An ancient ruler is 9 inches long. The only marks that remain are at 1 inch and 2 inches, 9 inches and one mark. It is possible to draw line segments of the whole number lengths from 1 to 9 inches without moving the ruler. What inch number is on the other mark

o find the coordinates of the gates in the third quadrant, we need to find the points where the circle and the line intersect in the third quadrant.

Substituting y = 2x into x² + y² - 4x = 9, we get:

x² + (2x)² - 4x = 9

5x² - 4x - 9 = 0

Using the quadratic formula, we find:

x = (-(-4) ± √((-4)² - 4(5)(-9))) / (2(5))

x = (4 ± √136) / 10

We can discard the positive root since it is in the first quadrant. The negative root corresponds to the x-coordinate of the point of intersection in the third quadrant:

x = (4 - √136) / 10 ≈ -0.433

Substituting this value into y = 2x, we get:

y = 2(-0.433) ≈ -0.866

Therefore, the ordered pair that represents the location of the gates in the third quadrant is (-0.433, -0.866).

We denote triangle ABC, angle A measures 90°, angle B measures 30° and angle C measures 60°.

We apply the cosine of 30 degrees, becuase m(∡A) = 90° and find the hypotenuse of triangle ABC:

cos = (adjacent side) / (hypotenuse)

⇔ cos B = AB/BC ⇔

⇔ cos 30° = 8√3/v ⇔

⇔ √3/2 = 8√3/v ⇔

⇔ √3 • v = 2 • 8√3 ⇔

⇔ v√3 = 16√3 ⇔

⇔ v = 16√3 ÷ √3 ⇔

⇔ v = 16 millimeters

Hope that helps! Good luck! :)

The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.


1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).

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_____________________________

_____________________________

To test the claim that the outcomes of rolling the modified die are not equally likely, we can use a chi-square goodness-of-fit test. We will use a significance level of 0.05.

The null hypothesis is that the outcomes are equally likely. The alternative hypothesis is that the outcomes are not equally likely.

First, we need to calculate the expected frequencies assuming that the outcomes are equally likely.

Since the die has six sides, each outcome has a probability of 1/6. Therefore, the expected frequency for each outcome is 200/6 = 33.33.

To calculate the test statistic [tex]x^2[/tex], we can use the formula:

[tex]x^2 = Σ (observed frequency - expected frequency)^2 / expected frequency[/tex]

where Σ is the sum over all outcomes.

Using the observed and expected frequencies given in the problem, we get:

[tex]x^2 = (27 - 33.33)^2 / 33.33 + (31 - 33.33)^2 / 33.33 + (42 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33 + (28 - 33.33)^2 / 33.33 + (32 - 33.33)^2 / 33.33[/tex]

[tex]x^2 = 3.02[/tex]

The degrees of freedom for this test is 6 - 1 = 5 (since there are 6 sides on the die).

Using a chi-square distribution table (or calculator), we can find the critical value for a significance level of 0.05 and 5 degrees of freedom to be 11.070.

Since the test statistic x^2 = 3.02 is less than the critical value of 11.070, we fail to reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the outcomes of rolling the modified die are not equally likely.

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The probability of randomly selecting a quarter from the bag is 5/16

Assuming that all the coins have the same probability of being randomly drawn, the probability of getting a quarter is equal to the quotient between the total number of quarters and the total number of coins in the bag.

There are 6 quarters, and the total number of coins is 16, then the probability of randomly selecting a quarter is:

P = 5/16

The correct option is the last one.

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Answer:

C. Triangles A and C.

Step-by-step explanation:

In triangles A and C, the ratios of corresponding sides are equal, and the corresponding angles are congruent.

The weight of the statue to the nearest ounce is 576 ounces.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is given as 10 inches, the radius is half of that, or 5 inches.

Using the formula, we can find the volume of the sphere:

V = (4/3)πr^3

V = (4/3)π(5^3)

V = (4/3)π(125)

V = 523.6 cubic inches (rounded to one decimal place)

Since we know the weight of the clay per cubic inch, we can find the weight of the statue by multiplying the volume by the weight per cubic inch:

Weight = Volume × Weight per cubic inch

Weight = 523.6 in^3 × 1.1 oz/in^3

Weight = 575.96 oz (rounded to two decimal places)

Therefore, the weight of the statue is approximately 576 ounces or 36 pounds (rounded to the nearest pound).

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Out of the 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b and does not like cola a is 0.2 or 20%, which is the answer. The answer is option B.

The probability that the student likes cola b and does not like cola a can be calculated as follows

Let's start by finding the number of students who like only cola b. We know that 50 students like cola b in total, but 30 of those students also like cola a. Therefore, the number of students who like only cola b is

50 - 30 = 20

So, out of 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b is

P(likes only cola b) = 20/100 = 0.2

Therefore, the probability that the student likes cola b and does not like cola a is 0.2.

The answer is option B: 0.2.

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--The given question is incomplete, the complete question is given

" In a class of 100 students, 60 students likes cola a, 50 students likes cola b  and 30 students likes both.  

From class a student is randomly chosen from the group.

what is the probability that the student likes cola b and does not like cola a?

0.1

0.2

0.3

0.4 "--

This situation represents exponential decay because the depth of the lake decreases over time.

Exponential decay is a mathematical term used to describe the process of decreasing over time at a constant rate where the amount decreases by a constant percentage at regular intervals. It is a type of exponential function where the base is less than 1.

In other words, the quantity is decreasing by a fixed percentage at regular intervals.

The rate of decay, r, is equal to 0.98 because the depth decreases by 2% per year.

So the depth of the lake each year is 0.98 times the depth in the previous year. It will take between 5 and 6 years for the depth of the lake to reach 26.7 meters.

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The value of sin(θ) = √15/4

The value of csc(θ) = [tex]\sqrt[4]{\frac{15}{15} }[/tex]

The value of sec(θ) = 4

The value tan(θ) = ±√15

The value of cot(θ) = ±√15/15

We can use the identity sec²(theta) - 1 = tan²(theta) to find the value of tan(theta).

Given sec(θ) = 4, we have:

sec²(θ) = 4² = 16

Then, using the identity:

tan²(θ) = sec²(θ) - 1 = 16 - 1 = 15

Taking the square root of both sides, we get:

tan(θ) = ±√(15)

Since sec(θ) is positive, we know that cos(theta), which is the reciprocal of sec(θ), is also positive. This tells us that θ is in the first or fourth quadrant, where sin(θ) is also positive.

Therefore:

sin(θ) = √(1 - cos²θ))

= √(1 - (1/16))

= √15/16)

= √(15))/4

Using the reciprocal identities, we can find the values of csc(θ) and cot(θ):

csc(θ) = 1/sin(θ)

= 4√(15)

[tex]\sqrt[4]{\frac{15}{15} }[/tex]

cot(θ)

= 1/tan(θ)

= ±√(15)/15

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Answer:

-7 feet

Step-by-step explanation:

-3-4 = -7, so it is -7 feet

The height of the right circular cone ,candle is approximately 6.8 inches.

To find the height of the third candle, which is a right circular cone with a volume of 16 cubic inches and a radius of 1.5 inches, we will use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

1. Substitute the given values into the formula: 16 = (1/3)π(1.5)^2h
2. Simplify the equation: 16 = (1.5^2 * π * h) / 3
3. Solve for h:
  a. Multiply both sides by 3: 48 = 1.5^2 * π * h
  b. Divide by π: 48/π = 1.5^2 * h
  c. Divide by 1.5^2: (48/π) / 1.5^2 = h
4. Calculate the height, and round to the nearest tenth: h ≈ 6.8 inches

The height of the candle is approximately 6.8 inches.

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Answer: Box and whisker plots are plots on number lines with a box and two lines off the edges, called whiskers. The box has a line at the upper quartile(1), one at the lower quartile(2), and one in the center of the box at the median(3). The two lines go to the ends of the data, one at the minimum(4) and one at the maximum(5).

  4     2     3       1             5

   |-----[___|____]-----------|

₀__₁__₂__₃__₄__₅__₆__₇__₈

I hope this helps.

This function is not differentiable at all points in [tex]R^2[/tex]. To see this, consider the points on the x-axis, where y = 0. At these points, the function is not differentiable because it has a sharp corner.

To show that the function f(x, y) = |y| is differentiable at (0, 0), we need to show that there exists a linear transformation L such that:

[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2)} = 0[/tex]

where f(0,0) = 0 since |0| = 0.

We have:

f(0+h,0+k) - f(0,0) = |k|

Now we need to find L(h,k), which is a linear transformation of (h,k) that approximates f(0+h,0+k) - f(0,0) near (0,0). We can take:

L(h,k) = 0

Since L is a constant function, it is a linear transformation. Also, we have:

f(0+h,0+k) - f(0,0) - L(h,k) = |k|

So we have:

[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2) } = lim (h,k) - > (0,0) |k| / \sqrt{(h^2 + k^2)}[/tex]

Using the squeeze theorem, we can show that this limit is equal to 0, since[tex]|k| < = \sqrt{(h^2 + k^2)}[/tex] for all (h,k) and[tex]lim (h,k) - > (0,0)\sqrt{ (h^2 + k^2) } = 0.[/tex]

Therefore, f(x, y) = |y| is differentiable at (0,0).

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Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.

First, convert 15.8 liters to milliliters:

15.8 L = 15,800 mL

Let x be the number of 400 ml juice bottles filled, and let y be the number of 1 liter juice bottles filled.

The total amount of juice filled can be represented as:

400 ml/bottle * x + 1000 ml/bottle * y = 15,800 ml

Simplifying, we get:

4x + 10y = 158

We also know that there are 3200 ml of juice left:

400 ml/bottle * (x - 3200/400) + 1000 ml/bottle * y = 0

Simplifying, we get:

x + 2.5y = 28

We now have two equations with two variables. Solving for x and y, we get:

x = 6

y = 8

Therefore, Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.

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The probability that cards #1, #2, and #3 are still in order on the top of the stack is 0.03%. Therefore, the correct option is D.

To find the probability, we need to calculate the number of ways in which the first 3 cards can remain in order on the top of the stack, and divide it by the total number of ways the cards can be arranged.

The number of ways in which the first 3 cards can remain in order is 3! (3 factorial), because there are 3 cards and they can be arranged in 3! = 6 ways.

The total number of ways the cards can be arranged is 10!, because there are 10 cards and they can be arranged in 10! = 3,628,800 ways.

So, the probability is:

3! / 10! = 6 / 3,628,800 = 0.000166 = 0.0166%

We can convert it to a percentage by multiplying by 100:

0.0166 x 100 = 1.66%

However, this is the probability that the first 3 cards are in a specific order, not necessarily the original order. Since the question asks for the probability that the original order is maintained, we need to divide the probability by 3!, which gives:

0.0166 / 3! = 0.000277 = 0.0277%

This is closest to answer choice D) 0.03%.

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It would take 1.53 years for the price of pizza to triple with a growth rate of 1.05.

To find the number of years it takes for the price of pizza to triple with a growth rate of 1.05, we need to use the formula for exponential growth:

A = P(1 + r)^t

Where:

A = final amount (triple the original price, or 3*$8 = $24)

P = initial amount ($8)

r = growth rate (1.05)

t = time in years

Substituting the values into the formula, we get:

$24 = $8(1 + 1.05)^t

Simplifying:

3 = (1 + 1.05)^t

Taking the logarithm of both sides with base 10:

log(3) = t*log(1 + 1.05)

t = log(3) / log(1 + 1.05)

Using a calculator, we get:

t ≈ 1.53

Therefore, it would take approximately 1.53 years for the price of pizza to triple with a growth rate of 1.05.

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The logarithmic expression log7 18 is equivalent to log 18 / log 7 using the change-base formula.

The change-base formula states that the logarithm of a number to a certain base can be converted to the logarithm of the same number to a different base by dividing the logarithm of the number to the first base by the logarithm of the number to the second base.

In this case, we want to convert log7 18 to a logarithm with base 10. Therefore, using the change-base formula, we can write:

log7 18 = log 18 / log 7

Using a calculator, we can evaluate the right-hand side of the equation to get:

log7 18 = 1.2553 / 0.8451

log7 18 = 1.4845 (rounded to four decimal places)

Therefore, the logarithmic expression log7 18 is equivalent to log 18 / log 7, which is approximately equal to 1.4845.

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There are 9 tables with 4 chairs in the restaurant.

Let's establish the variables:

Let x be the number of tables with 4 chairs

Let y be the number of tables with 5 chairs

Let z be the number of tables with 6 chairs

We know that there are a total of 19 tables, therefore:

x + y + z = 19 (equation 1)

We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:

4x + 5y = 64 (equation 2)

We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:

x + y + z - 16x - 20y = 19 - 256

Simplifying:

-15x - 19y = -237

Dividing both sides by -19:

x = 9

Therefore, there are 9 tables with 4 chairs.

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Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?

When x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.

Differential,

To find the differential dy, we use the formula:

dy = f'(x) * dx

where f'(x) is the derivative of the function y = tan(5x + 5) with respect to x.

Taking the derivative, we get: f'(x) = sec^2(5x + 5) * 5 Plugging in x = 3, we get: f'(3) = sec^2(20) * 5

Now we can find the differential dy for dx = 0.4 and dx = 0.8:

When dx = 0.4: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.4 dy ≈ 4.056

When dx = 0.8: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.8 dy ≈ 8.113

Therefore, when x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.

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The description concerns Uruguay, option B, since it is the only country among the answer choices that is located in South America to the South of Brazil.

South America is a continent located in the western hemisphere of the Earth. It is situated south of North America, east of the Pacific Ocean, and west of the Atlantic Ocean. The continent is home to 12 independent countries and 3 dependent territories, with a total population of approximately 422 million people.

The largest country in South America is Brazil, followed by Argentina, Peru, and Colombia. The continent is characterized by diverse topography, including the Andes mountain range, the Amazon rainforest, the Atacama Desert, and the Patagonian plains. The region is also known for its rich cultural heritage, including pre-Columbian civilizations such as the Incas and the Mayas, as well as colonial influences from Spain and Portugal. Today, South America is a rapidly developing region with a diverse economy, including agriculture, mining, and manufacturing industries.

Uruguay is also a part of South America. It is located South of Brazil and, as a matter of fact, during colonization, it was a part of Brazil. We can conclude option B is the right answer.

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The percent of the customers at Harris Teeter that are adults is 70%

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

Customers = 160

Children = 48

using the above as a guide, we have the following:

Adults = Customers - Children

substitute the known values in the above equation, so, we have the following representation

Adults = 160 - 48

So, we have

Adults = 112

Next, we have

Percentage = 112/160 * 100%

Evaluate

Percentage = 70%

Hence, the percentage is 70%

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To use the Evaluation Theorem to compute the definite integrals, follow these steps:

Step 1: Identify the function and the interval
In this case, we have three separate integrals to evaluate:
(a) ∫(e^3 - e) dx
(b) ∫0 dx
(c) ∫295/6 dx

Step 2: Find the antiderivative of the function
(a) The antiderivative of (e^3 - e) is (e^3x/3 - ex) + C.
(b) The antiderivative of 0 is simply C, where C is the constant of integration.
(c) The antiderivative of 295/6 is (295/6)x + C.

Step 3: Evaluate the antiderivative at the given interval
(a) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.
(b) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.
(c) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.

What are definite Intregal's: Definite integral is the area under a curve between two fixed limits.we can say that the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. Unfortunately, without specific intervals, we cannot use the Evaluation Theorem to compute the definite integrals. Please provide the intervals for each integral, and we can help you compute them.

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Considering the definition of probability, the probability that a randomly selected attraction at this amusement park would be a drink stand is 1/10.

Probability establishes a relationship between the number of favorable events and the total number of possible events.

The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:

P(A)= number of favorable cases÷ number of possible cases

In this case, you know:

Replacing in the definition of probability:

P(A)= 2÷ 20

Solving:

P(A)= 1/10

Finally, the probability in this case is 1/10.

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The amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.

Let's assume that there are three brothers, including Musa. Let X be the amount of money that the brother with the highest average takes, and let Y be the amount of money that the brother with the third rank takes.

According to the given conditions, we can write the following equations:

Let's simplify equation 1:

X + Y = 2900

Also, we know that:

X = (2Y + X)/2

(The amount that the third rank takes is half of what the first rank takes)

Simplifying this equation:

2X = 2Y + X

X = 2Y

Substituting this value of X in equation X + Y = 2900:

3Y = 2900

Y = 2900/3

Y ≈ 966.67

As the amount given must be a whole number between two consecutive natural numbers, we can round Y to the nearest natural number:

Y = 967

Then, X = 2Y = 2*967 = 1934

Therefore, the amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.

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The exact value of secθ secθ in simplest radical form is 106/81.

The length of the hypotenuse is the distance from the origin to the point (-9, 5):

√((-9)^2 + 5^2) = √(81 + 25) = √106

cosθ = adjacent/hypotenuse = -9/√106

Therefore, secθ = 1/cosθ = -√106/9.

In order to find the value of secθ secθ, we simply multiply secθ by itself:

secθ secθ = (-√106/9) * (-√106/9) = 106/81

The exact value of secθ secθ is 106/81.

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The simplified form of the expression 3(w+11) / 6w  is w + 11 / 2w .

Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.

In other words, we have to expand any brackets, next multiply or divide any terms and use the laws of indices if necessary, then collect like terms by adding or subtracting and finally rewrite the expression.

Therefore, let's simplify the expression:

3(w+11) / 6w

Hence, let's divide both the numerator and denominator by 3

Therefore,

3(w+11) / 6w =  w + 11 / 2w

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