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2 years ago

You are employed as the office manager at Clover Point Pediatries, Your

Mathematics

1 answer:

OlgaM077 [116]2 years ago

7 0

9514 1404 393

Answer:

$500

Step-by-step explanation:

There are 5 hours from 7 pm to midnight. At $100 per hour, the cost will be ...

($100/h)(5 h) = $500

The entertainment will cost $500.

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An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from e

laila [671]

Answer:

x=4 Inch

Step-by-step explanation:

Length of the Square = 24 Inches

If a Square of Length x cm is cut out from each corner

Length of the Box = 24-x-x=(24-2x) Inches

Width of the Box =24-x-x=(24-2x) Inches

Height of the box = x inches

Volume of a Cuboid = Length X Width X Height

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

Simplifying

V(x)=4x(12-x)(12-x)

To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.

V(x)=4x(12-x)(12-x)

$V^{'}(x)=12(x-12)(x-4)$

Set the derivative equal to zero to obtain the critical points

$V^{'}(x)=12(x-12)(x-4)=0\\Since \: 12\neq 0\\(x-12)(x-4)=0\\x-12=0 \:or\: x-4=0\\x=12 \:or\: x=4$

x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.

When x=4

V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches

When x=4 Inch, the volume, V of the open box is largest.

3 0

3 years ago

Use function notation to write a recursive formula to represent the sequence: 3, 6, 9, …

dlinn [17]

Answer:

f(n) = f(n - 1) + 3

Step-by-step explanation:

Substitute $n = 1, 2, 3,..$ to get the recursive formula.

OPTION 1: f(n) = f(n - 1) + 3

Substituting n = 1.

f(1) = f(1 - 1) + 3 = 0 + 3 = 3.

Substituting n = 2.

f(2) = f(2 - 1) + 3 = f(1) + 3 = 3 + 3 = 6.

Substituting n = 3.

f(3) = f(3 - 1) + 3 = f(2) + 3 = 6 + 3 = 9.

The numbers match the given sequence. So, we say the above recursive formula represents the sequence.

OPTION 2: f(n) = f(n - 1) + 2

Substituting n = 1

f(1) = f(0) + 2 $\ne$ 3.

So, this is eliminated.

Similarly, OPTION 3 and OPTION 4 can be eliminated as well.

4 0

2 years ago

I need help on this home work

Lady_Fox [76]

Where is the picture at?? I can’t help you

3 0

2 years ago

Read 2 more answers

The quotient of a number and 2<br>

alexgriva [62]

Answer:

what is the question?

Step-by-step explanation:

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4 0

2 years ago

Currently, Lupe and Hector are 61 and 67 years old, respectively. They have two daughters and a grandson, who are 37, 31 and 7 y

RSB [31]

Answer:

2 years

Step-by-step explanation:

We can check all the possibilities. Necessarily, Hector's age in years must be prime, then we consider the years when this happens and test for the other members of the family.

Hector is 67 years old, so in 25 years he will be 92 years old. The prime numbers between 67 and 92 are 71, 73, 79, 83 and 89.

When Hector is 71 years old, four years have passed the Lupe is 65 years old, so this case fails.

When Hector is 73 years old, six years have passed. Lupe is 67 years old, an their daughters and grandson are 43, 37 and 13 years old. All of these are prime numbers, therefore in this year the statement holds.

When Hector is 79, twelve years have passed. Then, the eldest daughter is 49, which is not a prime number thus this case fails.

When Hector is 83, sixteen years have passed, so Lupe is 77 which is not prime. This case fails too.

Finally, when Hector is 89, 22 years have passed. Lupe is 83, the daughters are 59 and 53 resp; the grandson is 29. All of these are primes, so the statement is true.

3 0

3 years ago