A circular playground is 60 feet wide and has a 3-foot wide path surrounding the playground.
1. The area of the playground is about
A. 377
B. 2,826
C. 11,304
2. The area of the circular path is about
A. 290
B. 396
C. 594

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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To find the probability of obtaining a value greater than or equal to 80 but less than or equal to 115 for a normal distribution with a mean of 100 and standard deviation of 10 using Excel, you can use the NORM.DIST function.

Here's how you can do it step-by-step:

1. Open Excel and enter the following formula in a cell: =NORM.DIST(115,100,10,TRUE) - NORM.DIST(80,100,10,TRUE)
  - The first argument (115) is the upper bound of the range (inclusive).
  - The second argument (100) is the mean.
  - The third argument (10) is the standard deviation.
  - The fourth argument (TRUE) specifies that you want the cumulative distribution.
  - Similarly, for the second part of the formula, use the lower bound (80).

2. Press Enter to calculate the formula. The result will be the probability of obtaining a value within the specified range.

The NORM.DIST function calculates the probability of a value occurring in a normal distribution. By subtracting the probability of the lower bound from the probability of the upper bound, you get the probability of obtaining a value within the desired range.

To find the probability using Excel, you can use the NORM.DIST function. By subtracting the cumulative distribution function (NORM.DIST) of the lower bound (80) from the cumulative distribution function of the upper bound (115), you can calculate the probability of obtaining a value within the specified range. The NORM.DIST function requires four arguments: the value you want to calculate the probability for, the mean, the standard deviation, and whether you want the cumulative distribution. In this case, the mean is 100 and the standard deviation is 10. By entering the formula in Excel, you can calculate the probability of obtaining a value between 80 and 115 for this normal distribution.

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True. Stokes' theorem states that if we have a surface r whose boundary is a curve c, and f is a vector field, that provided that c and r are oriented compatibly, the circulation of f around c is equal to the flux of the curl of f through r.

Stokes' theorem states "for surface R whose boundary is a curve C, and F is a vector field, then provided that C and R are oriented compatibly, the line integral of F around C is equal to the surface integral of the curl of F over R."

This theorem relates the circulation of a vector field around a closed curve to the flux of its curl through the enclosed surface.

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The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

The equivalent is the expression that is in different forms but is equal to the same value.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

\(\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\)

Simplify the expression, then we have

\(\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\\\\\rightarrow x^{-3/4 } \cdot y ^{(4/3)} \cdot (16x^2y^4)^{1/4}\\\\\rightarrow x^{-3/4 } \cdot y ^{4/3} \cdot 2x^{1/2}y\\\\\rightarrow 2 x^{1/2 - 3/4} \cdot y^{4/3 + 1} \\\\\rightarrow 2x^{-1/4} \ \cdot y^{7/3}\)

The given expression is \(\rm ax^by^c\). Compare the expression with given expressions, then we have

a = 2, b = - 1/4, and c = 7/3

Then the product of a, b, and c is given as,

⇒ 2 x (-1/4) x (7/3)

⇒ - 7/6

The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

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Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

m/7

Step-by-step explanation:

Answer:

m÷7=\(\frac{m}{7}\)

Step-by-step explanation:

quotient is the answer to a division problem, so m divided by 7 has a quotient of m over 7 or \(\frac{m}{7}\)

To simplify the expression 5b²+(a²+5b)(ab-b²), we can use the distributive property to expand the second term:

5b²+(a²+5b)(ab-b²)

= 5b²+a²ab-a²b²+5bab-5bb²

Then, we can use the associative property of addition to rearrange the terms:

= 5b²+a²ab-a²b²+ab5b-b²5b

Finally, we can combine like terms:

= (5b²-b²5b)+(a²ab-a²b²)+ab5b

= -4b³+a²*ab+5ab

Therefore, the simplified expression is -4b³+a²*ab+5ab.

The distributive property states that the product of a number and a group of numbers is equal to the sum of the products of the number and each individual number in the group. For example, a*(b + c) = ab + ac.

The associative property of addition states that the grouping of numbers being added does not affect the result. For example, (a + b) + c = a + (b + c).

Answer:

the simplified expression is 10ab*b.

Step-by-step explanation:

To simplify the expression 5b²+(a²+5b)(ab-b²), we can first use the distributive property to expand the second term:

5b²+(a²+5b)(ab-b²)

= 5b²+a²ab-a²b²+5bab-5bb²

Then, we can combine like terms:

5b²+a²ab-a²b²+5bab-5bb²

= 5b²-a²b²+5bab+5bab-5bb²

= 5b²+10abb-5b²

= 5b²-5b²+10abb

= 0 + 10abb

= 10abb

The minimum number of cameras that must be selected to ensure that p(at least 1 defective) ≥ 0.8 is either 0 (if selecting no cameras is allowed) or 1 (if at least one camera must be selected).

We can solve this problem using the complement rule:

p(at least 1 defective) = 1 - p(none defective)

Let X be the number of defective cameras selected. We want to find the minimum value of n (number of cameras selected) such that:

p(X ≥ 1) = 1 - p(X = 0) ≥ 0.8

If none of the cameras are defective, then we select 0 defective cameras out of 20, which can happen in C(20, 0) = 1 way. The probability of this is:

\(p(X = 0) = C(20, 0)\times (3/20)^0 \times (17/20)^{20\) ≈ 0.014

Using the complement rule, we have:

p(X ≥ 1) = 1 - p(X = 0) ≥ 0.8

1 - 0.014 ≥ 0.8

0.986 ≥ 0.8

This is already true, so we don't need to select any cameras. However, if we were required to select at least one camera, then the minimum number of cameras we would need to select would be 1, since selecting one camera and finding it defective would satisfy the requirement of having at least one defective camera.

Therefore, the minimum number of cameras that must be selected to ensure that p(at least 1 defective) ≥ 0.8 is either 0 (if selecting no cameras is allowed) or 1 (if at least one camera must be selected).

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Answer:

\(\sqrt{2000}\phantom{a}yards\)

Step-by-step explanation:

For a right triangle, \(a^{2} =b^{2} +c^{2}\), if a is the hypotenuse. So, \(60^{2} =40^{2} +c^{2}\), and c is the the distance we are trying to find:

\(60^{2} =40^{2} +c^{2}\)

\(3600=1600+c^{2}\)

\(c^{2} =2000\)

\(c=\sqrt{2000}\phantom{a} yards\)

Answer:

P(triangle) = 8/80 = 1/10 = 10%

P(circle) = 12/80 = 3/20 = 15%

P(triangle or circle) = 10% + 15% = 25%

Step-by-step explanation:

x=20

x aris is stright .right?

In economics, the theory of signalling is used to investigate the information conveyed by different actions of an individual. The two primary models of signaling are the pooling equilibrium and the separating equilibrium.

In a pooling equilibrium, an individual who is uninformed about another individual's quality acts in the same way towards both high-quality and low-quality individuals. In a separating equilibrium, individuals with different qualities behave in different ways. The theory of signalling assumes that the informed party and the uninformed party are aware of the type of the other party.The values of c for which both a pooling equilibrium and a separating equilibrium are possible are values such that the payoff to each type of worker is the same at the pooling equilibrium and the separating equilibrium, i.e., each type of worker is indifferent between the two equilibria.

The workers in the separating equilibrium earn more than the workers in the pooling equilibrium. In the separating equilibrium, the high-quality workers behave differently from the low-quality workers, and the informed party can distinguish between the two types. The uninformed party is willing to pay a premium for the high-quality worker, resulting in the high-quality worker receiving a higher wage than the low-quality worker. This premium compensates the high-quality worker for the cost of signalling.In the pooling equilibrium, the high-quality worker and the low-quality worker are indistinguishable, resulting in the same wage for both types of workers. Since the cost of signalling for the high-quality worker is greater than the cost of signalling for the low-quality worker, the high-quality worker will not signal their quality, resulting in a lower wage for both workers. Thus, workers in a separating equilibrium earn more than workers in a pooling equilibrium.

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Answer:

x = 8

y = 8

Step-by-step explanation:

y = 8

2x - 3y = -8

We substitute 8 in for y and solve for x

2x - 3(8) = -8

2x - 24 = -8

2x = 16

x = 8

Let's Check the answer.

2(8) - 3(8) = -8

16 - 24 = -8

-8 = -8

So, x = 8 and y = 8 is the correct answer.

Answer:

x = 8 and y = 8.

Step-by-step explanation:

To solve the system of linear equations using the elimination method, we'll eliminate the variable "y" by substituting the given value of y into the second equation. Let's start:

Given equations:

y = 8

2x - 3y = -8

Substitute y = 8 into equation 2:

2x - 3(8) = -8

2x - 24 = -8

Next, we'll solve this equation for x:

2x - 24 = -8

2x = -8 + 24

2x = 16

x = 16/2

x = 8

Now that we have the value of x, we can substitute it back into equation 1 to find the value of y:

y = 8

So, y = 8

Therefore, the solution to the given system of equations is x = 8 and y = 8.

Answer: All four friends would have to share paying the tip and the total so all of them would pay 1/4 of the bill and 1/4 of the tip

Step-by-step explanation: divide the bill and tip between the 4 friends and you get 1/4 which is how much of the bill and tip that all you and the friends have to pay

data:

radius=1.3 in

height=4.8 in

aluminum

After 20 years, the wetland will have decreased in area by 20/5 = 4 times.

If the area has decreased by a sixth every 5 years, it will decrease by 4/6 = 2/3 after 20 years.

Therefore, the percent of the total area that disappears after 20 years is 2/3 = 66.67%.

Rounding to two decimal places, the answer is 66.67%.

Answer:

$ 3513. 63

Step-by-step explanation:

Plug in the numbers :

3200 *  e ^(.017 * 5.5)  = 3513.63

In a residual plot if the linearity assumption is the points are scattered and there is no obvious pattern.

Residual plot:

in statistics, residual value is a measure of how much a regression line vertically misses a data point.

Given,

Here we need to find what would you expect to see in a residual plot if the linearity assumption is correct.

As per the definition of residual plot, there is no obvious pattern for this plot and the positive and negative values are evenly spread across the whole range.

Therefore, in the regression line there are some points are misses the line on the vertical base.

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Answer:

what is the question? this is a statement.

Step-by-step explanation:

The diagram of two similar triangles to complete the proportion is; Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.

From the concept of similar triangles, we know that If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor.

Applying this similar triangles theorem to our question, we can say that;

Height of a person/length of a person's shadow = Height of flower/length of a flower's shadow

We can rewrite this to get;

Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.

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a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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$3.879-$3.529=$0.35

hope this helps, ily!!! byesies have a nice day yar

Answer:

Length of A=6

Breadth of A=24/6=4

Length of B=6

Breadth of B=12/6=2

Step-by-step explanation:

Total surface area: 36

Ratio is 2:1

So, 2x + 1x = 36

3x=36

x=36/3

x=12

2*12=24

1*12=12

So areas are 24 and 12 respectively

Now, we can say that the sides of the square will be same, 6 cm

6*6=36

so the length of both rectangles will be 6

Hence we can divide each area by 6 and find the breadth.

Length of A=6

Breadth of A=24/6=4

Length of B=6

Breadth of B=12/6=2

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If a section of a highway is constructed with a 23% grade, the angle that the highway will make with a horizontal line will be: 13°.

Using the SOH CAH TOA formula, the angle that the highway will make with the horizontal line can be gotten by finding the tangent which is the

vertical/horizontal

Horizontal = 100 ft

Angle of inclination = 0.23

For the 23% grade, we will have

tan⁻1 of 0.23 = 12.9527°

= 13.0°

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The volume of the entire sphere is  (4/3)(249^(3/2) / π).

To find the volume of the entire sphere given that a hemisphere has a great circle with an area of 249, we can use the relationship between the area of a great circle and the volume of a hemisphere.

The area of a great circle is given by the formula A = πr², where A is the area and r is the radius of the great circle.

In this case, we are given that the area of the great circle is 249, so we have:

249 = πr²

Solving for r, we find:

r² = 249 / π

r ≈ √(249 / π)

Now, to find the volume of the entire sphere, we can use the formula for the volume of a sphere:

V = (4/3)πr³

Substituting the value of r, we have:

V = (4/3)π(√(249 / π))³

V ≈ (4/3)π(249 / π)^(3/2)

V ≈ (4/3)π(249^(3/2) / π^(3/2))

V ≈ (4/3)π(249^(3/2) / √π^3)

V ≈ (4/3)π(249^(3/2) / √(π * π^2))

V ≈ (4/3)π(249^(3/2) / π√π^2)

V ≈ (4/3)π(249^(3/2) / ππ)

V ≈ (4/3)(249^(3/2) / π)

Therefore, the volume of the entire sphere is approximately (4/3)(249^(3/2) / π).

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

A. P(3/4)

Step-by-step explanation:

Answer:

The question is not complete, here is a possible match to the complete question:

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units. What scale factor did Lin apply to the Triangle A to create the copy? Remember: A=1/2bh

a) 4

b) 8

c) 16

Answer:

Scale factor = 16

Step-by-step explanation:

From the diagram attached to this solution, the triangle was plotted on a graph sheet, and each grid on the graph represents 1 unit. hence the dimensions of Triangle A from the diagram is as follows:

Base = 3 units

Height = 3 units

Next, in order to determine the scale factor of the area of the triangle after scaling, let us calculate the area of the unscaled triangle.

Area of Triangle = 1/2 (base × height)

Area or Triangle = 0.5 × 3 × 3 = 4.5 square units

Therefore,

Area of unscaled triangle = 4.5 squared units

Area of scaled triangle = 72 squared units

since the area of the scaled triangle is larger than the unscaled triangle, the scale factor is simply the number of times by which the scaled triangle was enlarged, compared to the unscaled triangle. This can be calculated by dividing the scaled triangle by the unscaled triangle as follows:

Scale factor =(scaled triangle) ÷ (unscaled triangle)

Scale factor =  72 ÷ 4.5 = 16