Michelle wants to make a long-term investment. She wants to triple an initial investment of
$2,000. If she invests at a simple interest rate of 12% per year, approximately how long will it
take her principal to triple?

Answer:

Step-by-step explanation:

North America:

Climate: North America experiences a variety of climate types due to its large size. These include tundra climate in the far north, temperate climate in the central and eastern regions, arid or semi-arid climates in parts of the southwestern United States and Mexico, and tropical climate in southern Florida and parts of Mexico.

Mountains: North America is home to several major mountain ranges, including the Rocky Mountains in the western United States and Canada, the Appalachian Mountains in the eastern United States, and the Sierra Nevada range in the western United States.

South America:

Climate: South America exhibits diverse climate types. The northern part, near the equator, has tropical rainforest climates, while the central regions have a savanna climate. The western coast of South America, particularly Peru and Chile, experiences a desert climate. The southern regions, such as Argentina and Chile, have a variety of climates including Mediterranean, temperate, and subpolar.

Mountains: The Andes Mountains run along the western coast of South America, spanning several countries and forming the longest mountain range in the world.

Central America:

Climate: Central America has a tropical climate with high humidity and significant rainfall throughout the year. The region experiences wet and dry seasons, with the Caribbean coast receiving more rainfall than the Pacific coast.

Mountains: Central America is characterized by several mountain ranges, including the Sierra Madre range in Mexico and the Cordillera de Talamanca in Costa Rica and Panama.

Caribbean:

Climate: The Caribbean region generally has a tropical climate with high temperatures and humidity year-round. It experiences a wet season from June to November, coinciding with the hurricane season, and a drier season from December to May.

Mountains: The Caribbean islands consist of both volcanic and non-volcanic mountains. Some examples include the Blue Mountains in Jamaica, the Pitons in Saint Lucia, and the Central Range in Trinidad and Tobago.

It's important to note that these regions have variations within their climates and mountains due to geographical features, elevation, and other factors.

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The concave mirror is 36.7 cm away from the face.

The magnification equation is:

Magnification=m=-v/u where v is the image distance and u is the object distance.

Given that the upright image of a man's face is 2.54 times the size of the face, therefore magnification,

m=2.54 =-v/u.........(i)

Now, the mirror is a concave mirror and its radius of curvature, R=+36.7 cm.

Thus, the mirror's focal length, f=R/2=+18.35 cm.....(ii)

In terms of focal length, the object distance, u = -f.......(iii)

Substituting equation (ii) and (iii) in equation (i), we get:

2.54=-v/(-f)v=-2.54f

Now we have the relationship between v and f.

The object distance from the mirror is the sum of the focal length and the image distance.

Hence the object distance is:

u=f+v

u=-f+v

=-f-2.54f=-3.54f

Substituting the value of f=-18.35 cm, we get:

u= -3.54f

=3.54×18.35 cm = 64.99 cm

Therefore, the concave mirror is 64.99 cm away from the face of the man.

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Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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In a self-selection problem, the explanatory variables can be endogenous.

Endogenous variables are those that are determined within the system, meaning they are affected by other variables in the model. In self-selection problems, individuals or units choose whether to participate in a particular group or program based on their own characteristics.

As a result, the explanatory variables that influence the decision to participate can be correlated with unobservable factors that also affect the outcome of interest. This correlation creates endogeneity, which can lead to biased estimates if not properly addressed in the analysis.

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Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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Answer:

36

Step-by-step explanation:

If Connor is paid £54 for 8 hours in a supermarket, the cost for 10 hours in the supermarket is

The cost per unit of an item is represented by the unit price.

To determine the unit price of an item, we divide the price of a specific number of units by the number of units. In this case the number of item is is measured in time hence we use unit rate

If Connor is paid £54 for 8 hours in a supermarket, this means that the unit rate will be

= 54 / 8

= 6.75

the cost for 10 hours in the supermarket

= 6.75 * 10

= £67.5

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

From the graph of the parent logarithmic function f and transformed function, to produce g

It is clear from the given graph that, the function g has a graph that is the stretch of f by a factor of 2.

For instance, for X=4, Y is 2 for f and 4 for g.

This proofs that, the g function is double to that of f function.

Therefore,

To produce g , function f was vertically stretched or expand by a factor of 2.

Function g is defined as 2f.

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stretched, 2, g(x)=2f(x)

Answer:

x=5, y=8

Step-by-step explanation:

we can use subsitution to solve this so:

5x-17=x+3 since they bot equal y (y=y)

4x-17=13 subtract x from both sides

4x=20 add 17 to both sides

x=5

then, plug in x to solve for y (either equation) :

y = x+3

y = (5) + 3

y = 8

Answer: The value of G = 4.5

Step-by-step explanation:

As per given,

\(G\propto \dfrac{j^2}{m}\)

When we replace proportional sign with an equal to sign, we get

\(G=k\dfrac{j^2}{m}\), where k = constant

If G=0.05 when j = 0.4 and m=1.6, then

\(0.05=k\dfrac{0.4^2}{1.6}\\\\ 0.05=k(0.1)\\\\ k=0.5\)

Now,

\(G=0.5\dfrac{j^2}{m}\\\\\Rightarrow\ G=0.5\dfrac{6^2}{4}\\\\\Rightarrow\ G=4.5\)

hence, when j =6 and m=4, the value of G = 4.5

Answer:

Neither

Step-by-step explanation:

Parallel lines need to have the same slopes, but lines A and B have different slopes, so parallel is off the list.

Perpendicular lines need slopes that multiply to -1, meaning one of them must be negative. This is not possible if both are greater than 1, making them positive. The lines cannot be perpendicular.

If they are the same line, they need the same slopes. However, they have different slopes, making this option impossible.

We are left with neither.

Step-by-step explanation:

the general slope intercept formula is

y = ax + b

a is the slope of the line.

b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).

we get b by using the point coordinates in the equation and solve for b :

-2 = (1/4)×0 + b

b = -2 (as expected)

the full line equation is

y = (1/4)x - 2

Answer:divideing by the whole number

Step-by-step explanation:

Answer:

The value of the experimental probability is greater

Step-by-step explanation:

For the theoretical probability;

the probability that a card with the number 3 is selected is 1/5

We consider that the probabilities of each selection are equal, for the theoretical probability

For the experimental, we simply place the frequency of the selection 3 over the total

that will be 128/400 = 8/25

As we know that 8/25 is greater than 1/5

We can conclude that the value of the experimental probability is greater than that of the theoretical

Answer:

I hate math

Step-by-step explanation:

Answer:X=2

Step-by-step explanation:first you simplify the left side by multiplying the 2 with both numbers which gets you 6x+8=4x+12 then you can subtract 8 from 12 which gets you 6x=4x+4 then you subtract 4x from 6x which then gets you to 2x=4 and finally you divide the 2 from the 4 to get X alone which then gets you the answer of x= 2

Answer:

2

Step-by-step explanation:

2(3x +4)=4x +12

6x +8=4x +12

6x - 4x =12-8

2x=4

x=4:2

x=2

Answer:

98

Step-by-step explanation:

u + xy

u = 18

x = 10

y =8

18 + 10*8 = 18 +80

= 98

Answer:

the answer is 98

Step-by-step explanation:

u+xy

18+10*8

18+80

98

The particular solution is Y(t) = Bt³ sin 5t + Dt cos 5t

The differential equation is y″ + 25y = 7t³ sin 5t

The auxiliary equation can be written as r² + 25 = 0 , which can be solved as: r = ±5i

Hence the homogeneous solution to the differential equation is yh(t) = c1 cos 5t + c2 sin 5t

We seek a particular solution of the form Y(t) = Asin 5t + Bt³ sin 5t + Ct² cos 5t + Dt cos 5t

The derivatives of Y(t) areY'(t) = 5A cos 5t + 15Bt² cos 5t + 2Ct sin 5t - 5D sin 5tY''(t)

= -25A sin 5t + 30Bt sin 5t + 20C cos 5t - 25D cos 5t

Let's substitute the above equations into the original differential equation;

y″ + 25y = 7t³ sin 5ty'' + 25y

= -25A sin 5t + 30Bt sin 5t + 20C cos 5t - 25D cos 5t + 25 (Asin 5t + Bt³ sin 5t + Ct² cos 5t + Dt cos 5t)

= 7t³ sin 5t

Collecting like terms we obtain 7t³ sin 5t = [25A sin 5t - 25Bt³ sin 5t + 25C cos 5t + 25D cos 5t - 30Bt sin 5t - 20C cos 5t] / 25

Dividing by 7 sin 5t we gett³ = A/7 - (5B/7)t³ + (6B/35)t + (4C/35) - (5D/7)cos 5t

Substituting t = 0 into the above equation yields

0 = A/7 + 4C/35

Solving for A and C we get A = 0 and C = 0

Answer: Yp(t)=t(B3t+B₂t² +B₁t+Bo) e' sin 5t

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Answer: below! ^^

Step-by-step explanation:

Hii, do you need an answer to your question? Let me help you out! (;

Perpendicular lines have slopes that are opposite inverses of each other.

The slope (m) of the line that is perpendicular to y=-2x-7 is \(\sf -\cfrac{1}{2}\).

\(\boldsymbol{y-y1=m(x-x1)}\)

\(\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}\)

\(\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}\)

Voila! There's our answer, cheers! (:

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

\(\underbrace\)

very easy my friendStep-by-step explanation:

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

10x+2

Step-by-step explanation:

3x+(2+7x)=3x+2+7x

               =10x+2

The volume of the sphere with a diameter of 13.6 miles is approximately 1663.17 cubic miles.

To find the volume of a sphere, we need to use the formula:
V = (4/3)πr³

where V is the volume, π is the constant pi, and r is the radius of the sphere.

But in this problem, we are given the diameter of the sphere, which is 13.6 miles.

We can use this information to find the radius by dividing the diameter by 2:
r = d/2 = 13.6/2 = 6.8 miles

Now we can substitute this value of r into the formula for the volume:
V = (4/3)πr³
V = (4/3)π(6.8)³
V = (4/3)π(314.432)
V = 1663.17 cubic miles (rounded to the nearest tenth)

Therefore, the volume of the sphere with a diameter of 13.6 miles is approximately 1663.17 cubic miles.

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Answer:

b=6 is your answer