Evaluate at the given value: g(x)=1/7x-1, g^-1 (6)

The ending pressure group after the second dive is R.

According to the statement

We have given that the

The first dive is on a reef in 22 metres of water for 20 minutes and The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes.

And we have to find the pressure group after second dive.

So, For this purpose, we know that the

Recreational scuba diving (R) – this diving has prescribed limits, including a depth no greater than 130 fsw, using only compressed air, and never requiring a decompression stop.

From the above situation, we could note that there was a prescribed limit 18m/60ft of water with a bottom time of 30 minutes.

And due to its the ending pressure becomes R.

So, The ending pressure group after the second dive is R.

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Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

According to the question,

The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

Customary units and its equivalent  

1 Fluid ounce = 2 Tablespoons

1 Cup = 8 fluid ounces

1 Pint = 2 cups

1 Quart = 2 pints

1 Gallon = 4 quarts

Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

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The total weight of the bag that the salesman is carrying for selling a machine including some personal stuff is 13.9 Kg.

A fraction is a rational number that consists of a numerator and a denominator, used to represent a part of the whole thing.

It is given that,

A salesman is carrying a big bag for selling a machine.

Consider the weight of the machine = w

So,

The weight of his machine is three kilograms and half a machine. I.e.,

w = 3kg +w/2

⇒ w/2 = 3kg

∴ w = 6kg

Thus, the weight of the machine is 6 Kg.

So, the weight of the repair tool for the machine = a half kilogram and one-fourth of the machine

⇒ 1/2Kg + 1/4w

⇒ 1/2 + 6/4

⇒ 2 Kg

The personal stuff weighs - four kilograms minus a fourth of the weight of the machine.

⇒ 4Kg - w/4

⇒ 4 - 6/4

⇒ 2.5 Kg

He has some supplies that weigh two-fifth of the machine and personal stuff combined.

⇒ 2/5(w + 2.5)

⇒ 2/5 × 8.5

⇒ 3.4 Kg

Thus, the total weight of the bag = 6 Kg + 2 Kg + 2.5 Kg + 3.4Kg =  13.9Kg.

Therefore, the total weight of the salesman's bag is 13.9 Kg.

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The correct standard form of the equation of the parabola is:

[tex](x+3)^{2}[/tex]= 4(y - 3).

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.

For the given question,

Vertex of parabola is (-3,3)

Thus, the equation of the parabola is:

[tex](x-h)^{2}=4(y-k)[/tex]

[tex](x+3)^{2}[/tex]= 4(y-3)

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The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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The true statement about these graph is that: B. the graph of the original function (y = 8/5x + 4) is perpendicular to the graph of the new function (y =- 5/8x + 8).

A graph can be defined as a type of chart that's commonly used to for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate, which are typically known as the x-axis and y-axis respectively.

Mathematically, the standard form of the equation of a straight line on a graph is given by;

y = mx + c

Where:

In Mathematics, the condition for perpendicularity of two (2) lines is as follows:

m₁ × m₂ = -1

8/5 × (-5/8) = -1

Based on the graph (see attachment) of the original function and new function, we can infer and logically deduce that the true statement about their graph is that the graph of the original function (y = 8/5x + 4) is perpendicular to the graph of the new function (y =- 5/8x + 8).

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Complete Question:

Suppose the following function is graphed. y = 8/5x + 4 On the same grid, a new function is graphed. The new function is represented by the following equation. y =- 5/8x + 8. Which of the following statements about these graphs is true?

A. The graphs intersect at (0,8).

B. The graph of the original function is perpendicular to the graph of the new function.

C. The graph of the original function is parallel to the graph of the new function.

D. The graphs intersect at (0,4).

The complete table is

x     y

-1     -2

0     3

1     8

2    13

The function is given as:

y = 5x + 3

On the table, we have

x = -1, 0, 1 and 2

Using the above values, we have:

y = 5(-1) + 3 = -2

y = 5(0) + 3 = 3

y = 5(1) + 3 = 8

y = 5(2) + 3 = 13

So, the complete table is

x     y

-1     -2

0     3

1     8

2    13

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The mean calculated shows that the Chemistry score will be 87.

From the information given, the total scores will be:

= 84 × 4

= 336

The addition of the scores given will be:

= 72 + 85 + 92

= 249

The Chemistry score will be:

= 336 - 249

= 87

Complete question:

If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.

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The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system

The above is represented in the (a) part of this solution

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

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[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]

[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]

[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]

[tex]\\ \rm\dashrightarrow B=10(5)[/tex]

[tex]\\ \rm\dashrightarrow B=50dB[/tex]

Answer:

50 Db

Step-by-step explanation:

Given:

[tex]L=10 \log \dfrac{I}{I_0}[/tex]

[tex]I_0=10^{-12}[/tex]

where:

To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:

[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies L=10 \log 10^{-7-(-12)[/tex]

[tex]\implies L=10 \log 10^5[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies L=5 \cdot 10 \log 10[/tex]

[tex]\implies L=50 \log 10[/tex]

As the given log does not have a specified base, assume the base is 10.

[tex]\implies L=50 \log_{10} 10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies L=50 (1)[/tex]

[tex]\implies L=50\:\:\sf Db[/tex]

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The area of the minor sector DFE is gotten as; D: 66.1 square cm

Formula for area of sector is;

A = (θ/360) * πr²

We are given;

minor angle; θ = 100°

radius; r = 8.7 cm

Thus;

A =  (100/360) * π(8.7²)

A = 66.1 square cm

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Answer:

Point Form: (- 1/4, 5/4)

Equation Form: x = - 1/4, y  = 5/4

Step-by-step explanation:

Answer: -8 points

Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.

42-50= -8, which is how you get the answer!

Answer:

-8

Step-by-step explanation:

42-50 is the same as 50-42, except the answer is negative

The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;

B. f(x) is an even function so both ends of the graph go in the same

direction

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Now, we are given the polynomial;

f(x) = -4x⁶ + 6x² - 52

Let us first test if the polynomial is even;

f(1) = -4(1)⁶ + 6(1)² - 52

f(1) = -50

Similarly;

f(-1) = -4(-1)⁶ + 6(-1)² - 52

f(-1) = -50

Since f(1) = f(-1), we can say that both ends of the graph go in opposite

directions.

Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.

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Answer:

the answer is b 455

Step-by-step explanation:

15/(4×12)=455

The angle bisector theorems is proved below.

It should be noted that the angle bisector theorem simply states that an angle bisector of a triangle divides the opposite side into two segments which are proportional to the other sides of the triangle.

The way to proof the theorem is illustrated:

Draw a ray CX parallel to AD and then extend BA to intersect this ray at E.

In triangle CBE, DA is parallel to CE.

BD/DC == BA/AE ......... i

Now we want to prove that AE = AC

Since DA is parallel to CE, we have:

DAB = CEA (corresponding angles) ....... ii

DAC = ACE (alternate interior angles) ...... iii

Since AD is the bisector of BAC, we've DAB = DAC.

From the above, ACE makes and isosceles triangle and since the opposite sides are equal, we've AC = CE.

Substitute AC for AE in equation i

BD/DC = BA/AC

Therefore, the angle bisector theorems is proved.

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Answer:

x = 25°

Step-by-step explanation:

Hello!

25° and x° are vertical angles, therefore they are equal to each other.

Vertical angles are angles formed by two intersecting lines that are non-adjacent.

The angle to the right of 80° would be 55°, because the sum of angles on a line is 180°.

Angle x would be 25° because the other straight line contains angles 80°, 50° and x°.

Answer: dfghj

Step-by-step explanation: xcfvghj

Answer: It's D

Step-by-step explanation:

Right on edge 2022

Answer:

1161 confirmed cases

Step-by-step explanation:

In 2000 the number of cases was 86

Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.

So, we must multiply 13.5 and 86 to get the amount of cases in 2019.

13.5*86 = 1161 confirmed cases in 2019

Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

-3x² + 150x - 1800 = 0.

The coefficients are a = -3, b = 150, c = -1800, hence:

He needs to charge $30 for a profit of $600.

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Answer:

[tex]\frac{13\pi }{9}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

degrees × [tex]\frac{\pi }{180}[/tex]

= 260 × [tex]\frac{\pi }{180}[/tex]

= 26 × [tex]\frac{\pi }{18}[/tex]

= 13 × [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{13\pi }{9}[/tex]

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

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