Write the equation of the line through (0, −2) and (3, 10) in point-slope form.

Answer:

b = 133

c = 47

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

An equation is used to show the relationship between two or more numbers and variables.

The pool holds 30 gallons of water. After 5 minutes, the pool is about one fourth full. Hence:

Time to full the pool = 5 minutes * 4 = 20 minutes

Rate of water flow = 30 gallons/20 minutes = 1.5 gallons per minute

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

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Answer:

12i

Step-by-step explanation:

2i×2i=4i

4i×3i=12i

The amount added each time increases because each initial population is larger. This type of growth is called exponential growth is the answer.

During each measured time period when the per capita growth rate of a population is positive (r > 0), a population will add a number to its population that equals exactly r times the initial population. This process continues with each succeeding time period. Exponential growth is a type of population growth that occurs when the number of individuals in a population increases at a constant percentage per unit of time. In exponential growth, the population increases by a fixed amount in each unit of time. Each time period, the amount added to the population increases because each initial population is larger. Population growth can be modelled by the equation dN/dt = rN, where N is the population size, t is time, and r is the per capita growth rate.

The solution to this differential equation is N = N₀e^(rt), where N₀ is the initial population size and e is the natural logarithm base (approximately 2.71828). The exponential growth model is useful in understanding the growth of populations with abundant resources and no natural limits on growth. However, in reality, no population can grow indefinitely because of environmental factors such as competition for resources, predation, disease, and other factors that limit population growth.

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Franco can read approximately 1.875 chapters of his history book in 1 hour, assuming his reading rate remains constant.

Franco read 3/8 of a chapter in 1/5 of an hour. To find out how many chapters he can read in 1 hour, we need to first determine his rate of reading.

To do this, we can set up a proportion:

3/8 of a chapter = x chapters
1/5 of an hour = 1 hour

Cross-multiplying, we get:

3/8 * 1 hour = x * 1/5

Simplifying:

3/8 = x/5

Cross-multiplying again:

15/8 = x

So Franco can read 15/8 or 1 7/8 chapters in 1 hour.

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Answer:

the data has 2 range

Step-by-step explanation:

you can subtract the largest number with the smallest

Answer:

Step-by-step explanation:

The data are evenly distributed with a mean of 7.1

Answer:45

Step-by-step explanation:

the factors for 90= 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

the factors for 135=1,3,5,9,15,45

the highest numbers that is divide both numbers is 45

if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.

The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.

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all the missing Angles in the triangles are:

A = 60°

B = 60°

C = 60°

D = 42°

E = 35°

F = 35°

G = 55°

H = 45°

I = 45°

J = 15°

K = 15°

L = 75°

M = 120°

N = 21°

O = 69°

P = 21°

Q = 55°

R = 55°

S = 42°

T = 42°

U = 69°

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a specific case of such an isosceles triangle.

An equilateral triangle in geometry is a triangle whose sides are all of the same length. The three angles opposing the three equal sides are equal in measure since the three sides are all equal. As a result, it is also known as an equiangular triangle since each angle is 60 degrees.

A = 60°

B = 60°

C = 60°

D = 42°

E = 35°

F = 35°

G = 55°

H = 45°

I = 45°

J = 15°

K = 15°

L = 75°

M = 120°

N = 21°

O = 69°

P = 21°

Q = 55°

R = 55°

S = 42°

T = 42°

U = 69°

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The complete question is as follows:

The range of the possible values of r^2 is 0 to 1. It represents the proportion of the dependent variable’s variance that can be explained by the independent variable(s).


The coefficient of determination, often denoted as r^2, measures the proportion of the dependent variable’s variance that can be explained by the independent variable(s) in a statistical model. The value of r^2 ranges from 0 to 1.
A value of 0 for r^2 indicates that the independent variable(s) does not explain any of the variance in the dependent variable. On the other hand, a value of 1 implies that the independent variable(s) fully explain the observed variance in the dependent variable.
Therefore, the range of the possible values of r^2 is 0 to 1. Any positive numerical value within this range indicates a degree of explanatory power, while values outside this range are not meaningful in the context of r^2. It serves as a useful tool for assessing the strength of a statistical relationship and the predictive ability of a model.

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The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

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The complete question is:

A kindergarten teacher has five books to distribute to 20 children in her class.

(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?

(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.

(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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The water must travel \(41\frac{1}{6}\)  feet to go from the bottom of the roots to the top of the tree's branches .

In the question ,

it is given that

the length of the tree = \(28\frac{1}{3}\) feet

length of the root under the grounds surface = \(12\frac{5}{6}\) feet

So , to find the travel distance of water from bottom of roots to the top of tree's branches , both the length's of tree and root must be added .

travel distance of water = length of the tree + length of the root under the grounds surface

Substituting the values  , we get

travel distance of water =  \(28\frac{1}{3}\) +  \(12\frac{5}{6}\)

= 85/3 + 77/6

taking LCM of 3 and 6 as 6 , and solving further we get

= 170/6 + 77/6

= (170+77)/6

= 247/6

= \(41\frac{1}{6}\) feet

Therefore , the water must travel \(41\frac{1}{6}\)  feet to go from the bottom of the roots to the top of the tree's branches .

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When you develop an argument with a major premise, a minor premise, and a conclusion, you are using deductive reasoning. When constructing an argument using deductive reasoning, three components are involved: a major premise, a minor premise, and a conclusion.

Deductive reasoning is a logical process where the conclusion is derived from the major and minor premises. The major premise is a general statement or principle that establishes a broad context or rule.

The minor premise is a specific statement or evidence that relates to the major premise. Finally, the conclusion is the logical inference or outcome that follows from the combination of the major and minor premises.

Deductive reasoning allows for the logical progression from general principles to specific conclusions, making it a valuable tool in fields such as mathematics, logic, and philosophy.

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Answer:

19x - 608

Step-by-step explanation:

Answer: 19x - 608

Step-by-step explanation: Basically 32 x 19 (not the way teachers would want, but it still works -v-

Hope I helped!

The diameter is 18 inches.

It should be noted that the area of a circle is represented by πr². This will be:

πr² = 254.34

(3.14 × r²) = 254.34

3.14r² = 254.34

r² = 254.34/3.14

r² = 81

r = ✓81

r = 9

Therefore the diameter will be:

= 2 × radius

= 2 × 9

= 18

The diameter is 18 inches.

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Answer:

The diameter is 18 inches.

Step-by-step explanation:

Area of a circle formula:

A=πr2 (Area equals pi times radius squared)

254.34/3.14  (3.14 substituted for pi)

=81

square root of 81

=9

9x2

=18

Therefore, the diameter is 18 inches.

Answer:

Answer as a fraction. Do not include spaces in your answer.

1st question

-31/15

2nd question

19/40

3rd = Answer as a decimal with four decimal places

0.8333…

4th = fraction

5th =rational

6th =rational

Step-by-step explanation:

edge 2021

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be reduced to 0.8333.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be written as shown below,

\(2.5 \times 0.\bar3\)

= (25/10) × (1/3)

= 25/30

= 5/6

= 0.8333....

Hence, the given expression can be reduced to 0.8333.

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Answer:

c) 95 feet

Step-by-step explanation:

perimeter = πd

3.14*18=56.52 in

20 revolutions =56.52*20=1130 in =95 feet

Answer:

\(\frac{40}{41}\)

Step-by-step explanation:

Sin = opposite / hypothenuse

Sin A = 40 / 41

Answer: \(\frac{40}{41}\)

Answer:

The answer is 40/41...............

We are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

In the given scenario:

The boldface number "12.2" represents a statistic.

The boldface number "15.1" represents a statistic.

A statistic is a numerical value that summarizes a sample of data, while a parameter is a numerical value that summarizes a population.

In this case, we are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

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Answer:

a

Step-by-step explanation:

The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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The fraction of the check and tip did John pay is 5/24.

What are rational numbers?

It is possible to express rational numbers in the form pq, where p and q are integers and q0. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative. As a result, the numerator and denominator of a fraction are whole numbers (denominator 0), as opposed to integers in the case of rational numbers.

Here, we have

Given: A group of three friends ate dinner at a restaurant. When they settled the check and tip, Peter paid 4/5 as much as John paid, and John paid 1/3 as much as Ralph paid.

we have to find a fraction of the check and tip did John pay.

p, j, r, the fractions that each paid.

p + j + r = 1....(1)

p = (4/5)j and j = (1/3)r

From equation(1), we get

(4/5)j + j + 3j = 1

j(4/5 + 1 + 3) = 1

(24/5)j = 1

j = 5/24

We have

r = 3j

r = 3(5/24)

r = 5/8

Hence, the fraction of the check and tip did John pay is 5/24.

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The Rotate Array problem requires rotating an array of n elements to the right by k steps. Three different approaches to solve this problem are: using extra space, the reverse method, and the cyclic method.

Here are three different approaches to solve the Rotate Array problem:

1. Using extra space: We can create a new array of the same size as the input array, and then copy the elements of the input array into the new array in rotated order. Finally, we can copy the new array back to the input array. The time complexity of this approach is O(n), where n is the size of the input array.

2. Reverse method: We can reverse the entire array, and then reverse the first k elements and the remaining n-k elements separately. The time complexity of this approach is O(n), where n is the size of the input array.

3. Cyclic method: We can rotate the array in a cyclic manner, where we move the elements in a cycle of k steps until we have moved all the elements. This approach involves swapping the elements in place, without using any extra space. The time complexity of this approach is also O(n), where n is the size of the input array.

Here's the Python code for each of these approaches:

1. Using extra space:

```
def rotate(nums, k):
   n = len(nums)
   new_nums = [0] * n
   for i in range(n):
       new_nums[(i+k) % n] = nums[i]
   nums[:] = new_nums
```

2. Reverse method:

```
def rotate(nums, k):
   n = len(nums)
   k = k % n
   nums.reverse()
   reverse(nums, 0, k-1)
   reverse(nums, k, n-1)

def reverse(nums, left, right):
   while left < right:
       nums[left], nums[right] = nums[right], nums[left]
       left += 1
       right -= 1
```

3. Cyclic method:

```
def rotate(nums, k):
   n = len(nums)
   k = k % n
   count = start = 0
   while count < n:
       curr = start
       prev = nums[start]
       while True:
           next_idx = (curr + k) % n
           nums[next_idx], prev = prev, nums[next_idx]
           curr = next_idx
           count += 1
           if start == curr:
               break
       start += 1
```

Note that in each of these solutions, we first calculate the effective value of k by taking the modulus of k and n, since rotating an array by n+k steps is equivalent to rotating it by k steps.

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Answer:the function is linear

Step-by-step explanation:

Answer:

it linear

Step-by-step explanation:

AP3X verified

Answer:

Step-by-step explanation:

-7x > 21.

-x>3

x<-3

The answer is:

Work/explanation:

To solve the inequality, we should divide each side by -7.

Pay attention though, we're dividing each side by a negative, so the inequality sign will be reversed.

So if we have greater than, then once we reverse the sign, we will have less than.

This is how it's done :

\(\sf{-7x > 21}\)

Divide :

\(\sf{x < -3}\)

Answer:

\(d\approx 17.5 \text{ g/mL}\)

Step-by-step explanation:

We can use the formula

\(\text{density}=\dfrac{\text{mass}}{\text{volume}}\)

to calculate the density of the gold in the cylinder:

↓ plugging in the given values

\(d = \dfrac{447\text{ g}}{25.5\text{ mL}}\)

↓ evaluating using a calculator

\(d\approx 17.5 \text{ g/mL}\)

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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The amount of acres has the farmer planted will be 27/16.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A farmer plants the same amount every day, adding up to 2 1/4 acres at the end of the year.

If the year is 3/4 over.

Then the amount of acres has the farmer planted will be

2 1/4 = 9/4

Then we have

⇒ 9/4  x  3/4

⇒ 27 / 16

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