What are the dimensions of the poster at 1/3 its current size?

Answer:

\(\ln 4 -2 \ln x +5 \ln y\)

Step-by-step explanation:

\(\ln \dfrac{4y^5}{x^2}\\\\=\ln(4y^5) - \ln(x^2)~~~~~~~~~~~;\left[ \log_b\left( \dfrac mn \right) = \log_b m - \llog_b n \right]\\\\=\ln 4 + \ln y^5 - 2\ln x~~~~~~~~~~~~;[\log_b m^n = n \log_b m ~\text{and}~\log_b(mn) = \log_b m + \log_b n ]\\\\=\ln 4 + 5 \ln y -2 \ln x\\\\=\ln 4 -2 \ln x +5 \ln y\)

Answer: Answer B

Step-by-step explanation: Let's begin

Answer: B in 4 - 2 in x + 5 in y

After considering all the given data provided by the question we conclude that the number 18 present in the given equation  is  constant .

The equation for the sunflower's height is h = 18 + 2.5w.
Here, the number 18 shows the height of the sunflower during the time it was planted, so it is the constant term present in the equation and hence it does not relie on the duration of weeks that have passed.
The coefficient of w is 2.5, which represents the rate at which the sunflower grows in height per week.
Therefore, after one week, the sunflower would be 20.5 inches tall (18 + 2.5 x 1), after two weeks it would be 23 inches tall (18 + 2.5 x 2), after four weeks it would be 28 inches tall (18 + 2.5 x 4), and after six weeks it would be 33 inches tall (18 + 2.5 x 6).

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Answer:

B

Step-by-step explanation:

Given g(x) then g(x + a) is a horizontal translation of g(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

h(x) = g(x - 3) = (x - 3)² with a < 0

The graph of h(x) is the graph of g(x) horizontally shifted right 3 units

The correct option is b which tells that an optimal solution to a linear programming problem must lie at the intersection of at least two constraints.

Linear programming is an optimization technique that is fine for the purpose of getting the best solution such as maximizing profit or certain 4th-era quantities.

When there are just two choice variables, the graphic method of solving a linear programming issue can be employed.

It is fine by modelling real-life problems into mathematical models that have linear relationships or constraints such as in the form of objective functions.

In linear programming, an objective function defines the formula for quantity optimization and the goal from this is to determine variable values that maximize or minimize the objective function depending on the problem robbery solved.

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Answer:

75

Step-by-step explanation:

300/4 = 75

Change of y/ change of x = gradient

You can suggest that managers should avoid the quick-fix mentality that makes management by best-seller so tempting by implementing the following strategies:

1. Understand the Unique Nature of Your Business: Managers should take the time to understand the unique nature of their business. They should realize that what worked for another company may not work for their own company.

2. Avoid Short-Term Solutions: Managers should avoid short-term solutions that provide quick results. They should focus on long-term solutions that will benefit the organization in the long run.

3. Develop a Comprehensive Strategy: Managers should develop a comprehensive strategy that includes long-term goals and objectives. They should also have a plan in place to achieve those goals.

4. Invest in Employee Development: Managers should invest in employee development by providing training and development opportunities. This will help to build a strong workforce that is capable of handling complex challenges.

5. Encourage Collaboration: Managers should encourage collaboration among team members. This will help to create a culture of teamwork and cooperation.

6. Monitor Progress: Managers should monitor progress and adjust strategies as necessary. This will help to ensure that the organization is on track to achieving its goals.

By following these strategies, managers can avoid the quick-fix mentality that makes management by best-seller so tempting. They can focus on long-term solutions that will benefit the organization in the long run.

Hope this helped you...

Answer:

7. -3

8. 4.4

9. 11

Answer:

54 mailboxes

Step-by-step explanation:

9*6=54

Answer: 54

Step-by-step explanation: 9x6=54

The events A and B are not mutually exclusive; not mutually exclusive (option b).

Explanation:

1st Part: Two events are mutually exclusive if they cannot occur at the same time. In contrast, events are not mutually exclusive if they can occur simultaneously.

2nd Part:

Event A consists of rolling a sum of 8 or rolling a sum that is an even number with a pair of six-sided dice. There are multiple outcomes that satisfy this event, such as (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). Notice that (4, 4) is an outcome that satisfies both conditions, as it represents rolling a sum of 8 and rolling a sum that is an even number. Therefore, Event A allows for the possibility of outcomes that satisfy both conditions simultaneously.

Event B involves drawing a 3 or drawing an even card from a standard deck of 52 playing cards. There are multiple outcomes that satisfy this event as well. For example, drawing the 3 of hearts satisfies the first condition, while drawing any of the even-numbered cards (2, 4, 6, 8, 10, Jack, Queen, King) satisfies the second condition. It is possible to draw a card that satisfies both conditions, such as the 2 of hearts. Therefore, Event B also allows for the possibility of outcomes that satisfy both conditions simultaneously.

Since both Event A and Event B have outcomes that can satisfy both conditions simultaneously, they are not mutually exclusive. Additionally, since they both have outcomes that satisfy their respective conditions individually, they are also not mutually exclusive in that regard. Therefore, the correct answer is option b: not mutually exclusive; not mutually exclusive.

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The distance that the bus travels between Hawkes Meadow and Brunswick Street is; 7.3 km

The formula for distance here is;

Total distance = Speed * Time

Now, we are given the speed as 29 km/hour

Now, we want to find the total distance between Hawkes Meadow and Brunswick Street.

The time between Hawkes Meadow and Brunswick Street from the attached table is 14:40 - 14:25 = 15 minutes.

Converting to hours = 15/60 = 1/4 hours

Thus;

Total distance = 29 * 1/4 ≈ 7.3 km

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Answer:

Oblique rectangular prism

Step-by-step explanation:

4≥2-4x

2-4x≤4

-4x ≤ 4-2

-4x ≤ 2

x ≥ 2/(-4)

x ≥ -½

It will take 3.375 ft ³wrapping paper to cover a box that is 1.5ft x 1.5ft x 1.5ft

We can see that volume of a cube can be calculated as the cube of the sides of a given figure.

The volume of a cube = side³

We are given the dimensions as;

1.5ft x 1.5ft x 1.5ft

here the volume of the cube will be;

= side³

=1.5ft x 1.5ft x 1.5ft

= 3.375

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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is E. Pi.

The area of a circle is given by the formula A = π\(r^2\), where A is the area and r is the radius. If the area of the circle is increasing twice as fast as its radius, we can express this relationship as:

dA/dt = 2(dr/dt)

Here, dA/dt represents the rate of change of the area with respect to time, and dr/dt represents the rate of change of the radius with respect to time.

Since we are considering an expanding circle, both dA/dt and dr/dt are positive.

Now, let's solve for the relationship between dA/dt and dr/dt:

dA/dt = 2(dr/dt)

π\(r^2\) = 2(dr/dt)

Dividing both sides by \(r^2\):

π = 2(dr/dt) / \(r^2\)

Simplifying further:

π = 2(dr/dt) / \(r^2\)

π = 2/r

Therefore, the relationship between the rate of change of the area and the rate of change of the radius is π = 2/r.

To find the value of r, we rearrange the equation:

r = 2/π

Thus, the radius is 2/π, which is approximately 0.6366.

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Answer:

the triangle is right

Step-by-step explanation:

The Pythagorean theorem dictates that a^2 +b^2=c^2

6^2+8^2=10^2

36+64=100

100=100

\(y=19.08(1.129)^{-1}\) is the exponential model that describes the value of the land.

Exponential growth is a process by which quantity increases over time. When the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself, it is said to be proportional to the quantity itself. A quantity experiencing exponential growth is an exponential function of time, which means that the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth).

\($$Use the exponential model:$$y=a \cdot b^x$$Let $y$ be the value of the area of land in thousand dollars and $x$ be the number of years since 1950.Given two consecutive $x$-values $x=4$ (year 1954) and $x=5$ (year 1955), the growth factor $b$ is the ratio of their $y$ -values:$$b=\frac{35}{31} \approx 1.129$$Use the value of $b$ and one of the data points to find the initial value, $a$. Here, I used $(4,31)$ :\)

\($$\begin{gathered}31=a(1.129)^4 \\\frac{31}{(1.129)^4}=a \\19.08 \approx a\end{gathered}\\\\\\So, the function describing the value of the land is:$$y=19.08(1.129)^{-1}$$\)

Thus, \(y=19.08(1.129)^{-1}\) is the exponential model that describes the value of the land.

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In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

Given,

Ways 7 runners can places 1 through 4 be determined:

By using permutation:

7!

7 ×6 × 5 ×4×3×2×1

5040

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

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Answer:

Step-by-step explanation:

You just have to distribute all the equations. Start with the parenthesis. I'll do one for you. 2(x-5) +7 = x+8. Distribute 2(x-5) and you gest 2x-10+7=x+8. subtract x from the right and you get x-10+7=8. Combine like terms so you get x-3=8. Then add 3 on both sides and you get x=11.

By using the number line, we can infer that Miami, Florida is 50 degrees warmer than Buffalo, New York.

A visual representation of numbers on a straight line is known as a number line. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

Given that, the temperature in Buffalo, New York is 20 below zero and in Miami it is 30 degrees above zero.

So, the difference in temperatures is :

=30-(-20)

=30+20

=50 degrees.

We can count from -20 up to 30. If Buffalo, New York was 20 degrees warmer than it is on this winter morning, the temperature would be zero degrees. If Buffalo, New York was 30 degrees warmer still, the temperature would be 30 degrees, the same temperature as Miami, Florida. In order for Buffalo, New York to be the same temperature as Miami, Florida. Buffalo, New York would have to be 20+30=50 degrees warmer than it is.

Thus, Miami, Florida is 50 degrees warmer than Buffalo, New York.

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(A) The leading term is -8x^5.
(B) The limit of p(x) as x approaches 0 is 16.
(C) The limit of p(x) as x approaches infinity is negative infinity.

(A) The leading term of a polynomial is the term with the highest degree.

In this case, the highest degree term is -8x^5.

Therefore, the leading term of the polynomial p(x) = 16+2x^4-8x^5 is -8x^5.

(B) To find the limit as x approaches 0, we can simply substitute 0 for x in the polynomial p(x).

Doing so gives us:

p(0) = 16 + 2(0)^4 - 8(0)^5
p(0) = 16

Therefore, the limit of p(x) as x approaches 0 is 16.

(C) To find the limit as x approaches infinity, we need to look at the leading term of the polynomial.

As x gets larger and larger, the other terms become less and less significant compared to the leading term.

In this case, the leading term is -8x^5. As x approaches infinity, this term becomes very large and negative.

Therefore, the limit of p(x) as x approaches infinity is negative infinity.

In summary:

(A) The leading term is -8x^5.
(B) The limit of p(x) as x approaches 0 is 16.
(C) The limit of p(x) as x approaches infinity is negative infinity.

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Answer: I'd say reflection

Answer:

It is a reflection

Step-by-step explanation:

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Answer:

c

Step-by-step explanation:

the second question 65cent

Step-by-step explanation:

when you get a decimal like 0.02 and you want to express it in fraction,this is a simple trick.

first,put your pen at the point and move it forward till you end at the last number.

While you move the pen over each value, you will count the number of jumps and record the number of jumps in zeros i. e

2÷100 and it means that,the last 1or 3or 3whole numbers will become the numerator

Answer:

A is correct

Step-by-step explanation:

b has a negative value cause it's before 0

but -b will become a positive value thus >0

example:

b is -1

-b = -(-1)

= 1

hope you understand

Answer:

⇨ Choice A.

Step-by-step explanation:

We'll consider three choices and compare the answers with the given number line and points.

⟺ Choice A

This is the correct answer and here is why.

\(-b>0\)

Solving Inequality is similar to solving equation. The difference is if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.

Thus, our new Inequality would be \(b<0\) which is true by the number line itself.

⟺ Choice B

The reason why choice B is not correct because the point a is lesser than the point b. It's obvious that point a cannot be greater than point b.

⟺ Choice C

The reason why choice C is not correct because if we solve the Inequality.

\(-b<-c\)

We can either solve for b-term or c-term, the outcome would be the same. I'll solve for both terms.

⇨ Solve for b-term

\(-b<-c\\b>\frac{-c}{-1}\\b>c\)

Also remember that moving a negative coefficient would swap the sign/operator of Inequality.

⇨ Solve for c-term

\(-b<-c\\\frac{-b}{-1}>c\\b>c\)

As b>c is not true in the number line. We notice that c point is greater than b point.

Thus, the clear answer is A choice.  

The ratio of the surface area to the volume is 14/15 in²/in³.

To find the ratio of surface area to volume for a given object, we divide the surface area by the volume. In this case, we have a ratio of 280 in² to 300 in³.

The surface area represents the total area of all the exposed surfaces of the object, while the volume represents the amount of space occupied by the object.

To calculate the ratio, we divide the surface area by the volume:

Ratio = Surface Area / Volume

Ratio = 280 in² / 300 in³

Simplifying the ratio:

Ratio = (280/300) in²/in³

Ratio = (28/30) in²/in³

Ratio = (14/15) in²/in³

Therefore, the ratio of the surface area to the volume is 14/15 in²/in³.

This ratio represents the relationship between the amount of surface area and the amount of volume for the given object. It indicates that, for every 15 cubic inches of volume, there are 14 square inches of surface area.

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According to the Triangle Inequality Theorem, the sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.

In this case, you know the lengths of two sides of the triangle, and you also know that "x" represents the length of the third side. Then, you can set up the following:

Solving the inequality, you get:

You can rewrite it as:

Hence, the answer is:

The function P is given by:

Substitute t=0 into the formula:

Therefore, the number of insects at t=0 is 200

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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