What is
x + 9 = 18 + -2x

Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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Answer: I'm pretty sure its 14.

Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14

Answer:

P = 0.0438 ; We reject the Null and conclude that there is significant evidence that the discharge limit per gallon of waste has been exceeded.

Due to the small sample size.

Step-by-step explanation:

H0: μ = 500

H1 : μ > 500

Test statistic :

(xbar - μ) / S.E

Tstatistic = (1000 - 500) / 200

= 500 / 200

= 2.5

Pvalue from Test score ; df = 4 - 1 = 3 ; using calculator :

Pvalue = 0.0438

At α = 0.05

Pvalue < α ; We reject the Null and conclude that there is significant evidence that the discharge limit per gallon of waste has been exceeded.

The test above has a very small sample size, and for a distribution to be approximately Normal, the sample size must be sufficiently large enough according to the Central limit theorem.

For a two sided analysis ; the Pvalue is twice that for the one sided, hence, Pvalue = (0.0438 * 2) = 0.0876 yielding a less strong evidence against the Null.

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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Answer:

The Answe for the third side is 60

Answer:

About 75.36

Step-by-step explanation:

C = πd or 2πr, we'll use 2πr

2 x π x 12 = 24 x π = 24 x 3.14 = 75.36

Hope this helps :D

Answer:

\(x=\frac{26}{3}\)

Step-by-step explanation:

Lets solve for \(x\).

Subtract \(3x\) from both sides of the equation.

\(9x-20-3x=32\)

Add 20 to both sides of the equation.

\(9x-3x=32+20\)

Simplify both sides.

\(6x=52\)

Divide both sides of the equation by 6.

\(x=\frac{52}{6}\)

Write the fraction in simplest form.

\(52 \div 2 = 26\\6 \div 2 = 3\)

\(x=\frac{26}{3}\)

Answer:

Step-by-step explanation:

9x-20=3x+32

9x-20+20=3x+32+20

9x=3x+52

9x-3x=3x+52-3x

6x=52

6x/6=52/6

x=26/3

Answer:

88.8%

Step-by-step explanation:

Answer:

89% correct

Step-by-step explanation:

32 out of 36

32/36

8/9

0.89

89 percent correct

Answer:

D

Step-by-step explanation:

1 + 4x and 57° are corresponding angles and are congruent , so

1 + 4x = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

Answer:

Step-by-step explanation:

The maximum area of the rectangle is A = 9 units²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the function for area be f ( x )

where f ( x ) = - ( x - 3 )² + 9

Let the width of the rectangle be W.

The perimeter of a rectangle is given by:

Perimeter = 2(length + width) = 12 units

12 = 2(x + width)

Simplifying this equation, we get:

6 = x + width

width = 6 - x

Now, the area of the rectangle is given by:

Area = Length x Width

Substituting the value of width in terms of x, we get:

Area = x(6 - x)

Area of rectangle A = 6x - x²

This is a quadratic function of x, which has a maximum value at the vertex of the parabola. The vertex of the parabola can be found by completing the square or by using the formula:

x = -b/(2a)

In this case, a = -1 and b = 6, so we have:

x = -6/(2(-1)) = 3

Therefore, the maximum area of the rectangle occurs when x = 3, and the value of the maximum area is:

Area of rectangle A = 3(6 - 3) = 9 square units

Hence , area of rectangle is A = 9 units²

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The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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Answer:

54 degrees

Step-by-step explanation:

Original of lagos achii gege

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.

The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.

Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.

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Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

9514 1404 393

Answer:

Step-by-step explanation:

A graph can be helpful. It can show the locations of the maximum and minimum.

__

The maximum is found at the vertex of the parabola, located where ...

  x = -b/(2a)

  x = -1.42/(2(-0.015)) = 47 1/3

The value M(47 1/3) is ...

  M(47 1/3) = (-0.015(47 1/3) +1.42)(47 1/3) -7.8 = 0.71(47 1/3) -7.8 = 25 121/150

The maximum gas mileage is 25 121/150 ≈ 25.8067 mpg at 47 1/3 mph.

__

The minimum will be at one end or the other of the interval. Here, the maximum is farther from the lower end of the domain, so we expect to find the minimum there:

  M(30) = (-0.015(30) +1.42)(30) -7.8 = 0.97(30) -7.8 = 21.3

The absolute minimum gas mileage is 21.3 mpg at 30 mph.

Answer:

---------------------------------------

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

For n=6, the given vectors will be collinear.

Step-by-step explanation:

Collinear vectors are the vectors which lie on the same line or parallel lines. In order to find if two vectors are collinear, their ratio is found. If the ratio is same for all unit vectors then the vectors are collinear.

Given

\(a = (a_1, a_2) = (3,2)\\b = (b_1, b_2) = (9,n)\)

The ratio of first unit vectors is:

\(\frac{a_1}{b_1} = \frac{3}{9} = \frac{1}{3}\)

In order for the vectors to be collinear the other ratio should also be 1/3

\(\frac{a_2}{b_2} = \frac{1}{3}\)

Writing it mathematically

\(\frac{2}{n} = \frac{1}{3}\\2*3 = n\\n = 6\)

Hence,

For n=6, the given vectors will be collinear.

The functions f and g are inverse functions because f(g(x)) = g(f(x)) = x

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

f(x) = x + 6

g(x) = x - 6

To determine the inverse function, we calculate

f(g(x)) and g(f(x))

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

f(g(x)) = x + 6 - 6 = x

g(f(x)) = x + 6 - 6 = x

So, we have

f(g(x)) = g(f(x)) = x

Hence, the functions are inverse functions

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Answer:

Answer is (A.)

Step-by-step explanation:

Answer:

(A)

Step-by-step explanation:

Answer:

The formula for calculating the surface area of a cuboid is as follows.

Surface Area of Cuboid = 2lw + 2lh + 2hw

Where,

Therefore,

Surface Area of Cuboid = (2 x 20 x 5) + (2 x 20 x 10) + (2 x 10 x 5)

                                         = 200 + 400 + 100

                                         = 700 \(cm^{2}\)

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

The point-slope form is \(y+1=2(x-6)\).

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables.

                                              \(y-b=m(x-a)\)

When an equation is written in this form, \(m\) gives the slope of the line and \((a, b)\) is a point the line passes through.

We know that the line passes through (6, -1) with a slope of 2. Well, we simply plug \(m=2\), \(a=6\), and \(b=-1\) into point-slope form.

The point-slope form is:

\(y+1=2(x-6)\)

Answer:

Step-by-step explanation:

\(\sqrt{4^2+5^2}\)

= \(\sqrt{41}\)

The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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