Is 3/47 a rational number?

Answer:

The correct option is C. 120°

Step-by-step explanation:

For better explanation of the answer see the attached figure :

Since, Angle formed at the center is equal to the angle measure of its opposite arc

⇒ ∠AOD = 104°

Also, The angle formed in the segment is half the angle formed at the center of the circle

⇒ ∠DOB = 2 × ∠BAD

⇒ ∠DOB = 2 × 68°

⇒ ∠DOB = 136°

Now, ∠AOB = 360 - ∠BOD + ∠AOD

⇒ ∠AOB = 360 - 136 - 104

⇒ ∠AOB = 120°

Now, Angle formed at the center is equal to the angle measure of its opposite arc

⇒ b = ∠AOB

⇒ b = 101°

Hence, the correct option is C. 120°

when x =1 , y = 3

 when x = 3, y =27

27-3 = 24

3-1 = 2

24/2 = 12

 rate of change = 12

The ratio of all books to used books in simplified form is 7 : 3.

Used the concept of ratio that states,

The ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.

Given that,

There are 14 books on a shelf.

8 of these books are new.

Here, the number of used books is,

14 - 8

= 6

Thus, the ratio of all books to used books is,

14 : 6

Simplified form;

14 : 6 = 7 : 3

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Answer: 1, 2, 5, and 10

Step-by-step explanation: To find the factors of 10, begin by dividing 10 by 1 which gives us 10. This tells us that 1 and 10 are factors of 10. Next, divide 10 by 2 which gives us 5. This tells us that 2 and 5 are also factors of 10. Next, divide 10 by 3. Notice that 10 doesn't divide evenly by 3 so 3 is not a factor of 10. Next, divide 10 by 4. Since 10 doesn't divide evenly by 4, then 4 is not a factor of 10. Next, divide 10 by 5 which gives us 2. This tells us that 5 and 2 are factors of 10 but notice that we already know that 5 and 2 are factors of 10. This means that 5 and 2 are repeat factors.

There is no need to repeat factors that we already know. In fact, as we are writing the factors of a number, it's important to understand that once we hit repeat factors, all other factors that we try will also repeat.

So here, dividing by anything greater than 5 will give us factors that we already know so we can stop here.

This means that the factors of 10 are 1, 2, 5, and 10.

To find out how much hardener should be added to 19 containers of resin, multiply 60 mL by 19 and then divide the result by 1000 to convert mL to liters. The answer is 1.14 liters.

To find out how much hardener should be added to 19 containers of resin, we can use the given formula of adding 60 mL of hardener to each container of resin. Since we have 19 containers, we can multiply 60 mL by 19 to get the total amount of hardener needed.

60 mL × 19 = 1140 mL

To convert mL to liters, we need to divide the amount in mL by 1000. Therefore, the answer is:

1140 mL ÷ 1000 = 1.14 liters

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To determine which shapes are similar to shape A, we must evaluate the pattern, repetition, and geometrical structure, while understanding the differences in geometrical and organic forms.

When identifying shapes similar to shape A, we must look at the pattern and repetition of the figures while noting the differences. Shapes that are similar will have proportionally equivalent angles and sides, despite potential differences in size. We analyze the given shapes by comparing their properties such as angles, sides, and overall geometrical structure.

In a more complex composition, identifying positive and negative shapes can be challenging due to the presence of implied shapes that are created by the arrangement of other shapes or colors around them. Therefore, an in-depth inspection is needed to determine similarity.

Lastly, it is necessary to understand that shapes can be geometric, like circles and squares, or organic, which are more freeform and less regular. When comparing shapes to shape A, recall that similar shapes must relate in the ways mentioned, despite their geometric or organic nature.

To solve this problem, we can set up an equation using the amount invested at each rate. Solving the equation will give us the amount invested at 8% and 7%.

To solve this problem, let's assume that the amount invested at 8% is x dollars. Therefore, the amount invested at 7% would be (23000 - x) dollars. Now we can set up an equation to represent the given information:

0.08x + 0.07(23000 - x) = 1800

Solving this equation will give us the amount invested at each rate.

0.08x + 0.07(23000 - x) = 1800

0.08x + 1610 - 0.07x = 1800

0.01x = 1800 - 1610

0.01x = 190

x = 190 / 0.01

x = 19000

Therefore, $19000 is invested at 8% and $4000 (23000 - 19000) is invested at 7%.

To solve the problem, set up a system of equations using x and y as variables to represent the amounts invested at 8% and 7%. Solve the system to find x and y. The amount invested at 8% is $19,000 and the amount invested at 7% is $4,000.

To solve this problem, we can set up a system of equations. Let x represent the amount invested at 8% and y represent the amount invested at 7%. The total amount invested is $23,000, so we have the equation x + y = 23,000. The total return is $1,800, so we have the equation 0.08x + 0.07y = 1,800. We can solve this system of equations to find the values of x and y.

By substitution, we can solve for x:

x + y = 23,000

x = 23,000 - y

Substituting this into the second equation:

0.08(23,000 - y) + 0.07y = 1,800

1,840 - 0.08y + 0.07y = 1,800

-0.01y = -40

y = 4,000

Substituting the value of y back into the first equation, we can find x:

x + 4,000 = 23,000

x = 19,000

So, $19,000 was invested at 8% and $4,000 was invested at 7%.

To find the radian measure between adjacent spokes of a wheel, you divide 2π by the number of spokes. In this case, the wheel has 22 spokes, leading to a radian measure of approximately 0.286 radians for the angle between adjacent spokes.

The topic of the question pertains to geometry and radian measures. In a full circle, there are 2π radians. If a wheel has 22 spokes, each spoke defines a section of the circle equally. So, you would divide 2π by 22 to determine the measure, in radians, of the central angle formed by adjacent pairs of spokes.

Step-by-step calculation: The formula for calculating this is 2π/n, where n is the number of sections (or spokes). Therefore, the radian measurement of the angle between adjacent spokes would be 2π/22 = 0.286 radians when rounded up.

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see the attached figure with letters to better understand the problem  

we know that

the scale factor is equal to

[tex]scale\ factor=\frac{A'B'}{AB}[/tex] or  [tex]scale\ factor=\frac{B'C'}{BC}[/tex]

we have

[tex]A'B'=8\ units \\AB=2\ units[/tex]

substitute in the formula

[tex]scale\ factor=\frac{8}{2}[/tex]

[tex]scale\ factor=4[/tex]

therefore

the answer is

the scale factor is equal to [tex]4[/tex]

Answer:

this is the correct answer for plato (Roger should make 10 fire trucks and 15 dolls in order to minimize the time spent making toys.)

Step-by-step explanation:

Answer:

Number of Fire trucks made= 10.

Number of Dolls made =   15  

Step-by-step explanation:

Let x denote the number of fire trucks made.

and y denote the number of dolls made.

Now we are given:

Hence, the inequality that can be made  from this information is:

                       [tex]x+y\geq 25[/tex]

He sells each fire truck for $15 and each doll for $10.

He needs to earn at least $300 to cover his costs.

The inequality that can be made from this piece of information is:

                 [tex]15x+10y\geq 300[/tex]

           Also,

                      x≥0

                 and y≥0

Each fire truck takes 50 minutes to make and each doll takes 45 minutes to make.

Now we are asked to minimize the time function let it denote by 'z'.

Hence, the system that is formed is:

Optimization function       Min.   z=50x+45y

    subject to                     x+y ≥ 25[/tex]

                                and   15x+10y ≥ 300[/tex]

Non-negative constraint         x ≥ 0

                                                 y ≥ 0

Now on solving the constraints we get the boundary points as:

(25,0) , (0,30) and (10,15)

Hence, the optimal solution is checked at these points.

(25,0)             z=1250

(0,30)            z=1350

(10,15)             z=1175

Hence, the minimal time spent is: 1175 minutes.

Number of Fire trucks made= 10.

Number of Dolls made =15  

Bills father weight is 76 kilograms.

Here,

Bills weight is 48 kilograms. This is 10 grams more than one half his fathers weight.

We have to find, Bills father weight.

What is Linear expression?

Linear Equations deal with Equations with linear expression in one or two variables . Such Equations are known as Linear Equations.

Now,

Let Bills father weight is x kilograms.

According to given condition,

Bills weight is 48 kilograms. This is 10 grams more than one half his fathers weight.

⇒ [tex]\frac{x}{2} + 10 = 48[/tex]

⇒ [tex]\frac{x}{2} = 48 - 10[/tex]

⇒ [tex]\frac{x}{2} = 38[/tex]

⇒ [tex]x = 76[/tex]

Hence, Bills father weight is 76 kilograms.

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find the least common denominator then change fractions to have the same denominator, add them together and then reduce the fraction if possible