7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
They should build the airport at the
They should build the airport at the
n be found by locating the intersection of at least
which can be found by locating the intersection of a
a circumcenter
medians

The length of OP in the given circle figure is 2.

We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,

A = (A/360)*πr²

Here length of OP represents the radius of the circle with center O.

Let OP = R.

The area of the whole circle will be = πR²

Given that the sector which intends an angle of 72 degrees in center has area 4π/5.

According to the condition,

(72/360)* πR² = 4π/5

R²/5 = 4/5

R² = 4

R = 2 [since length cannot be negative so the negative value of square root is ignored.]

Hence the length of OP is 2.

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Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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Answer:

So we can be 95% confident that the true proportion of people with kids in the population is between 0.044 and 0.096.

Step-by-step explanation:

To construct a confidence interval, we need to use the formula:

CI = p ± zsqrt((p(1-p))/n)

Where:

CI = confidence interval

p = sample proportion (in this case, 42/600 = 0.07)

z = the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval)

n = sample size (in this case, 600)

Plugging in the numbers, we get:

CI = 0.07 ± 1.96sqrt((0.07(1-0.07))/600)

Simplifying this, we get:

CI = 0.07 ± 0.026

Therefore, the 95% confidence interval for the true population proportion of people with kids is:

0.044 ≤ p ≤ 0.096

The percentage of percentage of the apples have diameters that are between 6.34cm and 8.5cm is given as follows:

99.7%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The measures of 6.34 cm and 8.50 cm are the bounds exactly within three standard deviations of the mean, hence the percentage is given as follows:

99.7%.

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You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:

where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.

To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:

From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.

To find the value of a, you can compare the equation with the standard form of the quadratic equation:

where h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:

So the equation of the parabola is:

To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.

The area of the shaded part is 42.14 ft² .

Area of the shaded part of the figure = area of square - area of quarter circle

Area of shaded part of the figure = s² - 1/4πr²

Where s = 14 ft and r = 14 ft

Substitute into the formula:

Area of shaded part = 14² - 1/4(3.14)(14²)

                                  = 42.14 ft²

Therefore, the area of the shaded part is: 42.14 ft² .

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Complete Question

Check image

The recursive formula for the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The first term of the sequence is given as follows:

[tex]a_1 = -\frac{1}{8}[/tex]

Each term is the previous term multiplied by two, hence the common ratio is given as follows:

q = 2.

Then each term is the previous term multiplied by two, and the recursive rule is given as follows:

[tex]a_n = 2a_{n - 1}[/tex]

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1. normally distributed if the sample size is 30 or larger.

2. Not always normally distributed.

3. Skewed to the right is still normally distributed

4. normally distributed.

1. normally distributed if the sample size is 30 or larger.

2. If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is not always normally distributed. It depends on the sample size and the shape of the population distribution.

3. The sampling distribution of the sample mean for a sample of 10 elements taken from a population with a bell-shaped distribution that is skewed to the right is still normally distributed, by the central limit theorem, as long as the sample size is sufficiently large (typically at least 30) or the population distribution is approximately normal. Therefore, the answer is normally distributed.

4. The sampling distribution of the sample mean for a sample of 36 elements taken from a population with a bell-shaped distribution is normally distributed regardless of the population's skewness. Therefore, the answer is "normally distributed".

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Answer: 64

Step-by-step explanation:

multiple all of them

The total cost of the fence needed for the Perimeter of the work site is $8,800. So the answer is option B.

Because the question involves many units of measurement, we must convert them all to the same unit in order to determine the answer.

1/4 mile is equivalent to 1320 feet (1 mile = 5280 feet).

The length of the fence required to surround the work site equals the perimeter of the work site. To calculate the length of the fence in yards, divide 1320 feet by 3 (since a yard is 3 feet long).

1320 feet ÷ 3 = 440 yards

So the length of the fence needed is 440 yards.

The fence costs $20.00 per yard, thus to get the total cost, multiply the length of the fence by the cost per yard:

440 yards x $20.00/yard = $8,800.00

Therefore, the total cost of the fence needed for the perimeter of the work site is $8,800.00.

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Answer:  D.  -1

Step-by-step explanation:

Your equation:

[tex]\sqrt[4]{(\sqrt[3]{64}) ^{2} } =(\frac{1}{2} )^{x}[/tex]       >We are going to work from the inside first then out

                                   The cube root of 64 is 4 because 4*4*4=64

[tex]\sqrt[4]{(4) ^{2} } =(\frac{1}{2} )^{x}[/tex]            > 4² = 4*4=16

[tex]\sqrt[4]{(16) } =(\frac{1}{2} )^{x}[/tex]           > the 4th root of 16 is 2 because 2*2*2*2=16

[tex]2 =(\frac{1}{2} )^{x}[/tex]                   > if you have the same bases you can set the

                                   exponents equal.  They are not the same but we

                                    are going to make them the same.  

[tex]2^{1} =(\frac{1}{2} )^{x}[/tex]                  > 2 is the same as 2^1,  i can make the bases the

                                   same if I can make the 2 a reciprocal.  That

                                   happens when I take the negative exponent of the

                                   number

[tex](\frac{1}{2} )^{-1} =(\frac{1}{2} )^{x}[/tex]             >Now that my bases are the same, I can make the

                                exponents =

-1 = x

Answer:

12.8

Step-by-step explanation:

Quotient means the answer of two things divided.

62.72/4.9=12.8

Answer:

1,110

Step-by-step explanation:

it's that because I added it all up in got thatv

The part of the cake with vanilla or lemon frosting is 1/5 by using arithmetic and algebraic expression.

Let's start by defining the variable "x" as the part of the cake with vanilla or lemon frosting.

According to the problem, Jonah uses vanilla frosting on 1/5 of the cake, which can also be written as x = 1/5.

Similarly, he uses lemon frosting on 2/5 of the cake, which can be written as x = 2/5.

We know that the sum of the parts of the cake with vanilla, lemon, and chocolate frosting should equal the whole cake. Since there are only three types of frosting, we can write:

x + x + chocolate frosting = 1

2x + chocolate frosting = 1

We also know that chocolate frosting covers the remaining part of the cake, which is 3/5. Therefore, we can write:

chocolate frosting = 3/5

Substituting this value into the previous algebraic expression, we get:

2x + 3/5 = 1

Subtracting 3/5 from both sides of the equation, we get:

2x = 2/5

x = 1/5

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x = -6.

[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]

Applying the distributive property of multiplication on the left hand side:

[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]

Applying the distributive property of multiplication:

[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]

Check the image below to see an illustration of this process.

[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]

Now simplifying on the right hand side (applying the same logic as last step).

[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]

[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]

[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]

[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]

[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]

That's correct!

x = -6 is the corect answer.

I'm taking linear algebra right now so this one hits home :)

Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!

You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):

[tex]\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}[/tex]

Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.

Simply subtract row 2 from row 1, shown below:

[tex]\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}[/tex]

Now, simplify and you will have the answer:

[tex]\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}[/tex]

Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!

Answer:

We can write 4x^2 + y^2 - 4xy - 16 as the product:

(2x - y + 4)(2x - y - 4)

Step-by-step explanation:

To write 4x^2 + y^2 - 4xy - 16 as a product, we can use the technique of completing the square. First, we can rearrange the terms to group the x terms and the y terms:

4x^2 - 4xy + y^2 - 16

Next, we can complete the square for the x terms and the y terms separately. For the x terms, we can add and subtract (2x)^2:

4x^2 - 4xy + (2x)^2 - (2x)^2 + y^2 - 16

Simplifying the first three terms gives:

(2x - y)^2 - (2x)^2 + y^2 - 16

For the y terms, we can add and subtract 16:

(2x - y)^2 - (2x)^2 + (y - 4)^2 - 16^2

Simplifying the second term gives:

-(4x^2) + 16x - (y^2) + 16y - 16^2

Therefore, we can write 4x^2 + y^2 - 4xy - 16 as the product:

(2x - y + 4)(2x - y - 4)

Answer:

$\boxed{52}$ dog owners would be expected to brush their dog's teeth.

Step-by-step explanation:

The value of B is 6 when the value of sin x degrees equals to 4/5.

In the given triangle diagram, the opposite side of x = 3b

The hypotenuse of the given triangle = 22.5

Given triangle is a right-angled triangle, in trigonometry, we know that in a right-angled triangle the sin x = opposite side of x / hypotenuse side

So, sin x = 3b/22.5

But, the given value is 4/5. So,

3b/22.5 = 4/5

3b = 90/5

3b = 18

b = 18/3

b = 6

From the above explanation, we can conclude that the value of b is 6.

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Answer:

the answer to the question provided is y = x

The solution set for each rational inequality:

Case 1: - 9 ≤ x < - 5

Case 3: Every real number except x = 1.

In this problem we find two cases of rational inequality, whose solution sets can be found by using algebra properties and sign laws. Now we proceed to solve on each case:

Case 1

(3 · x + 7) / (x + 5) ≥ 5

(3 · x + 7) / (x + 5) - 5 ≥ 0

[(3 · x + 7) - 5 · (x + 5)] / (x + 5) ≥ 0

(- 2 · x + 18) / (x + 5) ≥ 0

- 2 · (x - 9) / (x + 5) ≥ 0

The inequality is positive for - 9 ≤ x < - 5.

Case 3

(- x² - 1) / (- x² + 2 · x - 1) > 0

[(- 1) · (x² + 1)] / [(- 1) · (x² - 2 · x + 1)] > 0

(x² + 1) / (x² - 2 · x + 1) > 0

(x² + 1) / (x - 1)² > 0

The inequality is positive for all real number except x = 1.

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"The line has a positive slope and passes through the x-axis at -2. Additionally, it crosses through point (2, 1).

The formula in this case is 2x-y = -4. When we set the value of y to 0, we can use this equation to calculate the x-intercept: 2x0=42x=4. When we multiply both sides by 2, we obtain 2x2=42x=2. The x-intercept is therefore -2.

We may use the slope-intercept version of the equation, y = mx + b, where m is the slope and b is the y-intercept, to graph the line y = 4x - 2.

We can observe that the slope is m = 4 and the y-intercept is b = -2 by comparing y = 4x - 2 to y = mx + b.

Starting with the y-intercept of -2 on the y-axis, we can graph line by finding other points on it using the slope of 4.

To get to the point, if we move two units to the right, we must move up eight units. (2, 6). To get to the point, if we move two units to the left, we must move down eight units. (-2, -10).

According to the description and choices given, "The line has a positive slope and passes through the x-axis at -2" is the option that most closely matches our graph. Additionally, it crosses through point (2, 1).

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Answer:

14

Step-by-step explanation:

line from center to chord bisect chord

so x = 14

The equation of the line representing Main Street is option C. y = -2x + 11

The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.

[The product of slopes of perpendicular Lines is -1.)

y - 1 = -2 (x -5)

y - 1 = -2x +10

y = -2x + 10 + 1

y = -2x + 11

Therefore, the best choice is option C. y = -2x + 11

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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.

We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).

Using the point-slope form of a line, we have:

y - 3 = 2(x - 0)

y - 3 = 2x

y = 2x + 3

Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.

To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:

y - 1 = -1/2(x - 5)

y - 1 = -1/2x + 5/2

y = -1/2x + 7/2

Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).

Answer:

the temperature at 7 am was -36.7 degrees.

Step-by-step explanation:

Let's denote the temperature at 7 am by "x". Since the temperature increased by 8.4 C between 7 am and 11 am, we can set up the equation:

x + 8.4 = -28.3

Subtracting 8.4 from both sides, we get:

x = -36.7

Therefore, the temperature at 7 am was -36.7 degrees.

The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0

From the question, we are to calculate the probability of choosing a ball numbered 29

From the formula for probability

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given information,

"A lottery game contains 28 balls numbered 1 through 28"

This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.

Now,

We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,

Number of favorable outcomes = 0

Total number of possible outcomes = 28

Thus,

Probability of choosing a ball numbered 29 = 0/28

Probability of choosing a ball numbered 29 = 0

Hence,

Probability of choosing a ball numbered 29 is 0

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The transformation of f(x) to g(x) is (a) f(x) is shifted up 1 unit to g(x).

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the graph, we can see that

So, we have

Difference = 1 - 0

Evaluate

Difference = 1

This means that the transformation of f(x) to g(x) is (a) f(x) is shifted up 1 unit to g(x).

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The volume of each cup shown above are as follows;

Volume of small cup = 50.24 in³.

Volume of medium cup = 127.56 in³.

Volume of large cup = 226.08 in³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have:

Volume of small cylinder, V = 3.14 × 2² × 4

Volume of small cylinder, V = 50.24 in³.

Volume of medium cylinder, V = 3.14 × 2.5² × 6.5

Volume of medium cylinder, V = 127.56 in³.

Volume of large cylinder, V = 3.14 × (6/2)² × 8

Volume of large cylinder, V = 226.08 in³.

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