The depth in feet, D. of a scuba diver can be modeled by the function D(x) = -x + 12x + 4. where x is the number of seconds spent diving.
What is the number of seconds spent diving when the scuba diver reaches their maximum depth?
Respond in the space provided

Answer:

L= 12

Step-by-step explanation:

area= L×B

108= 9×L

108= 9L

Divide both sides by 9

108/9= 9L/9

L= 12

Answer:

8:20 or if you want it simplified 2:5

Step-by-step explanation:

Using an exponential function, it is found that the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868}[/tex]

Which means that approximately 16.22 mg remain.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the equation is:

[tex]f(h) = m(0.5)^h[/tex]

We work with a 50 mg Cobalt-60 sample, hence m = 60, and considering a half-life of 5.3 years, in 10 years we have h = 10/5.3 = 1.8868. Hence the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868} = 16.22[/tex]

Approximately 16.22 mg remain.

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Answer:

10. s = 1.50x

11. s = 28x + 5

Step-by-step explanation:

10. s (money); so multiply x (the amount of pencils) by the price which is 1.50. Which is equal to 112.50.

11. s (money); multiple x (the amount of shoes) by the price, 28, which equals 84. Then add 5 for the shipping. This equals 89.

This is closed under addition because the sum of the polynomial produces another polynomial.

A polynomial is an expression that involves the addition, subtraction and multiplication of variables.

Polynomials will be closed under an operation if the operation produces another polynomial.

(3x⁴ + 5x - 7) + (2x - (2x)² + 4x - 1) + [(-8x)⁻² - (3x)³ + 7]

= 3x⁴ - 27x³ - 4x² + 9x - 1 + (-8x)⁻²

This is closed under addition because the sum of the polynomial produces another polynomial.

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Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:

[tex]A(t) = 64(0.5)^t[/tex]

32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:

[tex]A(4) = 64(0.5)^4 = 4[/tex]

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The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

[tex]V(n) = n * 1[/tex]

This gives

[tex]V(n) = n[/tex]

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27.

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27

Answer:

Step-by-step explanation:

Answer:

  Tina is 12 and MIna is 15

Step-by-step explanation:

Age problems can often be worked by backing out any of the changes in age so as to match the conditions specified at a given time.

Here, the ratio is given for now. The sum of the two ages is 6 years less now than it will be after 3 years, so is now 33 -6 = 27.

The sum of ratio units now is 4+5 = 9, so each ratio unit stands for 27/9 = 3 years of age. The ratio of current ages is ...

  3×4 : 3×5 = 12 : 15

Tina is 12 and MIna is 15.

_____

Check

After 3 years, their ages will be 15 and 18, which will total 33.

Answer: 47.28 miles

Step-by-step explanation: 5.91 times 8= 47.28

Answer:

Here I graphed it for you.

Step-by-step explanation:

Answer:

the median is 55.6

Step-by-step explanation:

The average annual temperatures (°F) from 1991 to 2000 for Kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

We have to evaluate the measures of center.

Firstly, we will calculate the mean.

Mean = (Sum of all the observations)/ (Total number of observations)

Mean =  

=

= 55.62

Now, we will calculate mode.

Mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.

Consider the data 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

Mode = 55.6

Now, we will calculate the median.

Firstly, we will arrange in the ascending order.

52.2, 54.4, 54.4,55.1 ,55.6, 55.6, 55.7, 57.3, 57.5, 58.3

Since there are 10 terms.

Median = th observation

Median = 5th observation.

Since, the 5th observation is 55.6.

Therefore, the median is 55.6

Answer:

C. 15 cm

Step-by-step explanation:

The formula to find the area of a circle is: π × r²

But since we need to solve for the radius, we use the formula:

[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]

r = radius

A = area

π = 3.14

Now we substitute the information given in the text into the equation

[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]

Substitute values into the equation

[tex]r = \sqrt{ \dfrac{ 706.5 }{ 3.14 } \phantom{\tiny{!}}}[/tex]

Divide 706.5 by 3.14

[tex]r = \sqrt{ 225 }[/tex]

Take the square root of 225

[tex]r = {15 }[/tex]

So, the radius of the pie is 15 cm

Answer:

1

Step-by-step explanation:

definite integral from 0-2 of root x dx

root x = x^½

integral of x^½ = ⅔x^(3/2)

Sales tax amount:-

Price:-

Answer:

$17,280

Step-by-step explanation:

Given

Solving :

Answer:

$26.42

Step-by-step explanation:

P = 30 * 0.82 * 1.074 = 26.42

Equation in slope intercept form

Now

Answer:

diameter is half the value of circumference 15/2 =7.5 diameter

Answer:

19.6

Step-by-step explanation

= Sum of terms / number of terms

= ( 20 + 19 +18+ 20 +19 +22 ) / 5

= 19.6

Answer:3 or 3/10

Step-by-step explanation:

Answer:

10+5 =15 thanks for asking

Answer:

Question (a)

Given equation:

[tex]8^{2x} = 32^{x+3}[/tex]

8 can be written as [tex]2^3[/tex]

32 can be written as [tex]2^5[/tex]

Therefore, we can rewrite the equation with base 2:

[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]

------------------------------------------------------------------------------

Question (b)

To solve:

[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]

Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]

[tex]\implies 2^{6x} = 2^{5x+15}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :

[tex]\implies 6x = 5x+15[/tex]

Subtract [tex]5x[/tex] from both sides:

[tex]\implies x = 15[/tex]

The inputs of the function are -8, 2, 4, and 6.

The input is the number that we put into the given function to get the output function.

x  and y of the function are given below

X    –8      2     4    6

f(x)  –6    –3     1     5  

From the given table, the inputs are given as the set of x values.

outputs are given as the set of y values. here, x is the input value that gives the output f(x).

Since x represents the input values and y represents the output values.

So, inputs of the function are -8, 2, 4 and 6

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Answer:

C. work backwards

Step-by-step explanation:

I did it

Answer:

D

Step-by-step explanation:

I have done this before
Top row units is 8 i then multiplied both sides so 5*2 which = 10 then multiplied 8*10 to get 80

Answer:

80 square units (D)

Step-by-step explanation:

Base is 16 units, height is 5 units. 16 * 5 = 80

Step-by-step explanation:

I don't understand this question

come again