What type of reasoning is used to find the next amount of train cars? Explain your answer.

Holly ate two [tex]\frac{1}{6}[/tex] fractions.

Holly ate 1 more brownie, then Tori

     = 1+2

      = 3

She ate [tex]\frac{3}{9}[/tex] fraction

Two equivalent fractions = [tex]\frac{3}{9} = 2x[/tex]

           [tex]x = \frac{1}{6}[/tex]

Holly ate two [tex]\frac{1}{6}[/tex] fractions.

What are Fractions?

Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the bottom part represents the denominator, and the top part the numerator. This article's focus is on going to learn the meaning of fractions in mathematics, different sorts of fractions, how to convert fractions to decimals, and a ton of problems that have been solved and well explained.

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Given the Linear Equation:

(a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:

Where "m" is the slope of the line and "b" is the y-intercept.

Then, you get:

Notice that:

(b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:

Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":

Because the value of "y" is zero when the line intersects the x-axis.

Therefore, you get:

Now you know that the line passes through these points:

Hence, you can graph it.

Therefore, the answers are:

(a) Equation in Slope-Intercept Form:

(b) Graph:

A rotation of 270 degrees about the origin would transform the figure as follows:

Which does not maps the A to A'.

Now, one sequence of transformations that take A to A' is:

1)First, a reflection over the x-axis would transform the figure as follows:

2) We translate the figure 3 units up and 4 units to the right:

Answer: Reflection over the x-axis, translation 3 units up and 4 units to the right.

Given: Linh buys $11.23 worth of groceries and pays for them with a $20 bill.

So, the change will be = 20 - 11.23 = $8.77

Answer:-900 feet. I think this is correct so don't use it unless you think its right

Step-by-step explanation:

Length of the given arc

So the length of the given arc is 1.57 cm

They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.

One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition.

The sum of 5 + 6.

They can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.

Therefore, 5 + 6 = 11.

Estimating other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.

Repeat the doubles facts so they can use them to solve equations.

They can also use doubles-minus-one facts to enable them solve equations.

Write down 9 + 10 and have your children find the sum.

If they know that 10 + 10 = 20, they know that the sum of 9 + 10 will be one less. Therefore, 9 + 10 = 19.

Practice solving different number sentences together.

Therefore, they can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.

Therefore, the correct answer is option A 5 + 5 = 10.

The complete question is:

Which doubles fact helps you solve 5 + 6 = 11? Circle the number sentence.

A 5+5=10

B6+6=12

C7+7= 14

D 8+8=16

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1) Solving that linear system using the elimination method, we'll proceed this way.

1.1 Choose one variable to be canceled out firstly. Let's choose the x variable:

6x + 5y = -15

-2x -3y= 17 Multiply this whole equation by 3

6x + 5y = -15

-6x -9y= 51 Add both equations

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

0 -4y =36 Divide both sides by -4

y = -9

2) Now let's plug into any equation, usually the one with smaller numbers y= -9

-2x -3(-9) = 17

-2x +27 = 17 Subtract 17 from both sides

-2x =17-27

-2x = -10 Divide both sides by -2

x= 5

3) So the solution is (5, -9)

-

Measure of ∠B = 16°

∠A and ∠B are Vertical angles with ∠A = x+12° and ∠B = 6x-8°.

Vertical angles are angles formed between two lines at the intersection of them and are opposite to each other.

Also measures of Vertical angles are equal.

Now to find the measure of ∠B, we need to find x.

So here,  ∠A = ∠B

⇒ x+12° = 6x-8°

⇒ 6x - x = 12 + 8

⇒ 5x = 20

⇒ x = 4

Hence, ∠B = 6x-8° = 6 x 4 -8 = 16°

So measure of ∠B = 16°

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Total ribbon Pam needs = 2 yards

Total ribbon Pam purchased = 0.497 + 0.91 + 0.40 = 1.807

The amount of ribbon Pam needs is calculated as,

Thus the amount of ribbon needed is 0.193 yards .

Answer:

The answer is (1,4,2)

Explanation: First of all we need to know if our triangle is a right triangle (has one 90° inner angle) to be able to use the law of sines to calculate the distance between Amanda and the helicopter.

Step 1: Once we know that the sum of all inner angles of a triangle is equal to 180° we can calculate the unknown angle as follows

As we can see above the missing inner angle is 90° which means it is a right triangle.

Step 2: Now we can use the law of sines as follows

once sin (90°) = 1 and sin (30°) = 0.5, let's calculate "x" below

Final answer: As we can see above, the final answer is 2000 ft

Answer:

3

Step-by-step explanation:

Hello!

A simple way to find if the number is a multiple of 9 is if the sum of the digits in the number is a multiple of 9, then the number itself is a multiple of 9.

So that means: 7 + 2 + b + 3 + 8 + 4 is a multiple of 9

If we add it up we should get: 24 + b

The multiples of 9 include 9,18,27,36,45,54....., and the closest multiple of 9 to 24 is 27. Therefore, the missing digit should be 3, as 27 - 24 is 3.

The next closest numbers would be 18 and 36, but you would need to add a negative number to get 18, and a two-digit number to get 36.

The dimension of the brick is given 110 cm x 655 cm x 1330 cm.

We know that 1 cm = 10^-2 m.

So, the dimensions of brick in meters will be 1.10 m x 6.55 m x 13.30 m.

The volume of the brick is calculated below:

Thus, the volume of the brick in cubic meters is 95.8265 m^3.

Answer:

Match that i have the step by step explanations

Step-by-step explanation:

A, F, C, D, E, F, B

From the question

By the bunkers rule

P = 18,000

R = 17.25% = 0.1725

For the time

Since the year is a leap year then

February has 29 days

Hence

From Feb.4 to Apr 21 implies

The number of days left in Feb. = 25

Number of days in March = 31

Number of days for April = 21

Therefore, Total number of days = 25 + 31 + 21 = 77

By Bankers rule, total days for the year will be 360

Hence the interest is

Therefore, the interest is 664.16

Answer:

Printer B prints the fastest

Distribution of

a(b + c) = ab + ac

Then

36 + 12 is equivalent to

Find composed numbers

36= 3•12

12 = 3•4

THEN ANSWER IS

3• (12 + 4)

The scientific notation of the expression is as follows:

The proper format for scientific notation is a x 10ᵇ where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.

Scientific notation is a special way of writing numbers.

The expression can be express in scientific notation as follows:

Therefore,

(7 × 10⁻⁶) (7 × 10⁻⁶)

Hence, we have to multiply the integers and add the exponents as follows:

(7 × 7) × (10⁻⁶. 10⁻⁶)

49 × 10⁻⁶⁻⁶

49 × 10⁻¹²

4.9 × 10⁻¹¹

Hence, the second can be express in scientific notation as follows:

(3.76 × 10⁵) + (7.44 × 10⁵)

(3.76 + 7.44) × 10⁵

11.2 × 10⁵

1.12 × 10⁵⁺¹

1.12 × 10⁶

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The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The system of the equations are,

3x + y - 2z = 22    .... (i)

x + 5y + z = 4       .... (ii)

x = - 3z                .... (iii)

Now,

Solve the equations as;

Substitute x = - 3z in both equations, we get;

⇒ 3x + y - 2z = 22

⇒ 3 × -3z + y - 2z = 22

⇒ - 9z + y - 2z = 22

⇒ - 11z + y = 22   .... (iii)

And, x + 5y + z = 4

- 3z + 5y + z = 4

5y - 2z = 4     ... (iv)

Solve equation (iii) and (iv) we get;

⇒ y = 44 and z = 2

So, x = - 3z    

⇒ x = - 3 × 2

⇒ x = - 6

Thus, The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

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Given a table represents a relation between x and y

As shown, the change of (x) and (y) vary with a constant rate

So, the table represents a linear function

The general equation will be: y = m * x + b

where (m) is the slope, (b) is the value of y when (x=0)

So, from the table, when x = 0 , y = 25

The slope will be as follows:

So, the equation will be:

When the input = 200, x = 200

So, substitute with (x) to find the output (y)

So, the answer will be:

For an input 200, the output is 1025

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

Another method to solve using the arithmetic sequence.

As shown in the table consider (x) represents the number of terms

So, (y) will be an arithmetic sequence

The first term = a = 30

The common difference = d = 35 - 30 = 5

the general rule of the arithmetic sequence is:

substitute with (a) and (d)

When x = 200

So, for an input 200, the output = 1025

Answer:  A) moves two places to the right

Example:

[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]

The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.

Answer:

See below

Step-by-step explanation:

Robert pays 35 %   in 12 monthly installments

6480 * .35 / 12 = 189 dollars per month

Let's start by completing the first table.

The questions gives the depth in two times:

- 2 hours after start -> 64 inches of water

- 4 hours after start -> 48 inches of water

From this, we can identifythe units:

- for time, we will use hours

- for depth, we will use inches

The first given values are:

- for time, 2

- for depth, 64

The second given valuesa are:

- for time, 4

- for depth, 48

So, the table is:

Quantity Name | Time | Depth of Pool

Unit | hour | inch

Given Value 1 | 2 | 64

Given Value 2 | 4 | 48

Now, we need to calculate the slope, which can be done using the given points and the equation:

So, the slope is -8 inches per hour.

The interceptwe the b in the equation:

Where y is the depth and x is the time. So, using the first given values and the slope, we can find b:

Thus, the intercept is 80 inches.

So, the formula we have for the pump is:

Using it, we can answer questions 1 and 2:

1. After 6 hours means x = 6, so:

So, y = 32, thus, the depth of the water will be 32 inches.

2. The level 24 inches mean y = 24, so:

Thus, x = 7, and the water will be at 24 inches after 7 hours.

The area of the wall whose length is 4y+8 and the height is 4y is 16y^2 + 32y.

How area is calculated?

Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2.

The area of a form is computed by dividing its length by its breadth.

It is given that the length of the wall is 4y+8 and height of the wall is 4y.

From this given information, we can conclude that the wall is rectangle.

Formula to calculate the area of rectangle is:

Area of rectangle = length x breadth

Putting the value given in the question:

Area of the wall = (4y+8)(4y)

Area of the wall = 16y^2 + 32y

Therefore, the area of the wall is 16y^2 + 32y

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[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]

ATTACHED IS THE SOLUTION

Answer:

(-104/15)

Step-by-step explanation:

    3              2

2 ------ × -2 -------

    5              3

5 × 2 = 10

10 + 3 = 13

3 × -2 = -6

-6 + -2 = -8

 13        -8            104

------- × ------- = (-) -------

  5          3             15

I hope this helps!

Given the interval of the distribution as

a) To find the mean, we will calculate the mid-value of the interval, this is shown below

Hence, the mean is 5.38

b) To find the standard deviation

Hence, the standard deviation is 0.2194

c) The probability that the child will be older than 5 years will be

Hence, the probability that the child will be older than 5 years is 1.0

d) The probability that the child age is between 5.4 and 5.6 years old will be

Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632

e) If the child is at the 53rd percentile, the age of the child will be

Hence, at the 53rd percentile, the age of the child is 5.4028 years old

The effect on the graph replacing f(x) by f(x)+k is a vertical shift k units.

According to the graph the resulting function is 2 units higher from the original one. This means k has a value of 2.