Are 2/6 equivalent to 10/12

Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

The number of ways for the first case will be 151,200. Then option A is correct. And the number of ways for another case will be 210. Then option D is correct.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Suppose 10 people run a race. Then the number of ways that they can be awarded first through the sixth place will be given as,

¹⁰P₆ = 10! / (10 - 6)!

¹⁰P₆ = 10 x 9 x 8 x 7 x 6 x 5 x 4! / 4!

¹⁰P₆ = 151,200

Suppose 10 people volunteer to help clean up the school, but you only need 6 of them. Then the number of ways is given as,

¹⁰C₆ = (10!) / [(10 - 6)! x 6!]

¹⁰C₆ = (10 x 9 x 8 x 7 x 6!) / (4 x 3 x 2 x 1 x 6!)

¹⁰C₆ = 210

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Answer:

x = 3

Step-by-step explanation:

x - 1.2 = 1.8

  +1.2  +1.2

---------------

x = 3

The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.

a(t) = eti - 6k

Since we know that v(t) = ∫ a(t) dt

= ∫ (eti - 6k) dt

= ∫6ti-6tk+c

where c is the arbitrary vector valued constant

since it is given that

v(0) = 2i + 9j + k

therefore from above

v(0) = e * 0i - 6(0) * k + c

2i + 9j + k =i+c

C= i +9j+k

therefore,

v(t) = eti - 6tk + i + 9j + k

= (et + 1) * i + 9j + (- 6t + 1) * k

Since we know that velocity vector can be found by integration of acceleration vector.

Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k

and we know that

R(t) = ∫ v(t)dt

= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C

where C is an arbitrary vector constant.

Now,

Since it given that r(0)=0 therefore

r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C

0=2i+ C

C= -2i

therefore

r(t)= (et+t)i+9tj+(-3t+t)k-2i

r(t)=(a+t-2)1+9tj+(-3t+t)k

Since we know that position vector can be found by integration of velocity vector

r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k

r(4) = (e4+2)1+36j-44k

Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:

v(t) =(et+1)i+9j+(-6t+1)k

r(t) =(et+t-2)i+9tj+(-3t2+t)k

r(4) = (e₄+2)i+36j - 44k

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The probability that both of them go back to prison is 4.48%.

The state recidivism rate is given by 22%.

So, the probability that both of the prisoners will go back to prison will be:

Hence, the probability that both of them go back to prison is 4.48%.

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The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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There are 8 to take Lara and Hayden to volunteer the same number.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara already volunteered 50 hours and will volunteer 5 hours more each week.

And, Hayden already volunteered to 10 hours and will volunteer 10 hours each week .

Now, For Lara;

⇒ 50 + 5x

And, For Hayden;

⇒ 10 + 10x

So, For same number of volunteer is,

⇒ 50 + 5x = 10 + 10x

⇒ 50 - 10 = 10x - 5x

⇒ 40 = 5x

⇒ x = 40/5

⇒ x = 8

Thus, There are 8 to take Lara and Hayden to volunteer the same number.

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The volume of the triangular prism as shown in the attached image is 30 cm³.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the height of the prism.

The area of the triangular base can be found using the formula:

Area = (1/2) × base × height

In this case, the base is 5 cm and the height is 4 cm, so the area of the triangular base is:

Area = (1/2) × 5 cm × 4 cm = 10 cm²

The height of the prism is 3 cm.

Therefore, the volume of the triangular prism is:

Volume = Area of triangular base × height

= 10 cm² × 3 cm

= 30 cm³

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Answer:

144mm²

Step-by-step explanation:

48mm / 4 = 12

12 × 12 = 144mm²

Area = 144mm²

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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Answer:

B

Step-by-step explanation:

rules:

add outside the function : f(x) ± a;  will shift  a + up / a- down

add inside the function: f(x ± a); will shift a + left  / a- right

so if

f(x)  becomes f(x) -4  will be shifting down 4 units

Answer:

18. 2,970 orbits.

19. 12,00 pounds

20. Vic’s town by 52,000

Step-by-step explanation:

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

(a)   x follows a poisson distribution with parameter λ = 8 / hour

(b)   P( X = 5 ) = 0.09160

      P( X ≥ 5 ) = 0.9004

(c)   the expected value  of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes

The standard deviation = 4

(d)   P(X ≥ 20) = 0.5297

      P( X ≤  10) = 0.0108

Step-by-step explanation:

Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).

(a)  If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour

(b)

What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?

the probability that exactly 5 nonconforming parts are produced during a 1-hour period can  be computed as:

P( X = 5 ) = \(e^{- \lambda } \lambda^x /x!\)

P( X = 5 ) = \(e^{- 8 }(8)^5 /5!\)

P( X = 5 ) = 0.09160

the probability that at least 5 nonconforming parts are produced during a 1-hour period

P( X ≥ 5 ) = 1 -  P( X ≤ 4)

\(P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x!\)

\(P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )\)

\(P( X \geq 5 ) = 1 - 0.0996\)

P( X ≥ 5 ) = 0.9004

c)  What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?

the expected value  of the number of nonconforming parts produced during a 120-min period \(\lambda = 8 \times \dfrac {120}{60}\)

= 16 nonconforming parts per 120 minutes

The standard deviation = \(\lambda^{1/2}\)

The standard deviation = \((16)^{1/2}\)

The standard deviation = 4

(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

During a 2.5 - hour period , the expected value = 8 × 2.5 = 20

As such, the probability  that at least 20  nonconforming parts produced during a 2.5-hour period is:

P(X ≥ 20) = 1 - P(X ≤ 19)

\(P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x!\)

\(P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )\)

P(X ≥ 20) = 1 -  0.4703

P(X ≥ 20) = 0.5297

Probability that at most  10 nonconforming parts produced during this period is:

P( X ≤  10) = \(\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x!\)

\(P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}!\)

P( X ≤  10) = 0.0108

Following are the calculation to the given points:

For point a)

With parameter, x follows the poisson distribution is \(\lambda=\frac{8}{hour}\)

For point b)

The probability that exactly 5 nonconforming parts are generated in a one-hour period.

\(\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916\)

There is a good chance that at least 5 nonconforming parts exist.

\(\to P(X\geq 5) =1-P(X\leq 4)\)

                 \(=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004\)

For point c)

Expected value for 120-minute period \(\lambda=8\times \frac{120}{60} =16\) 120 minutes of nonconforming sections

\(\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4\)

For point d)

Expected value for 2.5 hours

\(\to \lambda =8\times 2.5=20\)

As a result, there is a good chance that at least 20 nonconforming items were manufactured.

\(\to P(X\geq 20)=1-P(X\leq 19)\)

                   \(=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297\)

There is a chance that no more than 10 nonconforming parts were created.

\(\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108\)

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Answer:

A rectangle I think

This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.

Given that,

For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.

We have to find what percentage of the initial purchase price was represented by the auction price.

Let us take the percentage as x%.

Necklace sold at auction=the percentage multiplied by the actual price

We get,

$11,379,600 =x%($54,000)

x%=$11,379,600/$54,000

x%=2.1%

Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.

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Answer:

16

Step-by-step explanation:

4x1 is 4

4x3 is 12

4+12 is 16

Answer:

16

Step-by-step explanation:

The answer would be 4/21 if divided 2/7 by 1.5 which is the correct option (C).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have to determine the divide 2/7 by 1.5

⇒ 2/7 ÷ 1.5

Here 1.5 = 3/2

⇒ 2/7 ÷ 3/2

Apply the division operation between both term

⇒ (2/7)/(3/2)

Reciprocal the terms, we get

⇒ (2/7)×(2/3)

⇒ (2×2)/(7×3)

⇒ 4/21

Therefore, the answer would be 4/21

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Answer:

The answer is 4 3/10

Step-by-step explanation:

If you first break this question up into two steps, you first must add the whole numbers and then the fractions, like this:

2 7/10   1 6/10

First, add the whole numbers [Bold]

2 + 1

That equals the whole number 3

2 7/10    1 6/10

Next you add the fractions [Underlined]

7/10 + 6/10

this equals 13/10

Since this fraction is higher than 10/10, it equals a whole number too. This fraction, 13/10, will be simplified to 1 whole and 3/10. After simplifying this number you add the whole numbers once again resulting in 3 + 1, giving you 4. after finding this out you add your fractions back in, creating the answer of 4 3/10.

Hope this helps you out!

Answer:460

Step-by-step explanation:on delta math

The total number of action figures in Genesis's collection will be 460.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Genesis offers a variety of action figures. She hangs the remainder and keeps some in a display cabinet. 253 of her action figures are hung on the wall, and the display case holds 45% of her collection.

The obtained expression for the given condition,

=253 / (1-0.45)

=253/0.55

=25300/55

=460

Thus, the total number of action figures in Genesis's collection will be 460.

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Answer:

80

Step-by-step explanation:

These angles are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

12x+8 = 13x+2

Subtract 12x from each side

12x+8-12x = 13x+2-12x

8 = x+2

subtract 2 from each side

8-2 =x

6 =x

Find the measure of the angle

12x+8

12*6+8

72+8

80

As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

Let JK be = x.

GF/GH = JI/JK

⇒ 11/18 = 36 /x

⇒ x = 36 × 18/11

⇒ x = 63.8.

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Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

367.75

Step-by-step explanation:

21+23.3+323.45

Add the three terms.

= 367.75

The sum of theses numbers is 367.75.

Answer:

\(= 367.75 \\ \)

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: 21 \\ + \: \: \: \: 23.3 \\ = \: \: 44.3 \\ + 323.45 \\ = 367.75\)

Answer:

Step-by-step explanation:

fraction decomposition for the expression

13x - 7/(x+2)(4x-3)

Answer: A

Step-by-step explanation: