the tuition at a certain college was $ 23, 472 last year and increased 5.5 % from last year to the current year . How much this is year 's tuition is $

Answer: 4 boxes.

Step-by-step explanation:

We know that each box has 18 ounces of cereal.

We know that:

1 lb = 16 oz

Then:

1 = (1lb/16oz)

Then we can write:

18 oz = 18oz*(1lb/16oz) = (18/16) lb

This means that each box has (18/16) pounds of cereal.

Now, how many boxes we need to buy if we want to have at least 4 pounds of cereal?

If we buy N boxes, we will have N*(18/16) lb boxes of cereal.

Let's find N such that:

N*(18/16) lb = 4lb

N = 4*(16/18) = 3.56

But you can not have a 0.56 of a box, so we should round our number up to the next whole number, then we get:

N = 4.

She should buy 4 boxes.

Answer:

4

Step-by-step explanation:

Good Luck

Answer:

Dilation

Step-by-step explanation:

There are two main broad types of transformations: rigid and non-rigid. Rigid transformations keep the general shape the same while changing its position, rotation, direction, etc. Non-rigid transformations, on the other hand, may change how big it is.

For the image to have a different area than the original triangle, it would have to be a different size. Therefore, the original triangle must have gone through a non-rigid transformation. The only non-rigid transformation is dilation, so that is the answer.

There is another type of non-rigid transformation called shearing; however, this is fairly uncommon. If you want, you can include that as a possibility in your answer as well or just put "non-rigid transformation."

Let me know if you want more clarification. :)

Answer:

1

Step-by-step explanation:

Answer:

69.314718056

Step-by-step explanation:

Answer:

\(\frac{56}{125}\)

Step-by-step explanation:

112/250

Reduce the fraction \(\frac{112}{250}\) to the lowest terms by extracting and canceling out 2.

\(\frac{56}{125}\)

Hope it helps and have a great day! =D

~sunshine~

Answer:

The simplest form of 112/250 is 56/125. Steps to simplifying fractions. Find the GCD (or HCF) of numerator and denominator. GCD of 112 and 250 is 2

Answer:

18

Step-by-step explanation:

\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)

Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

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Answer:c

Step-by-step explanation:

Did the test

Answer:

D. 2:1 & 6:3

Step-by-step explanation:

Proportion means equal so we need to see which ratios are equal.

To do that we need to make one fo the numbers in the ratio equal the corresponding number in the other ratio, then see if the other matches.

A:

1:2 & 4:2

The second number is already the same but the first isn't, therefore it is not proportional.

B:

1:2 & 6:3

To get 1 to equal 6 we must multiply it by 6, and what you do to one side you must do to the other so we have to multiply 2 by 6 as well

6:12 & 6:3

The first numbers are the same but the second isn't, therefore it is not proportional.

C:

2:1 & 2:4

The first numbers are the same but the second isn't, therefore it is not proportional

D:

2:1 & 6:3

to get 2 to equal 6 we need to multiply it by 3, which means we have to multiu 1 by 3 too

6:3 & 6:3

These are equal so this is proportional.

Answer:

2.92

Step-by-step explanation:

Normal price

4 * 6.98 =27.92

Sale price

2 for 12.50   means 4 at 2* 12.50

2*12.50 = 25

Subtract

27.92-25=2.92

He saved 2.92

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

Answer:

\(\boxed {\boxed {\sf 15}}\)

Step-by-step explanation:

Distance is calculated using this formula:

\(d=\sqrt {(x_2-x_2)^2+(y_2-y_1)^2\)

where (x₁, y₁) and (x₂, y₂) are the points. We are given (-3,8) and (-3,7). Therefore;

\(x_1= -3 \\y_1= 8 \\x_2= -3 \\y_2= -7\)

Substitute the values into the formula.

\(d= \sqrt {(-3--3)^2+(-7-8)^2\)

Solve inside the parentheses.

\(d= \sqrt {(0)^2+(-15)^2\)

Solve the exponents.

\(d=\sqrt {0+225\)

\(d=\sqrt {225\)\(d= \pm 15\)

A negative number for distance doesn't make sense, so the distance must be 15.

Answer:

The original cost of the digital camera is Rs. 18,500.

Step-by-step explanation:

Let c be the original cost of the digital camera

Since VAT of 13% was added then we can say that the amount that was paid was 13% more than the original price. So the payment made was 113% of the original amount or 1.13 in decimal

Payment = original cost + 13% VAT

20, 905 = c + 0.13c

20, 905 = 1.13c

Divide both sides of the equation by 1.13

20905/1.13 = 1.13c/1.13

18,500 = c

c = Rs. 18,500

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

Answer:

9

Step-by-step explanation:

Answer:    >

Step-by-step explanation:

Answer:

Step-by-step explanation:

the measure of <c is 56

180 - 124 = 56

Answer: supplement <17

Step-by-step explanation:

1. 17 is greater

2. supplement is smaller

Answer:

es 8

Step-by-step explanation:

In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

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Answer:

6x^5-5x^4+6x^3-x^2+12x-31

Step-by-step explanation:

(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)

To add, combine like terms

6x^5-5x^4+6x^3-x^2+12x-43+12

6x^5-5x^4+6x^3-x^2+12x-31

Standard form means from the highest power of x to the lowest power of x

Given:

Find: the another equivalent value of

Explanation:

Final answer: The required answer is

To find the local and absolute maximum and minimum points of the function f(x) = (3/5)x^5 - 9x^3 + 2 on the closed interval [-4,5], we need to follow these steps:

a) Find all critical numbers (x-coordinates only):

To find the critical numbers, we need to identify where the derivative of the function is zero or undefined. Let's find the derivative of f(x) first:

f'(x) = 3x^4 - 27x^2

Now, set the derivative equal to zero and solve for x:

3x^4 - 27x^2 = 0

Factoring out a common factor of 3x^2, we get:

3x^2(x^2 - 9) = 0

This equation is satisfied when either 3x^2 = 0 or x^2 - 9 = 0.

For 3x^2 = 0, we have x = 0.

For x^2 - 9 = 0, we have x = -3 and x = 3.

Therefore, the critical numbers (x-coordinates) are 0, -3, and 3.

b) Find the intervals on which the graph is increasing (mark critical numbers):

To determine the intervals of increasing, we need to analyze the sign of the derivative on each side of the critical numbers. We create a sign chart for f'(x):

Interval (-∞, -3): Choose a test point x < -3, e.g., x = -4

f'(-4) = 3(-4)^4 - 27(-4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Interval (-3, 0): Choose a test point x between -3 and 0, e.g., x = -1

f'(-1) = 3(-1)^4 - 27(-1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (0, 3): Choose a test point x between 0 and 3, e.g., x = 1

f'(1) = 3(1)^4 - 27(1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (3, ∞): Choose a test point x > 3, e.g., x = 4

f'(4) = 3(4)^4 - 27(4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Therefore, the graph is increasing on the intervals (-∞, -3) and (3, ∞).

c) Find the intervals on which the graph is decreasing (mark critical numbers):

From the analysis above, we can see that the graph is decreasing on the intervals (-3, 0) and (0, 3).

d) Find all local maximum points:

To find the local maximum points, we need to examine the points where the graph changes from increasing to decreasing. By observing the sign changes in the derivative, we can identify potential local maximum points.

From our analysis in part b, we can see that the graph changes from increasing to decreasing at x = -3 and x = 0. Therefore, these are the local maximum points.

e) Find all local minimum points:

To find the local minimum points, we need to examine the points where the graph changes from decreasing to increasing. By observing the sign changes in the derivative, we can identify potential local minimum points.

From our analysis in part c, we can see that the graph changes.

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Explanation:

Let's say the mother will temporarily take the place of all the sisters. Wherever the mother sits will represent the block of girls.

Taking out the 6 sisters and replacing them with the mother leads to 7+1 = 8 people in a line.

There are 8! = 8*7*6*5*4*3*2*1 = 40,320 different ways to arrange 8 people.

----------

Again, the mother's position is where the sisters block will go. So let's say the mother was in seat #2. This would mean one brother would take seat #1, and all of the sisters would take the next six seats, until we reach seat #7 is when another brother would take the next seat.

Within any given permutation (the 40320 mentioned), there are 6! = 6*5*4*3*2*1 = 720 different ways to arrange just the girls in that girls block/group.

All together, there are 40320*720 = 29,030,400 different ways to arrange the 13 siblings where all the girls are seated together.

Answer:

Width = 12in, Length = 17in

Step-by-step explanation:

We can create two expressions from the given statements:

1) L (length) = 5 + W (width)

and

2) 58 = 2L + 2W (the equation for rectangular perimeter)

Substituting L from the first equation into the second equation yields:

58 = 2(5+W) + 2W

Distributing the 2 and solving for W yields:

12in = W

Plug this back into the first expression,

L = 5 + 12

L = 17in

Answer:

width = 12 in

length = 17 in

Step-by-step explanation:

Let width of rectangle = x

⇒ length of rectangle = x + 5

Given:

Perimeter = 2 × width + 2 × length

⇒ 58  = 2x + 2(x + 5)

⇒ 58  = 2x + 2x + 10

⇒ 58  = 4x + 10

⇒ 48  = 4x

⇒ x = 12

Therefore,

width = x = 12 in

length = x + 5 = 12 + 5 = 17 in

Answer:

7-16=-9

.

...................

Answer:

1/9

Step-by-step explanation:

probability equals number of desired outcomes over total possible outcomes

Total possible outcomes = 36

possible sums of 5:

2,3   1,4  3,2.  4,1

4/36= 1/9

Answer:

53.5

Step-by-step explanation:

First, set the numbers out as a data set:

{51 , 51 , 52 , 53 , 54 , 54 , 54 , 55}

The median is the number that is found in the middle of the set. In this case, there are 8 numbers, and the middle numbers are 53 & 54. Find the mean of the numbers:

(53 + 54)/2 = (107)/2 = 53.5

53.5 is your answer.

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