using the substitution y = 3^x, show that the equation 9^x - 3^(x+1) + 2 can be written as (Y-1)(Y-2) = 0

The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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The table with the numeric values of g(x) is given by:

Researching it on a search engine, it is found that we have to calculate the numeric values of g(x) = 3x + 5 for x = -5, -1, 1, 3 and 5.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is given by:

g(x) = 3x + 5.

Hence the numeric values are:

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The capacity of the elevator is 15 children or 11 adults. If 9 children are currently on the elevator, then there are 15 - 9 = 6 spots available for either children or adults.

However, since the maximum number of adults the elevator can hold is 11, the answer to the question is 11 - 9 = 2 adults can still get in.

You can act for the unknown amounts by the use of variables. Follow ignoring the description is and convert it one by one mathematically. For example, if it is asked to increase some item by 5, then you can add 5 in that item to increase it by 5.

If a thing is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

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For Snowman A:

The initial height of Snowman A is 28 inches, and it decreases by 4 inches per hour. So, the equation for the height of Snowman A in terms of t hours after sunrise is:

A = 28 - 4t

For Snowman B:

The initial height of Snowman B is 46 inches, and it decreases by 7 inches per hour. So, the equation for the height of Snowman B in terms of t hours after sunrise is:

B = 46 - 7t

To find when both snowmen have an equal height, we need to set A and B equal to each other and solve for t:

28 - 4t = 46 - 7t

3t = 18

t = 6

Therefore, both snowmen will have an equal height of 16 inches after 6 hours.

Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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\(\bigstar\:\boxed{\bf{\dfrac{a^m}{a^n}=a^{m-n}}}\)

\(\dag\sf\:\:a^m\times a^n=a^{m+n}\)

\(\dag\sf\:\:\dfrac{a^m}{a^n}=a^{m-n}=\dfrac{1}{a^{n-m}}\)

\(\dag\sf\:\:a^{-m}=\dfrac{1}{a^m}\)

\(\dag\sf\:\:(a^{m})^n=a^{mn}\)

\(\dag\sf\:\:a^1=a\)

\(\dag\sf\:\:a^0=1\)

\(\dag\sf\:\:\sqrt[n]{a^m}=a^{\frac{m}{n}}\)

Answer:

The answer is B

Step-by-step explanation:

none

Answer: 1 left, 3 down. (+1,-3)

Step-by-step explanation: Addition and subtraction

We can use the M/M/1 queuing model to solve this problem.

(a) The arrival rate of customers is λ = 10 per hour, and the service rate of the teller is μ = 15 per hour (since the average service time is 4 minutes or 0.067 hours). Using the formula for the utilization factor, we have:

ρ = λ/μ = 10/15 = 0.67

(b) Using the formula for the average number of customers in the system, we have:

L = λ/(μ-λ) = 10/(15-10) = 2

(c) Using the formula for the average time spent by a customer in the system, we have:

W = 1/(μ-λ) = 1/(15-10) = 0.2 hours or 12 minutes

In summary, the utilization factor of the teller is 0.67, the average number of customers in the system is 2, and the average time spent by a customer in the system is 12 minutes. These results indicate that the bank is operating at a relatively high level of congestion, with customers experiencing a significant amount of waiting time.

One possible solution to this problem is to add another teller to the bank to increase the service rate and reduce the average waiting time for customers. Alternatively, the bank could implement a system for scheduling appointments or prioritizing certain types of transactions to better manage the flow of customers.

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The variance of the actuary's wait time is 36 / 121.

From the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,

From the complete question, the variance of the actuary's wait time will be:

= 1 / (11/6)²

= (6/11)²

= 36 / 121

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The numbers in the quotient of 88 divided by 5 are 17 (the whole number part) and 0.6 (the decimal part).

When dividing 88 by 5, we get a quotient of 17.6.

The quotient is a decimal number, and it consists of two parts: the whole number part and the decimal part.

In this case, the whole number part is 17, and the decimal part is 0.6.

Therefore, the two numbers in the quotient of 88 divided by 5 are 17 (the whole number part) and 0.6 (the decimal part).

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Answer:

k = - 9

Step-by-step explanation:

Since the triangle is right- angled at Q then PQ is perpendicular to RQ

Calculate the slope of PQ using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = P(1, 4) and (x₂, y₂ ) = Q(- 3, - 4)

\(m_{PQ}\) = \(\frac{-4-4}{-3-1}\) = \(\frac{-8}{-4}\) = 2

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{2}\) , thus

\(m_{RQ}\) = - \(\frac{1}{2}\)

Calculate the slope of RQ and equate to - \(\frac{1}{2}\)

\(m_{RQ}\) = \(\frac{k+4}{7+3}\) = - \(\frac{1}{2}\) , that is

\(\frac{k+4}{10}\) = - \(\frac{1}{2}\) ( multiply both sides by 10 )

k + 4 = - 5 ( subtract 4 from both sides )

k = - 9

The right-angled triangle PQR has two perpendicular sides PQ and QR, such that the value of k is -9

Given that:

\(P =(1,4)\)

\(Q = (-3,-4)\)

\(R = (7,k)\)

Calculate the slope of PQ using:

\(m_1 = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m_1 = \frac{-4-4}{-3-1}\)

\(m_1 = \frac{-8}{-4}\)

\(m_1=2\)

Calculate the slope of QR using:

\(m_2 = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m_2 = \frac{k--4}{7--3}\)

\(m_2 = \frac{k+4}{7+3}\)

\(m_2 = \frac{k+4}{10}\)

Because the triangle is right-angled at Q, then sides PQ and QR are perpendicular.

The relationship between perpendicular sides is:

\(m_1 \times m_2 = -1\)

So, we have:

\(2 \times (\frac{k + 4}{10}) = -1\)

\(\frac{k + 4}{5} = -1\)

Multiply through by 5

\(k +4 = -5\)

Subtract 4 from both sides

\(k = -9\)

Hence, the value of k is -9

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Approximately 100 cells will contain values less than or equal to 0.1.
The RAND() function in Excel returns a pseudo-random number between 0 and 1. If you enter this function into 1000 cells, approximately 10% of these cells (0.1 probability) will contain values less than or equal to 0.1. Therefore, a number relatively close to 100 cells will have values less than or equal to 0.1.

The RAND() function is a built-in function in Excel that generates a random decimal number between 0 and 1. Each time the function is used, a new random number is generated.

The syntax for using the RAND() function is: =RAND() The function takes no arguments and simply returns a random decimal number.

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Mining has a negative effect on home prices in the county, reducing the price of a 2,000-square-foot house with three bedrooms by approximately $8,400.

Comparative statics is a method used to analyze how changes in one variable affect another. In this case, we are examining the effect of mining on home prices in the county. We are given that the company mines 300,000 tons of coal per year, which is worth $79 per ton. Therefore, the annual value of coal production is 300,000 tons * $79 = $23,700,000.

Now, let's consider the effect on home prices. We are given that the average price for a 2,000-square-foot house with three bedrooms located more than 20 km away from the mining site is $210,000. However, for a similar house within 4 km of the mine, the price is 4 percent lower.

To calculate the price reduction, we can multiply $210,000 by 4 percent (0.04). The reduction in price is $210,000 * 0.04 = $8,400. Therefore, the effect of mining on home prices in the county is a decrease of approximately $8,400 for a 2,000-square-foot house with three bedrooms.

It's important to note that this analysis assumes a linear relationship between the proximity to the mine and home prices. Other factors, such as environmental concerns or changes in the local economy, may also influence home prices in the area.

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Answer:

4:5

Step-by-step explanation:

Answer:

80% shining

20% not shining

It will take 119 x 10⁶ yr for the amount of u-235 to reach 5% of its initial amount.

In the radioactive nuclides, the time for decay is;

t = -2.303 /k log (A/A₀)

In which, k is the decay constant .

k = 0.693/ t₁/₂  for- ₁/₂ is the half-life.

k = 0693/ 703 x 10⁶ yrs = 9.85 x 10⁻¹⁰ /yr

A = amount left after time t

A₀ = Original amount present

Thus,

t = -2.303 / 9.85 x 10⁻¹⁰ /yr x log (0.95)

t = 119 x 10⁶ yr

Thus, it will take 119 x 10⁶ yr for the amount of u-235 to reach 5% of its initial amount.

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Answer:

6) 567

7)160

Step-by-step explanation:

The probability that exactly five students among the 12 visiting Mexico will contract a stomach virus is approximately 0.2173 and the probability that more than two students among the 12 visiting Mexico will contract a stomach virus is approximately 0.4866.

What is probability?

Probability is a branch of mathematics that deals with quantifying the likelihood or chance of an event occurring.

Probability that exactly five students contract a stomach virus:

Using the binomial probability formula, we have:

\(P(X = 5) = (12C5) * (0.23^5) * (0.77^7)\)

\(P(X = 5) = (792) * (0.23^5) * (0.77^7)\)

P(X = 5) ≈ 0.2173 (rounded to four decimal places)

Therefore, the probability that exactly five students among the 12 visiting Mexico will contract a stomach virus is approximately 0.2173.

Probability that more than two students contract a stomach virus:

We need to calculate the probabilities of three, four, and five students contracting a stomach virus and then sum them up.

P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial probability formula for each case:

\(P(X = 3) = (12C3) * (0.23^3) * (0.77^9)\\\\P(X = 4) = (12C4) * (0.23^4) * (0.77^8)\)

P(X = 5) ≈ 0.2173 (calculated previously)

Now, let's calculate each probability and sum them up:

P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5)

\(P(X > 2) = (12C3) * (0.23^3) * (0.77^9) + (12C4) * (0.23^4) * (0.77^8) + 0.2173\)

P(X > 2) ≈ 0.4866 (rounded to four decimal places)

Therefore, the probability that more than two students among the 12 visiting Mexico will contract a stomach virus is approximately 0.4866.

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After 1 month, there will be approximately 9,750 Brand A users, 20,350 Brand B users, and 69,900 non-users.

After 2 months, the numbers change to approximately 9,532.5 Brand A users, 20,783.5 Brand B users, and 69,684 non-users.

Finally, after 18 months, the numbers are approximately 9,524.90 Brand A users, 20,805.48 Brand B users, and 69,669.62 non-users.

To determine the number of people in each group after a certain number of months, we can use a transition matrix and matrix multiplication.

Let's define the following matrices:

X = [A, B, N], where A represents Brand A users, B represents Brand B users, and N represents non-users.

P = [[0.75, 0.10, 0.15], [0.20, 0.75, 0.05], [0.10, 0.15, 0.75]], which is the transition matrix representing the probabilities of switching or staying with each brand or becoming a non-user.

To calculate the number of people in each group after 1 month, we can multiply the initial population matrix X0 by the transition matrix P:

X1 = X0 * P

To calculate the number of people in each group after 2 months, we multiply X1 by P:

X2 = X1 * P

To calculate the number of people in each group after 18 months, we multiply X0 by the transition matrix raised to the power of 18:

X18 = X0 * P^18

Now, let's calculate the results:

Initial population matrix:

X0 = [10,000, 20,000, 70,000]

After 1 month:

X1 = X0 * P

X1 = [10,000, 20,000, 70,000] * [[0.75, 0.10, 0.15], [0.20, 0.75, 0.05], [0.10, 0.15, 0.75]]

X1 = [9,750, 20,350, 69,900]

After 2 months:

X2 = X1 * P

X2 = [9,750, 20,350, 69,900] * [[0.75, 0.10, 0.15], [0.20, 0.75, 0.05], [0.10, 0.15, 0.75]]

X2 = [9,532.5, 20,783.5, 69,684]

After 18 months:

X18 = X0 * P^18

X18 = [10,000, 20,000, 70,000] * P^18

X18 = [9,524.90, 20,805.48, 69,669.62]

Therefore, after 1 month, there will be approximately 9,750 Brand A users, 20,350 Brand B users, and 69,900 non-users. After 2 months, the numbers change to approximately 9,532.5 Brand A users, 20,783.5 Brand B users, and 69,684 non-users. Finally, after 18 months, the numbers are approximately 9,524.90 Brand A users, 20,805.48 Brand B users, and 69,669.62 non-users.

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Hi there!

\(\large\boxed{x \leq -9}\)

3x - 7 ≥ 4x + 2

Subtract 3x from both sides:

3x - 3x - 7 ≥ 4x - 3x + 2

-7 ≥ x + 2

Subtract 2 from both sides:

-7 - 2 ≥ x + 2 - 2

-9 ≥ x

x ≤ -9

Answer:

See below

Step-by-step explanation:

Looking at the numbers, we can see that:

So we can make:

Each first aid bag will have:

Answer:

$33.30 or $33.35

Step-by-step explanation:

Hi,

So the question says that you get paid $50 per hour and you want to know how much you get paid in 40 minutes:

First of all I will write 40 minutes as an hour:

\(40/60=2/3\)

It is 2/3 of an hour so we will keep that in mind:

\(2/3 * 50 = $33.33 or if you want to round it $33.30\)

So this person earns: $33.30(rounded according to Australian Dollar) or $33.35

\( \large \bf \implies{28}\)

\(\bf{P = \frac{1}{2}} \)

\(\implies\)Even numbers are equal to odd number

\(\implies\)x is even number

[Graph analysis]

7 fishes οf the new released initially in the given expοnential pοpulatiοn grοwth. (οptiοn c)

Expοnential pοpulatiοn grοwth means that whatever the pοpulatiοn size is, it keeps increasing because the pοpulatiοn per individual remains the same, accelerating pοpulatiοn grοwth that is limited by limited resοurces. Hence, this increase in pοpulatiοn size is knοwn as expοnential pοpulatiοn grοwth.

The grοwth οf their pοpulatiοn is mοdeled by the expοnential functiοn

P(t)=\(7b^{t}\) ,where t is the time in weeks after the release and b is a pοsitive unknοwn base.

Initially that is t=0

sο fοr t=0,

p(0)=7×1 [since sοmething tο the pοwer zerο is equal tο 1]

Hence, P(0)=7

sο there were 7 fishes initially.

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The line passes through the y-axis at point (0,4).

Step-by-step explanation:

On a coordinate plane, line DF goes through points (-1,-3) and (2,3).

So, the slope of the line DF is \frac{- 3 - 3}{- 1 - 2} = 2

−1−2

−3−3

=2

Then the straight line which is parallel to DF will be given by

y = 2x + c.

Where, c is any constant and we have to evaluate it if this line passes through the point (-4,-4).

So, - 4 = 2(- 4) + c

⇒ c = 4

So, the straight line which is parallel to DF and passes through the point (-4,-4) is y = 2x + 4.

Now, putting x = 0, we get, y = 4.

Therefore, the line passes through the y-axis at point (0,4). (Answer)

Answer:

The answer would be D

Step-by-step explanation:

Answer: The actual height of the tower is 91m

\(\frac{14}{x}=\frac{2}{13} \\x=\frac{14\times13}{2} \\x=91 m\)

The actual height of the tower is 91 m.

An indication of the relationship between the distances on a map and the corresponding actual distances.

Given that, The height of a tower on a scale is 14 centimeters. The scale is 2 cm: 13 m.

Since, 2 cm = 13 m

1 cm = 13 /2 m

Therefore, 14 cm = 14 × 13/2 = 91 m

Hence, the actual height of the tower is 91 m.

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