In January, Emma was 62.25 in tall. In December, she was 65.5 inches tall. How much did Emma grow between January and December?

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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The right answer is g(x)=(1/4x)^2 had the same question!!

Final answer:

The equation of the quadratic function f(x) = x² after a horizontal stretch by a factor of 4 is f(x) = x²/16.

Explanation:

When you horizontally stretch the quadratic parent function f(x) = x² by a factor of 4, you are stretching the function in the x-direction. This means that each x-coordinate of the graph is multiplied by the stretch factor. The new function is obtained by replacing x with x/4 in the original function. So the equation of the new function after a horizontal stretch by a factor of 4 is:

f(x) = (x/4)²

This simplifies to:

f(x) = x²/16

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]

This is about usage of direct proof.

m + p was proved to be even using direct proof.

m, n and p are integers

m + n and n + p are even integers.

If a is an even integer, then there will exist an integer b such that;

a = 2b

m + n = 2b

n + p = 2c

m + 2n + p = 2b + 2c

m + p = 2b + 2c - 2n

Factorizing, we have;

m + p = 2(b + c - n)

From earlier, b, c and n are integers. Therefore, from earlier formula about direct proof of even integers, we can equally say that m + p is also even.

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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 the expression 33-6(1 1/3+ 2/3), first simplify the expression within the parentheses with the Order of Operations. Then, perform the multiplication. Finally, subtract the result from the initial value of 33.

To solve the expression 33-6(1 1/3+ 2/3), we need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we simplify the expression within the parentheses:

1 1/3 + 2/3 = 2.

Next, we perform the multiplication: 6 * 2 = 12. Finally, we subtract the result from 33: 33 - 12 = 21.

Therefore, the expression 33-6(1 1/3+ 2/3) equals 21.

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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

Answer:

0.02($1,444.50)

Step-by-step explanation:

hope it helped i got it right

The required cost to ship her computer from store B is $28.89.

The percentage is defined as a ratio expressed as a fraction of a hundred.

We have been given that Sarah mailed her computer to Store B for repairs. Her bill was:

Initial Repair Cost = $1,350

Sales Tax of 7 percent = $94.50

Total Cost of Computer Repair = $1,444.50

We have to determine 2% of the total Cost of Computer Repair which is 1,444.50.

Shipping cost = 2% of 1,444.50

Convert percent into the fraction form,

Shipping cost = 2/100 × 1,444.50

convert the fraction into decimal form to get

Shipping cost = 0.02 × 1,444.50

Apply the multiplication operation, and we get

Shipping cost = $28.89

Therefore, the required cost to ship her computer from store B is $28.89.

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1 out of 12 can be written as 1/12

 now multiply 456 by 1/2

this is the same as dividing 456 by 12

456/12 = 38 students share a locker

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  

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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sqrt(16) = 4

sqrt4 = 2

2^2 = 4

 so now you have 4-6(4)/2

6*4 =24

4-24 = -20

-20/2 = -10