Write an equation in slope-intercept form for the perpendicular bisector of the segment with the given endpoints. Justify your answer. (Lesson 5-1)
D(-2,4) and E(3,5)

Answer: w+x=90

z=y+90

Step-by-step explanation: because the sum of the inner angles of triangle is 180. given that one angle is 90 degrees the sun of x and w has to be 180-90=90

for the second part, you have to use the triangle exterior angle theorem: an exterior angle of a triangle is equal to the sum of the opposite interior angles. The opposite interior angles in this case is 90 degrees and y

The direction and by how many units should f(x) be shifted to match g(x) is Left by 6 units. Option C

To determine the direction and magnitude of the shift needed for f(x) to match g(x), we can compare the corresponding values of f(x) and g(x) in the table.

For x = -2, f(x) = 4 and g(x) = 64.

For x = -1, f(x) = 1 and g(x) = 49.

For x = 0, f(x) = 0 and g(x) = 36.

For x = 1, f(x) = 2 and g(x) = 25.

For x = 2, f(x) = 4 and g(x) = 16.

By comparing the values, we can observe that the graph of f(x) is shifted to the right compared to g(x). To match the graph of g(x), we need to shift f(x) to the left.

The magnitude of the shift can be determined by the difference in x-values between the corresponding points of f(x) and g(x).

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Answer:

The 3 possible values of x are;

6, 4 and 2

Step-by-step explanation:

If the triangle is isosceles, then two of the sides must be equal

So we equate the sides, 2 at a time to get the different values of x

3x + 4 = 2x + 10

3x-2x = 10-4

x = 6

3x + 4 = x + 12

3x-x = 12-4

2x = 8

x = 8/2 = 4

2x + 10 = x + 12

2x - x = 12-10

x = 2

a) the unique ratio of equilibrium prices is p1/p2 = 1/1 = 1.

b) the Pareto efficient allocations occur when agent 1 consumes all of good 1 and agent 2 consumes all of good 2. This means that x11 = 1, x21 = 0, x12 = 10, and x22 = 10.

c) To make this a Walrasian equilibrium, we can adjust the endowments as follows:

Agent 1's new endowment: (1, 10 - x12) = (1, 0)

Agent 2's new endowment: (0, 10 - x22) = (0, 0)

By adjusting the endowments, we ensure that the total endowment matches the total demand at the Pareto efficient allocation, making it a Walrasian equilibrium.

a) To find the Walrasian equilibria of the economy, we need to determine prices at which the demand for each good matches the total endowment of the economy.

Let's denote the prices of goods 1 and 2 as p1 and p2, respectively. The demand for good 1 by agent i is given by x_i1^d = e_i1 - (p1/p2)e_i2, where e_i1 is the endowment of good 1 for agent i and e_i2 is the endowment of good 2 for agent i.

The total demand for good 1 in the economy is x_11^d + x_21^d = (1 - (p1/p2)) + 0 = 1 - (p1/p2).

Similarly, the total demand for good 2 in the economy is x_12^d + x_22^d = 10 + 10 = 20.

Since the total demand for each good must equal the total endowment, we have the following equations:

1 - (p1/p2) = 1 --> p1 = p2

20 = 10 + 10(p1/p2)

Simplifying the second equation, we get:

20(p2/p1) = 20

p2 = p1

Therefore, the unique ratio of equilibrium prices is p1/p2 = 1/1 = 1.

b) Pareto efficient allocations are those where it is not possible to make one agent better off without making the other worse off. To find the Pareto efficient allocations, we can compare the agents' utilities.

Agent 1's utility function is u1(x11, x12) = v(x11) + x12.

Agent 2's utility function is u2(x21, x22) = v(x21) + x22.

Since v is a strictly concave and increasing function, it implies that for a fixed value of x_i2, increasing x_i1 will always increase the utility of agent i. Similarly, increasing x_i2 will also increase the utility.

Therefore, the Pareto efficient allocations occur when agent 1 consumes all of good 1 and agent 2 consumes all of good 2. This means that x11 = 1, x21 = 0, x12 = 10, and x22 = 10.

c) To make a Pareto efficient allocation a Walrasian equilibrium, we need to adjust the endowments such that the total demand for each good matches the total endowment at the given Pareto efficient allocation.

In this case, the Pareto efficient allocation is x11 = 1, x21 = 0, x12 = 10, and x22 = 10.

To make this a Walrasian equilibrium, we can adjust the endowments as follows:

Agent 1's new endowment: (1, 10 - x12) = (1, 0)

Agent 2's new endowment: (0, 10 - x22) = (0, 0)

By adjusting the endowments, we ensure that the total endowment matches the total demand at the Pareto efficient allocation, making it a Walrasian equilibrium.

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The uppercase letter H has reflectional symmetry and does not have rotational symmetry or point symmetry.

The uppercase letter H has reflectional symmetry. Reflectional symmetry, also known as mirror symmetry, means that there is a line (axis) along which the shape can be divided into two equal halves that are mirror images of each other. In the case of the letter H, a vertical line passing through the center of the letter can be drawn as the axis of symmetry. When the letter H is folded along this line, the two halves perfectly match.

The letter H does not have rotational symmetry. Rotational symmetry refers to the property of a shape that remains unchanged when rotated by a certain angle around a central point. The letter H cannot be rotated by any angle and still retain its original form.

The letter H also does not have point symmetry, which is also known as radial symmetry or rotational-reflectional symmetry. Point symmetry occurs when a shape can be rotated by 180 degrees around a central point and still appear the same. The letter H does not exhibit this property as it does not have a central point around which it can be rotated and remain unchanged.

In summary, the uppercase letter H exhibits reflectional symmetry but does not possess rotational symmetry or point symmetry.

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To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

\(-4y^2-2x+13\)

Step-by-step explanation:

\(-6x +4y^2+3-8y^2+4x-7x+10\\4y^2-8y^2-6x+4x-7x+10+3\\-4y^2-2x+13\)

Answer: d

Step-by-step explanation:

Answer:

Step-by-step explanation:

True

False

False

Answer:

using the formula

y -y1 = m(x -x1)

y -6 = 2(x -5)

y -6 = 2x -10

y = 2x -10+6

y =2x -4(equation of the line)

Answer:

See below ↓↓↓↓

Step-by-step explanation:

Top left box

f(x) = 2x² + 4

g(x) = 2f(x) - 3

Top right box

f(x) = 2x² + 4

g(x) = 2f(x) + 3

Bottom left box

f(x) = 2x² - 4

g(x) = 2f(x) - 3

Bottom right box

f(x) = 2x² - 4

g(x) = 2f(x) +3

This circular swimming pool has 4595  ft³ of water in it.

According to what is said, the depth grows linearly from 2 feet at the south end to 7 feet at the north end and remains constant along east-west lines.

The given data in the question-

Diameter of  circular swimming Pool; d = 30 ft

Radius r = d/2 = 30/2 = 15 ft

The average depth is given as;

avg (h) = (4 + 9)/2

avg (h) = 6.5 ft

Formula for circular area is;

A = πr²

Put the values;

A = π × 15²

A = 225π

Formula for circular volume is;

Volume = Area × depth

Volume = 225π × 6.5

Volume = 4594.57 ft³

Rounding to a whole number;

Volume =  4595 ft³

Thus, this circular swimming pool has 4595  ft³ of water in it.

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The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer:

Step-by-step explanation:

i think that it is either -7 - -8 or -7 + 8 or -7+-8.

Two expressions that each represent the total change in Greg's bank account balance after his deposit and purchase are

Expression a  = 7 - 8

Expression b = -8 - (-7)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

For example, x + y is an expression, where x and y are terms having an addition operator in between.

Given,

Greg records deposit of $7

He records purchase of $8 b

Total change = 7 + (-8)

Expression a  = 7 - 8

Expression b = -8 - (-7)

Hence, 7 - 8 and -8 - (-7) are the two expressions for total change in Greg's bank account after his deposit and purchase.

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The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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The number of players the team brought to the tournament is 12.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Given that, Members of a softball team raised $1525.50 to go to a tournament.

Let x be the number of players the team can bring to the tournament.

Members of a softball team rented a bus for $1075.50 and they budgeted $37.50 per player for meals.

Now, the equation is

1075.50+37.50x=1525.50

37.50x=1525.50-1075.50

37.50x=450

x=450/37.50

x=12

Therefore, the number of players are 12.

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Answer:

-11y^5+2x

Step-by-step explanation:

subtract 3y^5 from -8y^5

Step-by-step explanation:

part1

the mean value is

(87+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+83) / 18

= 1665 / 18 = 92.5

part2

this is the sum of the absolute value of the differences bergen the individual sites and the mean value divided by the number of data points :

(5.5+7.5+1.5+13.5+0.5+7.5+2.5+9.5+3.5+6.5+7.5+1.5+3.5+2.5+7.5+0.5+3.5+9.5)/18

= 94/18 = 5.222222222... ≈ 5.2

part3

how many scores are less than 5.2 away (plus or minus) from the mean value ? in other words, how many differences in the part2 calculation were smaller than or equal to 5.2 ?

there are 9 scores meeting that criteria :

94, 92, 95, 89, 91, 89, 95, 93, 96

Answer:

ewfwefwfewfwfwe

Step-by-step explanation:

Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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The result of the expression in this problem is given as follows:

log3(27) - log5(5) = 1.

The logarithmic expression for this problem is given as follows:

log3(27) - log5(5)

The logarithms are given as follows:

Hence the result of the expression in this problem is given as follows:

log3(27) - log5(5) = 3 - 1 = 2.

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Answer:

350 hours

Step-by-step explanation:

Correlation coefficient helps us to know how strong is the relation between two variables. The strength of the model is a strong positive correlation.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

Hence, the strength of the model is a strong positive correlation.

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Answer:

B) a strong positive correlation

Step-by-step explanation:

The correct answer is a. high. In a one-sample chi-square test, the observed frequencies of the variable being studied are compared to the expected frequencies assuming a particular distribution or hypothesis.

The chi-square test statistic measures the difference between the observed and expected frequencies and determines whether this difference is statistically significant.

If the respondents are distributed very unequally across the levels of the variable being studied, the observed frequencies will be very different from the expected frequencies. This will result in a large difference between the observed and expected frequencies, leading to a high value for the chi-square test statistic.

The chi-square value is calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies. If the respondents are distributed very unequally across the levels of the variable being studied, the expected frequencies will be very different from the observed frequencies, resulting in a high value for the chi-square test statistic.

Therefore, in a one-sample chi-square test, if your respondents are distributed very unequally across the levels of your variable, your chi-square value will be high.

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Answer:

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

Hope this helps!

Step-by-step explanation:

Answer:

\(\frac{64}{x}\)  quotient means you divide

Step-by-step explanation:

The probability of selection of diagonal which is not shortest nor longest is 13/17.

We know very well that Icosagon has 20 sides.

If any diagonal is possible, it can be possible by connecting two points, so to choose r objects from n objects can be done by ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\)

So, number of ways to choose diagonal = \(^2^0C_{2}\)

After that we need to subtract 20 ways as single point can lead to diagonal making.

So, total number of ways to choose 20 diagonals =  170

Now, talking about the shorter diagonal

so, shorter diagonal =Diagonal connecting(A₁A₃, A₂A₄,.....) =20 diagonals.

Now, talking about longer diagonal=Diagonal connecting(A₁A₈,A₂A₉.........) = 20 diagonals

So, we have total chances of ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\) and possible number of chances of selection of shorter and longer diagonal

So, according to the formula,

Probability= Favorable outcome /Total outcome

Probability = [(Total ways to select diagonals - (Ways to select shorter diagonal) - Ways to select longer diagonal)]/(Total number of ways)

Probability = (170-20-20)/170

Probability = 130/170

Probability = 13/17

Hence, the probability of selecting a  diagonal such that it is not shortest nor longest is 13/17.

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When k = 5, the pair of linear equations has infinitely many solutions.

To find the value of k for which the pair of linear equations has infinitely many solutions, we need to check if the equations are dependent.

Let's rewrite the given equations:

Equation 1: 2x + 3y = 7
Equation 2: (k + 1)x + (2k – 1)y = 4k + 1

To determine if the equations are dependent, we need to check if the ratio of the coefficients of x and y in both equations is equal.

For Equation 1, the ratio of the coefficients is 2/3.
For Equation 2, the ratio of the coefficients is (k + 1)/(2k – 1).

For these two ratios to be equal, we can set up an equation:

2/3 = (k + 1)/(2k – 1)

Now, let's solve for k:

2(2k – 1) = 3(k + 1)
4k – 2 = 3k + 3
k = 5

So, when k = 5, the pair of linear equations has infinitely many solutions.

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