a reading shop enrolls novelists and poets in a ratio of 5 to 3 there were 24 people at the workshop how many novelists are there how many

Answer:    10. equal 0.27

                  11. 5.12

                  12. 3.35

Step-by-step explanation:

10. 0.9 * 0.3 = 0.27

11. 1.6 * 3.2 = 5.12

12. 0.5 * 6.7 = 3.35

13. 0.81*7.3 = 5.873

14. 5.6*3.9 = 21.84

15. 1.2 * 0.05 = 0.06

The scale factor from the cliff in the drawing to the actual cliff is equal to 1/3.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (actual figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 12/36

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

36ft/12in

36 divided by 12 =3 feet per inch

The fraction of the students that played the trumpet is 1/6

The school band has several students

1/4 play a brass instrument

2/3 of those students play the trumpet

Therefore the fraction of students that paly the trumpet can be calculated as follows

1/4 × 2/3

= 1/6

Hence the fraction of students that play the trumpet is 1/6

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The product of two matrices L and P is given as L × P = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex].

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
The product of matrices is only possible when the matrices have one of the matching orders with rows and columns.
Since among the given matrices, only matrix P and matrix L has the same order so,
[tex]L\times P = \left[\begin{array}{cc}2&-3\\1&2\end{array}\right]\times \left[\begin{array}{cc}0&0\\0&0\end{array}\right]\\L \times P = \left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Thus, the product of two matrices L and P is given as L × P = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex].

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Answer: 3 ovals and 3 rectangles and an even amount of rectangles and ovals

Answer:

Step-by-step explanation:

all internal angles in a triangle add to 180 degrees.

77+36=113

180-113=67

we know that the final angle in the triangle is 67 degrees

the left parallel line makes another triangle in the bottom left. we know that one angle is 41 and we just calculated that the other is 67.

41+67=108

180-108=72

so now we know that the small triangle in the bottom left has angles of 41,67 and 72.

all straight lines are 180 degrees, and we just figures out that the left side of the left parallel line is 72 degrees. therefore the other side is 108 degrees.

since they are parallel lines, the left angle of both of them on the bottom line is 72, while the right angle is 108.

this means that x=108 degrees

i hope this is right and it helps if it is correct. really sorry if it is wrong. have a good day :)

Answer:

Step-by-step explanation:

1.The square root function is a mathematical function that returns the positive number that, when multiplied by itself, gives the original number. It can be represented using the symbol √ or using the exponent 1/2. The cube root function is a mathematical function that returns the number that, when multiplied by itself three times, gives the original number. It can be represented using the symbol ∛ or using the exponent 1/3.

2.The ancient civilizations of Babylonia, Greece, and India all independently discovered the square root function. The concept of cube root was first mentioned in the ancient Indian text "Sulbasutras" around 800 BCE. The Greek mathematician Euclid also described the cube root function in his work "Elements" around 300 BCE.

3.The square root function is used in many areas of mathematics and science, including geometry, trigonometry, and physics. In real life, square root functions are used in many areas such as engineering, architecture, and finance. For example, in engineering, square root functions are used to calculate the stress and strain on materials. In architecture, square root functions are used to calculate the area of a building or room. In finance, square root functions are used to calculate the volatility of an asset. Similarly, cube root function is used in mathematics, physics, engineering, economics, and other fields. It is used to find the cube root of a number, to find the volume of a cube, to solve equations, and to calculate the cube root of a complex number.

The answer to the question is 90.

The sum of the five products x1x2x3 x2x3x4 x3x4x5 x4x5x1 x5x1x2 is divisible by 3 if and only if the sum of the exponents of each of the numbers 1, 2, 3, 4, and 5 in the expression is divisible by 3.

Since there are 5 numbers, and each number can appear in the exponent of each of the 5 products, there are 5^5 = 3125 ways to arrange the numbers. However, we need to subtract the cases where the exponents of each number don't add up to a multiple of 3.

For example, if the exponents of 1, 2, 3, 4, and 5 are (1, 1, 1, 1, 1), the sum of the exponents is 5, which is not divisible by 3. Similarly, if the exponents are (2, 1, 1, 1, 1), the sum of the exponents is 6, which is not divisible by 3.

After calculating this, we get that there are only 90 permutations that meet the condition. So the answer to the question is 90.

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Answer:

2.4%

Step-by-step explanation:

Answer:

if m stands for number of tickets

then amount would be

12+2.75*m

14.75m

Step-by-step explanation:

Answer:

x = 61

Step-by-step explanation:

Let's call the number of codes Jayvik can make, j, and the number of codes Fay can make, f. We know that since 0 cannot be used, Jayvick can have 5 number choices (1, 3, 5, 7, 9), and Fay can have 4 number choices (2, 4, 6, 8). To calculate the number of possible codes for Jayvick, we will have:

5 * 5 * 5 = 125

So Jayvick can make 125 codes. Then, for Fay we have:

4 * 4 * 4 = 64

So Fay can make 64 codes. We were told at the beginning that:

j = f + x

So, we substitute our numbers in, giving us:

125 = 64 + x

Minusing 64 from both sides gives us:

x = 61

So, x = 61.

Hope this helped!

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The number of sides of the regular polygon with the sum of interior angles  900 degrees is equal to 7 .

As given in the question,

Sum of the interior angles of any regular polygon is equal to 900 degrees.

Let us consider 'n' represents the number of sides of the regular polygon.

Relation between number of sides with the sum of the interior angles in the regular polygon is given by :

( n - 2 ) × 180° = Sum of the measure of interior angles of regular polygon

⇒ ( n - 2 ) × 180° = 900°

Divide both the sides by 180°

⇒ ( n - 2 ) = 900° /180°

⇒ ( n - 2 ) = 5

⇒ n = 5 + 2

⇒n = 7 sides

Therefore, the number of sides of the regular polygon whose sum of interior angles 900 degrees is equal to 7 sides.

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The rule for the given pattern is to subtract 13, then add 24.

The correct Option is (A.) subtract 13, then add 24.

A pattern or sequence in a series of numbers is called a number pattern. In general, this pattern builds a connection between all integers.

In this question we have the following pattern:

1, -12, 12, -1

Here we need to find the rule for this pattern.

Let's take the first number of the pattern, which is 1:

1

To obtain the second number of the pattern, which is -12, we must subtract 13, because:

1 - 13 = -12

To obtain the third number of the pattern, which is 12, we must add 24, because:

-12 + 24 = 12

Therefore, the correct answer is A.) subtract 13, then add 24

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The complete question is: "Which best describes the rule for this pattern? 1,-12,12,-1 A.) subtract 13, then add 24 B.) subtract -13, then add 24 C.) subtract -24, then add 13 D.) subtract 24, then add 13"

The area of the region enclosed by the inner loop of the curve is 8π/3.

The term area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Here we have Given the following values,

r = 2 + 4 sin (θ)

Now, we have to substitute the value of r = 0, then we get

⇒ 0 = 2 + 4 sin (θ)  

⇒ 4 sin (θ) = -2

⇒ sin θ = -1/2

⇒ θ = -π/6

Therefore, the limit lies in the interval -π/6 to + π/6

Now, the value of Area of polar region is calculated as,

=> A = ∫

Now, by Substituting the values

A=∫π/6−π/6 (2 + 4 sin (θ)) dθ

When we simplify this one then we get the value as,

=> A = 16 [θ + 1/6 sin6θ]

Apply the limit value, then we get

=> A = 16[(π/6 + 0) - (0 + 0)]

=> A = 8π/3

Therefore, the area of the region enclosed by the inner loop of the curve is 8π/3.

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The percentage of the total deliveries made by the Mary is equal to 95%.

As given in the question,

Total number of deliveries need to be delivered by the Mary this week = 40

Total number of deliveries completed by Mary is equal to 38

Percentage formula =  [( Number obtained ) / (Total number ) ] × 100

Substitute the value in the formula we get,

The percentage of the completed deliveries made by Mary is

= ( 38 / 40 ) × 100

= 3800 / 40

= 95%

Therefore, the total percentage of the completed delivery made by Mary is equal to 95%.

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By parallelogram opposite angles converse, the given quadrilateral is a parallelogram.

What is quadrilateral?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. Four non-collinear points are connected to form it. A quadrilateral's interior angles add up to 360 degrees in all cases.

There are four closed sides to a quadrilateral. These shapes below are quadrilaterals: a four-sided shape. One set of parallel sides make up the shape, and there are no right angles.

In given figure we can see that there is a quadrilateral given.

The opposite angles of quadrilateral are same.

Also the opposite sides of the quadrilateral are same.

It defines the properties of parallelogram.

Hence, by parallelogram opposite angles converse, the given quadrilateral is a parallelogram.

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There are 7 motorcycles and 4 cars in the parking lot

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of motorcycle and y represent the car. There could be a 2 wheel motorcycle or a 4 wheel car.

There are 11 vehicles in the parking lot, hence:

x + y = 11    (1)

There are 30 wheels, hence:

2x + 4y = 30    (2)

From both equations:

x = 7, y = 4

There are 7 motorcycles

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The measure of angle MQS is 18°.

In mathematics, angles are typically measured in degrees or radians.

An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of an angle, and the endpoint is called the vertex.

There are different types of angles:

Acute angle: an angle measuring between 0 and 90 degrees.

Right angle: an angle measuring exactly 90 degrees.

Obtuse angle: an angle measuring between 90 and 180 degrees.

Straight angle: an angle measuring exactly 180 degrees.

Reflex angle: an angle measuring between 180 and 360 degrees.

Draw QT  and QS

Angles TQP, SQT, and  SQR  will trisect the interior angle PQR

And PQR  = 108

So  ...angle  SQT  = 108 / 3   = 36

But...by symmetry....angle XQS  =  (1/2)angle SQT  = (1/2)36  = 18°

Therefore, The measure of angle MQS is 18°.

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Three-degree polynomials have 3 roots. Three-degree polynomials are called cubic polynomials.

Any cubic equation having a degree three has 3 roots. Just like linear polynomials have only one root which has only one degree and a polynomial of degree two is known as a quadratic polynomial. A Quadratic polynomial has two roots. The degree of zero polynomial is not defined. The degree of a non-zero constant polynomial is zero. Non-zero constant polynomials are represented in the equation as a constant real number.

A cubic polynomial can be represented as:

[tex]ax^3+bx^2+c[/tex]

We can find the roots of a quadratic polynomial using splitting the middle term and the Quadratic formula.

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Answer:

6700

Step-by-step explanation:

6.7*10³ to ordinary form. You simply move the decimal point three steps back because it's positive and put zeros before the decimal point which you have moved

a) The cube-shaped sculpture has edges that are 4 ft long, so the volume of the sculpture is 4^3 = 64 ft^3. The density of the marble is 170 lb/ft^3, so the weight of the sculpture is 64 ft^3 * 170 lb/ft^3 = 10,880 lb.

Since the sculpture weighs more than 10,000 lb, the pedestal should not be able to support it. The sculpture would require a pedestal that can support more than 10,000 lb.

b) The density of the marble is determined by the mass of the marble per unit volume. If the sculpture was half the size, it would have half the volume, but the same mass. So, the density of the marble would not change.

To estimate the number of sticks of butter needed to fill an empty bathtub, we can use the Fermi process.

First, we need to find the volume of the bathtub. A rectangular prism has a length of 60 inches, a height of 40 inches and a width of 20 inches. So, the volume of the bathtub is 604020 = 48000 cubic inches.

Next, we need to find the volume of a stick of butter. A stick of butter has a length of 4 inches, a width of 2 inches, and a height of 2 inches, so the volume of a stick of butter is 422 = 16 cubic inches.

Finally, we can divide the volume of the bathtub by the volume of a stick of butter to find the number of sticks of butter needed to fill the bathtub:

48000/16 = 3000 sticks of butter.

We can estimate that it would take around 3000 sticks of butter to fill an empty bathtub with the given measurements.

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On the coordinate plane , the point which lies on the y -axis is given by option ( 0 , 9 ).

As given in the question,

On the coordinate plane :

Point which lies on the y - axis is given by :

a. ( 9 , 9 )

This coordinate lies in the first quadrant. It will not lies on any of the axis.

False.

b. ( 9 , 0 )

In this coordinate has y-,coordinate is equal to zero , it lies on the x- axis.

False.

c. ( 0 , 9 )

In this coordinate has x-,coordinate is equal to zero , it lies on the y- axis.

True.

d. ( -9 ,-9 )

This coordinate lies in the third quadrant. It will not lies on any of the axis.

False.

Therefore, on the coordinate plane the point that lies on the y-axis is

( 0, 9).

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The solid figure that has the given net is C.rectangular prism.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Six faces, eight vertices (or corners), and twelve edges to up a rectangular prism. We would require either 12 edge pieces and 8 corner pieces to create the rectangular prism's frame or 6 rectangles that connect at the edges to form a closed three-dimensional shape.

Therefore, option C is correct.

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missing options:

square pyramid

cube

rectangular prism

square prism

Answer:

x = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 16[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 8[tex]\sqrt{3}[/tex]

The number of teaspoons of baking soda will be left will be 4 teaspoons.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Grace is making cookies. She has 6 tablespoons of baking soda left in the container. If she uses 2 teaspoons of baking soda for her recipe.

Then the number of teaspoons of baking soda will be left will be given as,

⇒ 6 - 2

⇒ 4

The number of teaspoons of baking soda will be left will be 4 teaspoons.

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Answer:

4 teaspoons is left.

Step-by-step explanation:

Now we have to,

→ find teaspoons of baking soda left.

Given information,

→ Total = 6 teaspoons

→ Used = 2 teaspoons

→ Left = x

Forming the equation,

→ 6 = x + 2

Then the value of x will be,

→ 6 = x + 2

→ x + 2 = 6

→ x = 6 - 2

→ [ x = 4 ]

Hence, the value of x is 4.

Answer:

Step-by-step explanation:

?

In this problem, x stands for the original quantity. To solve the problem, we can use algebra to rearrange the equation.

2x + 2x/3 = 19

Multiply each side by 3

6x + 2x = 57

Subtract 2x from each side

4x = 57

Divide each side by 4

x = 14.25

Therefore, x stands for 14.25, which is the original quantity.

Step-by-step explanation:

the other answer started correctly and then did a strange (to put it mildly) and wrong turn.

that is why I have to add my answer :

2x + 2x/3 = 19

yes, we need to multiply both sides by 3 to get rid of the fraction :

6x + 2x = 57

now we add terms of the same base and get

8x = 57

x = 57/8 = 7.125

Answer:

The 6th one is x=70 and <BCX=145

The equation represents the function on the graph is f(x)= cos 4x.

What is the function on the graph?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.

We have given,

A: f(x)= cos 1/4x

B: f(x)= sin 4x

C: f(x)= cos 4x

D: f(x)= sin 1/4x

To find the equation represent the function on the graph:

f(x) = cos 4x

let take the values on the x-axis of the graph,

x = п/2, п, 3п/2, 2п, 5п/2

For cos 360 degrees, the angle 360° lies on the positive x-axis. Thus cos 360° value = 1

Since the cosine function is a periodic function, we can represent cos 360° as, cos 360 degrees = cos(360° + n × 360°), n ∈ Z.

⇒ cos 360° = cos 720° = cos 1080°, and so on.

so, cos 4( п/2) = cos 4( 3п/2) = cos 4( 2п) = cos 4( 5п/2) = 1.

Hence, the equation represents the function on the graph is f(x)= cos 4x.

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Josh will cover a total distance of 38 kilometres while trekking in Glacier National Park, having already covered 17 km of the park's trails.

The idea that will be applied in this situation is the usage of models to simplify expression.

Josh was able to hike 17 km, and since this is 2 km short of being halfway done, we can create the equation that models the situation.

The model can be written as  [17 + 2 = (1/2)h ]

h =length of the hike.

then  we can substitute the values so that we can know the value of h,

[17 + 2 = (1/2)h ]

[19 =0.5h]

h = 38 km

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The properly written question:

Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, space, k, m and is 2 \text{ km}2 km2, space, k, m short of being \dfrac12 ​2 ​ ​1 ​​ start fraction, 1, divided by, 2, end fraction of the way done with his hike.