What is
(f + g)(x)?
f(x) = x2 – 36
g(x) = x3 + 2x2 – 10
Enter your answer in standard form in the box

a. To determine if the two populations of crawfish from Devon and Cornwall have the same mean carapace length, we can use the two-sample t-test.

This test compares the means of two independent samples to assess whether they are significantly different.

We can calculate the sample means and sample standard deviations for both groups:

Next, we calculate the t-value using the formula:

To determine if this t-value is statistically significant, we need to compare it to the critical value from the t-distribution for the given degrees of freedom

If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that the two populations have different mean carapace lengths. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean carapace length between the two populations.

b. To answer the question using the Wilcoxon rank sum test, we need to combine the observations from both samples, assign ranks based on their relative positions, and calculate the sum of ranks for one of the samples (either Devon or Cornwall). The null hypothesis for this test is that the two distributions are the same.

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Answer:

4.5

Step-by-step explanation:

Answer:

(x-4)^2 -4 = y

Step-by-step explanation:

The graph is translated 4 to the right and 4 downwards.

Answer:

a regular person would gave moved 4 to 5 times

Answer:

length = 9 in ; width = 4 in

Step-by-step explanation:

1) formula of the area of a rectangle

A = base x width

2) write an equation with the given informations:

w x (3w-3) = 36

3) solve the equation

-  multiply W by 3w and -3

3w^2 -3w = 36

- divide the two members by 3

w^2 - w = 12

- add up -12 at the two members

w^2-w -12 = 12 -12

w^2 - w - 12 = 0

- find two numbers whose sum is -1 and whose product is -12 and factorise the equation

(w-4)(w+3) = 0

- find the two solutions

w-4 = 0

w = 4

w+3 = 0

w = -3

4)remember that a length can’t be negative.

w = 4 is the only solution

5) find the length

4x3 - 3 = 9

Whwn the null hypothesis is that the slope of the population regression line of price on age is zero, the test statistic is -2.43.

The test statistic is calculated as follows:

t = (b - 0) / SE(b)

In this case, the slope of the regression line is estimated to be -11.50, the standard error of the slope is 4.77, and the hypothesized value of the slope is 0.

t = (-11.50 - 0) / 4.77

= -2.43

The test statistic is -2.43, The p-value for this test statistic can be calculated using a t-table. The degrees of freedom for this test are 5 - 2 = 3. The p-value for a t-statistic of -2.43 with 3 degrees of freedom is 0.048.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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Answer:

48 treats

Step-by-step explanation:

16 treats / 2 hours = 8 treats / hour

8 treats / hour x 6 hours =

48 treats

Hope that helps! :)

Answer:

2 cups

Step-by-step explanation:

16/8=2 so it is 2 cups

Answer:

1,250 millileters

Step-by-step explanation:

The computation of the number of milliters of the sports drink left is shown below:

Given that

The 2-liter sports drink is purchased

And, drank 250 millimeters and than drank one-half liter of the drink

Now convert liter to millileter

1 litre = 1000 milliliter.

2 liters = 2 × 1000 milliliters.

= 2000 milliliters.

Now the left drink would be

= (2000 - 250) - (250 × 2)

= 1,750 - 500

= 1,250 millileters

Answer: the answer is 6.06%, however if it is rounded it's 6.0%

Step-by-step explanation:

One faces a tradeoff between the number of courses and hours of work due to limited available time. Taking X courses while working X hours per week is impossible as it exceeds the time constraint.

The tradeoff between the number of courses and hours of work arises due to the finite number of hours available in a week. Assuming an individual has X hours per week, this time must be divided between courses and work.

To achieve a B or better in a course, it is necessary to dedicate at least X hours per course per week. Therefore, taking X courses while working X hours per week would require dedicating X hours per course, resulting in a total time commitment exceeding the available X hours.

Conversely, if only one class is taken while working X hours per week, the time commitment for a single course is less than X hours. This scenario leaves a significant amount of free time remaining, as the total time dedicated to the course and work does not exhaust the available X hours.

In summary, the tradeoff occurs because the time available is limited, and the minimum time requirement per course restricts the number of courses that can be taken while maintaining a specific work schedule.

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Answer:

Hopefully it makes sense

Step-by-step explanation:

Good luck

The correct option regarding the perimeter of the polygon in this problem is given as follows:

5/3mn³ + 3mn² + 3m².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the expression for the perimeter is given as follows:

1/3mn³ + mn² + m² + 2mn³ + 2mn² + 3m².

Combining the like terms, the perimeter is given as follows:

5/3mn³ + 3mn² + 3m².

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The probability that all 11 tests will be positive is 0.8007

The probability that at least one test will be negative is 0.1993

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

p = 0.98

n = 11

The probability that all 11 tests will be positive is

P = pⁿ

So, we have

P = 0.98¹¹

Evaluate

P = 0.8007

Here, we use

P = 1 - P(No negative)

So, we have

P = 1 - 0.8007

Evaluate

P = 0.1993

Hence, the probability is 0.1993

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Answer:

c - 13,600ft^2

Step-by-step explanation:

200 x 80 = 16,000ft^2

40 x 60 = 2,400ft^2

16,000ft^2 - 2,400ft^2 = 13,600ft^2

It is proved that if A1, A2,...,An and B are sets, then (A1 −B) ∩(A2 −B) ∩...∩(An−B) = (A1 ∩A2 ∩...∩An) −B.

To prove the given statement using induction, we need to show that it holds true for a base case and then demonstrate that if it holds for an arbitrary value of 'n', it also holds for 'n + 1'.

Base Case (n = 1):

Let's consider the base case where 'n = 1'. We have two sets A1 and B, and we want to prove that (A1 - B) = (A1 - B).

(A1 - B) ∩ (A1 - B) = (A1 - B)  [Using the definition of set difference]

This satisfies the given statement for the base case.

Inductive Step

Assuming that the given statement holds for 'n = k', let's prove that it holds for 'n = k + 1'.

We have sets A1, A2, ..., Ak+1, and B. We want to prove that:

(A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B) = (A1 ∩ A2 ∩ ... ∩ Ak+1) - B

Using the inductive hypothesis, we can rewrite the left-hand side (LHS) as:

[(A1 ∩ A2 ∩ ... ∩ Ak) - B] ∩ (Ak+1 - B)

To prove the equality, we need to show that each side is a subset of the other.

1. LHS ⊆ RHS:

Let x be an arbitrary element in LHS. This means that x belongs to each set in the intersection on the LHS: (A1 - B), (A2 - B), ..., (Ak+1 - B). By the definition of set intersection, x also belongs to (A1 - B), (A2 - B), ..., (Ak - B), and (Ak+1 - B).

Since x belongs to each set in the intersection (A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B), it follows that x belongs to (A1 ∩ A2 ∩ ... ∩ Ak) - B. Therefore, x ∈ RHS.

2. RHS ⊆ LHS:

Now let y be an arbitrary element in RHS. This means that y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1) - B. By the definition of set difference, y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1) and y does not belong to B.

Since y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1), it implies that y belongs to each set A1, A2, ..., Ak+1. By the definition of set difference, y does not belong to B, so y also belongs to each set (A1 - B), (A2 - B), ..., (Ak+1 - B).

Therefore, y ∈ LHS.

Since we have shown that LHS ⊆ RHS and RHS ⊆ LHS, it follows that (A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B) = (A1 ∩ A2 ∩ ... ∩ Ak+1) - B.

By the principle of mathematical induction, the statement holds for all 'n', completing the proof.

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Answer:

Step-by-step explanation:

I don’t know

We want to find the opening price of the stock in the beginning of the day. We will find that the solution is $89.50.

Let's say that the opening price of the stock was X.

Then, it is increased 6% to get to $94.87

This means that the 106% of X is equal to $94.87, then we can solve:

1.06*X = $94.87

Where we wrote 106% in decimal form, now we can just solve this for X:

X  = $94.87/1.06 = $89.50

This means that the price of the stock in the beginning of the day was $89.50

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Answer:

the mean and the standard deviation is 0.92 and 0.01808 respectively

Step-by-step explanation:

The computation of the mean and the standard deviation is shown below:

The mean is 0.92

And, the standard deviation is

= √0.92 × (1 - 0.92) ÷ √225

= √0.92 × 0.08 ÷ √225

= √0.0736 ÷ √225

= √3.27

= 0.01808

Hence, the mean and the standard deviation is 0.92 and 0.01808 respectively

Answer:

10,000 * (square miles in the city)

Step-by-step explanation:

You've been given a population of people for every square mile (10,000) and you're trying to figure out how many people live in the city.

To convert people per a square mile into people, you'll need to know how many square miles you have. I assume you've been given this as the size of the city or how many square miles the city takes up. Just multiply the amount of people per a square mile by the amount of square miles in the city, and it'll give you the population of people in every square mile of the city (the population).

Note:

This is people per a square mile, or in other words, for every square mile of city, 10,000 people live there. If you have 2 square miles of city, then 2 * 10,000 = 20,000 people live there.

The approximate Population density in the circular petri dish with a radius of 40 millimeters and 2,100 bacteria is approximately 0.418 bacteria per square millimeter.  After rounding up the bacteria becomes 0.42 per sq. meter hence the correct option is b  

The approximate population density in the circular petri dish, we need to calculate the area of the dish and divide the total number of bacteria by that area.

The formula to calculate the area of a circle is: A = πr^2, where A represents the area and r is the radius.

In this case, the radius of the petri dish is given as 40 millimeters. Therefore, the area can be calculated as follows:

A = 3.14 * (40)^2

A = 3.14 * 1600

A ≈ 5024 square millimeters

Next, we divide the total number of bacteria (2,100) by the calculated area to find the population density:

Population density = 2,100 bacteria / 5024 square millimeters

Population density ≈ 0.418 bacteria per square millimeter

Therefore, the approximate population density in the circular petri dish is 0.418 bacteria per square millimeter.

in scientific calculations, it is customary to use the value of π as 3.14 for simplicity, even though it is an irrational number with a longer decimal representation.

When writing about scientific concepts or calculations, it is crucial to ensure academic integrity by avoiding plagiarism. This can be done by understanding and explaining the concepts in your own words, citing any external sources used, and providing accurate calculations based on the given information.

In conclusion, the approximate population density in the circular petri dish with a radius of 40 millimeters and 2,100 bacteria is approximately 0.418 bacteria per square millimeter.  After rounding up the bacteria becomes 0.42 per sq. meter hence the correct option is b  

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The P(you win) = 1/16P(you lose) = 15/16 and Average winnings, µ, = -5/16.

The probability of winning (P) and the probability of losing (Q) are both possible outcomes from a coin toss experiment. The probability of winning is given by the formula

P = Number of ways to win/ Total number of possible outcomes.The probability of losing is given by the formula

Q = Number of ways to lose/Total number of possible outcomes.

Formulae used to calculate probability are:

P = Number of ways to win/ Total number of possible outcomes

P = Number of outcomes in which all four tosses are heads/ Total number of possible outcomes

When a coin is tossed four times, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

P = Number of outcomes in which all four tosses are heads/ Total number of possible outcomes

P = 1/16P (you win) = 1/16

The probability of losing is given by the formula

Q = Number of ways to lose/Total number of possible outcomes.

Q = 15/16P (you lose) = 15/16

Average winnings, µ, can be calculated as follows:

Let's say X represents the amount of money you win. When you win, you get $10, and when you lose, you lose $1.

X = -1 when you loseX = 10 when you winUsing the formula

µ = ∑ (X × P), we can calculate the average winnings,

µ = (-1 × 15/16) + (10 × 1/16)µ = -15/16 + 10/16µ = -5/16.

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Given information: A coin is tossed four times. You bet $1 that heads will come up on all four tosses. If this happens, you win $10. Otherwise, you lose your $1 bet.

Therefore, the answers are:

P(you win) = 0.0625

P(you lose) = 0.9375

Average winnings, µ, = -$0.31

Let A be the event of getting heads on the four tosses. Since the coin is tossed four times, the possible outcomes are 2^4 = 16. Thus the probability of getting heads on each toss is 0.5. Therefore, the probability of getting heads on all four tosses is:

P(A) = (0.5)^4

= 0.0625

Let B be the event of not getting heads on all four tosses. Thus:

B = 1 − P(A)

= 1 − 0.0625

= 0.9375

The winning amount for getting all four heads is $10, and the losing amount is $1. Thus, the average winnings is:

µ = (10 × 0.0625) − (1 × 0.9375)

µ = 0.625 − 0.9375

µ = -0.3125

Therefore, the answers are:

P(you win) = 0.0625

P(you lose) = 0.9375

Average winnings, µ, = -$0.31

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Answer:

C

Step-by-step explanation:

C

Answer:

9 - s = 4

Step-by-step explanation:

9 - 6 is 3, not 4, so thats the answer!

The equation is s = 6 not the solution is 9 - s = 4.

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

For which equation is s = 6 not the solution?

1. The solution of the equation 4 s = 24 is;

[tex]\rm4 s = 24\\\\s=\dfrac{24}{4}\\\\s=6[/tex]

2. The solution of the equation 9 - s = 4  is;

[tex]\rm 9 - s = 4\\\\s=9-4\\\\s=5[/tex]

3. The solution of the equation s + 6 = 12 is;

[tex]\rm s + 6 = 12\\\\s=12-6\\\\s=6[/tex]

4. The solution of the equation s - 4 = 2 is;

[tex]\rm s - 4 = 2\\\\s=2+4\\\\s=6[/tex]

Hence, the equation is s = 6 not the solution is 9 - s = 4.

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The "margin-of-error" is 3.6 and the "sample-mean" is 18.7 based on the given confidence interval (15.1, 22.3).

To find the "margin-of-error" and the "sample-mean" from the given confidence interval, we use the formula:

Confidence-Interval = Sample mean ± Margin of error,

In this case, the given confidence-interval is (15.1, 22.3),

To find the margin-of-error, we need to consider the range between the upper and lower bounds of the confidence interval and divide it by 2,

The "Margin-of-error" is = (Upper bound - Lower bound)/2,

"Margin-of-error" is = (22.3 - 15.1)/2 = 3.6,

So, the margin of error is 3.6.

To find "sample-mean", we calculate average of the upper and lower bounds of the confidence-interval,

The "Sample-Mean" is = (Upper bound + Lower bound)/2,

"Sample-Mean" is = (22.3 + 15.1)/2 = 18.7,

Therefore, the "sample-mean" is 18.7.

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The given question is incomplete, the complete question is

Use the confidence interval to find the margin of error and the sample mean. (15.1, 22.3).

If a and n are relatively prime (gcd(a, n) = 1), it does not guarantee that the equation x ≡ a (mod n) has solutions.

If a and n are relatively prime, denoted by gcd(a, n) = 1, it means that a and n do not have any common factors other than 1. However, this does not guarantee that the equation x ≡ a (mod n) has solutions.

The equation x ≡ a (mod n) represents a congruence relation, where x is congruent to a modulo n. This equation implies that x and a have the same remainder when divided by n.

To have solutions for this congruence equation, it is necessary for a to be congruent to some number modulo n. In other words, a must lie in the residue classes modulo n. However, the fact that gcd(a, n) = 1 does not ensure that a is congruent to any residue modulo n, hence not guaranteeing the existence of solutions for the equation.

Therefore, when n = 1, we cannot conclude that the equation x ≡ a (mod n) has solutions.

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The linear speed of a point on the circumference is approximately 9895 feet per minute.

(a) To find the angular speed in radians per minute, we need to convert the given rotational speed from rpm (revolutions per minute) to radians per minute. Since there are 2π radians in one revolution, we can use the conversion factor:

Angular speed (in radians per minute) = Rotational speed (in rpm) * 2π

Given that the rotational speed is 2100 rpm, we can calculate the angular speed:

Angular speed = 2100 rpm * 2π ≈ 13194 radians per minute

Therefore, the angular speed of the wheel is approximately 13194 radians per minute.

(b) To find the linear speed of a point on the circumference in feet per minute, we can use the formula:

Linear speed = Angular speed * Radius

Given that the radius of the wheel is 9 inches, we need to convert it to feet:

Radius = 9 inches * (1 foot / 12 inches) = 0.75 feet

Now, we can calculate the linear speed:

Linear speed = 13194 radians per minute * 0.75 feet ≈ 9895 feet per minute

Therefore, the linear speed of a point on the circumference is approximately 9895 feet per minute.

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Answer:

X = $9.00 for 1 pound of Jelly Beans

Y = $7.00 for 1 pound of Gummy Worms

Step-by-step explanation:

Ok, to start we need to make up some notation. It looks like you've chosen X and Y as your variables which works for me.

First lets say X = cost of one pound of jelly beans and Y = cost of one pound of gummy worms

Now let's put together our equations

2X + 4Y = 46

3X + 2Y = 41

Now we need to solve for one of the variables using substitution or elimination. Since none of the variables are isolated, let's use elimination by multiplying the bottom equation by -2.

2X + 4Y = 46

-6X - 4Y = -82

___________

-4X + 0 = -36

-4X = -36

X = 9 or $9.00 per pound

Now we can plug that back into own of the equations and solve for Y

2(9) + 4Y = 46

 18 + 4Y = 46

4Y = 28

Y = 7 or $7.00 per pound

The joint probability density function (pdf) is f(x,y) = 0.03 for 0 < x < 1 and 0 < y < 3.

The joint pdf, f(x,y), represents the probability density function for the random variables X and Y. Given that X is uniformly distributed on (0,10), we have fX(x) = 0.1 for 0 < x < 10. The probability of X being less than 1 is 1/10, so the conditional pdf f(x|X<1) = 0.1 for 0 < x < 1.

Furthermore, Y is uniformly distributed on (0,3), so fY(y) = 0.1 for 0 < y < 3. To find the joint pdf, we multiply the conditional pdf of X with the marginal pdf of Y: f(x,y) = f(x|X<1) * fY(y) = 0.1 * 0.1 = 0.01 for 0 < x < 1 and 0 < y < 3. Therefore, the joint pdf is f(x,y) = 0.01 for 0 < x < 1 and 0 < y < 3.

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