based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

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Ethical guidelines are established to help professional psychologists maintain Professional behavior.

Professional behavior refers to the conduct and standards expected of psychologists in their professional practice. Ethical guidelines provide a framework that outlines the principles, values, and standards that psychologists should follow in their interactions with clients, colleagues, and the broader community.

These guidelines promote ethical behavior by setting expectations for confidentiality, informed consent, competence, integrity, and avoiding conflicts of interest, among other aspects. They ensure that psychologists prioritize the well-being and rights of their clients, maintain professional boundaries, and uphold ethical standards in research and practice.

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The value of angle C is calculated by applying cosine rule as  50.67 ⁰.

The value of angle C is calculated by applying cosine rule as shown below;

c² = a² + b² - 2ab cosC

The given parameters in the diagram;

length a = 22

length b = 18

c = 20

The value of angle C is calculated as;

20² = 22² + 18² - (2 x 22 x 18) cos C

792 cos C = 502

cos C = 502/792

cos C = 0.6334

C = arc cos (0.6334)

C = 50.67 ⁰

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The values of the distance are;

1. 4. 49 feet

2. 7. 73 feet

We need to know the trigonometric identities and their ratios. We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Now, substitute the values, we have;

1. Adjacent = d

Hypotenuse = 12

Angle = 68 degrees

cos 68 = adjacent/hypotenuse

cos 68 = d/12

cross multiply the values, we get;

d = 4. 49 feet

2.

cos 25 = 7/x

cross multiply the values, we have;

x = 7/0. 9063

divide the values, we get;

x = 7. 73 feet

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A. A graph of the function is shown in the image below.

B. The illumination in foot-candles that the object receives at a distance of 20-feet from the light source is

C. In the context of the problem, a meaningful domain is {x | x ≤ 0} and a meaningful range is {y | y ≥ 0}.

In this exercise, we would plot the illumination on the y-axis (y-coordinates) of a graph while the square of the distance would be plotted on the x-axis (x-coordinate) of a graph on a coordinate plane.

Part B.

The illumination in foot-candles that this object would receive at a distance of 20-feet from the light source can be calculated by substituting the value of d, which is 20 feet into the function as follows;

I(d) = 4500/d²

I(20) = 4500/20²

I(20) = 4500/400

I(20) = 11.25 foot-candles.

Part C.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, 0] ∪ [0, ∞] or {x | x ≤ 0}.

Range = [0, ∞] or {y | y ≥ 0}

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Answer:60

Step-by-step explanation: because I Maltiply 6 by 6 times

The non-linear graph of the function y = -(x - 1)² + 1. is given by the image presented at the end of the answer.

We have to look at the graph of the function relative to the x-axis, as follows:

The function has a maximum point at (1,1), meaning that:

Considering the end behavior of the function, that it goes to negative infinity at both tails of the graph, a function that satisfies these features is given as follows:

y = -(x - 1)² + 1.

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a)

The cost per unit decreasing by 0.00001 for production levels above 12,000.

Given,

From the graph it is clear that the graph passes through the points (12000,0.85) and (38000,0.59).

Now,

If a line passes through two points then the slope of the line is

m = y2 - y1 / x2 - x1

The rate of change in cost per unit for production levels above 12,000 is

m = 0.59 - 0.85 / 38000 - 12000

m = -0.00001

Here negative sign represents the decreasing rate. It means the cost per unit decreasing by 0.00001 for production levels above 12,000.

b)

The function for the domain over [12000, 38000] is :

y = -0.00001x + 0.97

The point slope form of a linear function is,

(y-y1) = m (x - x1)

m = slope.

The slope of the line over [12000, 38000] is -0.00001 and the point is (12000,0.85). So, the function for the domain over [12000, 38000] is

y-0.85 = -0.00001(x-12000)

y =  -0.00001x + 0.97

c)

The cost per unit at the production level of 19,000 is 0.78.

Substitute x=19000 in the above equation, to find the cost per unit at the production level of 19,000.

y = -0.00001(19000) + 0.97

y = 0.78

Thus the cost per unit at the production level of 19,000 is 0.78.

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The angle the vector v, that has components of 9,6 makes with the x- axis is 33.7°

The angle of a vector with x and y components (x,y) is given by

Ф = tan⁻¹(y/x)

Given that vector v has components of 9,6. To determine the angle, Ф, in degrees , that vector v makes with the x-axis, we proceed as follows.

We know that the components of the vector are (9,6) which means that

So, we have that

So, substituting the values of the variables into the equation, we have that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(6/9)

Ф = tan⁻¹(2/3)

Ф = tan⁻¹(0.6667)

Ф = 33.69°

Ф ≅ 33.7°

So, the angle is 33.7°

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The function [tex]f(x) = \sqrt[3]{2x-1}[/tex] is a cubic root function with a linear transformation applied.

The expression inside the root, 2x-1, is a linear function that scales and shifts the input x. The cubic root function then takes the cube root of the result.

This function is defined for all real numbers x, as the cubic root can be calculated for any real number.

Its graph is a transformed version of the standard cubic root function, skewed and shifted depending on the coefficients in the linear function. The function increases monotonically as x increases, and it is continuous and differentiable everywhere.

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The Complete Question

[tex] f(x)=\sqrt[3]{2x-1}[/tex]

Identify this function and solve