On the blueprints for a building, 8 inches represents 28 feet. If the blueprints show a distance of 16 inches
between the two walls, how many feet separate the walls?

The diffusion time of the red blood cell to take oxygen through the membrane is 25uS.

The small capillaries in the lungs are in close contact and it takes a red blood cell 0.5 seconds to squeeze through the capillary.

The diffusion time for the oxygen across the 1 um thick membrane separating the air is given by,

t = x²/2D

Where,

t is the diffusion time,

x is the thickness of the membrane,

D is the diffusion coefficient.

Putting values,

t = (1 x 10⁻⁹)²/2 x 2 x 10⁻¹¹

t = 10⁻⁷/4

t = 25 x 10⁻⁹ seconds.

t = 25 uS.

so, the diffusion time is 25uS.

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Answer:

\(\sqrt{7}\), 2.8, \(\pi\), \(\sqrt{17}\), 4.6

Step-by-step explanation:

To order the numbers from least to greatest turn all the numbers into decimal form.

\(\sqrt{7}\): 2.65

\(\sqrt{17}\): 4.12

\(\pi\): 3.14

4.6

2.8

Now order them from least to greatest (make sure you put the numbers back into their original form)

\(\sqrt{7}\), 2.8, \(\pi\), \(\sqrt{17}\), 4.6

The numbers in the form of least to greatest will be \(\sqrt{7}\), \(2\overline{.8}\), π, \(\sqrt{17}\), 4.6.

Rational numbers are those numbers which have terminating,Repeating or recurring digits after the decimal place.

Irrational numbers have non-repeating, non-recurring non-terminating digits after the decimal place.

According to the given question we have to order the number from least to greatest.

Given number are 4.6, \(2\overline{.8}\), π, \(\sqrt{17}\), \(\sqrt{7}\).

We know the value of π is 3.14 approx and square root of 17 lies between square root of 16 and 25 which are 4 and 5 but more close to 4 and square root of 7 lies between square root of 4 and 9 which are 2 and 3.

∴  The given numbers in increasing order will be

\(\sqrt{7}\), \(2\overline{.8}\), π, \(\sqrt{17}\), 4.6.

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Answer: Option A.

Step-by-step explanation:

The first step is to place the point of the compass in the vertex of the angle and draw an arc that connects both rays.

Then you put the compass in the points where the arc intersected the rays and draw two new arcs (with the radius of the compass constant)

The point where the two new arcs intersect will be the interior point.

Then the first step is: place the compass in the vertex of the angle.

The vertex is the common point to the two rays, in this case, we can see that the vertex is the point A.

Then you should place the compass in the point A, the correct option is option A.

Answer:

After two seconds

h(2) = -16(2^2) + 115(2) + 19

h(2) = -64 + 115(2) +19

h(2) = 185

Let me know if this helps!

If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.

A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.

This document is used to determine how much tax was paid in excess of what was required during that time period.

In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.

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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:

April 15th.

October 15th.

August 15th.

November 15th.

None of the choices are correct.

the outward flux of F across the closed curve C is -5π/32 + √2π/72.

To find the outward flux of the vector field F = sin(6y)i + cos(4x)j across the closed curve C, we can apply Green's Theorem.

Green's Theorem states that for a vector field F = P(x, y)i + Q(x, y)j and a simple closed curve C with positively oriented boundary, the outward flux across C is given by the line integral of F along the curve C:

Flux = ∮C F · dr = ∬R (Qx - Py) dA,

where R is the region enclosed by C, Qx represents the partial derivative of Q with respect to x, and Py represents the partial derivative of P with respect to y.

In our case, the rectangle with vertices at (0,0), (π/6, 0), (π/6, π/4), and (0, π/4) can be denoted as R.

Let's calculate the partial derivatives of P and Q:

P(x, y) = sin(6y),

Q(x, y) = cos(4x).

Taking the partial derivative of Q with respect to x (Qx):

Qx = -4sin(4x).

Taking the partial derivative of P with respect to y (Py):

Py = 6cos(6y).

Now, we can evaluate the double integral using Green's Theorem:

Flux = ∬R (Qx - Py) dA

     = ∫[0, π/6]∫[0, π/4] (-4sin(4x) - 6cos(6y)) dy dx.

Integrating with respect to y first:

Flux = ∫[0, π/6] [∫[0, π/4] (-4sin(4x) - 6cos(6y)) dy] dx

     = ∫[0, π/6] [-4sin(4x)y - 6cos(6y)y]∣[0, π/4] dx

     = ∫[0, π/6] [-4sin(4x)(π/4) - 6cos(6(π/4))(π/4)] dx

     = -π/4 ∫[0, π/6] [sin(4x) + cos(9π/4)] dx

     = -π/4 [(-1/4)cos(4x) + (1/9)sin(9π/4)]∣[0, π/6]

     = -π/4 [(-1/4)cos(4(π/6)) + (1/9)sin(9π/4) - (-1/4)cos(0) + (1/9)sin(0)]

     = -π/4 [(-1/4)cos(2π/3) + (1/9)sin(9π/4) - (-1/4) + 0]

     = -π/4 [(-1/4)(-1/2) + (1/9)(-√2/2) + 1/4]

     = -π/4 [1/8 - √2/18 + 1/4]

     = -π/4 [5/8 - √2/18]

     = -5π/32 + √2π/72.

Therefore, the outward flux of F across the closed curve C is -5π/32 + √2π/72.

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complete question is below

Using Green's Theorem, find the outward flux of F across the closed curve C.  F=sin (6 y) i + cos (4 x) j C is the rectangle with vertices at (0,0), (π/6, 0), (π/6, π/4) and (0, π/4)

Answer:

C is the answer

Step-by-step explanation:

One key difference between Cousteau's argument and Kennedy's argument about space is that Cousteau believed that space exploration should not come at the expense of protecting and preserving our planet's oceans,

While Kennedy saw space exploration as a necessary and important component of national security and technological advancement. Jacques Cousteau and John F. Kennedy had different perspectives on the importance and priority of space exploration. While Kennedy argued that space exploration was crucial for national security and technological advancement, Cousteau believed that protecting and preserving the oceans on our planet should be the top priority. For Cousteau, the exploration of space should not come at the expense of neglecting our own planet and its natural resources. In contrast, Kennedy saw space exploration as a way to demonstrate American strength and leadership in the world and to gain a strategic advantage over other nations. Despite their different perspectives, both Cousteau and Kennedy recognized the importance of science and exploration in pushing the boundaries of human knowledge and achievement.

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Answer:

Explanation:

Here, we want to write the equation of the quadratic function

We have the general form as:

from the question, we have the horizontal intercepts at t= 3 and t =4

that means (t-3) is a factor and also (t-4) is another root of the equation

The product of these two is as follows:

Finally, we need to find the value of a

We can do this by making a substitution

We substitute 1 for t and -3 on the other side of the equation

Mathematically, we have this as:

Thus, we have the equation as:

1) Considering that y varies directly as the fourth power of x. So we can write:

2) But notice, we were told when x=1, y=6 so we can write out:

Note that now, we know the constant "k" of proportionality. Then we can write the following equation:

Thus, this is the answer.

Answer:

130 miles

Step-by-step explanation:

The number of miles is 20 times the number of inches.

6.5 * 20 = 130

Answer: 130 miles

Answer:

B

Step-by-step explanation:

A^2+B^2=C^2

Answer:

C: 131,073

Step-by-step explanation:

The pattern is multiplying by 2 and changing the operation each time, and if you repeat that 17 times and put the equation into a calculator you get 131,073.

It is estimated that many first-year college students gain 7-8 pounds. Students are more likely to gain weight during their first year of college than at any other time in their life. Many college students are known for gaining the infamous “freshman 15,” or the 15 pounds many students pack on during their first year of college.

However, studies show that the actual weight gain is often less than this estimate, with many first-year college students gaining around 7-8 pounds. The causes of this weight gain are multifaceted, and may include changes in dietary habits, increased alcohol consumption, stress, lack of exercise, and lack of sleep. College students are often faced with a variety of new experiences and responsibilities, which can make it difficult to prioritize healthy habits and maintain a healthy lifestyle.

For example, college students may find themselves eating more fast food or dining hall meals than they did at home, which can be high in calories and low in nutritional value. They may also have less time to exercise or get enough sleep, which can contribute to weight gain.In addition, college students are often exposed to high levels of stress, which can cause them to turn to food for comfort. This stress may be caused by academic pressures, social challenges, or financial difficulties. Finally, college students may find themselves drinking more alcohol than they did in high school, which can be high in calories and contribute to weight gain.While the freshman 15 may be a bit of a myth, there is no denying that many college students struggle with weight gain during their first year of college. By prioritizing healthy habits and making small changes to their lifestyle, students can maintain a healthy weight and avoid the weight gain often associated with college life.

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Answer:

5 x 3 =

Step-by-step explanation:

Length times width.

The multiplication equation represented by the model is 5 x 3.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The model has 5 rows and 3 columns shaded. The multiplication equation will be written below,

Multiplication equation = 5 x 3

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A card is drawn randomly from a standard 52-card deck. then the probabilities are a) 1/13 b) 3/13 and c) 10/13

There are four 3's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 3. This means that the probability will be:

p = 4/52

p= 1/13

b.

For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:

4*3 =12

The total possible cards are, still, 52, so, the probability will be

p= 12/52

p=3/13

c.

We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face card its:

p=52/52

p=1

so

p( the card is a face card ) + p( the card is not a face card) =1

but, we know that

p( the card is a face card ) =3/13

so

p( the card is not a face card) =1- 3/13

                                                 = 10/13

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The speed of the fox should be greater than the rabbit's speed in other to catch up, Hence, the speed of the fox must be 35/t + 40

The distance between the rabbit and fox, d = 35 feets

The rabbit's speed = 40 feets per second

Fox's speed = F

In other to obtain a specific speed for the fox, the time at which the fox is required to catch up with the rabbit should be given.

Let the time = t

Recall :

Speed = distance / time

Distance = speed × time

Rabbit's distance from fox after time t will be :

35 + (40 × t) = 35+40t

Fox's distance after time, t = fox speed × t = F × t

In other to catch up ; both fox and rabbit must be at the same distance ;

Rabbit's distance at time t = Fox's distance at time t

35+40t = Ft

To solve for F which is the fox's speed:

Divide both sides by t

(35+40t) / t = Ft/t

35/t + 40 = F

Hence, the fox' s speed must be : 35/t + 40

To obtain the exact speed of the fox, we must be given a specific time value.

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Answer:

Y= 8*x

Step-by-step explanation:

You can notice that the graph is a straight line that crosses the origin so it's a graph that has an equation written this way : y= a*x

a is the slope

You can easily find it by notice that the image of 1 is 8

So a = 8

Then y= 8*x

Answer:

\(y=8x\)

Step-by-step explanation:

Well drawing the line further then we can tell the y intercept is 0.

So we have to find the SLOPE using the following formula

\(\frac{y^2-y^1}{x^2-x^1}\)

So we need two points on the line, we can use the following

(1,8) and (2,16)

So 16 is y2 and 8 is y1 so 16-8 is 8.

2-1 is 1.

So the slope is 8x.

Do the equation is \(y=8x\)

We don’t have to put the y intercept because it is 0.

Answer:

X=11

Step-by-step explanation:

11-7=4 5(4)=20 So X equals 11

Answer: 3ab   IF a^b does NOT mean a to the power of b!

I believe you mean  9a²b and 30ab³

If you really mean 9aᵇ and 30ab³,  then the GCF is 3a.

Step-by-step explanation:

the factors of  9 are 3*3  The factors of 30 are 2*3*5.

The only common factor of 9 and 30  is 3

a is a common factor of a and a²

b is a common factor of b and b³

Answer:

b. x=2

Step-by-step explanation:

The axis of symmetry of a parabola gives us a line of symmetry where the parabola appears the same but flipped on either side. It passes through the parabola's vertex, or the minimum/maximum point of the parabola. Here, we can see that the parabola's minimum point occurs when x=2. Therefore, its axis of symmetry is x=2.

I hope this helps!

26 more students went to the football game than the volleyball game

The term ‘per cent’ means ‘out of a hundred’. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole.

Total students planning to attend football game is 120

25 percent of the students who said they were going to the football game did not attend. Therefore, total number of students who attended the football game is:

120 x (1 - 25%) = 120 x 0.75 = 90 students attended the football game

Total students planning to attend volleyball game is 80

20 percent of the students who said they were going to the volleyball game did not attend. Therefore, total number of students who attended the volleyball game is:

80 x (1 - 20%) = 80 x 0.80 = 64 students attended the volleyball game

Number of students who attended the football game more than the volleyball game is calculated thus:

(Total number of students who attended the football game) - (Total number who attended the volleyball game)

= 90 - 64

= 26 students.

Therefore, 26 more students attended the football game

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Answer:

140

Step-by-step explanation:

The sum of one interior angle and one exterior angle is 180

180-40=140 so an interior angle of the regular polygon would be equal to 140

Explanation

To solve the question, we will be aware that

There are 3 hours between 6PM and 9PM ,

The main pump's emptying rate is 1/4 tanker per hour. It will be open

the entire 3 hours, so it will empty 3/4 of the tank.

this means that the auxiliary pump must empty the remaining 1/4

Thus

Thus, we will have

Therefore

The auxiliary pump should start by 6pm + 45 minutes = 6:45pm

a. There are numbers that when multiplied are less than their difference. (True)
b. There is a number whose square is less than itself. (False)
c. For any positive whole number, its square is greater than or equal to the number itself. (True)
d. For any real numbers, the absolute value of their product is less than or equal to the product of their absolute values. (True)

To explain further, the statements are reformulated in a less formal manner without using variables.

a. The statement asserts that there exist some numbers (without specifying which numbers) that, when multiplied together, result in a product smaller than their difference. This statement is true. For example, consider u = 5 and v = 7. In this case, 5 * 7 = 35, which is less than the difference u - v = -2.

b. The statement suggests that there is a number x (without specifying its value) such that its square is less than x. This statement is false. It contradicts the fundamental property that for any real number x, x^2 is always greater than or equal to x. This is because the square of any real number, positive or negative, is either zero or a positive value.

c. The statement claims that for any positive integer n (without specifying a particular value), the square of n is greater than or equal to n itself. This statement is true. It is a fundamental property of positive integers that their squares are always greater than or equal to the original number. For example, when n = 4, 4^2 = 16, which is indeed greater than 4.

d. The statement asserts that for any real numbers a and b (without specifying specific values), the absolute value of their product is less than or equal to the product of their absolute values. This statement is true. The absolute value of the product of two real numbers is always less than or equal to the product of their absolute values. This can be understood by considering different cases, including when both a and b are positive, one is positive and the other is negative, or both are negative. In each case, the inequality holds true based on the properties of absolute values and multiplication.

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In Exercises 1-4, determine if the system has a nontrivial solution. Try to use as few row operations as possible.

1. 2x1 – 5x2 + 8x3 = 0
-2x1 – 7x2 + x3 = 0
4x1 + 2x2 + 7x3 = 0
-3x1 + 5x2 – 7x3 = 0

This system has a nontrivial solution since it has three equations and three variables. We can use row operations to put this system in reduced row echelon form and find the solution.

2. x1 – 3x2 + 7x3 = 0
-2x1 + x2 - 4x3 = 0
x1 + 2x2 + 9x3 = 0

This system has a nontrivial solution since it has three equations and three variables. We can use row operations to put this system in reduced row echelon form and find the solution.

3. -5x1 + 7x2 + 9x3 = 0
x1 – 2x2 + 6x3 = 0

This system has a nontrivial solution since it has two equations and three variables. We can use row operations to put this system in reduced row echelon form and find the solution.

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Mari put 1/2  of a bottle of water at the water fountain .

Let the capacity of the bottle holding water be 100 .

It is given that Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.

The amount of water is given by :

 2/3 of 100 - 1/6 of 100 =  2/3 × 100 - 1/6 × 100

                                       = 100( 2/3 - 1/6)

                                        = 100(1/2)

                                        = 50

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Based on the information, we can infer that the multiplication equation with 1/2 as a factor that models the image of the 6 pear halves is 3 pears = 1/2 x 6 pear halves.

To identify the correct equation we have to perform the following procedure: We have to consider that the image shows 6 pear halves, which equals 3 full pears, since each pear has two halves. Therefore, we can model the image as follows:

And if we want to represent it as a multiplication equation with 1/2 as a factor, we can divide both sides by 2:

Therefore, the multiplication equation with 1/2 as a factor that models the image of the 6 pear halves is:

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Out of the 85 people surveyed, approximately 33 individuals said that ten was not their favorite number.

To determine the number of people who did not choose ten as their favorite number, we subtract the percentage of people who selected ten (39%) from the total number of people surveyed (85).

39% of 85 is approximately (0.39 * 85 = 33.15). Since we can't have a fraction of a person, we round down to the nearest whole number. Therefore, approximately 33 people said that ten was not their favorite number.

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The first four derivatives of f(t) are \(f'(t) = 12t + 9e^t, f''(t) = 12 + 9e^t, f'''(t) = 9e^t\), and \(f''''(t) = 9e^t\).

The given function is \(f(t) = 6t^2+ 9e^t\).

To find its derivative, we can apply the power rule and the derivative of exponential function, which states that the derivative of \(e^t\)is \(e^t\)itself.

Thus, we get \(f'(t) = 12t + 9e^t\).

Applying the power rule again, we get \(f''(t) = 12 + 9e^t\).

Taking the derivative one more time, we get \(f'''(t) = 9e^t\).

Finally, taking the fourth derivative, we get \(f''''(t) = 9e^t\).

In summary, the first four derivatives of f(t) are \(f'(t) = 12t + 9e^t\), \(f''(t) = 12 + 9e^t\), \(f'''(t) = 9e^t\), and\(f''''(t) = 9e^t\).

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