60+12x=6 (_+_)

Simplifying Algebraic Expressions

The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

\(\huge\boxed{y=4x-7}\)

Step-by-step explanation:

Linear equations will always be in the form \(y=mx+b\), where m is the slope and b is the y-intercept

Since we know nothing about this equation, other than the fact that there are two points in it, we must find the slope and the y-intercept.

Luckily, we have two points to work with. We know that the slope between two points will be the change in y divided by the change in x (\(\frac{\Delta y}{\Delta x}\)), so we can use the two points given to us to find both changes.

The y value goes from 1 to 17, which is a \(17-1=16\) change.

The x value goes from 2 to 6, which is a \(6-2=4\) change.

Now that we know both changes, we can divide the change in y by the change in x.

\(\frac{16}{4}=4\)

Now that we know the slope (4), we can plug it into our equation (\(y=mx+b\)).

\(y=4x+b\)

Now all we need to do is find the y-intercept. Since we know the slope and one of the points the line passes through, we can find the y-intercept by substituting in the values of x and y. Let's use the point (2, 1).

Therefore our y-intercept is -7. Now that we know the slope and the y-intercept, we can plug it into our equation.

\(y=4x-7\)

Hope this helped!

Answer:hard stuff

Step-by-step explanation: i need help on same thing

Answer:

5

Step-by-step explanation: The 3 over the root sign is a cubed root (^3 instead of ^2) so the answer is 5^3. This is a very common calculation and is on most calculators.

This situation should be analyzed using a two-sample independent method. The two-sample independent method is used when comparing two independent groups, in this case, taxi ride times in San Diego and Phoenix. The two-sample paired method is used when comparing the same group under two different conditions, which is not the case here, as the taxi ride times are taken from two separate cities. There is no common characteristic that makes these data paired.

A two-sample independent method is used to compare the means of two independent populations, which is appropriate for this situation. The independent samples t-test is a common statistical test used to compare the means of two independent populations.On the other hand, if the data were obtained from the same set of taxis in both cities or from the same set of riders in both cities, then the situation would be a paired situation, and a two-sample paired method would be more appropriate.Paired data refers to data that is collected from the same sample, subject, or group at different points in time or under different conditions. For example, if the data were obtained from the same set of taxis in both cities, then the data would be paired because each taxi in San Diego would have a corresponding taxi in Phoenix. Similarly, if the data were obtained from the same set of riders in both cities, then the data would be paired because each rider in San Diego would have a corresponding rider in Phoenix.In summary, since the data in this situation were obtained from two different cities, a two-sample independent method is appropriate. If the data were obtained from the same set of taxis or riders in both cities, a two-sample paired method would be appropriate.

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The value of x in the given scenario is 8. Substituting x = 8, both angles A and B have a measure of 37°, confirming the solution.

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures. In this case, we have vertical angles A and B, and we need to find the value of x.

Given that m/A = (x + 29)° and m/B = (6x - 11)°, we can set up an equation by equating the measures of vertical angles:

m/A = m/B

(x + 29)° = (6x - 11)°

Now we can solve for x by simplifying and solving the equation:

x + 29 = 6x - 11

Combine like terms:

29 + 11 = 6x - x

40 = 5x

Divide both sides by 5 to isolate x:

40/5 = 5x/5

8 = x

Therefore, the value of x is 8.

To confirm, let's substitute x = 8 into the angle measures:

m/A = (x + 29)° = (8 + 29)° = 37°

m/B = (6x - 11)° = (6 * 8 - 11)° = (48 - 11)° = 37°

As expected, both angles A and B have a measure of 37°, confirming that x = 8 is the correct value.

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Answer:

B. The function shown on the graph has a smaller rate of change but a higher starting point

Step-by-step explanation:

Question options obtained from a similar question are;

A. The function shown on the graph has a greater rate of change and a higher starting point

B. The function shown on the graph has a smaller rate of change but a higher starting point

C. The function shown on the graph has a greater rate of change but a lower starting point

The function shown on the graph has a smaller rate of change but a higher starting point

Explanation;

The given function with which the graph is compared is y = 4·x + 2

From the given function, we have;

The rate of change of the function is the coefficient of 'x', therefore, the rate of change of the function = 4

When y = 0, 4·x + 2 = 0,

∴ x = -2/4 = -0.5

The y-intercept is given when x = 0

∴ The y-intercept, y = 4 × 0 + 2 = 2

The starting point of the function, is (0, 2)

From the graph, we have;

The y-intercept = (0, 4)

Therefore, the starting point of the line, the y-intercept, (0, 4), is higher than the starting point of the given function, (0, 2)

The coordinates of two (clear) points on the line in the graph are (0, 4) and (-2, -2)

The rate of change of the line, m = (4 - (-2))/(0 - (-2)) = 3

Therefore, the graph has a lesser rate of change, 3, than the rate of change of the given function, 4

When compared with the given function, 'the function shown on the graph has a smaller rate of change and a higher starting point'.

Answer:

x = 18

Step-by-step explanation:

the angles pictured are supplementary angles.

supplementary angles are angles whose sum equals 180°

ex: <1 + <2 = 180°

\(5x - 11 + 6x - 7 = 180\)

\(11x - 18 = 180\)

\(11x = 198\\x = 18\)

Answer:

\(\boxed{\sf{x=18}}\)

Step-by-step explanation:

To find the value of x, you have to use the supplementary angles which is equal to 180°.

Supplementary angles = 180°

5x-11+6x-7=180

Combine like terms.

\(\sf{5x+6x-11-7=180}\)

5x+6x=11x

\(\sf{11x-11-7=180}\)

Subtract the numbers from left to right.

-11-7=-18

\(\sf{11x-18=180}\)

You have to add by 18 from both sides.

11x-18+18=180+18

Solve.

Add the numbers from left to right.

180+18=198

11x=198

Divide by 11 from both sides.

11x/11=198/11

Solve.

198/11=18

\(\rightarrow \boxed{\sf{x=18}}\)

Therefore, the final answer is x=18.

Answer:

7 seconds, 6 seconds

Step-by-step explanation:

a) For the object to reach the ground, the height from the ground has to be 0. therefore, let the function h = 0

0 = -16t^2 + 700

the amswers are + or - 6.61

we cant have negative time so it is approximately 7 seconds.

b) for the object to reach a 100 feet, h =100

100 = -16t^2 + 700

0 = -16t^2 + 600

solve: + or - 6.12

therefore it takes approximately 6 seconds to reach 100 feet.

If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.

∠RTU = ∠RTG + ∠GTU

∠RTU = 5.8° + 113.6°

∠RTU = 119.4°

The measure of the angle ∠RTU will be 119.4°.

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Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10

Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

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A circular pie cut in 8 pieces and sold at a fractional form 4(2/8) and 5(1/2), yields a total sale of 78 pieces of pie.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

A pie is made in a circular shape.

Number of pieces in one pie = 8 pieces

Number of pieces of pie sold by first class of fifth grades = 4(2/8)

Number of pieces of pie sold by second class of fifth grades = 5(1/2)

The total number of pieces sold is = Pieces sold by first class + Pieces sold by second class

To find the pieces sold by first class multiply the fractional form by number of pieces -

4(2/8) × 8

34/8 × 8

34

The first class sold 34 pieces of pie.

To find the pieces sold by second class multiply the fractional form by number of pieces -

5(1/2) × 8

11/2 × 8

11 × 4

44

The second class sold 44 pieces of pie.

The total number of pies sold is -

The total number of pieces sold is = 34 + 44

The total number of pieces sold is = 78

Therefore, 78 pies were sold.

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Answer:

$5 for one person to rent a locker

Step-by-step explanation:

Assuming the $18 is for one person, then two people it would be $36, since $18 + $18 = $36 and it's stated there's two people. If you subtract $36 from $46 you get $10, and since it's for two people you split it in half (so basically divide by 2) you get $5 for a locker.

Hope this helps!

The f(x) value for each x-value in the table is

-2    36

-1     6

0      1

1       1/6

2       1/36

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

f(x) = (1/6)ˣ

From the table, we have the values of x to be integer values from -2 to 2

Using the above as a guide, we have the following:

f(-2) = (1/6)⁻² = 1/36

f(-1) = (1/6)⁻¹ = 6

f(0) = (1/6)⁰ = 1

f(1) = (1/6)¹ = 1/6

f(2) = (1/6)² = 1/36

So, the complete table of values is

-2    36

-1     6

0      1

1       1/6

2       1/36

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Answer

f(n)=4•(0.5)^n-1

The statement is false because in a Poisson distribution, the probability of success does not vary from trial to trial.

The Poisson distribution is a discrete probability distribution that describes the number of times an event occurs in a fixed time interval or spatial region, given the average rate of occurrence and assuming that the events are independent and random.

The Poisson distribution has only one parameter, λ, which represents the average rate of occurrence of the event.

The probability of observing k events in the interval is given by the Poisson probability mass function:

P(k) = (e^(-λ) * λ^k) / k!

where e is the base of the natural logarithm, and k is a non-negative integer.

The Poisson distribution assumes that the probability of observing an event at any given point in time or space is constant, and that the events are independent of each other.

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer:not

Step-by-step explanation:

Quadratic equations involve exponents

To reparametrize the curve with respect to arc length, we need to find the arc length function s(t) and then solve for t in terms of s.

The arc length function is given by:

s(t) = ∫√[r'(t)·r'(t)] dt

where r'(t) is the derivative of r(t) with respect to t.

We can calculate r'(t) as:

r'(t) = (2e^(2t)cos(2t) - 4e^(2t)sin(2t))i + (12e^(2t)sin(2t))j + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))k

Now we can substitute this into the arc length formula and integrate:

s(t) = ∫√[(2e^(2t)cos(2t) - 4e^(2t)sin(2t))^2 + (12e^(2t)sin(2t))^2 + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))^2] dt

This integral looks quite complicated, so we will use a numerical integration method to approximate s(t).

We can use the trapezoidal rule to numerically integrate s(t) between t = 0 and some value t = T:

s(T) ≈ ∑[s(iΔt) + s((i+1)Δt)]/2 * Δt

where Δt = T/n is the step size, and n is the number of intervals we use.

Once we have approximated s(t), we can solve for t in terms of s using numerical methods such as the bisection method or Newton's method.

For example, if we want to find the value of t that corresponds to s = 10, we can solve:

s(t) = 10

for t using numerical methods. Once we have t, we can plug it back into r(t) to get the reparametrized curve in terms of arc length s.

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Step-by-step explanation:

The price is $30.

please make me brainalist and keep smiling dude

The factor in the graph that supports the idea that the greater the rainfall in June through August, the fewer acres are burned by wildfires is the negative correlation between rainfall and acres burned.

The graph shows a negative correlation between the amount of rainfall in June through August and the number of acres burned by wildfires. As the amount of rainfall increases, the number of acres burned decreases. This suggests that wetter weather can help reduce the risk of wildfires.

The graph provides a visual representation of the relationship between rainfall and wildfires. It shows that there is a clear negative correlation between the two variables. This means that as one variable increases, the other decreases. In this case, the variable of interest is the number of acres burned by wildfires. The graph shows that when there is less rainfall in June through August, more acres are burned by wildfires. Conversely, when there is more rainfall during these months, fewer acres are burned. This makes sense because rainfall can help reduce the risk of wildfires by making vegetation less dry and therefore less susceptible to catching fire. Additionally, wetter weather can help firefighters contain and extinguish fires more quickly and effectively.

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Answer:

y=-20x-12

Step-by-step explanation:

The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.

The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:

f(x) = 1 / (b - a)

where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:

f(x) = 1 / (3.5 - 2.5) = 1

To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:

Probability = (width of range) / (total width)

= 0.2 / 1

= 0.2

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Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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Answer:

Step-by-step explanation:

88 / 184 ≈ 0.48

96 / 184 ≈ 0.52

104 / 166 ≈ 0.63

62 / 166 ≈ 0.37

To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

Answer:

(6, 5) will be the point after the rule is applied

The required translation as of the given condition is (6, 5).

Given that,
To apply the following rule to the point (-5,6): (x,y)-->(y, -x).

Coordinate, is represented as the values on the x-axis and y-axis of the graph

Translation of a point is defined as changing the location of the point on an arbitrary space with the help of any function and instructions.

Here,
In the question, a rule is mentioned for the transposition of the coordinates,
(x,y)-->(y,-x)
we just need to simply poor the coordinate in the given translation equation,
(-5, 6) - - -> (6, -(-5))
(-5, 6) - - -> (6, 5)

Thus, the required translation as of the given condition is (6, 5).

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The radius of the largest circular tabletop that can be cut from the given rectangular wood is 0.60 meters.

To determine the radius of the largest circular tabletop that can be cut from a rectangular piece of wood measuring 1.20 m by 1.80 m, we need to find the maximum possible diameter that fits within the dimensions of the wood.

The largest circle will have a diameter equal to the shorter side of the rectangle, which is 1.20 m. This is because the circle must be entirely contained within the rectangular wood, and placing the circle's diameter along the shorter side ensures it fits perfectly without exceeding the wood's dimensions.

Now that we know the diameter of the largest circle is 1.20 m, we can easily find the radius by dividing the diameter by 2:

Radius = Diameter / 2

Radius = 1.20 m / 2

Radius = 0.60 m

So, the radius of the largest circular tabletop that can be cut from the given rectangular wood is 0.60 meters.

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