Jack is constructing the circumscribed circle of ∆abc with just a compass and a straightedge. which step should he take next in completing the construction?

B. 3y = 2x – 9

is not perpendicular to the given line.

The slopes of perpendicular lines are negative reciprocals

Given the line

y = -1.5x + 11

The slope is -1.5 or -3/2

Any line perpendicular to the one above must have its slope as 2/3

A. The slope is 2/3 . CORRECT

B. The slope is 2/3. CORRECT

C. The slope is 3/2. WRONG

D. The slope is 2/3. CORRECT

Answer:

89.6 is 67.571644% of 132.6

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

The probability that the sample average amount of time taken on each day is at most 11 min is 0.5167

To solve for the probability proportion, we make use of the z statistic. The procedure to do is to calculate for the z value and using the standard probability tables, we can look up for the p value. The formula for z score is:

z =(x – μ) / (σ / √n))

where,

x = sample score = 11

μ = sample mean= 10

σ = standard deviation = 4

n = sample size

Calculating for the z and p value when n = 5:

z =(11 – 10) / (2 /√(5))

z = 0.55

Using the tables, p(5) = 0.7088

Calculating for the z and p value when n = 6:

z =(11 – 10) / (4/ √6))

z = 0.61

Using the tables, p(6) = 0.7290

If both days should be occurring, therefore the total probability that each day is at most 11 min is:

p total = p(5) * p(6)

p total = 0.7088 * 0.7290

p total = 0.5167

Hence the average amount of time taken on each day is at most 11 min.

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The correct statement is "If an appropriate confidence interval does not contain 25%."

To determine whether the pamphlet needs updating, we can construct a confidence interval for the proportion of high school students planning to attend a community college based on the survey results. If the confidence interval does not contain the value stated in the pamphlet (25%), it would suggest that the pamphlet needs updating.

In this case, the sample proportion is 46/150, or 0.3067 (approximately). To construct the confidence interval, we can use the formula for a proportion confidence interval:

p ± z * √(p * (1 - p) / n)

where p is the sample proportion, z is the z-score corresponding to the desired confidence level (95% in this case), and n is the sample size.

Using a z-score of 1.96 (for a 95% confidence level), the confidence interval would be:

0.3067 ± 1.96 * √(0.3067 * (1 - 0.3067) / 150)

Calculating this interval would give us the lower and upper bounds. If this interval contains 25%, then it would suggest that the pamphlet does not need updating. However, if the interval does not contain 25%, it would indicate that the pamphlet needs to be updated.

Therefore, the correct statement is "If an appropriate confidence interval does not contain 25%."

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The market rate of return on the Dayton Rapur stock is approximately 4.59%.

To calculate the market rate of return on the Dayton Rapur stock, we need to use the dividend discount model (DDM). The DDM calculates the present value of expected future dividends and divides it by the current stock price.

First, let's calculate the expected dividend for the next year. The annual dividend is $2.17 per share, and it increases by 2.56% annually. So the expected dividend for the next year is:

Expected Dividend = Annual Dividend * (1 + Annual Dividend Growth Rate)

Expected Dividend = $2.17 * (1 + 0.0256)

Expected Dividend = $2.23

Now, we can calculate the market rate of return using the DDM:

Market Rate of Return = Expected Dividend / Stock Price

Market Rate of Return = $2.23 / $48.49

Market Rate of Return ≈ 0.0459

Finally, we convert this to a percentage:

Market Rate of Return ≈ 0.0459 * 100 ≈ 4.59%

Therefore, the market rate of return on the Dayton Rapur stock is approximately 4.59%.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

Step-by-step explanation:

Total surface area of a cone \(S\) = \(\pi r^{2}+\pi rl\\\)

Since the diagram is half of a cone, its surface area will be \(S = \frac{\pi r^{2} +\pi rl}{2}\)

r = radius of the cone

l = slant height

From the diagram diameter of the cone = 16m;

r = 16/2 = 8m

l = 17m

\(S = \frac{\pi (8)^{2} +\pi (8)(17)}{2}\\S = \frac{64\pi + 136\pi }{2} \\S = 32\pi + 68\pi \\S = 100\pi cm^{2}\)

We have the next system of equations

First, we need to substitute the value of y of the second equation in the first equation.

Then we simplify the expression

then we sum like terms

then we isolate the x

the value of x is 1.

Then to know the value of y we will substitute the value of x in the second equation

the value of y is 4.

The solution of the system of equations is x=1, y=4 in point notation (1,4) this system only has one solution.

Answer:

The price of the socks is dollar 8

Pls mark nrainliest

Answer:

$8

Step-by-step explanation:

Using the information we already know, we can form an equation:

Let x be the socks' original price.

\((24+x)\) × \(0.75=24\)

Divide both sides by 0.75

\(24+x=32\)

Subtract 24 from both sides

\(x=8\)

The socks' original price was $8.

Step-by-step explanation:

Las organizaciones son estructuras administrativas y sistemas administrativos creadas para lograr metas u objetivos con el apoyo de las propias personas, o con apoyo del talento humano o de otras características similares.

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Safety data sheets (SDS) are not only required when there are 10 gallons. This statement is false. SDS, also known as material safety data sheets (MSDS), are required for hazardous substances, regardless of the quantity.

Safety data sheets provide detailed information about the potential hazards, handling, and emergency measures for substances. They are required under various regulations, such as the Occupational Safety and Health Administration (OSHA) Hazard Communication Standard (HCS) in the United States.

The quantity of the substance does not determine the need for an SDS. For example, even if a small amount of a highly hazardous substance is present, an SDS is still necessary for safety reasons.

SDS help workers and emergency personnel understand the risks associated with a substance and how to handle it safely. It is essential to follow proper safety protocols and provide SDS for hazardous substances, regardless of the quantity.

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Answer:

x ≥ 5

Step-by-step explanation:

3x - 8 ≥ 7 ( add 8 to both sides )

3x ≥ 15 ( divide both sides by 3 )

x ≥ 5

Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

Answer:

Step-by-step explanation:

Remark

There is only 1 way that you can get 1 2 3 4 5 in that order.

There are many possibilities of drawing 5 numbers from a total of 9 possible ones.

Total number of drawing 5 numbers.

Total = 9 * 9 * 9 * 9 * 9

Total = 59049

So putting the two facts together you get

Chance of getting (1 2 3 4 5)  = 1/59049

Answer: .000016935

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:hpe this helps

Answer:

B) 2:5

Step-by-step explanation:

it should be 2:5 since the girls are only 10, while the boys are 25 in number which makes their ratio bigger.

The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.

We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).

The probability of getting exactly 2 tails is given by:

P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5

= (21 * 9/16 * 1/1024)

= 189/16384

So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.

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Answer:

y = 1/3x − 6

Step-by-step explanation:

Answer:

y = 1/3x − 6

Step-by-step explanation:

:)

The x-intercepts with multiciplity greater than 1 is x = 0

The number of distinct intercepts is 3 and the number of zeros is 4

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

f(x) = x²(x + 2)(x - 7)

The x-intercepts with multiciplity greater than 1 is the factor that has a power greater than 1

So, we have

x² = 0

This gives

x = 0

The number of distinct intercepts is the number of factors i.e. 3

The number of zeros is the sum of powers

i.e. Zeros = 2 + 1 + 1

Zeros = 4

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The expression for cot(5π/9) in terms of the cotangent of a positive acute angle is (1/2)(√(5 - 2√5)/√(5 + 2√5)) - (1/2)(√(5 + 2√5)/√(5 - 2√5)).

Let's start by calculating the angle for cot5π9.

From the given angle of cot5π/9, we can find the value of its complementary angle, which is equal to 4π/9.

We know that the cotangent of an angle is the reciprocal of the tangent of its complementary angle.

We'll start by calculating the tangent of the complementary angle:

tan(4π/9) = sin(4π/9)/cos(4π/9)

Let's compute the values of sin(4π/9) and cos(4π/9)

individually:

cos(4π/9) = cos(π - 5π/9) = -cos(5π/9)sin(4π/9) = sin(π - 5π/9) = sin(5π/9)

We know that the value of sin(5π/9) can be derived from the formula for the golden ratio as follows:

sin(5π/9) = sin(π - 4π/9) = sin(4π/9)/2 + cos(4π/9)/2 = (1/2)(√(5 + 2√5)/2) + (1/2)(√(5 - 2√5)/2)cos(5π/9) = cos(π - 4π/9) = -cos(4π/9)/2 + sin(4π/9)/2 = -(1/2)(√(5 + 2√5)/2) + (1/2)(√(5 - 2√5)/2)
So, we get,

tan(4π/9) = (1/2)(√(5 + 2√5)/2) - (1/2)(√(5 - 2√5)/2) / -(1/2)(√(5 + 2√5)/2) + (1/2)(√(5 - 2√5)/2)

We can simplify this equation to get the expression for cot5π/9.

Thus, the expression for cot(5π/9) in terms of the cotangent of a positive acute angle is (1/2)(√(5 - 2√5)/√(5 + 2√5)) - (1/2)(√(5 + 2√5)/√(5 - 2√5)).

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Answer:

79.2 kilometres per hour

Step-by-step explanation:

1 km = 1000 m

1 hr = 3600 sec. To convert km/hr into m/sec,

We multiply the speed which in this case is 22m/s

by 3.6 giving 79.2 kmh. Therefore 22m/s into kilometer is 79.2 kmh.

For any value of n, the expression evaluates to (n+1)/1, which is equivalent to n+1.

To determine a formula for the expression 11⋅2 12⋅3 ... 1n⋅(n-1) for a given value of n, we can observe the pattern and derive a general formula.

Let's examine the terms of the expression for different values of n:

For n = 1: 11⋅2 = 22

For n = 2: 11⋅2 12⋅3 = 88

For n = 3: 11⋅2 12⋅3 13⋅4 = 528

For n = 4: 11⋅2 12⋅3 13⋅4 14⋅5 = 3168

From these examples, we can observe that each term in the expression is the product of two consecutive numbers, with the first number ranging from 11 to n and the second number ranging from 2 to (n+1).

Based on this pattern, we can derive a general formula for the expression. Let's denote the expression as f(n):

f(n) = (11⋅2) (12⋅3) ... (1n⋅(n-1))

To find the formula, we can rewrite the expression using a product notation:

f(n) = ∏(i=1 to n) (i(i+1))

Expanding the product notation, we have:

f(n) = (1⋅2)(2⋅3)(3⋅4)...(n(n+1))

Next, we can observe that the terms in the numerator and denominator cancel out:

f(n) = 1⋅(n+1)

Therefore, the formula for the expression 11⋅2 12⋅3 ... 1n⋅(n-1) for a given value of n is:

f(n) = n+1

In fraction form, this can be expressed as:

f(n) = (n+1)/1

In conclusion, the formula for the expression 11⋅2 12⋅3 ... 1n⋅(n-1) is f(n) = n+1.

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Answer:

C = 4 + 0.5d

Step-by-step explanation:

General equation: y = ax + b, with b is fixed term and a is rate per x.

Here,

C = y

fixed term b = 4

rate a = 0.5 per kilometer (d)

1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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To differentiate the expression Y(X) = 2V*-1, we can use the power rule of differentiation. First, we need to consider that V* is a variable and treat it as a constant when differentiating with respect to X.

So, differentiating the expression Y(X) = 2V*-1 with respect to X, we get:

dY/dX = d/dX (2V*-1)
= 2dV*/dX

We can simplify this expression by storing the result in a variable called "firstder":

import sympy as sp
Vstar = sp.Symbol('V*')
X = sp.Symbol('X')

firstder = 2*sp.diff(Vstar,X)

Now, the variable "firstder" contains the symbolic expression for the derivative of Y with respect to X.

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Answer:

140 in^2

Step-by-step explanation:

Take the outside dimensions of the LARGE rectangle

11 x 17 = 187 in^2

 subtract the two corner cutout rectangles

    187 - 8x4   -  3 x 5   = 140 in^2

Diagram

Answer:

9

Step-by-step explanation:

Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's  much easier to form a rectangle and multiply the width and the length and then divide it by 2  

the interval in which g(x) is positive is [3, ∞].

Here we have the function:

g(x) = ∛(x - 3)

The interval in which the function is positive is defined by:

g(x) > 0.

Then we have:

∛(x - 3) > 0.

We need to solve that inequality for x.

∛(x - 3) > 0

The cube root respects the sign of the argument, then:

x - 3 > 0

x > 3

Then the interval in which g(x) is positive is [3, ∞].

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