not sure how to do 13-18.

The ratio c:g:t in its simplest form is 10/3 : 5 : 4.

The ratio of c:g is 2:3 and the ratio of g:t is 5:4.

To write the ratio c:g:t in the simplest form, we need to express c,g and t in terms of a common value and simplify.

Let's begin;Let g be a common value between the ratios c:g and g:t. We can express c and t in terms of g as;

The ratio of c:g is 2:3. That means c is 2/3 of g.The ratio of g:t is 5:4.

That means t is 4/5 of g.We can now express the ratio c:g:t in terms of g, as;

c:g:t = 2/3 : 1 : 4/5

Multiplying by 15 (the LCM of 3 and 5) to get rid of the fractions, we have;

c:g:t = 10 : 15 : 12

Simplifying, we can divide each term by 3 to get the simplest form of the ratio;c:g:t = 10/3 : 5 : 4

Therefore, the ratio c:g:t in its simplest form is 10/3 : 5 : 4.

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The object is moving to the right or to the left. s'(t) is positive if t is in the interval (0, 3) and (6, ∞), indicating that the object is moving to the right. s'(t) is negative if t is in the interval (- ∞, 0) and (3, 6), indicating that the object is moving to the left.

Given, the position of an object at any time t is given by s (t) = 3t^4- 44t^3+ 108t^2+ 20.

(a) To find velocity, differentiate the given function with respect to t.

Here, s'(t) = ds(t)/dt = 12t³ - 132t² + 216t.

For the given position function, the velocity of the object at any time t is s'(t) = 12t³ - 132t² + 216t.

(b) The position of the object never stops changing, since the velocity is always changing.

When the object's velocity is zero, the position of the object is changing at a constant rate.

As a result, it never stops changing.

(c) To find when the object is moving to the right or to the left,

we must first find the zeros of s'(t).

The zeros of s'(t) can be found by factoring it and then using the zero-product property, 12t³ - 132t² + 216t = 0.

Factoring gives 12t (t - 3) (t - 6) = 0.

Therefore, the zeros of s'(t) are t = 0, t = 3, and t = 6.

For the intervals (- ∞, 0), (0, 3), (3, 6), and (6, ∞),

we can determine whether the object is moving to the right or to the left.

s'(t) is positive if t is in the interval (0, 3) and (6, ∞), indicating that the object is moving to the right.

s'(t) is negative if t is in the interval (- ∞, 0) and (3, 6), indicating that the object is moving to the left.

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Answer: 5.708333

Step-by-step explanation:

68.5 inches (in) is equivalent to 5.71 feet (ft).

To convert inches (in) to feet (ft), you need to divide the number of inches by the number of inches in a foot.

There are 12 inches in a foot.

Step 1: Set up the conversion equation

68.5 inches ÷ 12 inches/foot

Step 2: Perform the division

68.5 ÷ 12 = 5.70833333333

Step 3: Round the result

Since feet are typically expressed as whole numbers or with a decimal point, we can round the result to a desired decimal place.

In this case, let's round to two decimal places.

The rounded value of 5.70833333333 is 5.71.

Step 4: Write the final answer

68.5 inches is equal to 5.71 feet.

Therefore, 68.5 inches (in) is equivalent to 5.71 feet (ft).

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The required answer is the population of the country grew by 0.2% based on the given information on births, deaths, immigrants, and emigrants.

To calculate the percentage growth rate for a country, we can use the formula:

Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population * 100

Given the following information:

Initial Population = 5 million

Births = 100,000

Deaths = 70,000

Immigrants = 30,000

Emigrants = 50,000

Let's substitute these values into the formula:

Percentage Growth Rate = ((100,000 + 30,000) - (70,000 + 50,000)) / 5,000,000 * 100

Simplifying the numerator:

Percentage Growth Rate = (130,000 - 120,000) / 5,000,000 * 100

Percentage Growth Rate = 10,000 / 5,000,000 * 100

Performing the division:

Percentage Growth Rate = 0.002 * 100

Percentage Growth Rate = 0.2%

Therefore, the percentage growth rate for the country is 0.2%.

This indicates that the population of the country grew by 0.2% based on the given information on births, deaths, immigrants, and emigrants.

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Using the z table, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

\(\alpha\)=1−0.82

\(\alpha\)=0.18

Now finding the value of \(\alpha\)/2

\(\alpha\)/2=0.18/2

\(\alpha\)/2=0.09

Now finding the value of \(z_{a/2}\).

\(z_{0.82}\) = 1.34

Hence, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

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Answer:

Step-by-step explanation:

1) 3 + 4*2*29 = 3 + 232  = 235  

First we have to do multiplication and then we have to add

2) 5n + 1

Term 1 ; n = 1  ;  5n + 1 = 5*1 + 1 = 5 + 1 = 6

Term 2 ; n = 2 ; 5n + 1 = 5*2 + 1 = 10 + 1 = 11

Term 3 ; n = 3 ; 5n+ 1 = 5*3 + 1 = 15 + 1 = 16

Term 4; n = 4  ; 5n + 1 = 5*4 + 1 = 20 + 1 = 21

The sequence : 6 , 11, 16 , 21 ..........

The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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ANSWER:

a. 1950 people per square mile

b. The island's area got smaller

c.

STEP-BY-STEP EXPLANATION:

Population density is the average number of people living per unit area. It is calculated by dividing the total number of population of a geographical unit (in this case it is the island) by the total amount of surface.

a.

Therefore:

b.

Since the size of the island is halved without losing any people, we can conclude that the area has become smaller.

Therefore:

The island's area got smaller

c.

Since it is half the area, the new density would be:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

Step-by-step explanation:

ok so 16 is she will make a 100 dollars and 15 means how much money she will make per mile

\(\\ \sf\longmapsto 3y=z-2x\)

\(\\ \sf\longmapsto -2x=3y-z\)

\(\\ \sf\longmapsto 2x=-3y+z\)

\(\\ \sf\longmapsto 2x=z-3y\)

\(\\ \sf\longmapsto x=\dfrac{z-3y}{2}\)

Answer:

\( x = \frac{z - 3y}{2} \)

Step-by-step explanation:

Question :

\(3y = z - 2x\)

First take 2x to the left to make the 2x as a positive number (So, It's easy to solve)

\(3y + 2x = z\)

Then take 3y to the right side

\(2x = z - 3y\)

Now, divide both sides by 2 to make the x as the Subject

\( \frac{2x}{2} = \frac{z - 3y}{2} \\ x = \frac{z - 3y}{2} \)

hope this helps you.

Please let me know if you have another questions :-)

Answer:

4, 5 and 27.

Step-by-step explanation:

There are 2 cube numbers between 0 and 36 .

They are 8 and 27.

36 - 27 = 9 so the other 2 numbers could be 4 and 5 because they are both factors of 20.

36 - 8 = 28  whose factors are 2 * 2 * 7 which are not factors of 20.

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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The approximate value of x in the equation 5 to the power of 2x=20 is 0.93

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

5 to the power of 2x=20

As an expression, we have

5^(2x) = 20

Take the natural logarithm of both sides

so, we have the following representation

2x = ln(20)/ln(5)

Evaluate the quotients

This gives

2x = 1.86

So, we have

x = 0.93

Hence, the value of x is 0.93

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Therefore, the area of the region enclosed by the curves y = 2x² and y = 2x is 1/3 square units.

To find the area of the region enclosed by the curves y = 2x² and y = 2x, you need to solve for their intersection points and integrate the difference between the two functions.

This can be done as follows: Setting y = 2x² equal to y = 2x, we get:2x² = 2x Dividing both sides by 2x, we get: x = 0 or x = 1

Substituting x = 0 into y = 2x², we get: y = 2(0)² = 0 Substituting x = 1 into y = 2x, we get: y = 2(1) = 2

Therefore, the intersection points of the two curves are (0,0) and (1,2). To find the area enclosed by the curves, we integrate the difference between the two functions from x = 0 to x = 1.

This can be done as follows:∫[2x - 2x²]dx from x = 0 to x = 1= [x² - (2/3)x³] from x = 0 to x = 1= [1 - (2/3)] - [0 - 0]= 1/3

Therefore, the area of the region enclosed by the curves y = 2x² and y = 2x is 1/3 square units.

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Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression that represents the number of inches the plant grew this week is:

8 - x

This is because we are looking for the difference between the plant's height this week (which is 8 inches) and its height last week (which is x inches). Subtracting x from 8 gives us the amount by which the plant grew this week.


Hope this helped!

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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14x^2 + x - 9 expressions to represent the area of the shaded regions.

To determine what the area of the shaded region is, simply find the area of the large rectangle and subtract the product from the smaller one.

Since they are polynomials. Multiply one binomial to the other and first obtain the product, before subtracting the product of the smaller rectangle.

(5x + 2)(3x - 1) - (x)(x + 7)

15x^2 - 5x + 6x - 2 - x^2 - 7

14x^2 + x - 9.

A phrase sample definition is a commonly used word or phrase or a way of expressing your thoughts, feelings, or feelings. An example of an expression is the phrase "A dime saved is a dime earned". An example of a facial expression is a smile. A special way to bring your ideas to life.

A facial expression that expresses what you are feeling. Examples of phrases in sentences. 1. Seeing her daughter's excited face, Donna was happy to make her daughter's dream come true.

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This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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a) Counterexample: \(m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},\)

b) Counterexample:\(m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},\)

c) Counterexample:  length=16, width=4

d) Counter example:  angle ABD= 50 degree, angle CBD=10 degree

What is the interior?

Something's interior or related to its interior; inward.

a) An acute angle is one that measures less than 90 degrees.

Counterexample: \(m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},\)

(90 degrees is not an acute angle)

b) When the sum of two angles is 90°, then the angles are known as complementary angles

Counterexample:\(m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},\)

( None of the angles is greater than 45 degrees )

c) Area of rectangle = length*width=16*4

Counterexample:  length=16, width=4

d)  Since C is the interior of the angle ABD, then, angle ABD+angle CBD=60 degrees

Counterexample:  angle ABD= 50 degree, angle CBD=10 degree

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Answer:

Awsten Knight

Step-by-step explanation:

Answer:

\(\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1\)

Step-by-step explanation:

We are given:

\(\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)\)

And we want to evaluate it using L'Hopital's Rule.

First, using direct substitution, we will acquire:

\(=(1-1)^\ln(1)}=0^0\)

Which is indeterminate.

In order to apply L'Hopital's Rule, we first need to manipulate the expression. We will let:

\(y=(x-1)^\ln(x)\)

By taking the natural log of both sides:

\(\ln(y)=\ln(x)\ln(x-1)\)

And by taking the limit as x approaches 1 from the right of both functions:

\(\displaystyle \lim_{x\to 1^+}\ln(y)=\lim_{x\to 1^+}\ln(x)\ln(x-1)\)

Rewrite:

\(\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{\ln(x-1)}{\ln(x)^{-1}}\)

Using direct substitution on the right will result in 0/0. Hence, we can now apply L'Hopital's Rule:

\(\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}\)

Simplify:

\(\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}\Big(\frac{-x\ln(x)^2}{-x\ln(x)^2}\Big)\)

Simplify:

\(\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-\frac{x\ln(x)^2}{x-1}\)

Now, by using direct substitution, we will acquire:

\(\displaystyle \Rightarrow -\frac{1\ln(1)^2}{1-1}=\frac{0}{0}\)

Hence, we will apply L'Hopital's Rule once more. Utilize the product rule:

\(\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-(\ln(x)^2+2x\ln(x))\)

Finally, direct substitution yields:

\(\Rightarrow -(\ln(1)^2+2(1)\ln(1))=-(0+0)=0\)

Thus:

\(\displaystyle \lim_{x\to 1^+}\ln(y)=0\)

By the Composite Function Property for limits:

\(\displaystyle \lim_{x\to 1^+}\ln(y)=\ln( \lim_{x\to 1^+}y)=0\)

Raising both sides to e produces:

\(\displaystyle e^{\ln \lim_{x\to 1^+}y}=e^0\)

Therefore:

\(\displaystyle \lim_{x\to 1^+}y=1\)

Substitution:

\(\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1\)

As k increases (from 1 to 8), the critical value increases. This is because as k increases, the probability of a Type I error decreases.

A Type I error is the probability of rejecting the null hypothesis when it is true. By increasing the critical value, it is making it less likely to reject the null hypothesis when it is true.

Power is the probability of rejecting the null hypothesis when it is false. As k increases, power also increases. This is because as k increases, the difference between the two populations becomes more pronounced. This makes it more likely that we will be able to detect a difference between the two populations.

In conclusion, as k increases, the critical value increases and power also increases. This is because as k increases, the probability of a Type I error decreases and the difference between the two populations becomes more pronounced.

The critical values for a sample size of 24 participants (N = 24) given the following values for k is attached.

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Answer:

The correct answer would be B) Decomposition

Step-by-step explanation:

Edge Cumulative Exam 2022

The type of reaction is Decomposition reaction.

A decomposition reaction occurs when one reactant breaks down into two or more products. This can be represented by the general equation:

AB → A + B.

Examples of decomposition reactions include the breakdown of hydrogen peroxide to water and oxygen, and the breakdown of water to hydrogen and oxygen.

Given reaction:

\(C_{12}H_{22}O_{11}\) → 12C + 11\(H_{2}O\)

(Sucrose)

Here  \(C_{12}H_{22}O_{11}\) has been decomposed or break into C and 11\(H_{2}O\)molecule.

Hence, the given reaction is decomposition reaction.

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Answer: 24 children

Step-by-step explanation:

Answer:

Step-by-step explanation:

So if 25% have blue eyes, 75% do not.

100% - 25% = 75%

What is 75% of 32?

Change 75% to a decimal by movinf g the decimal two places to the left.

and multiply.

32 × .75 = 24

This is how to calculate the solution.

The value of the triple integral is π/2 - 2.

In spherical coordinates, the radial distance is denoted by ρ, the angle of elevation (measured from the positive z-axis) is denoted by θ, and the angle of rotation (measured from the positive x-axis) is denoted by φ.

To set up the integral, we begin by writing the expression for the volume element in spherical coordinates:

dV = ρ² sin(θ) dρ dθ dφ

Next, we write the function in terms of spherical coordinates. In this case, the function is 1/(x²+y²+z²), which can be written as 1/ρ² in spherical coordinates.

Finally, we set up the integral as follows:

∫∫∫E1/(x²+y²+z²) dV = \(\int _0 ^ {\pi /2} \int_0^{\pi/2-\theta sin(\theta)}\) ρ² sin(θ) (1/ρ²) dρ dθ dφ

Note that we integrate from 0 to π/2 for θ and φ because we are only considering the first octant. Also note that we integrate over ρ from the smaller sphere (ρ=3) to the larger sphere (ρ=4).

Now, we can simplify the integral by canceling out the ρ² term in the integrand and evaluating the resulting integral:

∫∫∫E1/(x²+y²+z²) dV = \(\int _0 ^ {\pi /2} \int_0^{\pi/2-\theta sin(\theta)}\) sin(θ) dρ dθ dφ

= \(\int _0 ^ {\pi /2} \int_0^{\pi/2-\theta sin(\theta)}\) (π/2-θ) dθ dφ

= \(\int _0 ^ {\pi /2}\) (1-cos(π/2-θ)) dθ

= \(\int _0 ^ {\pi /2}\) (1-sin(θ)) dθ

= π/2 - 2

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