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3 years ago

Multiply. 8 1/2 -2 2/3

Mathematics

2 answers:

MrRissso [65]3 years ago

5 0

Answer: $-\frac{68}{3}$ or $-22\ 2/3$

Step-by-step explanation:

To solve this problem you must:

- Convert the mixed numbers to fractions, as following:

$8\ 1/2=\frac{((8*2)+1)}{2}=\frac{17}{2}$

$2\ 2/3=\frac{((3(2)+2)}{3}=\frac{8}{3}$

- Multiply both fractions. Mutilply the numerators and the denominators:

$(\frac{17}{2})(-\frac{8}{3})=-\frac{136}{6}$

- Simplify. Therefore, you obtain that the answer is:

$-\frac{68}{3}$ or $-22\ 2/3$

zavuch27 [327]3 years ago

4 0

<h2>Answer:</h2>

Answer is 5 5/6.

<h2> Explanation:</h2>

For solution check the attached picture below.

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Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i

serious [3.7K]

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches,
the width of the box = 12 inches
and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³ - 72x² + 324x - 432 = 0

x³ - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³ - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So, x³ - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So, x³ - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches,
the width of the box = 12 inches
and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0

2 years ago

Find the quotient 3,085 +3

dem82 [27]

3,088 is the answer

5 0

3 years ago

What is the approximate value for the modal daily sales?

Aleksandr [31]

Answer:

Step-by-step explanation:

Hello!

The table shows the daily sales (in $1000) of shopping mall for some randomly selected days 

Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5 

Days 18 27 31 40 56 55 23 

Use it to answer questions 13 and 14. 

13. What is the approximate value for the modal daily sales? 

To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)

The modal interval is [3.1-3.5]

Now using the following formula you can calculate the Mode:

$Md= Li + c[\frac{(f_{max}-f_{prev})}{(f_{max}-f_{prev})(f_{max}-f_{post})} ]$

Li= Lower limit of the modal interval.

c= amplitude of modal interval.

fmax: absolute frequency of modal interval.

fprev: absolute frequency of the previous interval to the modal interval.

fpost: absolute frequency of the posterior interval to the modal interval.

$Md= 3,100 + 400[\frac{(56-40)}{(56-40)+(56-55)} ]= 3,476.47$

A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53 

Of all options the closest one to the estimated mode is A.

14. The approximate median daily sales is … 

To calculate the median you have to identify its position first:

For even samples: PosMe= n/2= 250/2= 125

Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.

F(1)= 18

F(2)= 18+27= 45

F(3)= 45 + 31= 76

F(4)= 76 + 40= 116

F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]

$Me= Li + c[\frac{PosMe-F_{i-1}}{f_i} ]$

Li: Lower limit of the median interval.

c: Amplitude of the interval

PosMe: position of the median

F(i-1)= accumulated absolute frequency until the previous interval

fi= simple absolute frequency of the median interval.

$Me= 3,100+400[\frac{125-116}{56} ]= 3164.29$

A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664

Of all options the closest one to the estimated mode is C.

5 0

3 years ago

A cup of coffee has approximately 310 mg of caffeine. Each hour, the caffeine in your system decreases by about 35%. How much ca

Alex787 [66]

Answer:

∴35.97 mg caffeine would be left in the system after 5 hours.

Step-by-step explanation:

Given that,

A cup of coffee has approximately 310 mg of caffeine.

Caffeine decrease at a rate 35% per hour.

Exponential Function:

$y(t)=y_0(1-r)^t$

y(t)= Amount caffeine after t hours

$y_0$ = Initial amount of caffeine

r= rate of decrease

t = Time in hour.

Here y(t)=?, $y_0$ = 310 mg, r=35%=0.35, t= 5 hours

$y(t)=310(1-0.35)^5$

=35.97 mg

∴35.97 mg caffeine would be left in the system after 5 hours.

3 0

4 years ago

3[(15 - 3) squared divided by 4]

Ronch [10]

3[(15 - 3) squared divided by 4]
=3[(15 - 3)^2 / 4]
=3[(12)^2 / 4]
=3[144 / 4]
=3[36]
=108

8 0

3 years ago