can 130 students all be seated at a table of 6 explain your answers

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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These are a legitimate probability distribution:

To have a legitimate probability distribution, the probabilities for all possible values of X must satisfy two conditions:

Each probability value must be between 0 and 1, inclusive.

The sum of all probability values must equal 1.

Check if the given probabilities satisfy these conditions:

P(X=-3) = 0.14 (valid)

P(X=1) = 0.1 (valid)

P(X=3) = 0.135 (valid)

P(X=5) = 0.306 (valid)

Now, calculate the remaining probability to check if it satisfies the second condition:

P(X=6) = 1 - (P(X=-3) + P(X=1) + P(X=3) + P(X=5))

P(X=6) = 1 - (0.14 + 0.1 + 0.135 + 0.306)

P(X=6) = 1 - 0.681

P(X=6) = 0.319

Since the calculated probability is valid (between 0 and 1), There is a legitimate probability distribution for the discrete random variable X:

P(X=-3) = 0.14

P(X=1) = 0.1

P(X=3) = 0.135

P(X=5) = 0.306

P(X=6) = 0.319

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Answer:

Step-by-step explanation:

The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.

To calculate for the volume of a rectangular base pyramid, we use the formula:

volume = 1/3 × area of base rectangle × height

volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units

volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.

Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.

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Following are the numbers correct to 3 significant figures

Answers to the following questions:

(1) Round to the needed significant figure: 37400;

(2) Round to the required significant figure: 84600;

(3) Round to the required significant figure: 261;

(4) Round to the needed significant figure: 0.00262

(5) Round to the required significant figure: 0.368

(6), round to the needed significant figure: 0.00257

The most significant number in the number is rounded up. Check the first non-zero digit if you want to round to one significant figure while doing so. If rounding to two significant numbers, have a look at the digit that comes after the first non-zero digit.

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Answer: 2.4

Step-by-step explanation: Given the angles below, the length of EF will be 2.4

Answer:

B) 3.8.

EF = 3.8

Use the law of sines to find the unknown length EF

Answer:

3/4 and 1/6 are already reduced the farthest they can go.

Answer:

glassA=1/3×22/7×4²

=16.76

glass B=1/3×22/7×3²

=9.42

glass A is the correct answer

Answer:

Let B(a,b) be x1, y1

A(-6,1) be x2,y2

midpoint M(-3,2) be (x,y)

using midpoint formula

(x,y)= [(x1+x2)/2, (y1+y2)/2)

(-3,2) = [(a-6)/2, (b+1)/2}

comparing corresponding value

-3 = (a-6)/2                           (b+1)/2 = 2

-6= a-6                                  b+1=4

a=0                                         b=3

coordinates of B = (0,3)

Answer: 23.76 miles

Step-by-step explanation:

You are basically finding the perimeter for question a

given that perimeter is \(\pi\)d

Subsitute the values

So perimeter = \(\pi\) x 5.5 = 5.5 \(\pi\) miles = 17.28 miles (2.d.p)

For question b, the area of the surface of Crater lake is finding its area

Given that area of a circle is \(\pi r^{2}\)

Substitute the values

Because 5.5 is the diameter, to find the radius, divide by 2 to get 2.75

Area = 2.75^2 x \(\pi\) = 7.5625\(\pi\) = 23.76 miles^2 (2.d.p)

Answer:

2.5 Grams

Step-by-step explanation:

You divide 25 by 10 giving you 2.5 Grams.

Answer: The answer is A

Step-by-step explanation:

Step-by-step explanation:

2500x=5000000

2500x/2500=5000000/2500

x=2000

I think the answer is this

Answer:

see the attachment

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

First, we factorize each integer:

\(12 = 2^{2}\times 3\), \(48 = 2^{4}\times 3\)

Then the highest common factor and the least common multiple are, respectively:

\(LCM = 2^{4}\times 3 = 48\), \(HCF = 2^{2}\times 3 = 12\)

The highest common factor and the least common multiple are 12 and 48, respectively. \(\blacksquare\)

First, we factorize each integer:

\(24 = 2^{3}\times 3\), \(36 = 2^{2}\times 3^{2}\)

Then, the highest common factor and the least common multiple are, respectively:

\(LCM = 2^{3}\times 3^{2} = 72\), \(HCF = 2^{2}\times 3 = 12\)

The highest common factor and the least common multiple are 12 and 72, respectively. \(\blacksquare\)

First, we factorize each integer:

\(32 = 2^{5}\), \(40 = 2^{3}\times 5\)

Then, the highest common factor and the least common multiple are, respectively:

\(LCM = 2^{5}\times 5 = 160\), \(HCF = 2^{3} = 8\)

The highest common factor and the least common multiple are 8 and 160, respectively. \(\blacksquare\)

First, we factorize each integer:

\(24 = 2^{3}\times 3\), \(48 = 2^{4}\times 3\), \(60 = 2^{2}\times 3 \times 5\)

Then, the highest common factor and the least common multiple are, respectively:

\(LCM = 2^{4}\times 3 \times 5 = 48\), \(HCF = 2^{2}\times 3 = 12\)

The highest common factor and the least common multiple are 12 and 48, respectively. \(\blacksquare\)

First, we factorize each integer:

\(42 = 2\times 3 \times 7\), \(56 = 2^{3}\times 7\), \(70 = 2\times 5\times 7\)

Then, the highest common factor and the least common multiple are, respectively:

\(LCM = 2^{3} \times 3 \times 5 \times 7 = 840\), \(HCF = 2\times 7 = 14\)

The highest common factor and the least common multiple are 14 and 840, respectively. \(\blacksquare\)

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Answer:

7 is the constant

Step-by-step explanation:

7 is the only number that has no variable, therefore it is a constant

Answer: The McGee family would pay $52 either way if they rented the truck for 2 additional days.

Step-by-step explanation:

Luther's Moving Company:

38 is how much they'll pay on the first day plus 7 per every additional day

This is represented by 7x+38

Springdale Rent-a-Truck

44 is how much they'll pay on the first day plus 4 per every additional day

This is represented by 4x+44

Set the equations equal to each other

7x+38=4x+44

Move the 38 to the other side by subtracting

7x=4x+44-38

7x=4x+6

Move 4x to the other side by subtracting

7x-4x=6

3x=6

Divide 3 to get x alone

3x/3=6/3

x=2

They'll be equal after 2 additional days

Plug in 2 to each equation

Luther: 7(2)+38

14+38=52

Springdale: 44+4(2)

44+8=52

The mass of the 10% sugar syrup that mixes with the 25% sugar syrup to result in the 120 grams 15% sugar syrup solution is 80 grams

A solution is a mixture of one or more of a substance, known as the solute with another substance, known as the solvent, such that the solute is spread through the space occupied by the solvent.

The concentration of the sugar syrup Samantha mixes = 25%

The mass of the 10% sugar syrup with which the 25% sugar syrup is mixed = x grams

The mass of the resulting solution = 120 grams

The concentration of the resulting solution = 15%

The dilution formula can be applied to find the mass x of the 10% sugar solution as follows;

M₁·C₁ + M₂·C₂ = M₃·C₃

Where;

M₁ = The mass of the 25% sugar syrup

C₁ = 25% = The concentration of the 25% sugar syrup

M₂ = The mass of the 10% sugar solution

C₂ = 10%

M₃ = The mass of the resulting solution = 120 grams

C₂ = The concentration of the resulting solution = 15%

The principle of the conservation of mass indicates that we get;

M₁ + M₂ = M₃

Therefore;

M₁ + x = 120

M₁ = 120 - x

M₁·C₁ + M₂·C₂ = M₃·C₃

(120 - x) × 0.25 + x × 0.1 = 120 × 0.15 = 18

(120 - x) × 0.25 + x × 0.1 = 18

30 - 0.25·x + 0.1·x = 18

30 - 0.15·x = 18

0.15·x = 30 - 18 = 12

x = 12/0.15 = 80

The mass of the 10% syrup, x = 80 grams

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Answer: 0.10x grams

Step-by-step explanation:

Answer:

V = (1/3)π(3^2)(11) = 33π = 103.4

we know the diameter of the cone is 6, so its radius must be half that, or 3.

\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=11 \end{cases}\implies V=\cfrac{\pi (3)^2(11)}{3} \implies V\approx 103.7\)

Answer:

C

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

here [ a, b ] = [ - 1, 2 ] , then

f(b) = f(2) = 2.5 ← value of y from graph

f(a) = f(- 1) = - 5 ← value of y from graph , then

average rate of change = \(\frac{2.5-(-5)}{2-(-1)}\) = \(\frac{2.5+5}{2+1}\) = \(\frac{7.5}{3}\) = 2.5

Answer:

C

Step-by-step explanation:

Formula for average rate of change :

\(A(x) = \frac{f(b)-f(a)}{b-a}\)

Here :

b = 2

a = -1

f(b) = 2.5 (according to the graph)

f(a) = -5 (according to the graph)

Solving :

A(x) = 2.5 - (-5) / 2 - (-1)

A(x) = 7.5/3

A(x) = 2.5

Answer:

The answers are 3 and 5

The only thing u had to do is

x-5=0

x=5

7x-21=0

7x=21

x=3

Answer:

a. 1.2

Step-by-step explanation:

b. 0.4

Answer:

Find answer below

Step-by-step explanation:

f(x)=2x-6

Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}

Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}

Parity of 2x-6: Neither even nor odd

Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)

inverse of 2x-6: x/2+6/2

slope of 2x-6: m=2

Plotting : y=2x-6

For the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters is the right triangle.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that, A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters.

We have to verify whether it is a right-angle triangle or not.

A right-angle triangle must follow the Pythagoras theorem.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

If the longest side is the hypotenuse.

h²=p²+b²

LHS

68² = 1424

RHS

60²+25²

3600+625

4225

L.H.S=R.H.S

Thus, the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters in the right triangle.

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Answer:

1 and 20    or   2 and 10   or   4 and 5

Step-by-step explanation:

the divisors of 20 are 1 , 2 , 4 , 5 , 10 , 20

Then

20 = 1 × 20

     = 2 × 10

     = 4 × 5

Answer:

BCDE

Step-by-step explanation:

You can see it in the image. Parallel = if the line keeps going and will never touch each other.

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

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Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation: