A chipmunk population is experiencing exponential growth with a population growth rate of 265 individuals/year, and a per capita rate of increase of 0.15. How many chipmunks are currently in this population

Answer:

The dimensions of the square, that will result in a box of maximum volume is a square with side length of approximately 1.585 inches

Step-by-step explanation:

The  given dimension of the steel sheet are;

The width = 8.5 inches

The length = 11 inches

Let 'x' represent the side length of the squares cut out, we have;

The length of the box formed, l = 11 - 2·x

The width of the box formed, w = 8.5 - 2·x

The height of the box, h = x

The volume of the box, V = (11 - 2·x) × (8.5 - 2·x) × (x) = 4·x³ - 39·x² + 93.5·x

The maximum or minimum volume is found from dV/dx = 0 at max. or min.

dV/dx = d(4·x³ - 39·x² + 93.5·x)/dx = 12·x² - 78·x + 93.5 = 0

Which gives;

x = (78 ± √((-78)² - 4×12×93.5))/(2 ×12)

x = 4.915 or 1.585

When x = 4.915, V = 4 × 4.915³ - 39 × 4.915² + 93.5 × 4.915 = -7.65

When x = 1.585, V = 4 × 1.585³ - 39 × 1.585² + 93.5 × 1.585 = 66.15

Therefore, the local maximum occurs at x ≈ 1.585

Therefore, the dimensions of the square, 'x' that will result in a box of maximum volume is x ≈ 1.585 inches.

Probability that both Rebecka and Aaron select poodles is  4/81

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

A pet store has 9 puppies.

includes 2 poodles, 5 terriers, and 2 retrievers.

Rebecka selects one puppy at random.

The probability of selection one pet from store is 1/9

After Rebecka selects one puppy at random pet store replaces the puppy with a puppy of the same breede. Now store has same number of pets.

Aaron chooses a puppy at random.

The probability of Aaron selecting a pet is 1/9.

As they both selects a poodle,

Rebecka : Probability of selection one poodle from store is 2/9

Aaron: Probability of selection one poodle from store is 2/9

The probability that both Rebecka and Aaron select poodles is 2/9 × 2/9 = 4/81

Hence probability that both Rebecka and Aaron select poodles is  4/81

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The inequality equation is x ≥ ( by - c - d ) / a

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

by - d ≤ ax + c    be equation (1)

On simplifying the equation , we get

Subtracting c on both sides of the equation , we get

by - d - c ≤ ax

And , ax ≥ by - d - c

Divide by a on both sides of the equation , we get

x ≥ ( by - c - d ) / 2

Hence , the inequality is x ≥ ( by - c - d ) / a

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Answers:   49,   1,   49

Those values go in the blanks from left to right

=====================================================

Explanation:

The rule we use is x^(-k) = 1/(x^k)

That means if we're evaluating something like 7^(-1), then it's the same as 1/(7^1) = 1/7 which explains how x = -1 leads to y = 1/7.

Similarly, 7^(-2) = 1/(7^2) = 1/49 is the y value when x = -2. So you'll type 49 into the first box to fill in that missing denominator.

Raising any nonzero value to the zeroth power leads to 1. That rule is x^0 = 1 where x can be anything you want but it can't be zero. Therefore 7^0 = 1 goes in the second box.

Lastly, 7^2 = 7*7 = 49 will go in the third box.

Answer:

55 inches

Step-by-step explanation:

4 feet x 12 inches per foot = 48 inches + 7 inches = 55 inches

The required value of the given expression is 6x3 - 13x2 - 13x + 20. Option B is correct.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,
= (3x² + x - 4)(2x - 5)
= [6x³-13x² - 13z + 20]

Thus, the required value of the given expression is 6x3 - 13x2 - 13x + 20. Option B is correct.

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Answer:

5 + 2√6 or 9.898979

Step-by-step explanation:

(√3 + √2) (√3 + √2)

= 5 + 2√6

decimal = 9.898979

Answer:

I’ll put a picture because I can’t like write down the answer…. So yeah.

Step-by-step explanation:

1) expand expression: (sqrt3 + sqrt2)^2

Then calculate: 3 + 2sqrt6 + 2

Andddd: 5 + 2sqrt6

* sqrt: square root

I hope this helps! Good luck :)

Answer:

8 quarts, in 2 gallons

Step-by-step explanation:

Answer: x^2 (the ^ represents that the next number is an exponent)

Step-by-step explanation:

Any number squared (to the power of 2) is just itself multiplied by itself. Remember, multiplication is repeated addition and exponents are repeated multiplication.

Answer:

(0, -8)

Step-by-step explanation:

Answer:

ok so the answer is 28² - 21 to the power of 4

Step-by-step explanation:

Answer:

$10,400

Step-by-step explanation:

Figure 1

Since the diameter is 8, this cuts in half to the radius of r = 4. Plug the given values into the cone volume formula below

V = (1/3)*pi*r^2*h

V = (1/3)*pi*(4)^2*4

V = (64/3)pi  ..... exact volume in terms of pi

V = (64/3)*3.14

V = 66.98667 .... approximate volume when using pi = 3.14

========================================================

Figure 2

V = volume of cylinder

V = pi*r^2*h

V = pi*4^2*4

V = 64pi ..... exact volume

V = 64*3.14

V = 200.96 .... approximate volume when using pi = 3.14

========================================================

Figure 3

b and h* are dimensions along the bottom face, aka floor

h is the height or vertical dimension of the 3D room

V = volume of rectangular prism = volume of 3D room

V = length*width*height

V = (b)(h*)(h)

V = (32)(12)(4)

V = 1536 is the exact volume

There is no approximate volume for this figure because the result above is an integer.

========================================================

Combining the figures

Adding up the volumes for figures 1 through 3 gets us

(64/3)pi + 64pi + 1536 = (256/3)pi + 1536

The exact total volume in terms of pi is (256/3)pi + 1536

If we used pi = 3.14, then it leads to

(256/3)pi + 1536 = (256/3)*3.14 + 1536 = 1803.94667

The approximate total volume of all three figures combined is roughly 1803.94667 cubic units

Answer:

yes

Step-by-step explanation:

yes

Answer:

4/5

Step-by-step explanation:

5cosA=4

divide both sides by 5

cosA=4/5

Answer:

1/3 chance she will chose a Mystery Book.

Step-by-step explanation:

I hope This helps?

Total= 18

mystery=6

6/18= 1/3

Answer:

the answer is 1/3 or 6 out of 18

Answer:

its basically the relationship between sets of numbers. the anwser is D if the line on the graph is curved it is a function and if the number repeat on the x value it is a function.

-by-step explanation:

Answer:

1

Step-by-step explanation:

depends if you have a table , to pick the right one always choose a one that pass more through and between the points and the one that is straight

Step-by-step explanation:

a)

[tex]\sin^{2}x + \cos^{2}x = 1[/tex]

Dividing both sides by sin^2x, we get

[tex]1 + \frac{\cos^{2}x }{ \sin^{2}x} = \frac{1}{\sin^{2}x } [/tex]

The 2nd term on the LHS is simply cot^2x and the RHS is simply csc^2x

[tex]1 + \cot^{2}x = \csc^{2}x[/tex]

b)

[tex]2 \sin x = 1[/tex]

[tex] \sin x = \frac{1}{2} [/tex]

[tex]x = \sin^{ - 1} (\frac{1}{2}) = \frac{\pi}{6} [/tex]

You can also graph it to arrive at the solution.

Did u get help

On you question?

Answer:

Look at the image.

Step-by-step explanation:

(36 ÷ 4) - (36 ÷ 9)

9 - 4

5

(8 × 3) - 12 = 12

24 - 12

12

Answer:

1.) Set the data set in the ascending order

2.) Start cancelling out numbers each side, like if u cancel out the first number, then cancel out the last as well.

3.) Keep doing the step 2 until u reach the middle most number.

4.) Sometimes there are 2 middle numbers left, in that case find their average (add both numbers together and divide the sum by 2) which would be ur middle most number.

Hope this helps!

Answer:

The answer is "A mean of 0 and a standard deviation of 1".

Step-by-step explanation:

The standard answer of its following formula is calculated by:

[tex]\to z=\frac{X-\mu}{\sigma}[/tex]

Its standard score relates to the sampling distribution with the normal distribution average standard variation of 0 and 1, correspondingly. The mean for a standard scoring is 0, and the normal deviation is 1. that's why the mean=0, standard deviation=1.

Answer:

D) Identifies the transaction and is located at the top right corner of the check

Step-by-step explanation:

The check number on a check is the number located at the top right corner of the check, and it can also be found at the bottom of the check, located in lower right corner after the routing number and the account number

The check number aids in the tracking and identifying bank transactions such as to identify checks that the bank has processed and to know outstanding checks that are yet to be processed.

The check number also aids in balancing of the checkbook.

Therefore, the check number on a check identifies the transactions and is located at the top right corner of the check.

Answer:

Its 13

Step-by-step explanation:

Good luck