What is the list price 45 off 1/4

A parcel delivery service will deliver a package only if the length plus girth (distance around) does not exceed 84 inches. (A

Kisachek [45]

Answer:

A. 14x14x28

B. The maximum volume is 5488 cuibic inches

Step-by-step explanation:

The problem states that the box has square ends, so you can express volume with:

$v=x^{2} y$

Using the restriction stated in the problem to get another equation you can substitute in the one above:

$4x+y=84\\\\$

Substituting y whit this equation gives:

$v=x^{2} (84-4x)\\\\v=84x^{2} -4x^{3}$

Now find the limit of x:

$\frac{84x^{2}-4x^{3}}{dx}=168x-12x^{2}\\\\x=\frac{168}{12}=14$

Find the length:

$y=84-4(14)=28$

You can now calculate the maximum volume:

$v=(14)^{2}(28)= 5488$

6 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

Using the given points and line, determine the slope of the line. (1, 2) and (2, 1) slope = 2 slope = 1 slope = -1

Bas_tet [7]

Answer:

-1

Step-by-step explanation:

Slope formula: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (1 - 2)

= -1

8 0

3 years ago

1.A bag has 4 green blocks, 3 red blocks, 2 blue blocks, and 1 yellow block. Find the probability of randomly selecting a block

maks197457 [2]

Answer: 1) 7/10 2) 15 3) 240 4) 1/4 5) 4/9 6) 1/20 7) No, not independent

Step-by-step explanation:

1. 4 green+3red+2blue+1yellow = 10 total

if 3/10 are red, then 7/10 are not red. So the second option, 7/10

2. 3 cartons in every 40

40*5 = 200

so do 3*5 = 15

so 15 or the third option

3. 40 out of 110

110*6 = 660

so do 40*6 = 240

so 240 or the fourth option

4.

Flipping heads: 1/2

rolling even: well, there is 2, 4, and 6, or 3 even numbers so 3/6 or 1/2

do 1/2*1/2 = 1/4

so 1/4 or the third option

5. Numbers more than 2: 3, 4, 5, 6 (4 numbers)

4/6 or 2/3 chance the first time, 2/3 chance the second time

do 2/3*2/3 = 4/9

so 4/9 or the second option

6. 5 dishes and 4 desserts

1/5 chance of picking the dish

1/4 chance of picking the dessert

do 1/5*1/4 = 1/20

so 1/20 or the fourth option

7. Since you don’t replace the marble after picking it, it affects the outcome of the second draw. Therefore the events are dependent, or not independent. So the second option.

7 0

3 years ago

Consider a graph of the equation and -3x + 4. What is the y-intercept?

Andreas93 [3]

Answer:0,4

Step-by-step explanation: are there multiple choice answers because I wasn’t to make sure this answer is correct

3 0

3 years ago