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The work required to pump the water out of the spout is 5000ft⋅lb

Given

The volume V=12(4ft)(5ft)(6ft)=60ft3,

Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.

Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.

Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.

In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.

We have to lift that slice 4ft−y, so work is

w = [tex]\int\limits^4_0[/tex] (62.5)(4 − y) (7.5y)

dy = (62.5)[15y2−2.5y3]40  = 5000ft⋅lb

The work required to pump the water out of the spout is  5000ft-lb

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Option B is right perpendicular bisectors of the sides of the triangle

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.

One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.

When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.

When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C

In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC

Therefore Option B is right perpendicular bisectors of the sides of the triangle.

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Answer:

62 and 150

Step-by-step explanation:

let the 2 numbers be x and y , x > y , then

x + y = 212 → (1)

x - y = 88 → (2)

add the 2 equations term by term to eliminate y

2x + 0 = 300

2x = 300 ( divide both sides by 2 )

x = 150

substitute x = 150 into (1)

150 + y = 212 ( subtract 150 from both sides )

y = 62

the 2 numbers are 62 and 150

Answer:

28) Y=1x+c

29)-2/3x+c

Step-by-step explanation:

Answer:

Drag and drop 6(2x-1) to 12x-6.

Drag and drop 6(4x-2) to Neither.

Drag and drop 3(8x+4) to 24x+12.

Drag and drop 6(4x+2) to 24x+12.

Drag and drop 2(6x-3) to 12x-6.

Step-by-step explanation:

To check these, use distributive property to solve each one.

6(2x-1) = 12x-6

6(4x-2) = 24x-12

3(8x+4) = 24x+12

6(4x+2) = 24x+12

2(6x-3) = 12x-6

Hope this helps!

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[tex]{(x-h)}^2 + {(y-k)}^2 = {r}^2[/tex] represent the equation of the new circle.

Given: (h,k) is center of circle

           and (x,y) remains on edge of circle.

The distance formula is used to determine the distance, d, between two points. If the coordinates of the two points are (x1, y1) and (x2, y2), the distance equals the square root of x2 − x1 squared + y2 − y1 squared.

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points.

In a Cartesian grid, to measure a line segment that is either vertical or horizontal is simple enough. You can count the distance either up and down the y-axis or across the x-axis

Using Distance formula which says,

[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r\\\sqrt{{(x - h)}^2 + {(y - k)}^2} = r\\\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]

Hence, the equation of the new circle will be [tex]\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]

[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r[/tex]

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Answer: B

Step-by-step explanation:

Answer:

{x:x is a multiple of 3, x ≤ 15}

In set builder notation, the set Q is written as

Q = {x | x ∈ N, 1 ≤ x ≤ 15, x ∈ {1, 3, 6, 9, 10, 15}}

The set Q can be rewritten using the set-builder notation as:

Q = {x | x ∈ N, 1 ≤ x ≤ 15, x ∈ {1, 3, 6, 9, 10, 15}}

In the set-builder notation, the expression "x |" indicates that x belongs to the set being defined.

The vertical bar (|) is read as "such that." The condition "x ∈ N" specifies that x is a natural number, and the condition "1 ≤ x ≤ 15" indicates that x must be greater than or equal to 1 and less than or equal to 15.

Finally, the expression "{1, 3, 6, 9, 10, 15}" specifies the specific elements that belong to the set Q.

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The value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.

According to the properties of similar triangle, the corresponding sides of similar triangles are in proportion.

In the question, we are given that ΔQRS ~ ΔXYZ.

By properties of similar triangles, we know that:

QR/XY = RS/YZ = SQ/ZX.

From this, we can show that:

RS/SQ = YZ/ZX ...(i).

We are asked to find the value of tan(Q).

By trigonometric ratios, we know that:

tan(Q) = Perpendicular/Base = RS/SQ.

From (i), we know that RS/SQ = YZ/ZX.

From figure, we know that YZ = 9, and ZX = 12.

Thus, YZ/ZX = 9/12 = 3/4.

Thus, tan(Q) = RS/SQ = YZ/ZX = 3/4.

Hence, the value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.

The question is incomplete. The complete question can be seen in the figure.

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A dependent means t-test determines if the differences between scores on the pretest and post-test measures differ significantly from Zero(0).

Benefits of pre-test measurements

This design is superior to the post-test-only control design because it adds pre-tests. Addition of pre-test: Improve your design ability to detect effects. You can investigate the impact of interventions on various sublevels of pretesting.

The design of the pre-test and post-test is similar to the in-subject experiment. In this experiment, each participant is first tested in control conditions and then in therapeutic conditions.

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By applying basic proportionality theorem (BPT), the length of side PC and BR are 25 cm and 9 cm respectively.

In order to determine the length of side PC and BR, we would apply basic proportionality theorem (BPT) as follows:

PC/CQ = AR/AQ

PC/15 = 20/12

Cross-multiplying, we have:

12PC = 20 × 15

PC = 300/12

PC = 25 cm.

For the length of side BR, we have:

PC/CQ = PB/BR

PC/15 = 15/BR

25/15 = 15/BR

25BR = 225

BR = 225/25

BR = 9 cm.

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Answer:

Julia and Liz worked 10 hours to finish the project.

Step-by-step explanation:

I don't know if I am 100% right, but I believe this is the answer.

If you take the 24 hours it will take Julia to finish the project on her own and subtract the time it would take Liz you would have 12 hours left then take the 2 hours Liz has already been working on the project you would have 10 hours for both of them to finish the project together.

24 -12 = 12

12 - 2 = 10

sin(Q) = -(12/13)

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.  It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.

cot(Q) = 5/12

sin(Q) = 1/cosec(Q)

[tex]sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}\\[/tex]

sin(Q) = ±12/13

Because, π < Q < (3/2)π

Therefore, sin(Q) = -12/13

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Answer:

A- -12/13

Step-by-step explanation:

Answer:

x=0. The explanation is below.

Step-by-step explanation:

So, it is run 2 rise 6. We can fact-check that with 1 to 3 to 5 and 1 to 7 to 13. So, the slope is 3 because of rise over run. So, we can make an equation with y = mx + b. m = 3 because that is the slope. 1=3(1) + b. b=-2. So, the equation is y=3x-2. We can find any x using y and vice versa if we find the equation.

For this part, -2=3x-2. 3x=0. x=0.

Find equation of line

Slope

Equation

Now

put y=-2

Answer: D: SSS Congruency

Step-by-step explanation:

- SSS congruency stands for side-side-side congruency

- if the 3 side lengths are equal for both triangles they are equivalent

- the reflexive property states that an angle, line segment, or shape is always congruent to itself

- so the reflexive property is just saying that WY = YW, therefore creating 3 equal sides for both triangles

- so the triangles are congruent by SSS

hope this helps :)

Step-by-step explanation:

p=2L+2w

factorise

p=2(L+w)

p=2(20+14)

p=2(34)

p=68

This is also a perimeter of a rectangle

Hello!

Here, the 2 mathematical operations involved are : multiplication and addition.

From the order of operations, we know multiplication is followed by addition.

⇒ P = 2(20) + 2(14)

⇒ P = 40 + 28

⇒ P = 68

∴ The answer will be [tex]\fbox {68}[/tex]

Answer:

Radius = 8 units

Length of arc AB = 8.37758 units

Step-by-step explanation:

The sector COD is 1/4 the size of the circle.

the vertex angle is 90° and a circle has 360° at the center.

So the area of sector COD/area of Circle = 90/360 = 1/4

This means the area of the circle is 4 * 50.24 = 200.96 square units

Area of circle = πr² where r is the radius
πr² = 200.96

r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units

The circumference of the circle is 2πr = 16π units

arc AB has a vertex angle of 30°.

30°/360° = 1/6

So the length of the arc is 1/6th the circumference of the circle =

(1/6) * 16π  = 2.67π  units or 8.37758 units

The formula speed = distance ÷ time can be rearranged, just like any other equation. The formula can be rearranged in three ways: speed = distance ÷ time , distance = speed × time.

Speed tells us how slow or fast an object moves.  Distance refers to extent of space between two events. Time refers to an interval separating two events.

ASSUME a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

Distance that the ferry would be able to trave in 1 hour can be found out by :

unit rate=distance / time

=1/7÷3/5

Reciprocal:

=1/7×5/3

=5/21th of distance per hour

The distance that the ferry would be able to travel in 3.5 hours:

= (5/21 ) ×3.5

=(5/21)×(7/2)

Further solving:

=(5/3)×(1/2)

5/6th of the distance between two ports.

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Disclaimer:

Your question was incomplete. Please check below the full content.

Complete question could be a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

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The answers are:

Note that the graph depict the depth, y, in meters, of a shark that moves from the surface of an ocean for a given amount of time, x, in minutes.

So:

Part A :

We  look at the two right triangles:  Δ ABD and Δ BCE, and where D(2,100) and E(1,60) points.

Since the  triangle are the same and thus, the slope of line segment AB: tan θ = AD/BD

= 140 - 100 / 2 - 1

= 40

Since the the slopes of line segment BC will be:

tan a = BE/CE

= 100 - 6 / 1 - 0

= 40

So, θ = α and the slope of AB and BC are similar.

Part B :

Using the graph, one can see that  the initial value of the graph is 60 m and it stands for the initial position of the shark

e.g.  at point t = 0 min, the shark was seen at a depth of 60 m from the water surface.

So therefore, since the slope of the graph is 40 it implies that the rate of change of distance from the Ocean surface of the shark in regards to the  time in minutes have to be 40 m per min.

Therefore, The answers are:

Part A: The slope of AB and BC are the same.

Part B :The initial value is 60 m and the slope is 40 m/min.

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Answer:

120

Step-by-step explanation:

For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120

Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.

The area of the composite figure is the sum of two areas, the area of a semicircle and the area of a right triangle. The formula for the area of the composite figure is described below:

A = (1/2) · AB · BC + (π/8) · BC²     (1)

If we know that AB = 6 cm and BC = 6 cm, then the area of the composite figure is:

A = (1/2) · (6 cm)² + (π/8) · (6 cm)²

A ≈ 32.137 cm²

Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.

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Answer:

Step-by-step explanation:

Michelangelo went 30 feet for a pizza to a pizza restaurant.

It is given that,

Michelangelo was starving for a slice of pizza. He started -50 feet in the sewer, climbed the ladder to the street, and ran 20 feet to the pizza restaurant.

So, the total feet he traveled is,

= -50 feet + 20 feet = 30 feet.

Therefore, Michelangelo went 30 feet for pizza.

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Answer:

1679616

Step-by-step explanation:

Answer:

it's 6^8 (6 to the 8th power)

Step-by-step explanation:

put 8 in the box

hope this helps :) <3

The permutation illustrates that when the teacher decides to only use 6 posters, the number of arrangements that can be made will be 665280 ways.

When the teacher decides to only use 6 posters, the number of arrangements will be:

= 12P6

= 12!/(12 - 6)!

= 12!/6!

= 665280 ways.

The fundamental principle will be:

= 12 × 11 × 10 × 9 × 8 × 7

= 665280 ways

When the teacher uses all 12 posters, but wants to have a black & white poster at each end, the number of arrangements will be 203212800 ways.

When the teacher uses all 12 posters, but wants all the colored posters to be side-by-side, the number of arrangements will be:

= 4!8!

= 4 × 3 × 2 × 1 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 967680 ways.

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Answer:

24.8°

Step-by-step explanation:

Complementary angles sum 90°

65.2° + B° = 90°

B° = 90° - 65.2°

B° = 24.8

Angle B from the information given is 24. 8°

Note that complementary angles sum up to 90°

From the information given, we have that

Angle A + Angle B = 90°

If angle A = 65. 2°

Angle B = 90 - 65. 2

Angle B = 24.8°

Thus, angle B from the information given is 24. 8°

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The range of a function is all possible y values that a function can take on.

In the case of the given function, the y values fluctuate between -1 and 1. Therefore, the range of the function is -1 <= y <= 1 (Option A).

Hope this helps!