A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that

The triangles can be proved congruent by SAS theorem.

Two or more triangles are said to be congruent if and only if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.

To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.

Therefore. in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;

It can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.

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Answer:29,697

Step-by-step explanation: multiply 57x521 and you get 29,697

Answer:

Step-by-step explanation:

2 or 6 i think im probaly wrong

Answer:

The container can hold 6 cups.

Step-by-step explanation:

Since the container is 1/3 full, and it currently has 2 cups, we know that it can only hold 6 cups as 3 × 2 is equal to 6.

Answer:

7.5 which rounds to 8

Step-by-step explanation:

2,722 divided by 360 equals 7.56

check if needed <3

Answer:

  1056

Step-by-step explanation:

You want the product of the LCM and the GCF of 22 and 48.

One way to find the LCM of two numbers is to start with their product, then divide out the extra factor:

  LCM(A, B) = (A×B)/GCF(A, B)

Since we want the product of the LCM and the GCF, we can start with this and multiply by the GCF:

  LCM(A, B) · GCF(A, B) = ((A×B)/GCF(A, B)) · GCF(A, B)

  LCM(A, B) · GCF(A, B) = A×B

Using this for the given numbers, we get ...

  LCM(22, 48)·GCF(22, 48) = 22·48 = 1056

__

Additional comment

If you want to go to the trouble of finding the LCM and GCF, you get ...

  22 = 2·11

  48 = 2·24

  LCM(22, 48) = 2·11·24 = 528

  GCF(22, 48) = 2

  LCM·GCF = 2·528 = 1056

Answer:

If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.

Step-by-step explanation:

Answer:

<1=75°[corresponding angles are equal]

<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]

<3=<2=105°[Vertically opposite angles are equal]

<4=75°[Alternate angles are equal]

<6=<2=105°[Corresponding angles are equal]

<7=<6=105°[Vertically opposite angles are equal]

<8=75°[Vertically opposite angles are equal]

*mark me brainliest

A total of 785 planks Andy Mann needs to order to make sure he has enough to complete the fence.

As the planks are 10cm wide to the nearest cm.

The total length of the fencing is = 75 m

From above, we can conclude that,

Range of the planks' lengths: 9.5 cm <= Plank's length < 10.5 cm

Range of fencing needed: 74.5 m <= Fence length < 75.5 m

We should consider the worst-case scenario where all the planks are 9.5 cm.

To complete the job, he only needs 74.5 m in total.

So, the total number of planks needed for completing the Job will be

= (74.5 * 100) / 9.5 = (7.84210*100) = 784.210

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well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

The capacity of an object is expressed in terms of volume. The quantity of space a three-dimensional item takes up can also be referred to as volume.  It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

Given

The bounds for z are 0 ≤ z ≤ x.

The bounds in the xy-plane are x ≤ y ≤ 5 - x and x in [0, 5/2]

So, V = ∫∫ (x - 0) dA

= ∫(x = 0 to 5/2) ∫(y = x to 5 - x) x dy dx

= ∫(x = 0 to 5/2) x (5 - 2x) dx

= ∫(x = 0 to 5/2) (5x - 2x^2) dx

= (5x^2/2 - 2x^3/3) {for x = 0 to 5/2}

=  125/24.

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

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Answer:

a) 110

b) 250

Step-by-step explanation:

Read the top row of numbers for a.  We are starting at zero and going to 110

Reflex is when two angles add up to 360

360 - 110 = 250

Hello!:

Let's take this problem in steps:

   [tex]sinx-\sqrt{3-3sin^2(x)}=0\\\\\text{We know that } sin^2(x) + cos^2(x)=1 \text{ and that } cos^2x=1-sin^2(x)\\\\sin(x)-\sqrt{3(1-sin^2(x))}=0\\\\sin(x)-\sqrt{3*cos^2(x)}=0\\\\sin(x)-\sqrt{3}*cos(x)=0[/tex]

Now we need to find the value of sin(x) and cos(x) where the value becomes zero:

  --> and it so happens to be:

        [tex]sin(30)=\dfrac{1}{2} \\\\cos(120)=\dfrac{\sqrt{3}}{2}[/tex]

Thus:

 [tex]sin(30)-\sqrt{3}*cos(120)=0\\\\\dfrac{1}{2} -\sqrt{3}*\dfrac{\sqrt{3} }{2} =0\\\\\\\dfrac{1}{2} -\dfrac{1}{2} =0\\\\0=0[/tex]

Answer: (B)

A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.

The expression can be written as,

[tex]y = 840(1.25)^x[/tex].

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The length AB of the roof is 3.20 m.

What is the Pythagorean theorem.

The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.

The theorem states that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.

Now applying the Pythagorean theorem, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

/AB/^2 = /2/^2 + /2.5/^2

            = 4 + 6.25

/AB/^2 = 10.25

AB = (10.25)^ 1/2

AB = 3.20

Thus, the length of AB of the roof is 3.20 m.

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In a tank that is 36 inches long, 18 inches wide, and 12 inches tall have approximately 33 gallons of water.

The rectangular tank's volume may be calculated using the formula V = l*b* h, where "l" stands for the tank's length, "b" for its width, "h" for its height, and "V" for its volume.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume = length*width*height

V=36*18*12

V=7776 inches^3

which is approximately 33 gallons.

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Answer:

C:  (-8, 2)

Step-by-step explanation:

Given parabola:

[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.  

Therefore, the x-value of the vertex of the given parabola is:

[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]

To find the y-value of the vertex, input x = -8 into the given equation:

[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

Therefore:

[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]

Answer:

Step-by-step explanation: (11c + 8) (-9c - 1)

Then expand

which would be 11c ( -9c - 1) + 8 ( -9c - 1)

-99c^2 -11c - 72c - 8

It becomes -99c^2 - 83c -8

I hope this was helpful

Answer:

Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes

1.3584655000

2.85760000

3.146737000

4.5555627000

5.7777000

please help

Step-by-step explanation:

1. Eliminate any constant that is on the same side as the variable.

2. Use inverse operations to isolate the variable by itself.

3. Whatever you do to one side you do to the other.

Total 400 calories is expected to have a meal has 300 calories from fat  the relationship between the total calories a meal has and the number of calories from fat .

A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables). There are points on a scatter (XY) plot that depict the connection between two sets of data. The sample illustrates the weight and height of one person for each dot. Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another. The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.

given

300 calories from fat

total = 100 + 100 + 200

= 400 calories

Total 400 calories is expected to have a meal has 300 calories from fat  the relationship between the total calories a meal has and the number of calories from fat .

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The value of a perfect square is either a positive number or zero. They cannot be neutral.

Perfect squares are generated when you square an integer. For instance, the number 81 is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since 12 is squared to produce it. 169 is a perfect square since 13 may be squared to obtain it. Mathematical language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the outcome is referred to as a square number, a perfect square, or simply "a square." Therefore, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

The value of a perfect square is either a positive number or zero. They cannot be neutral.

Square differences can be positive, negative, or zero depending on the order in which the numbers are obtained.

One squared term will be added to the difference of squares, and another squared term will be subtracted.

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The group that would probably give you the most reliable data is tourists who have visited the beaches. Option C is the correct answer.

In order to gather information about a service, product, or process, a survey is described as an act of looking at a process or interviewing a predetermined sample of people. Surveying beachgoers who have previously been there will yield more accurate results regarding the greatest beaches because they can share their personal experiences.

Surveying those in charge of the beaches is not a smart idea since they would be prejudiced in saying that their beaches are the finest. As a result, the third choice is the best one.

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Step-by-step explanation:

[tex] = {x}^{2} \div {x}^{2} + 3x - 5x + 6 - 10 \\ = 1 - 2x - 4 \\ = - 2x - 4 + 1 \\ = - 2x - 3 \\ = - 1(2x + 3)[/tex]

HI,HOPE THAT IS HELPFUL.

Answer:

Step-by-step explanation:

because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,

we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD

The equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].

What is slope intercept form of the line?

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.

Given:

The line passes through the points (7, 6) and (- 1, 2).

We have to find the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.

First to find the slope of the line using the formula,

Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1, y_1)= (7, 6), (x_2,y_2)=(-1, 2)[/tex]

Plug the values in the above formula.

[tex]m = \frac{2-6}{-1-7} = \frac{-4}{-8}=\frac{1}{2}[/tex]

Now consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)\\y-6=\frac{1}{2}(x-7) \\y-6=\frac{1}{2}x-\frac{7}{2}\\ y=\frac{1}{2}x -\frac{7}{2}+6 \\y=\frac{1}{2}x+\frac{5}{2}[/tex]

Hence, the equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].

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Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.

A calculation or problem-solving procedure is known as an computation or algorithm. Algorithms serve as a thorough set of instructions that direct hardware- or software-based routines through a sequence of planned actions step by step. In all areas of IT, algorithms are commonly employed.

Here,

If it is impossible to develop an algorithm that reliably returns a true or false result for each input value, the problem is said to be undecidable.

The category of inherently unknowable questions, a subtype of insoluble problems, only includes questions that ought to receive a yes-or-no response .

Thus ,incomputable. is another word for undecidable.

Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.

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Answer:

x=40º

Step-by-step explanation:

A straight line is 180º

180-40=140º

180-140=40º

x=40º

Hope this helps :)

The line parallel to 6y = -36x -3 will have the same slope which will be -6.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation of the line is

6y = -36x -3

⇒y = -6x - 1/2

From slope intercept form of the equation we know that

equation of the line is y = mx + c

where m is the slope.

Therefore,

slope the line is -6

The line parallel to 6y = -36x -3 will have the same slope which will be -6.

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The number of asset is 15.698.89

Assets = liabilities + equity

liabilities= 3,241.77

equity= 12,457.12

Assets= 3,241.77 + 12,457.12

=  15.698.89

Hence Lloyd has 15.698.89 number of assets

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