MATHEMATICS COLLEGE

Which fraction is bigger 7/36, or 4/9

Answers

Answer 1

Answer:

Answer:

4/9 is bigger

Step-by-step explanation:

For the 1st fraction, since 9 × 4 = 36,

4/9 = 4 × 4

9 × 4 = 16/36

Likewise, for the 2nd fraction, since 36 × 1 = 36,

7/36= 7 × 1

36 × 1 = 7/36

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/36> 7/36 or 4/9 > 7/36

Answer 2

Answer: 7/36 is bigger
7 goes into 36 5 times
and 4 goes in 9 only 4 times

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To calculate approximately the amount or value of something is called _________.

Answers

to calculate approximately the amount or value of something is called estimate

(5.1 x 103) • (3.2 x 103)

Answers

Answer:

11480.22

Step-by-step explanation:

5.1x3.2 + 5.1x103 + 103x3.2 + 103x103

16.32 + 525.3 + 329.6 + 10609

11480.22

One table at a bake sale has 75 oatmeal cookies. Another table has 60 lemon cupcakes. Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?

Answers

75 = 3·5², so has 6 divisors. 6 rectangles are possible if you make the distinction between 1×75 and 75×1.

60 = 2²·3·5, so has 12 divisors. 12 rectangles are possible under the same conditions.

The cupcake table can be arranged more ways.

_____

When 1 is added to each exponent of the prime factors, the product of those sums is the number of divisors. For 75: (1+1)(1+2) = 6; for 60: (1+2)(1+1)(1+1) = 12.

Arrangement is simply the order, which items are displayed or presented.

The table of 60 lemon cupcakes allow more rectangular arrangements

The given parameters are:

$\mathbf{Oatmeal = 75}$

$\mathbf{Lemon = 60}$

The rectangular arrangement (R) is calculated as follows:

$\mathbf{R = (Area)/(n)}$

Where n represents the number of items, and Area represents the area of the rectangular table

For the oatmeal, we have:

$\mathbf{R_1 = (Area)/(75)}$

$\mathbf{R_1 = 0.0133Area}$

For the lemon, we have:

$\mathbf{R_2 = (Area)/(60)}$

$\mathbf{R_2 = 0.0167Area}$

By comparison, 0.0167Area is greater than 0.0133Area

Hence, the table of 60 lemon cupcakes allow more rectangular arrangement

Answers

The domain is all real numbers expect -2, and the domain is -4 to 4 expect 2.

A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this store in week t after its release is R=f(t)=350 ln tR=f(t)=350lnt with t>1. Find f(5), f'(5), and the relative rate of change f'/f at t=5. Interpret your answers in terms of revenue.

Answers

Solution :

It is given that :

$f'(t) = (350 \ln t)'$

$=350(\ln t)'$

$=(350)/(t)$

So, $f(5)=350 \ln (5) \approx 563$

$f'(5) = (350)/(5)$

$=70$

The relative change is then,

$(f'(5))/(f(5))=(70)/(350\ \ln(5))$

$=(1)/(5\ \ln(5))$

$\approx 0.12$

$=12\%$

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

candy box is made from a piece of cardboard that measures 45 by 24 inches. Squares of equal size will be cut out of each comer. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? inches should be cut away from each corner to obtain the maximum volume. A square with a side of length (Round to the nearest hundredth as needed.)

Answers

Answer:

Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

= x(1080 - 138x + 4x²)

= 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.

$(dV)/(dx)=12x^(2)-276x+1080=0$

12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

Final answer:

The size of the square that should be cut away from each corner to obtain the maximum volume for a box made from a cardboard measuring 45 by 24 inches is 3 inches.

Explanation:

To find the size of the square that should be cut from each corner to obtain the maximum volume, we should first make an equation for the volume of the box. If x is the length of the side of the square, then the dimensions of the box are (45-2x) by (24-2x) by x, thus the volume of the box V is (45-2x)(24-2x)x.

By using calculus, we can find the derivative of this function, set it to zero and solve, this will give the critical points where the maximum and minimum volumes will be.

The derivative is found to be -4x^2 + 138x - 1080. Setting this to zero and solving, we find that x = 3 and x = 90 are the critical points for the maximum and minimum volumes. Since we cannot cut corners more than 24 inches (this would make the width negative), x = 3 inches is the only feasible solution.

So, 3 inches should be cut away from each corner to obtain the maximum volume.

Learn more about Optimization here:

brainly.com/question/37742146

#SPJ3

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