Please help with this question; I need to prove to my parents I am not as much of a disappointment to them as they think I am.

The domain to plot the growth function is 0 ≤ x < 7

Given that

f(d) = 11(1.01)ᵇ

When the radius is approximately 1179 mm

We have

11(1.01)ᵇ = 11.79

Divide

(1.01)ᵇ = 1.072

Take the logarithm

d = log(1.072)/log(1.01)

Evaluate

d = 6.99

So, the reasonable domain is 0 ≤ x < 7

Here, we have

f(d) = 11(1.01)ᵇ

The y-intercept is 11

This means tha the initial radius of the algae is 11 mm

For the average rate, we have

f(7) = 11(1.01)⁷ = 11.79

f(2) = 11(1.01)² = 11.22

So, we have

Rate  = (11.22 - 11.79)/(2 - 7)

Evaluate

Rate  = 0.114

So, the average rate of change from day 2 to day 7 is 0.114 mm per day

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The amount of the money after 7 years with a rate of 13% with an initial amount of $400 will be $ 941.04.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Tanvi opened a savings account and deposited $400.00 as principal.

The account earns 13% interest, compounded annually.

Then the balance after 7 years will be

We know the compound interest formula.

A = P (1 + r)ⁿ

We have

P = $ 400

r = 13%

n = 7 years

Then we have

A = 400 x (1 + 0.13)⁷

A = 400 x 1.13⁷

A = 400 x 2.3526

A = $ 941.04

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Answer:

the 3 steps

Step-by-step explanation:

1. Rearrange the equation so "y" is on the left and everything else on the right.

2. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

3. Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

In the question ,

it is given that ,

a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x²  ,

let the coordinate of the upper right corner be P(x,y) ,

and A be the area of the rectangle .

the point P lies on the parabola , given y = 12 − x² ,

So,  P = P(x,12−x²)

Due to symmetry of the rectangle,  the width of rectangle is half the distance between P and the y axis ,

that means width = 2x   and length = y .

Area of the rectangle = width × Length

= 2x * y

= 2x (12 − x²)

= 24x - 2x³

To maximize the area we differentiate Area with respect to x ,

we get ,

dA/dx = 24 - 6x²

for critical point dA/dx = 0 ,

24 - 6x²  = 0

6x² = 24

x² = 4

x = ±2 ,

since length cannot be negative ,

So , x = 2 .

to check for maximum and minimum ,we differentiate Area with respect to x,

we get

d²A/dx² = -12x

substituting , x = 2 ,

we get -12 < 0, So , the area is maximum .

hence the width = 2*2 = 4

and length = 12 - 4 = 8

and the maximum area is 32 .

Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

The given question is incomplete , the complete question is

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?

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The union of  sets a and b is a ∪ b, includes all the numbers that satisfy conditions of either a or b. Here a ∪ b consists all real numbers that fall within ranges −3 ≤ x ≤ 0 or −1 < x < 2, resulting in the interval −3 ≤ x < 2.

Set a is defined as {x ∈ ℝ | −3 ≤ x ≤ 0}, which represents the closed interval from -3 to 0, including both endpoints. Set b is defined as {x ∈ ℝ | −1 < x < 2}, representing an open interval from -1 to 2, excluding both endpoints.

To find the union of a and b, we combine the elements that satisfy either the conditions of set a or the conditions of set b. In this case, the union of a and b (a ∪ b) consists of all real numbers that fall within the ranges −3 ≤ x ≤ 0 or −1 < x < 2.

Combining these intervals, we obtain the interval −3 ≤ x < 2. This means that a ∪ b includes all real numbers from -3 up to (but not including) 2, covering the interval −3 ≤ x < 2.

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Naomi must make 6 visits to the movie theater to earn a free movie ticket.

Naomi earns 40 rewards points for signing up for a movie theater points card, and she earns 4.5 points for each visit to the movie theater. She needs 67 points to earn a free movie ticket. Now, let's write an equation to determine the number of visits, v, Naomi must make to earn a free movie ticket: 40 + 4.5v = 67

To solve this equation, we can simplify it and isolate the variable v by subtracting 40 from both sides. 4.5v = 27

Divide both sides by 4.5 to solve for v:v = 6

Therefore, Putting it all together, we can write the equation:

40 + 4.5vv = 67

vv = 27 / 4.5

vv = 6

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Answer: 5 over 28 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Step-by-step explanation:

To create a table of values for the equation 2x - 6y = 12, we can choose different values of x and solve for y. We will start with x = 0 and then choose other values of x to generate more points.

When x = 0, the equation becomes:

2(0) - 6y = 12

-6y = 12

y = -2

So the first point on the table is (0, -2).

When x = 2, the equation becomes:

2(2) - 6y = 12

4 - 6y = 12

-6y = 8

y = -4/3

So the second point on the table is (2, -4/3).

When x = 4, the equation becomes:

2(4) - 6y = 12

8 - 6y = 12

-6y = 4

y = -2/3

So the third point on the table is (4, -2/3).

When x = 6, the equation becomes:

2(6) - 6y = 12

12 - 6y = 12

-6y = 0

y = 0

So the fourth point on the table is (6, 0).

Therefore, the table of values for the equation 2x - 6y = 12 is:

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Answer: approx. 75 cents / muffin

Step-by-step explanation: divide 6.8 by 9

Answer:

$0.75

Step-by-step explanation:

6.8 divide by 9=0.755555556 and so its 0.75 cents per muffin

The rest allowance for chopping down a tree is 0.67 hours (rounded to two decimal places) or 40 minutes. In an 8-hour shift, approximately 40 minutes should be allowed for rest.

To calculate the rest allowance, we need to determine the energy expenditure for chopping down a tree and convert it into a time duration.

Given that the energy expenditure associated with chopping down a tree is 8.0 kcal/min, we can calculate the rest allowance using the following formula:

Rest allowance = Energy expenditure (kcal/min) * Time duration (min) / Energy content of food (kcal).

As the rest allowance is typically a fraction of the energy expenditure, we can use the value of 0.25 (25%) as the input for the rest allowance calculation.

Rest allowance = 8.0 kcal/min * Time duration (min) / Energy content of food (kcal) = 0.25.

Solving for the time duration, we find:

Time duration (min) = 0.25 * Energy content of food (kcal) / 8.0 kcal/min.

To determine the time duration in hours, we divide the time duration in minutes by 60:

Time duration (hours) = Time duration (min) / 60.

The specific energy content of food is not provided in the question. Therefore, without knowing the energy content, we cannot calculate the exact time duration for the rest allowance.

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Answer: 0.949

Step-by-step explanation:

I took the test

Given that

Then

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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The difference between sampling error and measurement error lies in the sources and causes of variation in data. Sampling error reflects the variation based on the probability of particular individuals or items being selected in a sample, while measurement error arises from errors in the process of measuring or collecting data, such as self-reporting or improper data collection methods.

Sampling error is the difference between the characteristics of a sample and the characteristics of the entire population. It occurs because we cannot measure the entire population, so we rely on a sample to make inferences. Sampling error is influenced by the probability of selecting specific individuals or items in the sample, and it can be reduced by increasing the sample size and using appropriate sampling techniques.

Measurement error, on the other hand, refers to errors that occur during the process of measuring or collecting data. This can be due to various factors, such as respondents providing inaccurate or incomplete information in surveys relying on self-reported data. Measurement error can also arise from using improper data collection methods or instruments that introduce bias or imprecision in the measurements. It represents the discrepancy between the true value and the measured value

In summary, sampling error is related to the representativeness of the sample and the probability of selection, while measurement error is associated with the accuracy and precision of data collection methods and instruments. Both errors contribute to the overall variability in data and can impact the reliability and validity of research findings.

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The area of the flat will be 600 ft².

Given that the apartment is having a length of 30 ft and the width is 20 ft,

We need to find the area of the flat,

So the area = length × width

Area = 20 × 30

= 600 ft²

Hence the area of the flat will be 600 ft².

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The distribution is roughly symmetric and unimodal, and the median and IQR best represent the data set.

If you plot a histogram of the data;

the distribution appears to be roughly symmetric and unimodal.

We can also calculate some summary statistics to better understand the center and spread of the data:

The range is a simple measure of spread, but it can be heavily influenced by outliers.

The IQR is a more robust measure of spread that is less affected by outliers.

Finally, the standard deviation is a commonly used measure of spread that takes into account how far each data point is from the mean.

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Answer: -10

Step-by-step explanation:

10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50

Answer:

x=-10

Step-by-step explanation:

-4x+10=50

10=50+4x

-50+10=4x

-40=4x

4x=-40

x=-40÷4

x=-10

Answer:

= 36

Step-by-step explanation:

Let us substitute x=2 to the equation: 3x(4+ x)

-

3(2)(4+ (2))

6*6 =36

Answer:

3x(4+x) when x=2 is 36

Step-by-step explanation:

3x(4+x) and x=2

Plug in 2 for every x and simplify:

(3(2))(4+(2))
6(6)

Now multiply:
6*6=36

Answer:

i think its 6 x 3 x 1

Step-by-step explanation:

There is 195 meters increase in distance for each additional 30 seconds

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for distance

d = 6.5t

where t is time in seconds,

Distance ran in 30 seconds

d = 6.5×30

d = 195 meters

Distance ran in 60 seconds

d' = 6.5 × 60

d' = 390 meters,

Increase in distance in 30 seconds

d' - d = 390 - 195 = 195 meters

Hence, 195 meters increase is there in distance every additional 30 seconds.

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Answer:

-16t² + 7,744 = 0

-16t² = -7,744

t² = 484

t = 22 seconds

The value x = 3 is not a zero of polynomial f(x) = x³ + 3 · x² - x - 3. (Correct choice: C)

Let p(x) be a polynomial, a value x is a zero of polynomial p(x) when p(x) = 0. Now we need to determine a value x such that polynomial f(x) = x³ + 3 · x² - x - 3 ≠ 0. The procedure is shown below:

Case A: x = 1

f(1) = 1³ + 3 · 1² - 1 - 3

f(1) = 1 + 3 - 1 - 3

f(1) = 4 - 4

f(1) = 0

Case B: x = - 1

f(- 1) = (- 1)³ + 3 · (- 1)² - (- 1) - 3

f(- 1) = - 1 + 3 + 1 - 3

f(- 1) = 0

Case C: x = 3

f(3) = (3)³ + 3 · (3)² - (3) - 3

f(3) = 27 + 27 - 3 - 3

f(3) = 48

Case D: x = - 3

f(- 3) = (- 3)³ + 3 · (- 3)² - (- 3) - 3

f(- 3) = - 27 + 27 + 3 - 3

f(- 3) = 0

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Using the binomial distribution, the probabilities are given as follows:

The probability mass function for the binomial distribution is presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters of the distribution are given by:

In the context of this problem, the values of these parameters are:

n = 5, p = 0.735.

The probability of all people ordering the breast sandwich is:

P(X = 5) = 0.735^5 = 0.2145 = 21.45%.

The probability of no people ordering the breast sandwich is:

P(X = 0) = (1 - 0.735)^5 = 0.0013 = 0.13%.

The probability of at least one person ordering the breast sandwich is:

P(X >= 1) = 1 - 0.0013 = 0.9987 = 99.87%.

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Step-by-step explanation:

125+680w>2,500+450w

You would divide 13 by 754=58

Then 58 times 8= 464

So 464 miles

The solution to the algebraic equation (a + 8/3) = 2/3 is given by a = -2

(a + 8/3) = 2/3

open parenthesis

a + 8/3 = 2/3

collect like terms

a = 2/3 - 8/3

a = (2-8) / 3

a = -6/3

a = - 2

Check:

(a + 8/3) = 2/3

-2 + 8/3 = 2/3

(-6+8) / 3 = 2/3

2/3 = 2/3

In conclusion, -2 is the solution to the unknown in the equation (a + 8/3) = 2/3

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Circumference = diameter x pi

Find the diameter:

75.36 = diameter x pi

Divide both sides by pi:

Diameter = 75.36/3.14 = 24 inches.

Area = pi x r^2

R = 1/2 diameter = 12

Area = 3.14 x 12^2

Area = 452.16 in^2

The answer is D.