The average rate of change of a function f between x = a and x = b is the slope of the ______ line between (a, f(a)) and (b, f(b)).

Answer:

the value of x is 2^9/4 then 2^3x-4=2^11/4

Answer: 1/125

I got it by multiplying 1/5 by itself twice. This helps account for all of the possibilities.

Answer:

1/125

Step-by-step explanation:

Edge (I don't know the explanation lol sorry)

a) The linear inequality: 2x + 2y ≤ 20.

b) Two possible sizes for the sandbox: 3 feet by 7 feet and 5 feet by 5 feet.

The graph  for the equation y + 2 = 3x + 3 is drawn below.

a) To write a linear inequality describing the situation, let's assume the length of one side of the rectangular sandbox is x feet and the width is y feet. The perimeter of the sandbox is given by the equation:

2x + 2y ≤ 20

This equation represents the constraint that the sum of the lengths of all sides of the sandbox should be less than or equal to 20 linear feet.

b) To find two possible sizes for the sandbox, we can choose different values for x and solve for y.

Let's consider two scenarios:

1) Setting x = 3 feet:

By substituting x = 3 into the inequality, we have:

2(3) + 2y ≤ 20

6 + 2y ≤ 20

2y ≤ 20 - 6

2y ≤ 14

y ≤ 7

So, one possible size for the sandbox is 3 feet by 7 feet.

2) Setting x = 5 feet:

By substituting x = 5 into the inequality, we have:

2(5) + 2y ≤ 20

10 + 2y ≤ 20

2y ≤ 20 - 10

2y ≤ 10

y ≤ 5

Thus, another possible size for the sandbox is 5 feet by 5 feet.

Therefore, two possible sizes for the sandbox are 3 feet by 7 feet and 5 feet by 5 feet.

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The distance from tire race to the rope climb is; 80 yards

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

We are given the coordinates of tire race and rope climb as;

Tire race = (-40, -30)

Rope climb = (40, -30)

Thus distance between tire race and the rope climb is;

D = √[(-30 - (-30))² + (40 - (-40))²]

D = √(80²)

D = 80 yards

Thus, we conclude that is the distance from tire race to the rope climb.

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A) The steady-state error for transfer function (20s² + 2s + 36) with reference r(t) = 1 and K = 20 is -35.

B) The steady-state error for transfer function (6s² + 22) with reference r(t) = 1 and K = 20 is -21.

A) Transfer Function: G(s) = (20s² + 2s + 36)

To calculate the steady-state error, we need to evaluate the transfer function G(s) at s = 0.

So let's substitute s = 0 into the transfer function:

G(0) = (20(0)²+ 2(0) + 36)

= 0 + 0 + 36

= 36

The steady-state value of the output for reference r(t) = 1 and K = 20 is 36.

Steady-State Error = r(t) - y(t)

= 1 - 36

= -35

B) Transfer Function: G(s) = (6s² + 22)

Let's evaluate the transfer function G(s) at s = 0:

G(0) = (6(0)² + 22)

= 0 + 22

= 22

The steady-state value of the output for reference r(t) = 1 and K = 20 is 22.

Therefore, the steady-state error is:

Steady-State Error = r(t) - y(t)

= 1 - 22

= -21

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Answer:

(x-2,y-4)

Step-by-step explanation:

Here, we want to calculate the rule for the translation

From the question, we can see that the new image was just formed as a movement of the old image by some particular units

The x-axis was move sideways while the y-axis was moved further down

The number of units is thus;

Y from 12 to 8

A movement of -4

For the x-axis

we have a movement of two units toward the left

So the rule is;

(x,y) to (x-2, y-4)

Answer:

i am pretty sure its 11

Step-by-step explanation:

bc if you look at the nymber next to 0 its .6 and they say 5 and up round UP!!

Answer:

11

Step-by-step explanation:

Rounded to Nearest Whole Number =  

11

Rounded to Nearest Tenth =  

10

Rounded to Nearest Hundredth =  

0

Rounded to Nearest Thousandth =

0

So, the quartiles are Q1 = 59, Q2 = 62, and Q3 = 65.

IQR = Q3 - Q1 = 65 - 59 = 6.

The data set does have one outlier, The value 77.

It is above the upper outlier limit of 74.

a)To find the quartiles, we first need to arrange the data in order:

55 56 57 59 60 60 61 62 62 62 63 64 65 65 77

The median is the middle value of the data set, which is:

Median = 62

To find the first quartile (Q1), we take the median of the lower half of the data:

Q1 = Median of {55, 56, 57, 59, 60, 60, 61} = 58

To find the third quartile (Q3), we take the median of the upper half of the data:

Q3 = Median of {63, 64, 65, 65, 77} = 65

b)The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 65 - 58 = 7

c) To identify any outliers, we can use the rule that considers any value that falls below Q1 - 1.5 IQR or above Q3 + 1.5 IQR to be an outlier.

Lower outlier bound: Q1 - 1.5 IQR = 58 - 1.5(7) = 47.5

Upper outlier bound: Q3 + 1.5 IQR = 65 + 1.5(7) = 76.5

Since one value (77) that falls above the upper outlier bound, this value is considered an outlier.

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Answer:

$1,248.00, or 1,248 dollars.

Step-by-step explanation:

First, multiply 4, which is the dollars per hour, by 2, which is 8. Then, multiply four with ten, which is 40. Next, multiply 4 with 3, which is 12, and add two zeros on the back, which is 1,200. Finally, add them all together for a total of $1,248.00, or 1,248 dollars.

Answer:

x = 2.8

Step-by-step explanation:

5/6 = 4/x+2

Cross multiply:

5 * x + 2 = 6 * 4

Simplifying

5 * x + 2 = 6 * 4

Reorder the terms:

5 * 2 + x = 6 * 4

2 * 5 + x * 5 = 6 * 4

10 + 5x = 6 * 4

Multiply 6 * 4

10 + 5x = 24

Solving

10 + 5x = 24

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.

10 + -10 + 5x = 24 + -10

Combine like terms: 10 + -10 = 0

0 + 5x = 24 + -10

5x = 24 + -10

Combine like terms: 24 + -10 = 14

5x = 14

Divide each side by '5'.

x = 2.8

Simplifying

x = 2.8

Answer: The answer is x= −6 4/5  ^^

Step-by-step explanation: I took the quiz!! look at the attached files for answers! ( I go to k12, this is the 1.09 Quiz: Solve a Proportion. )

Number of miles in 8,400 feet are 1.6 miles.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, there are 5,280 feet in 1 mile.

Let the number of miles in 8,400 feet be x.

So, 5280/1 = 8400/x

5280x=8400

x= 8400/5280

x= 1.6 miles

Therefore, number of miles in 8,400 feet are 1.6 miles.

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Answer:

37%

Step-by-step explanation:

Surface area of a cylinder = πr² + 2πrh

With r = 22 and h = (6 + 10) = 16

Area = π * 22² + 2 * π * 22 * 16

Area = 1520.728 + 2211.968

Area = 3732.696 in²

Percentage of green = surface area of green ÷ total surface area

Surface area of green = 2πrh

Surface area of green = 2 * π * 22 * 10

Surface area of green = 1382.48

Percentage of green = 1382.48 / 3732.696 * 100%

Percentage of green = 37%

Answer:

C) 2

fοf(2) =2

Step-by-step explanation:

Explanation

Given f(x) = 3 x-4 and g(x) = -x²

given f(x) = 3 x-4

fοf (2) = f(f(2))

         = f(3 (2)-4)) ( ∵ put x=2 in f(x))

        = f(2)

       = 3(2) -4

      =  6-4

      =2

∴  fοf (2) =2

The least positive integer that will be divisible by both 15 and 35 will be 105.

The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.

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Answer: $96.25

Step-by-step explanation:

Take 89.75 divided by 100% = 0.8975

Then times 7.25% = $6.5

Total is 89.75 + 6.5 = $96.25

Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The strength of the electric field at the position (0 cm, 5.0 cm) due to a -11 nC charge located at the origin will be; 0.004 N/C upwards.

To find the strength of the electric field, we can use Coulomb's Law and the principle of superposition.

Since we know that Coulomb's Law states that the electric field created by a point charge is directly proportional to the charge magnitude and inversely proportional to the square of the distance.

Now we have a -11 nC charge at the origin (0,0) and we want to find the electric field at the point (0 cm, 5.0 cm).

First, we need to calculate the distance between the charge and the point where we want to find the electric field. In this case, the distance is simply 5.0 cm.

Electric Field = (k * charge magnitude) / distance²

where k is the electrostatic constant. Plugging in the values;

Electric Field = (9 x 10^9 N m^2/C^2 * (-11 x 10^-9 C)) / (0.05 m)²

Simplifying this expression;

Electric Field = -0.004 N/C

The negative sign indicates that the electric field points in the opposite direction of the positive y-axis, therefore the field is directed upwards.

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The complete question is;

A -11 nC charge is located at the origin. What is the strength of the electric field at the position (x,y)=(0cm,5.0cm) ?

The percent decrease is 10.16%

Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100

The first step is to calculate the decrease

= 4.33 - 3.89

= 0.44

The percent decrease can be calculated as follows

= 0.44/4.33 × 100

= 0.1016 × 100

= 10.16

Hence the percent decrease is 10.16 %

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Answer:

(B)  10.16%

Step-by-step explanation:

Correct on my quiz.

The area of the rectangle is 105 square centimeters.

The perimeter of a rectangle is equal to the sum of the lengths of all its sides. If the perimeter of a rectangle is 44 centimeters, and we call the length of the rectangle "l" and the width "w", we can write an equation to represent this:

2l + 2w = 44

Now we can solve for one of the dimensions if we have the other one. For example, if the length is 15 centimeters, then:

2 * 15 + 2w = 44

30 + 2w = 44

2w = 44 - 30

2w = 14

w = 14 / 2

w = 7

So the length is 15 centimeters and the width is 7 centimeters. To find the area of the rectangle, we can multiply the length by the width:

15 * 7 = 105 square centimeters

So the area of the rectangle is 105 square centimeters.

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Answer:

Step-by-step explanation:

D Thombus

In approximately 11.41% of years, the rainfall will be between 50 and 70 centimeters in that town.

To solve this problem, we need to find the percentage of years where the rainfall is between 50 and 70 centimeters. We can do this by standardizing the rainfall values and using a standard normal distribution table.

First, we need to standardize the rainfall values of 50 and 70 centimeters using the formula

z = (x - μ) / σ

where

z is the standardized value

x is the rainfall value

μ is the mean

σ is the standard deviation

For x = 50

z = (50 - 95) / 28

z = -1.607

For x = 70

z = (70 - 95) / 28

z = -0.893

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two standardized values. This represents the percentage of years where the rainfall is between 50 and 70 centimeters.

Using a standard normal distribution table, we can find that the area under the curve between z = -1.607 and z = -0.893 is 0.1141. This means that approximately 11.41% of years will have rainfall between 50 and 70 centimeters in this town.

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9514 1404 393

Answer:

  72°

Step-by-step explanation:

In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.

  (6 swim days)/(30 days) = (swim pie angle)/(360°)

Multiply by 360° to find ...

  swim pie angle = (360°)(6/30) = 72°

72° of the circle should represent swimming.

After calculation, the average salary is 865.8644 thousands of dollars and average tenure is 7.955 years. Number of CEOs who are in their first year as CEO is equal to 5.

Here are the steps in R Studio to perform the tasks:

(a) Finding the average salary and the average tenure in the sample:

Load the CEOSAL2 data set in R Studio using the read.csv function.

       ceos <- read.csv("CEOSAL2.csv")

Calculate the average salary using the mean function:

       average_salary <- mean(ceos$salary)

Calculate the average tenure using the mean function:

average_tenure <- mean(ceos$ceoten)

(b) Finding the number of CEOs in their first year as CEO and the longest tenure as CEO:

Use the sum function and a logical test to count the number of CEOs in their first year as CEO:

first_year_ceos <- sum(ceos$ceoten == 0)

Use the max function to find the longest tenure as CEO:

longest_tenure <- max(ceos$ceoten)

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ATQ

\(\\ \tt\hookrightarrow 12+2.5r=95.75\)

\(\\ \tt\hookrightarrow 2.5r=95.75-12=83.75\)

\(\\ \tt\hookrightarrow r=83.75/2.5\)

\(\\ \tt\hookrightarrow r=33.5\)

Answer:

26 miles * 5280 ft/ 1 mile

Step-by-step explanation:

We know there are 5280 ft in 1 mile

26 miles * 5280 ft/ 1 mile

Answer:

C

Step-by-step explanation:

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Each outcome represents the result of two spins, with the first element indicating the outcome of the first spin and the second element indicating the outcome of the second spin in the sample space.

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is spinning a spinner twice with two equally sized sections labeled "stop" and "go."

The possible outcomes of the first spin are "stop" (s) and "go" (g). Similarly, the possible outcomes of the second spin are also "stop" and "go."

Therefore, the sample space can be represented by all possible combinations of the first and second spin outcomes, which gives us the following four outcomes:

(s,s): the spinner stops on "stop" twice

(s,g): the spinner stops on "stop" on the first spin and on "go" on the second spin

(g,s): the spinner stops on "go" on the first spin and on "stop" on the second spin

(g,g): the spinner stops on "go" twice

Hence, the sample space for spinning a spinner twice with two equally sized sections labeled "stop" and "go" is given by the set: {(s,s), (s,g), (g,s), (g,g)}.

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Answer:

Slope: -11/10

Step-by-step explanation:

always do    y2 - y1/x2 - x1

12 - 1 / -19 + 9 = -11/10