There are 13
books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?

The predicted femur length is 69 cm

From the question, we have the following parameters that can be used in our computation:

The scatter plot

On the scatter plot, we have

x = the length of two peoples femur (the long leg bone in thigh)

y = height in centimeters

So, we have

Height = 218 cm

From the graph, we have

x = 69

Hence, the femur length is 69 cm

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Answer:

“m + 5”

internet

Answer:

The interval notation for the set of all numbers greater than or equal to 1 and less than 6 is [1, 6).

Step-by-step explanation:

The required time duration is  0.13 s

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

[tex]h(t)=-5t^2 + v_{0}t+h_{0}[/tex]

Substitute given the values

2=-5t² + 15 t+0

=> 5t² -15t+2 =0

On solving this quadratic equation ,w e get

t= 0.13 s

The required time duration is  0.13 s

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To make 5 pizzas, Paula will use 45 sauce and 30 cheese.

Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.

The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.

Given,

Paula uses 18 sauce and 12 cheese to make two pizzas.

Ingredients needed to make one pizza = 18/2 sauce and 12/2 cheese

                                                                = 9 sauce and 6 cheese

Ingredients needed to make 5 pizzas = 9 × 5 sauce and 6× 5 cheese

                                                               = 45 sauce and 30 cheese

Hence, 45 sauce and 30 cheese is needed to make 5 pizzas.

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Value of variable x = 13/√2

Value of variable y = 13/√2

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

Given,

In the right triangle ABC

AC = 13

AB = x

BC = y

∠C = 45°

Sin 45° = AB/AC

1/√2 = x/13

x = 13/√2

AB = 13/√2

Tan 45° = AB/BC

1 = (13/√2)/y

y = 13/√2

BC = 13/√2

Hence, 13/√2 is the value of both variables x and y.

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Answer:

The volume of one marble can be calculated as follows:

V = (4/3) * π * (r^3)

where r = 1.25 cm (diameter of 2.5 cm divided by 2)

V = (4/3) * 3.14 * (1.25^3) = 5.20 cm^3

The mass of one marble is then:

m = V * 2.6 g/cm^3 = 13.52 g

And the total mass of 66 marbles is:

m = 66 * 13.52 g = 888.32 g

Rounding to the nearest gram, the total mass of the marbles in Keisha's pouch is 888 g.

The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:

A. a rotation of 180° about the origin and a translation of 1 unit left.

E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                  →     (-x, -y)

Point A = (-6, 2)  →  Point A' = (-(-6), -(2)) = (6, -2).

By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 1, y - 7)

Coordinate A' = (6, -2)   →    Coordinate A'' (6 - 1, -2) = (5, -2)

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A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as A weighted mean.

The weighted mean is defined as a type of mean that is calculated by multiplying the weight associated with a particular event or outcome and the associated with the quantitative outcome and then summarizing all the products together.

For each data point to contribute equally to the final mean, some data points contribute more weight than others.

The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products.

weighted average= The sum of variables/sum of all weights.

if the variables are denoted by x and their weights are denoted by y, then we have:

Weighted average = Σ(xy)/Σy

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Answer:

Step-by-step explanation:

Basically, we want to use the formula for the area of a sphere: V = 4/3πr^3

And plug-in our radius, 4 for r.

We get an answer around 67 sooooooo

The volume of the ball is about__67__cubic centimeters. The density of the ball is__1.343__grams per cubic centimeter. Based on its density, the ball will__sink__.

Answer:

The base should be sink

Calculation of the volume, density:

Since the density of water is 1 gram per cm^3.

The volume is

Here a = base area and h = height of the pyramid

So,

Now

Density is

Since The mass of the pyramid is 1.17 g.

So, the density is

Density

Since its density is more than that of water, so it will sink.

Hence, we can conclude that The base should be sink.

Step-by-step explanation:

Hope this helped!

The surface area of each face is 4 square inches.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A regular octahedron has a surface area of 32 square inches.

That means

all sides are equal.

The surface area of each face is,

= 32/8

= 4 square inches.

Therefore, the required area is 4 square inches.

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To find out how much each ticket costs, we can use this equation:

Total cost ÷ Number of tickets = Price of each ticket

Inserting the numbers into the equation would look like this:

To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.

Therefore, each ticket costs $8.

Answer:

Step-by-step explanation:

The perimeter of Wendy's math certificate is 7 inches + 7 inches + 9 inches + 9 inches = 32 inches.

So, the cost to frame Wendy's math certificate would be $2.00 per inch * 32 inches = $64.00.

Answer: 23/72

Step-by-step explanation:

180 degrees = half of circle

5 degrees = 1/72 of circle

5 degrees times 23 = 115 degrees

1/36*23 = 23/72

Answer:

23/72 of a circle

Step-by-step explanation:

4×sector=circle

90÷360=1/4

so,

115/360=23/72

Explanation:

First we add up those numbers

2+6+9+56+63+68 = 204

Then divide by 6 because there are 6 values in this list.

204/6 = 34

Answer:34

Step-by-step explanation:It's obtained by simply dividing the sum of all values in a data set by the number of values.

Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.

The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.

cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53

So, the cosine of ∠U is 28/53, written as a proper fraction.

Now let's convert cosine of ∠U is 28/53 in improper fraction:

The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.

gcd(28, 53) = 1, so the fraction cannot be further simplified.

Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.

Now let's convert cosine of ∠U is 28/53 in whole number:

The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.

28 ÷ 53 = 0.526087

So, the cosine of ∠U expressed as a whole number is approximately 0.52609

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_____ The given question is not correct, so correct Question is:

Find the cosine of ∠U in Triangle UTV with side:

UV=28

VT=45

TU=53

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

The area and the angle are matched as below.

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Diameter = 10 in

Radius = 5 in

Area of the circle in sector = 360°

πr² = 360

π x 5² = 360

25π in² = 360° _____(1)

Now,

From (1),

25π in² = 360°

Divide both sides with 8.

25/8 π in² = 45°

From (1),

25π in² = 360°

Divide both sides with 18.

25/18 π in² = 20°

From (1),

25π in² = 360°

Divide both sides with 36.

25/36 π in² = 10°

Thus,

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

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Answer:

To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.

Step-by-step explanation:

Year 1: 92,000 kilotons

Year 2: 92,000 * 0.95 = 87,400 kilotons

Year 3: 87,400 * 0.95 = 82,990 kilotons

and so on, until year 15.

To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:

92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)

This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:

S = a * (1 - r^n) / (1 - r),

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:

S = 92,000 * (1 - 0.95^15) / (1 - 0.95)

S = 92,000 * (1 - 0.556774) / 0.05

S = 92,000 * 0.443226 / 0.05

S = 92,000 * 8.86452

S = 814,178.24 kilotons

Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.

The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

2.45

Z score = (Observed value - Expected value) / Standard Deviation

Z score = (95 - 85) / √(85*(1-85)/30)

Z score = 2.45

We can calculate the Z score associated with our observation by taking the observed value, 95%, and subtracting the expected value, 85%, and dividing this by the standard deviation. To calculate the standard deviation, we use the formula: √(expected value*(1-expected value)/sample size). In this case, 85*(1-85)/30. The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

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The cost of an apple is $1 and the cost of an orange is $2

From the question, we have the following parameters that can be used in our computation:

x = apples

y = oranges

Using the above as a guide, we have the following:

5x + 2y = 9

7x + 3y = 13

Multiply (1) by 3 and (2) by 2

15x + 6y = 27

14x + 6y = 26

Subtract

x = 1

So, we have

5(1) + 2y = 9

This gives

y = 2

Hence, the cost of orange is $2

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Step-by-step explanation:

This is a trick question I think.

It says he managed to only travel 3 7/8. So wouldn't that mean the fraction of his planned trip that he travel would be... 3 7/8? Unless they want it as 31/8? Something is odd with the question

Value of expression 1 + 1 = 2

Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers.

Given expression,

1 + 1

+ is sign of Addition, Adding the numbers,

1 + 1 = 2

Hence, 2 is the value of expression 1 + 1.

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Answer:

There would be 600 fish after 12 months.

Step-by-step explanation:

The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:

F = 350 * (1 + 0.1)^n

where,

F is the number of fish after n months

We want to find the number of fish after 12 months, so:

F = 350 * (1 + 0.1)^12

F = 350 * 1.719178

F = 603.56 to the nearest 100, which is 600.

∠AFB = 73° is the angles of a triangles .

What does a math angle mean?

An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

because the angles of a triangles add up to 180 degree

      m∠A = 39° ,  m∠ADC = 107°

   so ∠c = 180 - 107 - 39

               = 34°

     BE ≅ BC

         ∠C = ∠E = 34°

        SO ∠EDF = 180 - 107 = 73°

   So ∠DEF = 180 - 34 - 73 = 73°

  Because m∠DFE and ∠AFB are vertical angle

  so  ∠DFE = ∠AFB

     ∠AFB = 73°

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a) 720 ways 3 boys and 3 girls sit in a row.

b) 48 ways boys and the girls are each to sit together.

c) 6 ways boys must sit together.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

Number of girls= 3

Number of boys = 3

a) Using Permutation

⁶P₆ = 6! / (6 - 6)!

⁶P₆ =  6! / (0!)

⁶P₆ = 6!

       = 6 × 5 × 4 × 3 × 2 × 1

        = 30 × 24

        = 720

b) 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together

= 3! x 2³

= 3 x 2 x 2 x 2 x 2

= 48 ways

c) the number of ways boys can sit together

= 3!

= 6 ways

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Answer: 1, 2, 3, 6, 1

Step-by-step explanation:

When listing all the factors for 18, 30 ,54....

18 , 30 , 54 to find the common factors. The common factors for 18,30,54 18 , 30 , 54 are 1,2,3,6 1 , 2 , 3 , 6 . The GCF (HCF) of the numerical factors 1,2,3,6 1 , 2 , 3 , 6 is 6 .

( Hope this helps )

The given expression (2x^3 + 2)/(x^3 - 2) can be written as a composition of two non-identity functions as follows:

Let f(x) = 2x^3 + 2 and g(x) = x^3 - 2.

Then, the expression can be written as:

f(x)/g(x) = (2x^3 + 2)/(x^3 - 2)

So, the expression is a composition of the two non-identity functions f and g, written as:

h(x) = f(g(x)) = (2x^3 + 2)/(x^3 - 2)