the dye dilution method is used to measure cardiac output with 7 mg of dye. the dye concentrations, in mg/l, are modeled by c(t)

The y-intercept of the equation of line  y = (7/9)x + 2/3 is 2/3.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question;

y = 7/9 x + 2/3

Simplify the right hand side

y = (7/9)x + 2/3

Using the slope-intercept form, the y-intercept is 2/3.

Therefore, the y-intercept in point form is (0,2/3).

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Complete question is;

The decibel level of sound is 50 dB greater on a busy street than in a quiet room where the intensity of sound is 10^-10 watt/m2. The level of sound in the quiet room is (10,20,100) dB, and the intensity of sound in the busy street is (10^-1, 10^-5, 10^-10) watt/m2.

Use the formula , β = 10log I/I 0 where β is the sound level in decibels, I is the intensity of sound you are measuring, and Io is the smallest sound intensity that can be heard by the human ear (roughly equal to 1 x 10^-12 watts/m2).

Answer:

A) The level of sound in the quiet room will be 20 dB

B) The intensity of sound in the busy street is 10⁻⁵ W·m⁻²

Step-by-step explanation:

Formula given is; β = 10log(I/I₀)

(a) For Quiet room:

We are given;

I = 10⁻¹⁰ W·m⁻²

I₀ = 1 × 10⁻¹² W·m⁻²

Plugging these values into the given equation, we have;

β = 10log[(10⁻¹⁰/(1 × 10⁻¹²)]

β = 10log(10²)

β = 10 × 2 = 20 dB

Thus, the level of sound in the quiet room will be 20 dB.

(b) For the Street;

We are given;

β(street) - β(room) = 50 dB

Now, let's rewrite the given intensity level equation;

β = 10logI - 10 logI₀

Now, Let the intensity level for the room be β₁ and let the intensity level for the road be β₂. Thus;

β₁ = 10logI₁ - 10log I₀ - - - - (eq 1)

β₂ = 10logI₂ - 10logI₀ - - - - (eq 2)

Subtract eq 1 from eq 2 to give;

β₂ - β₁ = 10logI₂ - 10logI₁

50 = 10logI₂ - 10log(10⁻¹⁰)

Divide each term by 10 to give:

5 = logI₂ - log(10⁻¹⁰)

5 = logI₂ - (-10)

5 = logI₂ + 10

Subtract 10 from each side to give;

-5 = logI₂

Taking the antilog of both sides to give;

I₂ = 10⁻⁵ W·m⁻²

Thus, the intensity of sound in the busy street is 10⁻⁵ W·m⁻².

Answer:

10⁻⁵ W·m⁻² THE ANSWER IS CORRECT

Step-by-step explanation:

Answer:

Solution given:

-7=12x-16

add both side by 16

16-7=12x-16+16

subtract like terms

9=12x

dividing both side by 12

9/12=12x/12

x=9/12

reduce fraction

x=\(\frac{3*3}{4*3}\)

x=¾

Answer: x=23/12 Is the answer

Step-by-step explanation:

Add 16 to both sides of the equation

17=12x-6

7+16=12x-16+16

Simplify

23=12x

Divide both sides of the equation by the same term

23=12x

23/12= 12x/12

Simplify

x=23/12

Solution

x=23/12

Answer: $22.50

Step-by-step explanation

In this case, x is what the original number was in case you didn’t know.

x - (x * 20/100) = 18

x -0.2x=18

0.8x=18

18/0.8=x

X = 22.5

Answer:

The surface area is 31.85 in.

Step-by-step explanation:

Tiffany gets 4 minutes of talk time on her cell phone per dollar cost.

If someone gets ' T ' minutes of talk time for the cost $ D so the rate of getting talk time per dollar is given by = T / D.

Given that the Tiffany pays a sum of $ 40 for talking 160 minutes on her cell phone.

So for $ 40 Tiffany gets the talk time of 160 minutes on her cell phone.

For $ 1 Tiffany gets the talk time of = 160 / 40 = 16 / 4 = 4 minutes on her cell phone.

Hence, Tiffany gets 4 minutes of talk time on her cell phone per dollar cost.

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Yes that is correct

Kugvuykvyukykvuuyvkkyvu

Answer:

76%

Step-by-step explanation:

At Bernard's Hats, there are 19 baseball caps and 6 other hats. What percentage of the hats are baseball caps?

total hats = 19 + 6

total hats = 25

baseball caps are: 19/25

19/25 = 0.76

0.76 = 76%

Answer:

-0.00572

Step-by-step explanation:

0.572 143/250 57.2%

then divide:)

Answer:

289 in^2

Step-by-step explanation:

1. Find side of the small square: (DG=a)

64= a^2

a= 8

2. Find hypotenuse of triangle being formed: (OG=c and DO=b)

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(8^{2}\) + \(15^{2}\) = \(c^{2}\)

c= 17

3. Find area of square:

\(c^{2}\)= A

(17)*(17)= 289 in^2

The area of the shaded square when the DOG is a right triangle formed by the placement of 3 squares so it should be 289 \(in^2\).

Find we have to determine the side of the small square i.e. (DG=a)

Now

64= \(a^2\)

So,

a= 8

Now find the hypothenuse

\(8^2 + 15^2 = c^2\)

c = 17

Now the area should be like

= (17) (17)

= 289 \(in^2\).

Hence, The area of the shaded square when the DOG is a right triangle formed by the placement of 3 squares so it should be 289 \(in^2\).

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we need to multiply this number by 100 to get the  as a percentage:

0.1806 * 100 = 18.06%

The probability of choosing a senior can be calculated using the formula:

P(senior) = (102/562) * 100

P(senior) = 18.06%

This means that there is an 18.06% chance of choosing a senior if a student is randomly selected from the school.

First, we need to calculate the total number of students in the school by adding together the number of students in each class:

Total = 165 + 145 + 114 + 102 = 562

Next, we need to calculate the probability of choosing a senior by taking the number of seniors enrolled in the school (102) and dividing it by the total number of students in the school (562).

102/562 = 0.1806

Finally, we need to multiply this number by 100 to get the probability as a percentage:

0.1806 * 100 = 18.06%

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(a) To find the derivative of g(x) = 3x * (u² - 1) / (u² + 1), where u = 3x, we can use the chain rule.

Let's differentiate each part separately:

d/dx (3x) = 3 (derivative of 3x with respect to x)

d/dx (u² - 1) = 2u * du/dx  (applying chain rule: derivative of u² with respect to u times the derivative of u with respect to x)

Now, substitute u = 3x and du/dx = 3:

d/dx (g(x)) = 3 * (2u * 3) / (u² + 1)

           = 9u / (u² + 1)

           = 9(3x) / ((3x)² + 1)

           = 27x / (9x² + 1)

Therefore, the derivative of g(x) is 27x / (9x² + 1).

(b) To find the derivative of g(x) = 1 - 2x^3, we differentiate each term separately:

d/dx (1) = 0  (derivative of a constant is zero)

d/dx (-2x^3) = -6x^2  (power rule: bring down the exponent and multiply by the coefficient)

The derivative of g(x) is -6x^2.

(c) To find the derivative of h(x) = √(2 + 3x) * (1 + 2x), we can use the product rule.

Let's differentiate each part separately:

d/dx (√(2 + 3x)) = (1/2)(2 + 3x)^(-1/2) * (3)  (derivative of the square root function)

d/dx (1 + 2x) = 2  (derivative of a linear function)

Now, apply the product rule:

d/dx (h(x)) = (√(2 + 3x) * 2) + ((1 + 2x) * (1/2)(2 + 3x)^(-1/2) * 3)

Simplifying, we get:

d/dx (h(x)) = 2√(2 + 3x) + 3(1 + 2x) / (2 + 3x)^(1/2)

Therefore, the derivative of h(x) is 2√(2 + 3x) + 3(1 + 2x) / (2 + 3x)^(1/2).

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The range of the function is y ≥ -2 so , correct option is option c

Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.

The graph of the range of the given function is attached below .

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ANSWER :

55.5 ft

EXPLANATION :

Recall the cosine law :

where a and b are the sides of the triangle with an included angle C as the angle between them.

and c as the opposite side to that included angle.

From the problem, the two sides are a = 95 ft and b = 114 ft

The included angle between them is C = 29 degrees

and c is the distance between kites

Using the formula above :

Answer:

C

Step-by-step explanation:

x+x-1-1-1-1-1-1-1 = -x-x-x+1+1+1+1+1+1+1+1+1

2x-7 = -3x +9

5x - 7 = 9

5x = 16

x = 16/5

x= 3⅕

x= 3.2

Answer:

12 miles

Step-by-step explanation:

From the graph given :

Mike's travel :

School to Mall= 16 miles

Mall to Library = 30 miles

Total travel = 16 + 30 = 46 miles

Henry's travel :

From school to Library = Hypotenus :

Distance can be obtained using Pythagoras :

Hypotenus = √(opposite² + adjacent²)

Hypotenus = √(30² + 16²)

Hypotenus = √1156

Hypotenus = 34 miles

Difference in Distance covered :

(46 miles - 34 miles) = 12 miles

Answer:

○ \(\displaystyle x^2 + 4x + 13\)

Step-by-step explanation:

Sinse this expression is unfactourable with rational quantities, use the Quadratic Formula:

\(\displaystyle -B ± \frac{\sqrt{B^2 - 4AC}}{2A} = x\\ \\ -4 ± \frac{\sqrt{[-4]^2 - 4[1][13]}}{2[1]} = x \hookrightarrow -4 ± \frac{\sqrt{16 - 52}}{2} = x \hookrightarrow -4 ± \frac{\sqrt{-36}}{2} = x \hookrightarrow \frac{-4 ± 6i}{2} = x \\ \\ \boxed{-2 - 3i, -2 + 3i = x}\)

I am joyous to assist you at any time.

It appears to be a constant connection that the square matrix has n eigenvalues, where n is the dimensions (not dimensions as in Rank, but as in # of Column values) of the square matrix.

similar to: a 3x3 matrix square, which has 3 Eigenvalues and only permits eigenvalue decomposition in the event that the matrix is diagonasible.

I think it has to do with how mirror-reflective and inverse the dimensional features of the Matrix can be, and how its linear structure is strong enough to support a dimensional cube.

When it comes to interaction, eigenvalue decomposition can be used to systematically eliminate it.

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Answer: solve for x

x ∈ R, h = 0 and g = 0

Step-by-step explanation:

Answer:

b^2 - 4ac ==> what's inside the square root

The answer is the 2nd option

Step-by-step explanation:

b^2 - 4ac represents the number of roots in the quadratic equation. If

b^2 - 4ac>0, then there are 2 roots in the quadratic equation. If

b^2 - 4ac=0, then there is only 1 root. If b^2 - 4ac<0, then the square root of b^2 - 4ac would be invalid since the square root of a negative number has no real solution. Hence, if b^2 - 4ac<0, then there are no roots.

Answer:

The answer should be option B. b^2-4ac

Step-by-step explanation:

...

Answer:

z = 18,9

Step-by-step explanation:

\(6.6 = 3(z - 16.9) - - 0.6\)

\(6.6 = 3z - 50.7 - ( - 0.6)\)

\(6.6 = 3z - 50.7 + 0.6\)

\(6.6 = 3z - 50.1\)

\(6.6 - 3z = - 50.1\)

\( - 3z = - 50.1 - 6.6\)

\( - 3z = - 56.7\)

\(z = 18.9\)

The balance that will be on the company account after the refunds have been paid is -R1130

To calculate the balance on the company account after the refunds have been paid, we need to subtract the total amount refunded from the current balance of R2195,00.

The total amount refunded will be the product of the refund amount and the number of clients, which is:

5 x R665,00 = R3325,00

Therefore, the balance on the company account after the refunds have been paid will be:

R2195,00 - R3325,00 = -R1130,00

Note that the negative sign indicates that the company's account will be overdrawn by R1130,00 after the refunds have been paid.

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Answer:

x= 67

y=40

z=40

Step-by-step explanation:

 A=C        B=D

67=X    Y&?= Z&73

73+ x aka(67) = 140

180-140= y = 40

Answer:

it would cost 35 each I think

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

950

Step-by-step explanation:

A=P*(1/2)^(t/h)

Answer:

Although this makes for a lot of potential fun with formulas, mind experiments and arguments, the answer is plain.

Infinity is already everything so there is no more to it, infinity plus infinity would be still just infinity, which is btw infinite.

Answer:

infinity + infinity =  infinity

Step-by-step explanation:

Mark brainliest please :)