A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 13,29 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Answer:

Step-by-step explanation:

X-intercept means y-coordinate of 0:

4x +7×0 = 28

 4x = 28

   x = 7         ← x-coordinate

Y-intercept means x-coordinate of 0:

4×0 +7y = 28

 7y = 28

   y = 4         ← y-coordinate

The nth Maclaurin polynomial for the function f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...

The nth Maclaurin polynomial for the function f(x) = (4x − 5)/(x + 1), we need to expand the function as a power series centered at x = 0 (the Maclaurin series) and then truncate it to the desired degree.

First, let's find the Maclaurin series expansion of f(x):

f(x) = (4x − 5)/(x + 1)

To expand this as a power series, we'll use the concept of geometric series expansion. We'll start by expressing f(x) as a product of two functions:

f(x) = (4x − 5)×(x + 1)⁻¹

Now, let's find the power series expansion for each factor separately.

1.The power series expansion for (4x - 5) centered at x = 0 is given by:

(4x - 5) = -5 + 4x

2.The power series expansion for (x + 1)⁻¹ centered at x = 0 is given by the geometric series formula:

(x + 1)⁻¹ = 1 - x + x² - x³ + x⁴ - ...

Note that this expansion is valid when |x| < 1 since it's based on a geometric series.

Now, we'll multiply these two expansions together to get the expansion for f(x). We'll keep terms up to the fourth degree (n = 4).

f(x) = (4x - 5) × (x + 1)⁻¹ = (-5 + 4x) × (1 - x + x² - x³ + x⁴)

Expanding this expression:

f(x) = -5 + 4x - 5x + 4x² - 5x³ + 4x⁴ + ...

Simplifying the terms:

f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...

This is the Maclaurin series expansion for f(x). The nth Maclaurin polynomial, we'll truncate the series at the fourth degree (n = 4):

f(x) ≈ -5 - x + 4x² - 5x³ + 4x⁴

Therefore, the fourth Maclaurin polynomial for f(x) is given by:

P₄(x) = -5 - x + 4x² - 5x³ + 4x⁴

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The expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B.

Difference of Squares is a squared quantity that can be represented as the difference of the squares of two variables or numbers. In simple terms, when two squares are subtracted, a difference of squares is produced. The squares of the two quantities, x and y, are subtracted from each other in the Difference of Squares.Here, the expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B. In this expression, we have the square of two quantities subtracted, which results in the Difference of Squares.Checking the other options, we can say that option A (10y² − 4x²) cannot be considered a difference of squares because there is no squared quantity subtracted from it. Similarly, option C (8x² − 40x + 25) and option D (64x² − 48x + 9) do not show the Difference of Squares as they do not have two squared quantities subtracted from each other.

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Answer:

75.935

Step-by-step explanation:

If V = Pe^rt and we are given P (the principle investment) =4630 ,

a rate of 5.7 % which as a decimal = 0.057 (% divided by 100 = decimal)

we can substitute this information in and get V=4630 e^(.057t).

then it says what will it be in 9 years? so we put 9 in for "t" and get

v = 4630 e^(0.057 * 9) simplify using a calculator and we will get our answer.

The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. What is multiple linear regression? Multiple linear regression is a regression method where the response variable is dependent on more than one independent variable. Multiple linear regression is an extension of linear regression, where one response variable is dependent on one independent variable. It helps to determine the nature of the relationship between dependent variables and independent variables in the form of linear equations. It is used to find out the relationship between variables and make predictions based on that relationship. Assumptions of multiple linear regression1. Linearity, It is assumed that the relationship between the independent variables and dependent variables is linear. This implies that as the value of the independent variable changes, the change in the dependent variable is constant.2. Independence, There should be independence among the observations. This implies that there should not be any relationship between the residuals of the observations.3. Homoscedasticity implies that the variance of residuals should remain constant across all levels of the independent variable.4. Multicollinearity, It is the condition where the independent variables are highly correlated with each other. If there is perfect collinearity, it will not be possible to obtain the estimates of regression coefficients.5. Normality, The residuals should follow a normal distribution with mean zero and constant variance. The residuals should be normally distributed and centered on zero. The assumptions that are true for multiple linear regression are: The independent variables are not correlated. The residuals are normally distributed. The relationship between dependent and independent variables is linear. The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. Hence, the correct option is D) There will be a multi-collinearity effect.

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Step-by-step explanation:

[tex]91.8 \div 12 = 7.65 \\ 19.35 \div 3 = 6.45[/tex]

3 months

Answer:

x = 6

y = 4

Step-by-step explanation:

5x - 7y = 2

x - 7y = -22 (Multiply by -1)

-x + 7y = 22

5x - 7y = 2

4x = 24

x = 6

x - 7y = -22

6 - 7y = -22

-7y = -28

y = 4

Answer:

5.5

Step-by-step explanation:

30-60-90 triangle rule is:

x - x[tex]\sqrt{3}[/tex] - 2x

11 = 2x

x = 5.5

Answer: 50

Step-by-step explanation:

because its rounded to its nearest 20ths'

Answer:

- 22719559.

Step-by-step explanation:

Answer:

y=4x+2

Step-by-step explanation:

Answer:

Complementary

x= 60

Step-by-step explanation:

Answer:

The angles are complementary.

X =  60

Step-by-step explanation:

The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Answer:

If you add teacher plus students which is 490+10=500

you get 500 people in total after that you divide 500 by 50 and you get 10 so you will need 10 busses in total hope this helped!

Step-by-step explanation:

Answer:

[tex]x = \frac{20}{ \sqrt{3} } \\ y = \frac{40}{ \sqrt{3} } [/tex]

Step-by-step explanation:

[tex]for \: \: x \\ \tan(60) = \frac{20}{x} \\ \sqrt{3} = \frac{20}{x} \\ x = \frac{20}{ \sqrt{3} } \\ \\ for \: y \: \\ \sin(60) = \frac{20}{y} \\ \frac{ \sqrt{3} }{2} = \frac{20}{y} \\ \sqrt{3} \: y = 20 \times 2 \\ y = \frac{40}{ \sqrt{3} } [/tex]

I hope that is useful for you :)

Answer:

1. 1/4

2. 43/10 or 4 3/10 either are correct.

3. 67/12 or 5 7/12 either are correct.

Step-by-step explanation:

I hope this helped.

A:  The alternative hypothesis is that the population mean is not equal to the specified value

B: p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C: 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970

A. The null hypothesis is that the population mean is equal to a specified value (μ = specified value), and the alternative hypothesis is that the population mean is not equal to the specified value (μ ≠ specified value).

B. To perform the hypothesis test,

we first need to calculate the sample mean and standard deviation.

Since we have,

Sample size (n) = 7

Sample mean (X) = (13+9+10+5+10+7+9) / 7 = 8.8571

Sample standard deviation (s) = 2.1561

Using the formula for the one-sample t-test, we get,

⇒ t = (X- μ) / (s / √(n))

Assuming the specified value is 8, then we have,

⇒ t = (8.8571 - 8) / (2.1561 / √(7))

⇒ t = 0.9945

Using a t-distribution table with 6 degrees of freedom (df = n - 1),

we find that the p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C. Based on this test, we cannot reject the null hypothesis that the true population mean is equal to 8 at a 5% level of significance since the p-value (0.3739) is greater than the significance level (0.05).

Therefore, we do not have enough evidence to conclude that the population mean is different from 8. In other words, we can state with 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970.

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Answer:

Y= 3/5-4

Step-by-step explanation:

What is slope-intercept form? Slope intercept form is an equation for graphing. It is y=mx+b. The "m" stands for the slope, or how much coordinates it takes to move to the next point. The "b" stands for the y-intercept, or where the line is perfectly on the y-line.

Step One: The first part of the equation is the slope, so let's figure that out. Since this one a graph, it is easy to tell the slope. The points are nicely marked, so we don't have to guess which points are visible. We are going up 3 jumps and then across 5 jumps. The slope is always "rise/run" where the "rise" is the y and "run" is x. So, the slope is 3/5x.

Step Two: For the last part, we need to know the y-intercept. It is clearly shown on the graph: -4. Because it is negative, we remove the plus sign because a plus with a negative is subtraction.

Step Three: We can combine both parts and that is the answer: y=3/5x-4.  

Approximately 12.5% percentage of the students could be expected to score between 80 and 90.

To determine the percentage of students who could be expected to score between 80 and 90, we need to calculate the z-scores for these scores and use the standard normal distribution.

First, we need to calculate the z-scores for 80 and 90 using the formula:

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values of μ = 100, σ = 60, and x = 80 or x = 90, we can calculate the z-scores.

For x = 80:

z = (80 - 100) / 60 = -0.3333

For x = 90:

z = (90 - 100) / 60 = -0.1667

Next, we need to find the area under the standard normal distribution curve between these two z-scores. This represents the percentage of students who scored between 80 and 90.

Using a standard normal distribution table or calculator, we can find that the area between -0.3333 and -0.1667 is approximately 0.1210 or 12.1%.

Therefore, approximately 12.5% of the students could be expected to score between 80 and 90.

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Correct Question is:

A car company charges x dollars to rent a car plus extra options as shown in table.

Car seat = 50 $

Insurance = 75 $

Car Wash = 15 $

Three people each rented a car with insurance and one more person rented a car with a car wash. What is the expression for the total cost?

Step-by-step explanation:

3 people rented with insurance = (x + 75) * 3) = 3x +225

one person rented with car wash = (15+x)

Total car rental will be adding both equations = 3x +225 + 15 + x = 4x + 240

Answer:

A

Step-by-step explanation:

Hello There!

This is the formula for volume of a cylinder

[tex]V=\pi r^2h[/tex]

where r = radius and h = height

we are given the height and diameter height - 10 ft diameter - 22 ft

we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2

22/2=11 so the radius is 11

now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)

[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]

so we can conclude that the answer is A

Answer:

24cm

Step-by-step explanation:

Assuming sides AC and BC are equivalent:

AC = 3cm + 9cm = 12cm

BC = AC = 12cm

AB = 3cm + 3cm = 6cm

AB + BC + AC = 12cm + 12cm + 6cm = 24cm

Answer:

30

Step-by-step explanation:

30

Main answer: fn(x) = xe converges uniformly to 0 on [0, ∞).

Supporting explanation: In order to prove that fn(x) = xe converges uniformly to 0 on [0, ∞), we need to use the definition of uniform convergence. Let ε > 0 be given. We need to find an N such that |fn(x) - 0| < ε for all n > N and x ∈ [0, ∞).So, we have|fn(x) - 0| = |xe| = xe < εfor all n > N and x ∈ [0, ∞).We can choose N = 1/ε, then we have|fn(x) - 0| = |xe| < εfor all n > N and x ∈ [0, ∞).This means that fn(x) = xe converges uniformly to 0 on [0, ∞). Hence, the proof is complete.

A series of fn(x) functions with n = 1, 2, 3, etc. For a set E of x values, is said to be uniformly convergent to f if, for each > 0, a positive integer N exists such that |fn(x) - f(x)| for n N and x E. An alternative definition for the uniform convergence of a series of functions is given below.

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Answer:

Diameter= 10.2  -  Radius=5.1

Step-by-step explanation:

5.1 x 2= 10.2

10.2/2=5.1

Answer:

80%

Step-by-step explanation:

Percent increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

Increase = $27 - $15 = $12 , then

percent increase = [tex]\frac{12}{15}[/tex] × 100% = 0.8 × 100% = 80%

Step-by-step explanation:

Percentage Increase = Amount of Increase/ Orginal Amount x 100%

27-15= 12

$12= Amount of Increase

Percentage Increase= 12/15 x 100

                                  = 80% increase in stock price

Hope this Helps

Answer:

19x−14y

Steps:

7x-3y+4x-5y+8x-6y

=19x-3y-5y-6y

= 19x−14y

plz mark as brainliest

Answer:

19x-14y

Step-by-step explanation:

rearrange

7x+4x+8x-3y-5y-6y

solve the coefficient and add the variables

Answer:

m∠R = 123°

m∠S = 91°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc

m of arc QRS = 2 m∠P = 2(57) = 114

Now m of arc SPQ = 360 - 114 = 246

So, m∠R = 1/2(246) = 123

m of arc RSP = 2 m∠Q = 2(89) = 178

m of arc PQR = 360 - 178 = 182

m∠S = 1/2(182) = 91

Multiply 6 by 1/2 to get 3

Ow you have :

3( h + 1) = 18

Distribute the 3:

3h + 3 = 18

Subtract 3 from both sides:

3h = 15

Divide both sides by 3:

H = 5

Answer: `h² + 18h + 108`

We have to evaluate the difference quotient of the formula `f(x) when `f(6+ h)?

f(6)` and the expression will be simplified by dividing it by 'h.'

Difference quotient:

The difference quotient is a formula used to find the average rate of change of a function over a specific interval. The difference quotient is defined as:```f(x + h) - f(x) / h```

To find the difference quotient for f(x) = x³, we need to substitute the values as shown below:

f(x + h) = (6 + h)³f(x) = 6³f(x + h) - f(x) = (6 + h)³ - 6³

Now we can substitute these values in the formula of the difference quotient :

'f (6+ h). f(6)`h = (6 + h)³ - 6³ - h/ h

By simplifying the difference quotient we get;`

(6 + h)³ - 6³ - h/ h = (6³ + 3 * 6²h + 3 * 6h² + h³ - 6³) / h`

After simplifying the expression above, the terms 6³ and -6³ cancel out.

We can then combine the like terms (3 * 6²h and 3 * 6h²) and further simplify the expression as follows:`= (3 * 6²h + 3 * 6h² + h³) / h`= (108h + 18h² + h³) / h`= h² + 18h + 108

Answer: `h² + 18h + 108`

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