a worker in a silver mine descends 71 feet. Use an integer to represent the change in the workers position.

The average rate of change of f is less than the average rate of change of g.

The symmetry axis for the functions f and g is either the same or different.The line that passes through the vertex's x value is known as an axis of symmetry. It is the line of symmetry, but for a quadratic equation, and it divides the equation in half.

By examining function f, we can determine the vertex's location by either the lowest point, or (-3, -10). This is so that the numbers before and after (-3, -10), which increase by the same amount, have the same interval as the x values. (For instance, the symmetric pairs x = -5 and x = -1 have y values of -2 and x = -4 and x = -2, respectively, have y values of -8.)

Consequently, x = -3 is the axis of symmetry for function F.because the vertex's x value is -3.The graph demonstrates that x = -3 is also the axis of symmetry for function g because an illustrative vertical line drawn through this value bisects the quadratic.As a result, the symmetry axis for the functions f and g is the same.

The relationship between f's and g's y-intercepts is (less than, equal to, greater than) Where an equation crosses the y axis is known as the y intercept. As x = 0 is the y axis, it always has a value of 0.Looking at function f, the y-intercept of the function is equal to 8 when x = 0.We can observe the y value of when the function g returns aOn the graph, the quadratic intercepts the y axis. It is y = -2.As a result, f's y-intercept is larger than g's y-intercept.The average rate of change of f is (equal to, less than, or greater than) the average rate of change of g across the range [-6, -3].The amount that the y value rises for each unit of x that passes is the rate of change.

For function f, we can see that the function declines by 18 between x = -6 and x = -3. The sum of the rate of change (the amount the y changed / difference between the x values of points) is therefore -18 / 3 = -6.For function g, we can see that the function grows between x = -6 and x = -3. In this instance y value, but we may calculate that it rises by around 9. 9 / 3 = 3.

The average rate of change of f is therefore lower than the average rate of change of g.

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In this simulation experiment, the population distribution represents the lifetimes of a certain type of electronic control and the density curve in the figure represents the population distribution.

The distribution is skewed and follows a lognormal distribution with an expected value of ln(X) equal to 3 and a variance of ln(X) equal to 0.16. The experiment consisted of 500 replications and examined different sample sizes: n = 5, n = 10, n = 20, and n = 30.

The density curve in the figure represents the population distribution, with an expected value of E(A) equal to 21.7584 and a variance of V(X) equal to 82.1449. The histograms shown illustrate the distribution of sample means for the different sample sizes. Additionally, a normal probability plot from MINITAB is included for the x-values based on a sample size of n = 30, allowing for an assessment of the normality assumption for the sample means.

These visual representations provide valuable insights into the characteristics of the simulated experiment's population distribution, as well as the behavior of the sample means for different sample sizes.

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The complete question is:

Consider a simulation experiment in which the population distribution is quite skewed. The figure below shows the density curve for lifetimes of_a certain type of electronic control [this is actually a lognormal distribution with E(ln(X)) = 3 and V(ln(X)) = 0.16]. The statistic of interest is the sample mean X. The experiment utilized 500 replications and considered these sample sizes: n = 5, n = 10, n = 20, and n = 30. The resulting histograms along with a normal probability plot from MINITAB for the x values based on n = 30 are shown in the figures below. Density curve for the simulation experiment (E(A) = 21.7584, V(X) = 82.1449].

Answer:

a = 40 + root(7) , b = 5 root(7)

Step-by-step explanation:

\(49 + \sqrt{7} - \sqrt{81} + \sqrt{-175}\\ = 49+\sqrt{7}-9+5\sqrt{7}i\\ = 40+\sqrt{7} + 5\sqrt{7}i\)

The formula to calculate the midpoint between two points is,

Checking the last option for confirmation

The coordinates are (10, 0) and (6, 6)

Where,

Therefore,

Hence, from the result above we can conclude that the coordinates with the pair (8,3) are (10, 0) and (6, 6).

Therefore, the answer is (10, 0) and (6, 6).

Answer:

The container can hold 280 liters of water.

Step-by-step explanation:

Proportions

The water originally fills 1/8 of a container. Then 35 lt of water are poured into the container and now it's 1/4 full.

If we subtract the final portion of the tank minus the original portion of the container, we obtain the portion that was poured into.

\(\mathrm{Portion\ poured }=\frac{1}{4}-\frac{1}{8}=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)

If 35 liters of water is 1/8 of the tank, then it can hold 35*8 = 280 liters.

The container can hold 280 liters of water.

The output of the following code snippet will be 1, 2, 3, and 4.

The reason is that the while loop runs infinitely until the break statement is executed. The break statement terminates the loop if the value of x is divisible by 5. However, the value of x is incremented at each iteration of the loop before checking the condition. Here is the step-by-step explanation of how this code works:

Step 1: Assign 1 to x.x = 1

Step 2: Start an infinite loop using the while True statement.

Step 3: Check if the value of x is divisible by 5 using the if x % 5 == 0 statement.

Step 4: If the value of x is divisible by 5, terminate the loop using the break statement.

Step 5: Print the value of x to the console using the print(x) statement.

Step 6: Increment the value of x by 1 using the x += 1 statement.

Step 7: Repeat steps 3-6 until the break statement is executed.

Therefore, the output of the code will be: 1 2 3 4.

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To solve this problem, we need to use some basic geometry concepts. First, we know that the diagonal of a unit square is the square root of 2, since the sides are of length 1.  The side length of the smaller square inscribed within a circle inscribed in a unit square is 1.

Next, we know that the circle inscribed in the square will have a diameter equal to the diagonal of the square, which is the square root of 2. The radius of the circle will therefore be half of the diameter, which is sqrt(2)/2.
Now we can use the radius of the circle to find the side length of the smaller square inscribed within it. If we draw the diagonal of the smaller square, it will be twice the radius of the circle, or sqrt(2). This is because the diagonal of the square passes through the center of the circle and therefore has a length equal to twice the radius.
We can then use the Pythagorean theorem to find the length of each side of the smaller square. If we let x be the side length of the smaller square, then we have:
x^2 + x^2 = 2
2x^2 = 2
x^2 = 1
x = 1
Therefore, the side length of the smaller square is 1, which makes sense since it is inscribed within a unit square.

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To correctly add x and x², Boswa needs to recognize that these are not like terms and cannot be combined. Instead, he can write the expression as x + x².

Polynomials are mathematical expressions consisting of variables and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation, but not division by a variable.

Boswa is incorrectly assuming that x + x² is the same as x2², but this is not true.

To add expressions, you need to have like terms, which are terms with the same variable and the same exponent. In this case, x and x² are not like terms, so they cannot be combined.

To remember the correct way to add expressions, it's helpful to use the following steps:

1. Identify like terms in the expression.

2. Combine the coefficients (the numbers in front of the variable) of the like terms, while keeping the variable and exponent the same.

3. Write the combined terms together, and any remaining terms that cannot be combined.

For example, to simplify the expression 2x² + 3x + x², we can follow these steps:

1. Identify the like terms: 2x² and x² both have the variable x raised to the power of 2.

2. Combine the coefficients of the like terms: 2x² + x² = 3x²

3. Write the combined terms together, and any remaining terms: 3x² + 3x

Therefore, to correctly add x and x², Boswa needs to recognize that these are not like terms and cannot be combined. Instead, he can write the expression as x + x².

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The correct slope of the tangent line to y = f(t)g(2) at the point where r = 3 is 21, not 14 as Adam entered.

To find the slope of the tangent line to the function y = f(t)g(2) at the point where r = 3, we can use the product rule of differentiation. Let's analyze Adam's approach and identify the mistake(s).

Adam's mistake is in assuming that the slope of the tangent line to y = f(x)g(x) at the point where x = 3 is simply the product of the slopes of the individual tangent lines to f(x) and g(x) at x = 3. This assumption is incorrect because the product rule accounts for the interaction between the two functions.

To find the slope of the tangent line to y = f(t)g(2) at the point where r = 3, we need to apply the product rule:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

Given the information provided, we know:

f(3) = 5

f'(3) = 2

g(3) = -7

g'(3) = 7

Now, let's substitute these values into the product rule equation:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

(dy/dt) = (2 * g(2)) + (f(t) * 7)

(dy/dt) = (2 * g(2)) + (5 * 7)

(dy/dt) = (2 * g(2)) + 35

Since we are interested in the slope at the point where r = 3, we substitute r = 3 into the equation:

(dy/dt) = (2 * g(2)) + 35

(dy/dt) = (2 * (-7)) + 35

(dy/dt) = -14 + 35

(dy/dt) = 21

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The discontinuity of the function f(x) = 1 / (2 tan x - 2) occurs when the denominator of the fraction becomes zero, as division by zero is undefined. Thus, we need to find the values of x that make 2 tan x - 2 equal to zero.

2 tan x - 2 = 0

tan x = 1

x = π/4 + nπ, where n is an integer, Therefore, the discontinuity of the function occurs at x = π/4 + nπ.
To find the discontinuity of the function f(x) = 1 / (2 tan x - 2), we need to determine the values of x for which the denominator becomes zero, as the function will be undefined at these points.

The denominator is given by:

2 tan x - 2

Let's find the values of x for which this expression becomes zero:

2 tan x - 2 = 0

Now, isolate tan x:

2 tan x = 2

tan x = 1

The tangent function has a period of π, so the general solution for x is:

x = arctan(1) + nπ

where n is an integer.

The arctan(1) value is π/4, so the general solution becomes:

x = π/4 + nπ

So, the function f(x) = 1 / (2 tan x - 2) has discontinuities at x = π/4 + nπ, where n is an integer.

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Answer:

1. x = 3

2. x = 6

3. not sure

Step-by-step explanation:

5x +2 (x+7) =14x -7

First expand the expandables

5x +2x +14 =14x-7

7x +14 =14x -7

14x -7x =14+7

7x=21 . Divide both sides by 7

x=3.

Step-by-step explanation:

1. 5x +2x + 2*7 =14x-7

7x + 14 = 14x - 7

14 +7 = 14x - 7x

21 = 7x

21/7 =x

4 =x

The Right triangular prism will result in a triangular cross-section.

In Geometry, the shape or the figure that has three (even higher) dimensions, are known as solids or three-dimensional shapes.

When a solid is cut by a plane that is parallel to its base, forming a two-dimensional cross-section, in order to have a triangular cross-section the base or bases of that solid must be a triangle.

So, 1) Rectangular pyramid will result in a rectangular cross-section.

2)Right hexagonal prism will result in a hexagonal cross-section.

3)Cube will result in a squared cross-section.

4)Right triangular prism will result in a triangular cross-section.

Therefore, The Right triangular prism will result in a triangular

cross-section.

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The solid that could have resulted in a two-dimensional cross section in the shape of a triangle when cut by a plane parallel to its base is the "rectangular pyramid."

When a rectangular pyramid is cut parallel to its base, the resulting cross section is a triangle. This is because one of the sides of the pyramid's base forms the base of the triangle, and the other edges of the pyramid converge to form the other sides of the triangle in the cross section.

The other listed solids—right triangular prism, right hexagonal prism, and cube—would not form a triangle as their cross sections when cut parallel to their base; they would typically result in polygons with more sides or shapes different from a triangle.

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Before the discount, the price of the table was $112.5.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the discount of 64% and the final sale price will be $72.

Assume the original price be {x}. Then, we can write -

72 = 64% of {x}.

72 = (64/100) x {x}

{x} = (72 x 100)/(64)

{x} = 7200/64

{x} = 112.5

Therefore, before the discount, the price of the table was $112.5.

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Jody has created a systematic sampling error by forgetting to include a segment of the population that is relevant to the study.

Systematic sampling is a sampling method where every nth member of a population is selected to be part of the sample. In Jody's case, she forgot to include a specific segment of the population, which means that the sampling process was not systematic. This error can introduce bias and affect the representativeness of the sample.

No calculations are required for this type of error.

Jody's mistake in not including a relevant segment of the population has resulted in a systematic sampling error. To ensure the accuracy and validity of the study, it is important to rectify this error by including the missing segment or adjusting the sampling method accordingly.

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The probability that the proportion of airborne viruses in a sample of 679 viruses would be greater than 8% is approximately 0.

To solve this problem,

Use the normal approximation to the binomial distribution.

We can assume that the sample proportion of airborne viruses follows a normal distribution with mean equal to the true proportion of 7% and standard deviation given by:

√(7%*(1-7%)/679) = 0.0155

Then, we want to calculate the probability that the sample proportion is greater than 8%.

Standardize the distribution as follows:

(z-score) = (sample proportion - true proportion) / std deviation (z-score)

              = (8% - 7%) / 0.0155

              = 64.52

Using a standard normal table, we can find the probability that a z-score is greater than 64.52, which is essentially 1.

Therefore, the probability of the sample proportion being greater than 8% is approximately 0.

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The ticket price of

A Senior citizen = $14

A Child               = $4

First day of ticket sales :

Senior citizen tickets (s) = 14

Child tickets (c)             = 14

Total price of both tickets = $252

14s + 14c = 252   eq. (1)

Second day of ticket sales :

Senior citizen tickets (s) = 9

Child tickets (c)              = 7

Total price of both tickets = $154

9s + 7c = 154   eq. (2)

Multiplying equation 2 with 2, we get

18s + 14c = 308    eq. (3)

Now, we will subtract eq. (1) from eq. (3)

18s + 14c = 308    eq. (3)

-14s - 14c = -252    eq. (1)

____________________

          4s = 56

            s = 56/4

            s = 14

We get the ticket price of one senior citizen which is 14 Dollars.  

Now, we will put s = 14 in eq. 2,

So,  9s + 7c = 154

 (9×14) + 7c = 154

              7c = 154  - 126

                c = 28 / 7

               c = 4

Ticket price of one child is 4 Dollars.

Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.

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Based on these observations, option (d) 30 seems to be the most reasonable choice for a longer distance down the fairway.

To determine how far down the fairway the ball hits the ground, we need to consider the horizontal range of the golf ball. The range is the horizontal distance traveled by the ball before it hits the ground.

The range can be calculated using the formula:

Range = (Initial Velocity)² * sin(2 * Launch Angle) / g

Where:

Initial Velocity is the initial velocity of the golf ball (180 ft/sec).

Launch Angle is the angle at which the ball is hit off the tee.

g is the acceleration due to gravity (approximately 32.2 ft/sec²).

Since you haven't provided the launch angle for each club, we cannot determine the exact range for each one. However, we can make some general observations based on the given answer choices:

(a) 15: This option implies a lower launch angle, which would likely result in a shorter range.

(b) 20: Similar to option (a), a lower launch angle would generally result in a shorter range.

(c) 25: This option suggests a moderate launch angle, which could correspond to a reasonable range.

(d) 30: A higher launch angle typically leads to a longer range, so this option may result in a greater distance.

Based on these observations, option (d) 30 seems to be the most reasonable choice for a longer distance down the fairway.

However, without specific launch angles for each club, we cannot determine the exact answer.

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Answer:

The missing angle is about 27.92°.

Step-by-step explanation:

This is a tangent equation, as there is no hypotenuse value. I'll use x as the missing angle.

tan(x) = opposite/adjacent

tan(x) = 20/38

tan(x) = 0.52631578947368421052631578947368

tan(x) ≈ 0.53

Now, we have to reverse.

tan⁻¹(0.53) = x

27.92358972 = x

x ≈ 27.92°

Since reaction time is measured and not constrained to a specific range of numbers, it is continuous quantitative data.

'What is continuous quantitative?'

A continuous data set is a quantitative data set that represents a scale of measurement that includes fractions and decimals in addition to whole integers. Values like height, weight, length, temperature, and other similar metrics would be included in continuous data sets. They are items that can be quantified in decimals and fractions. A continuous data set typically requires the use of a tool, such as a ruler, measuring tape, scale, or thermometer, to create the numbers.

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Answer:

B I think

Step-by-step explanation:

Because your dividing 4 into 5 things

Answer:

One solution

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

X is equal to 7 and will only be equal to 7 which is why you only have one solution,

Answer:

-168

Step-by-step explanation:

8 × -7 × 3

-56 × 3

-168

Answer:

4.51 ⁰ simplified would be 1 :)

It is 1 because anything to the 0 power is 1.

Answer:

try 2.32 trust me

Step-by-step explanation:

Answer: x= -10 , False B

x= -8, False B

x= -14, True A

Step-by-step explanation:

Answer:

I think its....73

cause you know...Cause you do 10+9qu43x8382_8234234+892q84=73

Step-by-step explanation:

Answer:

4 To 0

Step-by-step explanation:

it is 0-4=-4.

hence you can choose any other natural number too

Answer:

Step-by-step explanation:

y-y1=m(x-x1) ---> (point-slope form)

y-(-2)=10(x-8)

y+2=10(x-8) (Answer)

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

slope-intercept form: y=mx+b where m=slope and b=y-intercept

y+2=10(x-8)

y=10x-80-2

y=10x-82 (Answer)

Please mark me as Brainliest if you're satisfied with the answer.

Answer:

36

Step-by-step explanation:

Answer:

Solution,

X = 16 [ Given]

Now,

\(x - ( - 20)\)

Plugging the value of X

\(16 - ( - 20)\)

\( = 16 + 20\)

\( = 36\)

Hope this helps..

Good luck on your assignment..

Answer:

12-2=10

Step-by-step explanation:

Your welcome! :D

The inputs that are solutions for the inequality are:

x = 2

x= 1

Here we have the following inequality:

-5x < 2

We want to see which of the given inputs is a solution for this.

First we can isolate the variable in our inequality, so we get:

-5x < 2

-2 < 5x

-2/5 < x

-0.4 < x

So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:

x = 1

x = 2.

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