Identify the vertex, axis of symmetry, and direction of the graph of each function. Compare the width of the graph to the width of the graph of f(x)=x^2

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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Answer: 104.60736 kilometers

Step-by-step explanation:

If 1 mile = 1.609km

Then, you multiply 65 and 1.609 and you get your kilometers.

The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

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Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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The proof by contrapositive of the theorem is based on the following assumption and conclusion:

Assumption:

x and y are real numbers such that (x+y)/2≤0

Conclusion:

x<0 or y≤0

Only the assumption is taken as fact or is assumed, while the conclusion is proven by contrapositive. Therefore, the fact is assumed that the average of any two positive real numbers is also positive.

However, the proof by contrapositive involves taking the opposite of the original statement and negating it in order to prove its truth.

The contrapositive of the statement “The average of any two positive real numbers is also positive” is “If x≤0 and y≤0, then (x+y)/2≤0.”

This means that if either x or y is not positive, then the average of the two numbers cannot be positive. Therefore, it is proven that x>0 or y>0.

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In a multiple regression framework, the R-squared (R^2) increases whenever a regressor is added unless the coefficient on the added regressor is exactly zero.

If the added regressor has a non-zero coefficient, even if it is small, it will contribute to explaining additional variance in the dependent variable and increase the overall fit of the regression model.

However, it is important to note that the R-squared value does not directly indicate the significance or meaningfulness of the added regressor. It only measures the proportion of variance in the dependent variable that is explained by the entire set of regressors in the model. Therefore, an increase in R-squared does not necessarily imply that the added regressor is statistically significant or has a substantial impact on the dependent variable.

The other answer choices provided, "greater than 1.96 in absolute value" and "added unless there is heteroskedasticity," do not accurately describe the conditions for R-squared to increase when a regressor is added in a multiple regression framework.

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

B. No solution

Step-by-step explanation:

The module function | | makes all the results be positive. As the result isn't a positive number, there's no solution for this problem.

The limit of the given expression as x approaches 1 is 0.

To evaluate the limit of the given expression as x approaches 1, we can use L'Hopital's rule, which states that if the limit of a quotient of functions is of the form 0/0 or ±∞/±∞, then the limit can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the same point.

Using L'Hopital's rule on the given expression, we get:

lim x→1 [5x/(x-1) - 5/x] = lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)]

Plugging in x = 1 directly to this expression, we get:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = (5 - 10 + 5)/(1 - 1) = 0/0

Since the limit is still in an indeterminate form, we can apply L'Hopital's rule once again:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = lim x→1 [(10x - 10)/(2x - 1)] = 0

Therefore, the limit of the given expression as x approaches 1 is 0.

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Answer:

\(\huge\boxed{\sf 8:32\ AM}\)

Step-by-step explanation:

Woke up = 7:30 AM

Time to:

Altogether:

= 14 + 9 + 39 min

(As we know that, 1 hour = 60 minutes)

So,

Time he reached the school:

7 hr 30 min + 1 hr 2 min

Combine like terms

7 hr + 1 hr + 30 min + 2 min

OR

\(\rule[225]{225}{2}\)

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?

In this question we are asked to calculate the time paul reach the school.

Altogether time paul took to get ready, to finish his breakfast and to commute to school.

(14 + 9 + 39) minutes

→ (23 + 39) minutes

→ 62 minutes

Now we will convert minutes into hour.

62 ÷ 60

→ 1 hr 2 min

Now we will calculate the time he reached his school.

7 hr + 30 + 1 hr 2 min

\(\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}\)

He will reach the school at 8:32 AM.

Answer: x<*-3

It wont let me write the less or equal sign*

Answer:

I believe it would be X ≤ -3

Step-by-step explanation:

My answer is stating x is -3 or less. this means it is including -3 as a possible answer.

Answer:

15x+(-10)y

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

When you distribute the 5 it means you multiply it to everything inside the parentheses, so it'll be...

\(5*3x=15x\\5*-2y=-10y\\\)

so [15]x+[-10]y

Answer:

1)-9x^5 + 7x^2 + 3    2)  -2x2 • (x - 7)      3)  -23v^2 + 7v + 4    4) is just 7x

Answer:

True

Thx for the points :)

Answer:6

Step-by-step explanation:

Answer: third one

Step-by-step explanation:

Answer:

3√2

Step-by-step explanation:

the 2nd answer

y=3√2

Answer:

yeah sure i got you, whats the question?

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

i can because i am super smart

The boys ate 1/4 more than the girl.

Answer:

I fairly sure the answer is 12 days

It would 12 days to take to produce 4,512 phones.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that machine that makes cellphones can produce 47 cellphones per hour when running. The machine can only run for 8 hours per day.

We have to determine the number of days will it take to produce 4,512 phones.

Here machine produces (47×8) i.e 376 cellphones per day

Let x days would it take to produce 4,512 phones.

We can write this as a ratio as:

376 phones : 1 day = 4,512 phones : x days

⇒ 376/1= 4,512 /x    

⇒ (376)(x) = 4,512

Divide each side by 376

⇒ x = 4,512/376

⇒ x = 12

Therefore, it would 12 days to take to produce 4,512 phones.

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Regarding the relative maximums and relative minimums of the functions, we have that:

8. Functions h(x) and k(x) have relative maximums.

9. f(x) has one relative maximum and g(x) has two relative maximums.

In item 8, we want relative maximums, hence points in which the functions change from increasing to decreasing, hence the functions that have it are: h(x) and k(x).

In item 9, we have that:

Hence the sentence is:

f(x) has one relative maximum and g(x) has two relative maximums.

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Answer:

No solution

Step-by-step explanation:

Any equations with the same slope are parallel, or will never intersect.

In a slope-intercept equation, this would mean the 'm' values are the same.

y = mx + b

Two equations:

y = 5x - 4

y = 5x - 5

Since the two equations given have the same slope, they will never intercept and therefore have no solution.

The Nyquist sampling rate for x(t) is 1800 Hz.

Nyquist sampling theorem states that in order to accurately reconstruct a signal without aliasing, the sampling rate must be at least twice the highest frequency component in the signal.

For the given signal x(t), we need to determine the highest frequency component.

The first term in x(t) is 2 times the sinc function of 800pit. The sinc function has zeros at integer multiples of pi, and its first zero after the origin occurs at pi. Therefore, the highest frequency component in the first term of x(t) is 400 Hz (corresponding to the frequency at which the sinc function crosses zero after the origin).

The second term in x(t) is the square of the sinc function of 1800*t. The sinc function has zeros at integer multiples of pi, and its first zero after the origin occurs at pi/1800. Therefore, the highest frequency component in the second term of x(t) is 900 Hz (corresponding to twice the frequency at which the sinc function crosses zero after the origin).

Thus, the highest frequency component in x(t) is 900 Hz. According to the Nyquist theorem, the sampling rate must be at least twice this frequency, or 1800 Hz, in order to accurately reconstruct the signal without aliasing. Therefore, the Nyquist sampling rate for x(t) is 1800 Hz.

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Answer:

Perimeter = 18m

Area = 18m²

Step-by-step explanation:

On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18

The perimeter is 18m

To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18

The area is 18m²

Hope this helps!

Answer:

the slope becomes 3 and the graph moves up 7 units. 2. The slope becomes 5 and the graph moves down 2 units.

]

A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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Answer:

y = 4/3 x - 4

Step-by-step explanation:

The slope-intercept form of the equation of a line

The equation of a line can be expressed in several forms. One of them is the slope-intercept form:

y = mx + b

Where

m = slope

b = y-intercept

We are required to convert the equation of the line:

4x - 3y = 12

It can be done by solving for y.

Subtracting 4x:

- 3y = - 4x + 12

Dividing by -3;

y = 4/3 x - 4

The surface area of the figure is 200 square yards

The formula for calculating the surface area of a triangular prism is expressed as;

Surface area= b h + ( b 1 + b 2 + b 3 ) l

Given that;

substitute the values, we get;

Surface area = 6(4) + (5 + 5 + 6)11

add the values

Surface area = 24 + 16(11)

Surface area = 24 + 176

add the values

Surface area = 200 square yards

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To compute the effect size, we can use the formula:

ES = (|Ž - X|) / SD

where Ž is the mean for Group 1, X is the mean for Group 2, and SD is the standard deviation from either group as the given question.

Using the given values, we have:

Experiment 1: ES = (|78.6 - 73.4|) / 2 = 2.6

Experiment 2: ES = (|78.6 - 73.4|) / 4 = 1.3

Experiment 3: ES = (|78.6 - 73.4|) / 8 = 0.65

From the experiments 1, 2, 3, we can see that the standard deviation increases, the effect size decreases.

It means that the larger SD makes it harder to detect a meaningful difference between the two groups.

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Answer:

5

Step-by-step explanation: