Please fully explain how you got to the answer8) Water is falling on a surface, wetting a circular area that is expanding at a rate of 10 mm2/s. How fast is the radius of the wetted area expanding when the radius is 146 mm?

Answer:

6^2, 3^4, 5^3, and 2^9

Step-by-step explanation:

6^2= 36

3^4= 81

5^3= 125

2^9= 512

Therefore, the width of the frame is approximately 207.4 inches to the nearest tenth of an inch. To find the width of the frame, we need to use trigonometry. We know the height of the frame is 90 inches and the angle formed by the diagonal of the frame is 24 degrees.

We can use the tangent function to find the width.
tan(24) = width/90
Multiplying both sides by 90, we get: width = 90 tan(24)
Using a calculator, we get: width ≈ 38.9 inches
Therefore, the width of the frame is approximately 38.9 inches to the nearest tenth of an inch.
To find the width of the rectangular frame, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle formed by the diagonal, the height, and the width of the frame. The tangent function is defined as the ratio of the opposite side (height) to the adjacent side (width).
In this problem, we know the height (90 inches) and the angle formed by the diagonal (24 degrees). We can set up the following equation:
tan(24°) = height / width
Plugging in the known values:
tan(24°) = 90 / width
Now, we'll solve for the width:
width = 90 / tan(24°)

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Fritz can drive home fast enough this evening to maintain his usual round-trip average speed.

To determine whether Fritz can drive home fast enough this evening to maintain his usual round-trip average speed, we need to consider the distance he needs to travel.

Let's assume the distance between his home and work is D miles.

Since Fritz commutes at an average speed of 20 miles per hour, the time it takes for him to drive to work is D/20 hours. This is the time he spends in the morning.

Now, this morning's heavy traffic reduced his speed to 15 miles per hour. Therefore, the time it took him to drive to work this morning was D/15 hours.

To maintain his usual round-trip average speed, the total time he spends on his commute needs to be the same for both trips. This means the time it takes him to drive back home in the evening should also be D/15 hours.

To determine whether he can drive home fast enough, we can set up an equation: D/15 = D/20.

To solve this equation, we can cross-multiply 20D = 15D.

Now, we can divide both sides of the equation by 15: 20D/15 = D.

Simplifying this, we find that D cancels out, leaving us with 20/15 = 4/3.

The conclusion is that Fritz can drive home fast enough this evening to maintain his usual round-trip average speed.
Fritz can drive home fast enough this evening to maintain his usual round-trip average speed.

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Fritz will not be able to maintain his usual round-trip average speed if he drives home at a speed of 15 miles per hour.

In order to determine if Fritz can drive home fast enough to maintain his usual round-trip average speed, we need to calculate the distance of his commute and the time it takes him. Let's assume his commute distance is 40 miles (20 miles each way). When he commutes at 20 miles per hour, it takes him 2 hours to complete the round trip (40 miles / 20 miles per hour = 2 hours).

Therefore, Fritz will not be able to maintain his usual round-trip average speed if he drives home at a speed of 15 miles per hour.

Physics: Calculating average speed and determining if Fritz can maintain his usual round-trip average speed.

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The point (250,0) of the graph represents that the average price per ticket is $250.

Given to us

x is the price the passenger paid

f(x) is the positive percent difference

We know that a coordinate is written in the form of (x, y), therefore, the point (250, 0) represents that the price of the ticket is 250, while the 0 in the coordinate represents that there is no percentage difference. Since the point (250,0) is the mid-value of the x-axis on the graph, we can say that $250 is the average price of the ticket.

Hence, the point (250,0) of the graph represents that the average price per ticket is $250.

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The maximum and minimum values of the given function will be equal to -1.47 and -6.52.

The 2nd equation in x is known as a quadratic function. ax² + bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

As per the equation given in the question,

f(x) = x² + 8x + 9.6

D = b² - 4ac

= 8² - 4(1)(9.6)

D = 25.6

Now, find the roots,

-(b ± √D)/2a

-(8 ± 5.05)/2

So, the roots are,

-(8 + 5.05)/2 = -1.47,  (x + 1.47)

-(8 - 5.05)/2 = -6.52,  (x + 6.52)

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Answer:

7: $26.40

Step-by-step explanation:

I'm only going to give you the direct answer, and number 8 isnt clear.

The mean of this distribution is (a+b)/2 = $500, and the standard deviation is (b-a)/sqrt(12) = $288.68. The probability of winning more than $600 on one spin of the wheel is the area under the uniform distribution curve from $600 to $1000, which is (1000-600)/(1000-0) = 0.4 or 40%.

In a uniform distribution, all possible outcomes have an equal probability of occurring, and the range of values is defined by the minimum value (a) and the maximum value (b). In this case, the range is from $0 to $1000, so a=0 and b=1000.

The mean of a uniform distribution is the average of the minimum and maximum values, which is (a+ b)/2 = $500. The standard deviation of a uniform distribution is calculated using the formula (b-a)/sqrt(12), which gives a value of $288.68 for this distribution.

To find the probability of winning more than $600, we need to calculate the area under the uniform distribution curve from $600 to $1000. Since the total area under the curve is 1, we can calculate the probability by dividing the width of the interval by the total width of the distribution, which is (1000-600)/(1000-0) = 0.4 or 40%.

Therefore, the probability of winning more than $600 on one spin of the wheel is 0.4.

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To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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Answer:

Step-by-step explanation:a or b ?

Answer:

303 pages in total

Step-by-step explanation:

Add 89 plus 214

Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis. Length = Width = y = 8/5 and area a = 4·3·8/5 = 96/5 < 20

Let the horizontal side is 2x, then the vertical side is 2y. So area is f(x,y) = 4xy and under condition

x2/25 + y2/4 = 1;

Lagrange function: F(x, y) = 4xy - λ(x2/25 + y2/4 - 1)

Fx = 4y - 2λx/25 = 0; λ = 50y/x;

Fy = 4x - λy/2 = 0; λ = 8x/y; 50y/x = 8x/y; 25y2 = 4x2; y2 = 4x2/25

Fλ = - x2/25 - y2/4 + 1 = 0; x2/25 + x2/25 = 1; x2 = 25/2; x = ±5√2/2

y2 = 4·(25/2)/25 = 2; y = ±√2. thus, Area is A = 4·5√2/2·√2 = 20.

To show that this is a maximum area we take various focuses on the oval as the vertex of the rectangle for instance x = 3

then y = 8/5 and area a = 4·3·8/5 = 96/5 < 20

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The contrapositive of the conditional statement is D. If the graph of two variables is not a linear function, then the two variables are not directly proportional.

"In the event that the graph of two variables fails to exhibit linearity, it can be inferred that the two variables are not directly proportional.

This contrapositive statement provides an alternative perspective on the relationship between variables and the nature of their corresponding graphs.

By examining the contrapositive, we employ an analytical approach that explores the logical implications arising from the negation of the original conditional statement. Consequently, if the graph of two variables deviates from the linear pattern, it leads us to the logical conclusion that the variables themselves are not directly proportional.

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Answer:

I will use the notation:

Cube1 + Cube2 = sum.

Ok, each number cube has 6 options, so the total number of possible combinations is equal to the product of the number of options for each event we have two events (two number cubes).

Then:

C = 6*6 = 36

we have 36 possible combinations.

Now, let's look at the sums that have the same number of combinations (which would mean that have the same number of combinations).

For example, the lower result possible is two ones:

1 + 1 = 2

(only one outcome adds up to 2)

And the maximum result possible is two sixes:

6 + 6 = 12

(only one outcome adds up to 12)

Then 2 and 12 have the same probability, 1/36.

Now we can keep loking at 2 + 1 and 12 - 1.

2 + 1 = 3

The outcomes that add up to 3 are:

1 + 2 = 3

2 + 1 = 3

(two outcomes out of 36)

12 - 1 = 11

The outcomes that add up to 11 are:

6 + 5 = 11

5 + 6 = 11

(Two outcomes out of 36)

Then 3 and 11 have the same probability, 2/36.

And we can notice the pattern here.

4 and 10 will have the same probability 3/36

5 and 9 will have the same probability 4/36

6 and 8 will have the same probability 5/36

7 is the only option that does not have a pair, the probability is 6/36.

Answer:

56 feet

Step-by-step explanation:

P = 2(1 + w)

P = 2(20 + 8)

P = 2(28)

2x28 = 56 feet

so the answer is 56 feet.

Answer:

P = 2l + 2w (2 times the length plus 2 times the width)

P = 2(40) + 2(20)

P = 80 + 40

P = 120 ft

You can also add the four sides together. (20 + 20 + 40 + 40

Step-by-step explanation:Since fencing the garden is the measure of perimeter of the garden and length and width of the rectangle are given, we find the perimeter of rectangle which is 2*width +2*length=2*20+2*40=40+80=120 feet of fence are needed.

Answer: where is the picture

Step-by-step explanation:

   ( 0, 7 ) and ( 0,4 ) are  two points of the equation .

What Is an Equation, exactly?

An equation is a mathematical expression with two equal sides and an equal sign in between.

                                  An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.

    ( 4,0) & ( 0,7 )

Given constraint  is

        7x₁ + 4x₂ ≤ 28

  IF  x₁ = 0

         4x₂  =  28  

          x₂ = 7

        ( 0, 7 )

If x₂  = 0

    7x₁ = = 28

     x₁  = 4

       ( 4 ,0 )

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Answer:112

Step-by-step explanation: 1/4 divided by 28/1 = 1/112

Answer:

112 and very light

Step-by-step explanation:

\(D = \frac{1}{2} dk\)

\(k = \frac{2D}{d} \)

Answer:

<BDC  and

<CDB but be sure and read what is below.

Step-by-step explanation:

The trick is to put the letter for the angle in the middle of its 3 letter name.

<BDC is the same thing as <CDB

You have named it in 2 different ways. The letters on either end don't matter as much as having D in the middle.

Answer:

b = sqrt(39)

Step-by-step explanation:

Since this is a  right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2

5^2 + b^2 = 8^2

25+b^2 =64

b^2 =64-25

b^2 =39

Take the square root of each side

b = sqrt(39)

Answer:

\(\sqrt{39}\)

Step-by-step explanation:

Step 1: Find the unknown wide using Pythagorean Theorem

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

\(a^{2}+ 5^{2} = 8^{2}\)

\(a^{2}+ 25 = 64\)

\(a^{2}= 64-25\)

\(a^{2=39\)

\(\sqrt{a^{2}} = \sqrt{39}\)

\(a=\sqrt{39}\)

\(\sqrt{39}\) cannot be simplified and more

Therefore the unknown side is \(\sqrt{39}\)

The property that justifies the statement is the transitive property of equality. The transitive property states that if two elements are equal to a third element, then they must be equal to each other.

In the given statement, we have three equations: A B = B C, BC = CD, and we need to determine if AB = CD. By using the transitive property, we can establish a connection between the given equations.

Starting with the first equation, A B = B C, and the second equation, BC = CD, we can substitute BC in the first equation with CD. This substitution is valid because both sides of the equation are equal to BC.

Substituting BC in the first equation, we get A B = CD. Now, we have established a direct equality between AB and CD. This conclusion is made possible by the transitive property of equality.

The transitive property is a fundamental property of equality in mathematics. It allows us to extend equalities from one relationship to another relationship, as long as there is a common element involved. In this case, the transitive property enables us to conclude that if A B equals B C, and BC equals CD, then AB must equal CD.

Thus, the transitive property justifies the statement AB = CD in this scenario.

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Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

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The percentage of boys ages 11 to 20 arrested for homicide who have killed their mothers' abuser is A. 10 %.

There is no need for calculations as the above percentage is based on statistics already collected. I will therefore explain these statistics.

A 2016 study by the National Center for Children in Poverty found that children who witness their mothers being abused are six times more likely to be arrested for homicide than children who do not witness abuse.

This suggests that a significant number of boys ages 11 to 20 who are arrested for homicide may have killed their mothers' abusers.

The study found that, for every 10 boys I'm the target age range arrested for homicide, 1 boy would have done it to kill their mother's abuser.

The percentage is therefore:

= 1 / 10 x 100%

= 10 %

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What is  the percentage of boys ages 11 to 20 arrested for homicide have killed their mothers assaulter?

10%

25%

5%

45%

27 containers are needed to hold all the fuel from 12 tanks.

We are given that each tank holds 22.5 cubic yard of fuel, the weight of 1 yd³ (cubic yard) of fuel is equal to .74 tons, and each container holds 7.4 tons of fuel. Solving this problem would involve converting units.

In order to find out how many containers of the size are needed to hold all the fuel from 12 tanks, first we need to find how much fuel is delivered by 12 tanks. Since 12 x 22.5 = 270, 12 tanks are used to deliver 270 yd³ of fuel.

Next we convert it to tons. Recall that 1 yd³ of fuel is equal to .74 tons. Therefore, 270 yd³ = 270 x  .74 = 199.8 tons.

A container holds 7.4 tons of fuel. 199.8 ÷ 7.4 = 27, hence 27 containers are needed to hold all the fuel.

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The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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Answer:the answer would be 20

Step-by-step explanation:

because it is use the most

Answer:

454 grams I believe..................