What is the minute ventilation of an average adult male at rest breathing at a rate of 10 breaths per minute?

Answer:

[tex]C(h)=\$30+xh[/tex]

Step-by-step explanation:

Let

C-----> the cost of having a plumber spend h hours at your house

h----> the number of hours

x----> the cost per hour of labor

we know that

The linear equation that represent the cost C is equal to

[tex]C(h)=\$30+xh[/tex]

In this linear equation in the slope-intercept form (y=mx+b)

the slope is equal to [tex]m=x\frac{\$}{hour}[/tex]

the y-intercept b is equal to [tex]b=\$30[/tex] ---> charge for coming to the house

Answer:

C = 30 + x * h

Step-by-step explanation:

The total cost for the plumber is his initial fee plus the number of hours times the cost per hour

C = 30 + x * h

Answer:

1/4.

Step-by-step explanation:

I am assuming that there are 3 even and 3 odd tiles in each bag.

Probability( drawing an even tile form one bag) = 3/6 = 1/2.

The probability  of drawing  an even from the first and an even from the second = 1/2 * 1/2 = 1/4 (answer).

The individual probabilities  are multiplied because the 2 events are independent.

Answer:

9/36

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:Let

x------->the probability of its complement

we know that

The Complement Rule states that the sum of the probabilities of an event and its complement must equal

so

in this problem

2/7 + x = 1

solve for x

Adds 1- 2/7  both sides

x= 1 - 2/7

x= 5/7

Answer:

5/7

Step-by-step explanation:

Answer:

An Acute triangle

Step-by-step explanation:

It is an acute triangle, because the following characterization holds:

In this case,

[tex]6^2=36<5^2+4^2=25+16=41[/tex]

Answer:

-7

Step-by-step explanation:

7 and -7 squared both equal 49

Answer:

[tex]\large\boxed{B.\ a^2+2ah+h^2+3a+3h+5}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+3x+5\\\\f(a+h)\to\text{substitute}\ x=a+h\ \text{to the equation:}\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{Use}\ (x+y)^2=x^2+2xy+y^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]

Answer:

the slope-intercept form:

y = 5x - 9

Step-by-step explanation:

y = 5x - 5, this line has slope = 5

parallel line, slope is the same so slope of the parallel = 5

equation

y - 6 = 5(x - 3)

y - 6 = 5x - 15

y = 5x - 9   <------the slope-intercept form

Answer: [tex]y=5x-9[/tex]

Step-by-step explanation:

The slope-intercept form of a equation of the line is:

[tex]y=mx+b[/tex]

Where m is the slope and b the y-intercept-

If the lines are parallel then they have the same slope:

m=5

Find b substitutin the point and the slope into the equation and solving for b:

[tex]6=3*5+b\\b=-9[/tex]

Then the equation is:

[tex]y=5x-9[/tex]

Answer:

Final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].

Step-by-step explanation:

Given equation is [tex]3\cdot\sec\left(x\right)-2=1[/tex]

Now we need to find the solution of  [tex]3\cdot\sec\left(x\right)-2=1[/tex] in given interval [tex][0, 2\pi ][/tex].

[tex]3\cdot\sec\left(x\right)-2=1[/tex]

[tex]3\cdot\sec\left(x\right)=1+2[/tex]

[tex]3\cdot\sec\left(x\right)=3[/tex]

[tex]\frac{3\cdot\sec\left(x\right)}{3}=\frac{3}{3}[/tex]

[tex]\sec\left(x\right)=1[/tex]

which gives [tex]x=0[/tex] and [tex]x=2\pi[/tex] in the given interval.

Hence final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].

Answer:

x  = 0 and x = 2π

Step-by-step explanation:

We have given the equation.

3sec x -2 = 1

We have to solve it  interval [0,2pi].

3sec x -2 = 1

3secx = 1+2

3secx = 3

secx = 1

x= sec⁻¹(1)

x  = 0 and x = 2π is the answer in this interval.

Answer:

$41.50

Step-by-step explanation:

He would have to give her $41.50 in order for them to have an equal amount of money, which would be $51.50.

Answer:

He should give her $41.50

Step-by-step explanation:

Answer:

[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]

Step-by-step explanation:

Let's start by breaking down each of the radicals:

[tex]\sqrt[3]{16x^3y}[/tex]

Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of [tex]x^3[/tex], and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:

[tex]\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}[/tex]

We can apply this same technique of "extracting cubes" to the second term:

[tex]\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}[/tex]

Replacing those two expressions in the parentheses leaves us with this monster:

[tex]2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})[/tex]

What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:

[tex]4, \sqrt[3]{2} , x[/tex]

We can factor those out to give us a final, simplified expression:

[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]

Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.

Answer:

Step-by-step explanation:

(a) The Extreme Value Theorem.

(b)  We would differentiate the function and equate this to zero. The zeroes of the function will give us the values of the maxima / minima and we can find find the absolute maxima/minima from the results. Note we might have  multiple relative maxima/ minima  but only one absolute maximum and one absolute minimum.

Final answer:

The Extreme Value Theorem guarantees that a continuous function on a closed interval has an absolute maximum and minimum. To find these, one calculates the derivative to find critical points, analyzes the derivative's sign around these points, and evaluates the function at the critical points and the interval's endpoints.

Explanation:

Extreme Value Theorem and Finding Maximum and Minimum Values

The theorem that guarantees the existence of both an absolute maximum and minimum value for a continuous function defined on a closed interval a, b is known as the Extreme Value Theorem. This theorem plays a crucial role in calculus and mathematical analysis and is fundamental in understanding the behavior of continuous functions on closed intervals.

To find these maximum and minimum values, one would typically follow these steps:

Calculate f'(x), the derivative of the function f(x), to find the critical points.

Analyze the sign of f'(x) around the critical points to determine if they are local minima, local maxima, or saddle points.

Evaluate the function f(x) at each critical point as well as the endpoints of the interval [a, b] to determine the absolute extrema.

Moreover, if a function satisfies the criteria of being continuous on [a, b] and differentiable on (a, b), then by a related theorem called the Mean Value Theorem, there exists at least one c in (a, b) where f'(c) = 0.

These methods form the standard procedure for finding the extremal values that a continuous function may possess on a closed interval.

Answer: option b.

Step-by-step explanation:

To solve this exercise you must keep on mind the identities shown below:

1) [tex]sec\theta=\frac{1}{cos\theta}[/tex]

2) [tex]csc\theta=\frac{1}{sin\theta}[/tex]

3) [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]

Therefore, to rewrite [tex]\frac{sec\theta}{csc\theta}=1[/tex] you must substitute identities and simplify the expression, as following:

[tex]\frac{sec\theta}{csc\theta}=1\\\\\frac{\frac{1}{cos\theta}}{\frac{1}{sin\theta}}=1\\\\\frac{sin\theta}{cos\theta}=1\\\\tan\theta=1[/tex]

Therefore, as you can see, the answer is the option b.

Answer:

Step-by-step explanation: B

Answer: 9321 votes

Step-by-step explanation:

1- You can express the ratio as following:

[tex]5:8[/tex] or [tex]\frac{5}{8}[/tex]

2- Let's call the number of  no votes "N"

3- Therefore, if there were 3585 yes votes, then you can write the following expression to calculate the number of  no votes:

[tex]\frac{5}{8}=\frac{3585}{N}\\\\N=\frac{3585*8}{5}\\\\N=5736[/tex]

4- Then, the total number of votes is:

[tex]t=3585votes+5736votes=9321votes[/tex]

Answer:

9321

Step-by-step explanation:

We can simply make a ratio (fraction) to solve this. Let total number of  NO votes be N. Shown below is the ratio:

[tex]\frac{YesVotes}{NoVotes}=\frac{5}{8}=\frac{3585}{N}[/tex]

Now we can cross multiply and solve for N:

[tex]\frac{5}{8}=\frac{3585}{N}\\5N=8*3585\\5N=28,680\\N=\frac{28680}{5}=5736[/tex]

Hence, number of NO votes is 5736.

To get TOTAL number of votes, we add number of yes votes (3585) to that of number of no votes (5736).

Total votes = 3585 + 5736 = 9321

Answer:

See attached picture.

Step-by-step explanation:

Graph the function as (x,y) points.

(-3,5)

(4,6)

(6,-9)

(9,-10)

These are graphed in black on the picture.

To graph the inverse, switch the points from (x,y) to (y,x).

(5,-3)

(6,4)

(-9,6)

(-10,9)

These are graphed in red on the picture.

Answer:

105

Step-by-step explanation:

to get this you must first divide 17.5 by 2.5 to see how many times to multiply 15 by 2.5

sorry if it does not make scence

7 * 0.055 = 0.385  

631.40 / 0.385 = $1,640

Answer:

a. No the particles will never collide.

b. The second particle is moving faster.

Step-by-step explanation:

We can tell they never collide based on the fact that they will never have the same two points. We can tell this because there is only one time in which they will have the same x value. To find this amount of time, set the two x values equal to each other and solve for t.

5t - 5 = 4t

-5 = -t

5 = t

So we know the x value will only be the same at 5 seconds. Now we can input that value and see if the y values are the same.

2t + 6 = t^2 - 2t - 1

2(5) + 6 = 5^2 - 2(5) - 1

10 + 6 = 25 - 10 - 1

16 = 14 (FALSE)

Therefore they do not collide.

For the second part of the question, we know that the second one is moving faster based on the fact that there is a squared value in the y formula. This shows that it is moving at an exponential rate, which always changes faster than a linear rate.

Particle A and particle B never collide.

The value of k where the particles collide is k = -4

The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Two particles:

Particle A:

x(t) = 5t - 5

y(t) = 2t - k

Particle B:

x(t) = 4t

y(t) = t² - 2t - 1

We see that,

The x(t) of particle A and x(t) of particle B are the same only at t = 5.

x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20

x(t) = 4t = 4 x 5 = 20

Now,

y(t) = 2t - k = 2 x 5 - k = 10 - k

y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14

(a) If k = -6.

x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20

x(t) = 4t = 4 x 5 = 20

y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 6 = 16

y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14

In order to collide both the x(t) of particles A and B must be the same.

Similarly, y(t) must be the same.

So,

Particle A and particle B never collide.

(b)

The value of k where the particles collide.

k = -4

y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14

y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14

(c)

The time at which the particles collide.

t = 5 and k = -4

x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20

x(t) = 4t = 4 x 5 = 20

y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14

y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14

The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.

Thus,

Particle A and particle B never collide.

The value of k where the particles collide is k = -4

The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.

Learn more about equations here:

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Answer:

x=3

Step-by-step explanation:

Answer:

  C)  (x - 4)

Step-by-step explanation:

A root makes a factor be zero. The root of 4 will make the factor x-4 be equal to zero.

Answer:

(x-4)

Step-by-step explanation:

the roots of a polynomial are −3, 4, 5, and −7.

When 'a' is a root of the polynomial then (x-a) is a factor

Lets write the factors for all the root given

[tex](x-(-3))(x-4)(x-5)(x-7)[/tex]

[tex](x+3)(x-4)(x-5)(x-7)[/tex]

Check with the options, which factor is in our polynomial

(x-4) is one of the factor

Answer:

$77,380

Step-by-step explanation:

If she gets a 6% raise next year she will make 106% of what she makes this year.  

106% is 1.06 as a decimal.  Multiply her salary by 1.06 to find out how much she will make next year...

$73,000(1.06) = $77,380

Answer:

77,380

Step-by-step explanation:

divide 73000 by 100% and you get 730, then you multiply it by 6 since you need a 6% raise. once you get this value, you simply add it to the 73000 and you get the answer

Answer:

120 feet

Step-by-step explanation:

1. find the length of the pool (2*20 = 40 feet)

2. add the sides 2L + 2W

    2L = 2*40 = 80

    2W = 2*20 = 40

    80+40=120

Answer: 9 feet.

Step-by-step explanation: The formula to convert inches to feet is to divide the amount in inches by 12. 108/12 = 9.

Answer: 250km

Step-by-step explanation:

Answer:

The cities are 35 cm apart in map.

Step-by-step explanation:

The scale on a map is 5 cm : 8 km.

[tex]\texttt{Scale = }\frac{5cm}{8km}\\\\\texttt{Scale = }\frac{5cm}{8\times 100000cm}=\frac{5}{800000}[/tex]

Now we need to find how much is the distance in map if the original distance is 56 km.

Distance in map = Scale x Original distance

[tex]\texttt{Distance in map = }\frac{5}{800000}\times 56km=\frac{5\times 5600000cm}{800000}=35cm[/tex]

The cities are 35 cm apart in map.

Answer:

V = 960 ft^3

Step-by-step explanation:

The volume of a room can be found by

V = Area of base  time height

V = 120 * 8

V = 960 ft^3

Answer:

[tex]\large\boxed{\tan x(\cot x-\cos x)=1-\sin x}[/tex]

Step-by-step explanation:

[tex]Use\\\\(\tan x)(\cot x)=1\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\text{distributive property:}\ a(b-c)=ab-ac\\======================\\\\\tan x(\cot x-\cos x)=(\tan x)(\cot x)-(\tan x)(\cos x)\\\\=1-\left(\dfrac{\sin x}{\cos x}\right)(\cos x)=1-\sin x[/tex]

Answer:

[tex]6k[/tex]

Step-by-step explanation:

Let

k-----> the variable

we know that

The phrase " The product of a number and six" is equal to multiply the variable k ( the number) by 6

so

[tex]6k[/tex]

Answer:

The measure of the complement angle is [tex]18\°[/tex]

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to [tex](90-x)\°[/tex]

The supplement of an angle is equal to [tex](180-x)\°[/tex]

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

[tex](90-x)\°=(1/6)(180-x)\°[/tex]

solve for x

[tex](540-6x)\°=(180-x)\°[/tex]

[tex](6x-x)=(540-180)\°[/tex]

[tex](5x)=(360)\°[/tex]

[tex]x=72\°[/tex]

Find the measure of the complement angle

[tex](90-x)\°[/tex] ------> [tex](90-72)=18\°[/tex]

Answer:

18⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Supplement = 180 - x

Given:

90 - x = 1/6 × (180 - x)

540 - 6x = 180 - x

5x = 360

x = 72

Complement = 90 - 72 = 18⁰

The width of the rectangular park is 126 feet. This was found by setting up an equation based on the problem description and then solving for the width.

The subject of this question is Mathematics, specifically algebra. The problem states that the length of a rectangular park is 3 feet shorter than its width, with the length being given as 123 feet.

First of all, let's define the length with a variable L and the width with a variable W. From the problem, we can write the equation, L = W - 3. Since we know that L = 123 feet, we can substitute this value into the equation, getting 123 = W - 3.

To find W, all we need to do is add 3 to both sides of the equation. Hence, W = 123 + 3 = 126 feet. So, the width of the park is 126 feet.

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probably the formula is 4×(x-1.6)

Answer:

4) 4(x−32)

Step-by-step explanation: