Problem 3
The √2-1.4142135... This expansion is not exact (a finite decimal expansion cannot give the exact
5
10,000,000
10,000,000
14,142,135 is close to √2 and in fact, is within
(or half the size of the
answer). The fraction
denominator); however, the denominator is too large. There are fractions that match this
approximating power with much smaller denominators.
Part A: Find the fraction with the smallest denominator that matches √2 to three places.

The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The given parameters can be represented as:

M(0) = 30680

M(20) = 30970

The average rate of change is calculated as:

M'(t) = (M(20) - M(0))/(20 - 0)

This gives

M'(t) = (30970 - 30680)/(20 - 0)

M'(t) = 14.5

Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The average rate of change of M as t changes from 8 to 16.

This is calculated using

M'(t) = (M(16) - M(8))/(16 - 8)

M'(t) = (20 - 10)/(16 - 8)

M'(t) = 1.25

The average rate of change of M as t changes from 16 to 24.

This is calculated using

M'(t) = (M(24) - M(16))/(24 - 16)

M'(t) = (25 - 20)/(24 - 16)

M'(t) = 0.625

The average rate of change of M as t changes from 24 to 32.

This is calculated using

M'(t) = (M(32) - M(24))/(32 - 24)

M'(t) = (25 - 25)/(32 - 24)

M'(t) = 0

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Answer:

-2 =w

Step-by-step explanation:

9(w – 4) – 7w = 5(3w – 2)

The first step is to distribute

9w -36 - 7w = 15w -10

Combine like terms

2w -36 = 15w -10

Subtract 2w from each side

2w -36 -2w = 15w-10-2w

-36 = 13w -10

Add 10 to each side

-36+10 =13w-10+1-

-26 = 13w

Divide by 13

-26/13 =13w/13

-2 =w

The measures of the x is 6.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given : one angle= 6x-6 and another angle = 54

Using angle sum property, we have

6x-6 + 54 + 90 = 180

6x=180-144

6c= 36

x=36/6

x=6

Thus, value of x is 6.

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The price of one pen will be $1.5 and one highlighter is $4.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The cost of the pen and the highlighter will be calculated by forming the two expressions from the given data in the question the expressions are as follows:-

6p  +  3h  = 21

2p  +  4 h = 19

Solving the above linear equations by elimination method:-

( 6p  +  3h  = 21 ) x 2

( 2p  +  4 h = 19 ) x 6

The new equations are:-

12p  + 6h  =  42

12p  + 24h  = 114

Substracting the below equation from the above equation we will get:-

6h - 24h  =  -72

-18 h = -72

h  =  $4

Put the value of h in any of the above equations:-

2p  +  4 h = 19

2p  +  4 ( 4 )  = 19

2p  +  16  =  19

p  =  3 / 2

P  = $1.5

Therefore the price of one pen will be $1.5 and one highlighter is $4.

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Answer:

Approx. 2140.16 cubic centimeters

Step-by-step explanation:

[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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Answer: -12

Step-by-step explanation: When solving this problem, PEMDAS is a key component. What is PEMDAS?

PEMDAS stands for the following:

P- Parentheses

E- Exponents

M-Multiplication

D- Division

A-Addition

S-Subtraction

This is also known as order of operations. Following this order, we can easily simplify the problem.

P-Parentheses

(-2)(-3)^2-2(2-5)

Our parentheses is (2-5). We can simply this to -3. Our problem now is

(-2)(-3)^2-2(-3)

E-Exponents

We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is

(-2)(9)-2(-3)

M- Multiplication

We can simply to.

-18+6

These simplifies into

-12

Answer:

-12

Step-by-step explanation:

-2*9-2(2-5) : Raise -3 to the power of 2

-18-2(2-5) : Multiply -2 by 9

-18-2*-3 : Subtract 5 from 2

-18+6 : Multiply -2 by -3

-12 : Add -18 and 6

Answer:

x = 10

Step-by-step explanation:

If S is between R and T, then RS + ST will be equal to RT.

See image.

Use this idea to write an equation.

2x + 3 + 4x = 63

Combine like terms, Subtract 3, Divide by 6, to solve for x. See image.

Answer:

508?

Step-by-step explanation:

what is this factor? simplify?...etc

Answer:

(x-4)(x-4)

Step-by-step explanation:

Because the factors of 16 that add up to -8 can be -4 and -4.
Let's plug it in...
16 - 32 + 16 = 0

It works!!!

ANswer is (x-4)(x-4)

Answer: (x-1)(x+4)

the answer

Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.

In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.

Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)

Angle F + angle G = 180

4x - 2 + 34 = 180

4x + 32 = 180

4x = 180 - 32

4x = 148

x = 148/4

x = 37

Value of x is: E. 37.

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Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours  

Answer: 49π or 153.86

Explanation: To find the R, do 14 divide by 2 because since you're not multiplying pi with it. The circumference formula is 2πr
14 / 2 = 7
7 = Radius

Area of a circle is : πr^2
π(7^2)
π49
----------
π49
153.86

The rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

The function is given as:

d = √216 +h²

At a distance of 100 feet, it means that:

d = 100

So, we have:

√216 +h² = 100

Take the square of both sides

216 +h² = 10000

Subtract 216 from both sides

h²= 9784

Take the square root of both sides

h = 98.9

Hence, the rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

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Answer:

slope: -3

y-intercept: -2

equation: -3x-2

y intercept is the value of y at x=0

slope is how many units the graph moves per x

equation is (slope)x+(y-intercept)

The amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

The equation is given as:

y =1.5x + 5

For a 17-pound goat, we have:

x = 17

This gives

y =1.5 * 17 + 5

y = 30.5

For a 55-pound goat, we have:

x = 55

This gives

y = 1.5 * 55 + 5

y = 87.5

Hence, the amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

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The solution to the equation is y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

Analysis:

since number of items cannot be negative x and y are real number numbers since y or x can be a decimal so we do not use integers alone.

so  y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

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Answer: C

Step-by-step explanation:

Answer:

(14, -2)

Step-by-step explanation:

The coordinates of the midpoint is equal to the mean of the coordinates of the endpoints.

=============================================================

Solving :

⇒ 5 = -4 + x / 2

⇒ x - 4 = 10

⇒ x = 14

⇒ 2 = 6 + y / 2

⇒ y + 6 = 4

⇒ y = -2

===========================================================

Coordinates of Point Y :

⇒ Y = (x, y)

⇒ Y = (14, -2)

Answer:

Y (14, - 2 )

Step-by-step explanation:

using the midpoint formula for (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1+y_{2} } }{2}[/tex] )

equating the x- coordinates and the y- coordinates

let coordinates of Y = (x, y )

[tex]\frac{x-4}{2}[/tex] = 5 ( multiply both sides by 2 )

x - 4 = 10 ( add 4 to both sides )

x = 14

and

[tex]\frac{y+6}{2}[/tex] = 2 ( multiply both sides by 2 )

y + 6 = 4 ( subtract 6 from both sides )

y = - 2

coordinates of Y = (14, - 2 )

Answer: 8

Step-by-step explanation:

To find the diagonal, we need to use two formulas:

Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)

Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]  

Since  every side of a square is the same:

[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]

Our equation:

[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]

The picture below visually explains the problem

Hope this helps!

[tex]y+9-x =[/tex]

[tex]x=1 \\ y=3[/tex]

[tex]3 +9 -1=11[/tex]

Answer:

y+9-x = 3+9-1 which would end up equaling: 11

9-1=8+3=11

Answer:

44

Step-by-step explanation:

16.5 / 3/8 = 44

she will need 44 beads to complete that necklace

Using the normal distribution, it is found that 0.13% of American women CAN NOT use the bicycles designed by this company.

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 65\ \ \sigma= 3.5[/tex]

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{54.5-65}{3.5}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CAN NOT use the bicycles designed by this company.

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The size of the scalene triangle would be larger or smaller

Answer:

a/b = c/d

a*d = b*c

Ex:

a/2 = 2/4

4a = 4

a = 1

1/2 = 2/4

The correct answer is option A. Which is the solution of the given equation will be (15,15).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given equations are solved as:-

a - 1.2b = -3 or a = -3 + 1.2b

0.2a + 0.6b = 12

Put the value of a from equation 1 to the equation second.

0.2 ( -3 + 1.2 b)  + 0.6b = 12

-0.6 + 0.24b + 0.6b = 12

0.84b = 12  + 0.6

0.84 b = 12.06

b  = 15

Put the value of b in the first equation to find the value of a.

a = 1.2b - 3

a = (1.2 x 15) - 3

a = 15

Therefore the correct answer is option A. Which is the solution of the given equation will be (15,15).

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Answer:

C

Step-by-step explanation: