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Suppose we want to choose 6 letters with out replacement from 13 distinct letters.

a. The number of  ways this be done if the order of the choices is not relevant is   1,235,520  ways.

b.  The number of  ways this be done if the order of the choices is relevant is 1716 ways.

a. Number of ways if choice are not relevant

[tex]^nP_r = n!/ (n-r)![/tex]

Where:

n =13

r = 6

So,

[tex]^1^3P_6[/tex] = 13! / (13 - 6)!

[tex]^1^3P_6[/tex] =6,227,020,800 /7!

[tex]^1^3P_6[/tex] =6,227,020,800/5,040

[tex]^1^3P_6[/tex] =  1,235,520 ways

b. Number of ways if choice are relevant

[tex]^nC_r =n!/ r! (n-r)![/tex]

[tex]^1^3C_6[/tex] = 13! / 6!(13-6)!

[tex]^1^3C_6[/tex] = 13! / 6! × 7!

[tex]^1^3C_6[/tex] =6,227,020,800 / 720×5040

[tex]^1^3C_6[/tex] =6,227,020,800 / 3,628,800

[tex]^1^3C_6[/tex] = 1,716 ways

Therefore the number of ways are 1,235,520 ways  and 1,716 ways.

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One possible set of perimeters for the two figures is 4x and 16x.

Dilation is one of the type of transformation where the size of the object is made smaller or larger without affecting the shape.

Let A be the area of the original figure.

New area after dilation = 16A

Suppose that the figure is a square.

Area of a square is the square of it's side length and perimeter is four times the length of one side.

Let 'x' be the length of a side of the original figure.

Area of the original figure, A = x²

Perimeter of original figure = 4x

New area = 16 A = 16 x² = (4x)²

So the side length of new figure = 4x

Perimeter of new figure = 4 (4x) = 16x

Hence one of the possible set of perimeters for the two figures given is 4x and 16x.

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Answer:

Equivalent

Step-by-step explanation:

Two fractions are equivalent if the value, proportion, or quantity they represent is the same. Equivalent fractions can have different numerators and denominators. If you multiply the first one by 2/2, they will both be the same.

Answer:

equivalent

Step-by-step explanation:

2x/18y divided by 2 = x/9y

Answer: ( see image )

Step-by-step explanation:

Answer:

D) 19

Step-by-step explanation:

-7 + 19 = 12

Answer:

hiro ..................

Answer:

it just a released test from previous year. It is not the real test . I may be use as a practice.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6

17 percent of 24320 is 4134.4

basically minus that

so

24320 - 4134.4 = 20,185.60

Answer:

24320 - 4134.4 = 20,185.60

Step-by-step explanation:

:)

Answer:

m is 3. x is 2.

Step-by-step explanation:

if you mirror the variable, it is most likely the ssme

Answer:

615.44 m²

Step-by-step explanation:

the area of circle = 3.14 x 14² = 3.14×196

= 615.44 m²

Radius=r=14in

Area

Answer:

12(7-3) and 2-0.5

Step-by-step explanation:

All the rest are either terms or equations. The top left one is a term, and all the rest have equal signs, so they're equations. Only the bottom left and bottom right ones are expressions.

Answer:

The quantity of pepper cheddar cheese required = 2.5 kilograms

The quantity of Pennsylvania Jack required = 4.5 kilograms

Step-by-step explanation:

Let x = Quantity of pepper cheddar cheese

y=  Quantity of Pennsylvania Jack

As per given , we have the following system of equations:

Multiply 8 to equation(1) , we get

Eliminate (3) from (2) , we get

Put value of x in (1) , we get

Hence, the quantity of pepper cheddar cheese required = 2.5 kilograms

The quantity of Pennsylvania Jack required = 4.5 kilograms

Answer:

D.  X= -3/2, y= 4

Step-by-step explanation:

Just took the test

The radius of the circle with a circumference of 24π is 12 inches.

An equation shows how two or more numbers and variables are related to each other.

The circumference of a circle is the measure of the arc of the circle. It is given by:

Circumference (C) = 2π * radius

Given that the circumference is 24π, hence:

24π = 2π(radius)

Radius = 12 inches

The radius of the circle is 12 inches.

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The values of a , b and c from the equation is ( 3 , 0 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6   be equation (1)

Now , the number 6006.6 is written as

6000 + 6 + 0.6 = 6006.6

On simplifying the equation , we get

( 6 × 10ᵃ ) = 6000

Divide by 6 on both sides of the equation , we get

10ᵃ = 1000

So , 10ᵃ = 10³

Therefore , the value of a = 3

Now , ( 6 × 10ᵇ ) = 6

Divide by 6 on both sides of the equation , we get

10ᵇ = 1

when b = 0

10⁰ = 1

Therefore , the value of b = 0

Now , ( 6 × 10^c ) = 0.6

Divide by 6 on both sides of the equation , we get

10^c = 0.1

when c = -1

10⁻¹ = 0.1

Therefore , the value of c = -1

Hence , the value of a , b and c is 3 , 0 and -1 respectively

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Answer:

2 19/28 or 75/28

Step-by-step explanation:

Find common denominators then add, simplify if needed.

Answer:

15 cm

Step-by-step explanation:

This could help

go to you tube and paste Area of Shaded Region - Circles, Rectangles, Triangles, & Squares - Geometry

The Organic Chemistry Tutor

Answer:

Step-by-step explanation:

Required area is:

Answer:

The answer is 3/20 or 0.15

I wish you luck in your assignments.

9514 1404 393

Answer:

  -2, 3

Step-by-step explanation:

For the product to be negative, exactly one of the two numbers must be negative. For the sum to be positive, the positive number must be larger than the absolute value of the negative number.

One such pair of numbers is -2 and 3.

__

Their product is -6; their sum is +1.

First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

Answer: 158 feet

Step-by-step explanation: I’ve gotten this question right on a test.

The approximate perimeter of the pool will be 157.36 feet.

The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The perimeter of the shape is a combination of the perimeter of two small quarter circles, one big circle, and the sides of a rectangle. Then the perimeter is calculated as,

P = πr + 2L + w + πR

P = 3.14 x 9 + 2 x 35 + 12 + 3.14 x 15

P = 157.36 feet

The approximate perimeter of the pool will be 157.36 feet.

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If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

The amount earned In a month is 3250.

There are 12 months In a year.

The total month in 10 years = 10× 12 = 120 months

The total amount in the account for 10years = 120×3250 = 390,000

Therefore there will be 390000 in the account at the end of 10th year.

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Answer:

The profit is: [tex]Rs100000[/tex]

Step-by-step explanation:

Given

[tex]1 \to Rs20[/tex]

Required

Profit on 5000

Repesent this as: x

So, we have:

[tex]1 \to Rs20[/tex]

[tex]5000 \to x[/tex]

Cross Multiply

[tex]x * 1 = Rs20 * 5000[/tex]

[tex]x * 1 = Rs100000[/tex]

The profit is: [tex]Rs100000[/tex]

9514 1404 393

Answer:

  0 people ate dinner

  23 people ate lunch

Step-by-step explanation:

If the bill is split evenly between x people, then each pays 500/x.

Splitting the bill between x-1 people means each pays 500/(x -1).

When the difference in those amounts is 1.00, we have ...

  500/(x -1) -500/x = 1

  500 = x(x -1)

Completing the square gives ...

  500.25 = (x -0.5)²

  x = 0.5 +√500.25 ≈ 22.866 ≈ 23

Check

With 22 people splitting the $500 bill, the amount each pays is ...

  $500/22 ≈ $22.73

With 23 people splitting the bill, the amount each pays is ...

  $500/23 ≈ $21.74

The difference is $0.99, about $1.00. This is as close as you will get with these numbers.

__

23 people at lunch, including Stewart.

Answer:

[tex]\left \{ {{20} \atop {3}} }.[/tex]

Step-by-step explanation:

supply = Infinite

supposing you intend to package the marbles in bags of 17

Determine the number of distinguishable collections of marbles that could be in the bags

Given that ; n = 17 ,  K = 4

The distinguishable collections = [tex]\left \{ {{20} \atop {3}} }.[/tex]

attached below is the detailed solution

Answer:

-7

Step-by-step explanation:

-2(x+5)=4

First, distributive property,

-2x-10=4

Add 10 to both sides,

-2x=14

Divide both sides by -2

-7