in a water maze experiment, rats were injected with a drug 20 minutes before being placed in the maze. the rats quickly learned the task and, after 5 trials, would swim directly to the quadrant containing the hidden escape platform. one week later, the same rats were placed (one at a time) in the water maze after receiving an injection of saline. they performed at chance, spending equal amounts of time in each of the four quadrants. what is likely true about the drug (assuming all other variables were kept constant)?

The AD curve in an AS-AD diagram is most relevant to Keynes's Law. The correct option is d.

In an AS-AD (Aggregate Supply-Aggregate Demand) diagram, Keynes's Law is most relevant to the AD curve. Keynes's Law, proposed by economist John Maynard Keynes, states that aggregate demand (AD) determines the level of economic activity and that fluctuations in AD can lead to periods of economic expansion or contraction.

The AD curve represents the total demand for goods and services in an economy at different price levels. It shows the relationship between the overall price level and the quantity of real GDP demanded. When the AD curve shifts to the right, it indicates an increase in overall demand, leading to higher levels of output and employment. Conversely, a shift to the left indicates a decrease in overall demand, which may lead to lower output and employment.

Keynes's Law emphasizes the importance of aggregate demand management by the government through fiscal and monetary policies to stabilize the economy and achieve full employment. Thus, the AD curve plays a central role in illustrating the concepts and implications of Keynes's Law in an AS-AD diagram. The correct option is d.

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Answer:

3 and 4

36 and 48

Step-by-step explanation:

you got the 1 wrong

should be 5 and 4

20 and 16

The hiker's distance and bearing from their starting point are approximately 7.155 miles and 28.07°, respectively.

Given that two hikers travel 8 mi southeast and then 6 mi east, we are to find the hikers distance and bearing from their starting point at this time.Long ExplanationThe bearing of the hiker refers to the angle between the hiker's direction and North. So, let us assume that the hiker has initially moved at a direction East, as shown below:We are given that the hiker has traveled 8 miles to the southeast.

Therefore, from the diagram, the distance traveled in the East direction is 8 sin(45) miles, and the distance traveled in the South direction is 8 cos(45) miles. East = 8 sin(45) = 8/√2 = 4√2 miles South = 8 cos(45) = 8/√2 = 4√2 miles We are then told that the hiker travels 6 miles east, from the last position.

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Answer:

55

Step-by-step explanation:

\(\sqrt[3]{\frac{n}{4} } +\frac{n}{10} \\\\\sqrt[3]{\frac{500}{4} } +\frac{500}{10}\\\\\sqrt[3]{125} +50\\5+50\\55\)

A milkshake costs $3.50 and an ice cream sundae costs $4.75.

A system of linear equations is a set of two or more linear equations that contain the same variables. A linear equation is an equation of a straight line and has the form ax + by = c, where a, b, and c are constants and x and y are variables.

The goal of a system of linear equations is to find the values of the variables that satisfy all the equations in the system simultaneously. This can be done by different methods, such as substitution, elimination, or matrix methods.

Systems of linear equations are widely used in mathematics, science, engineering, and economics to model and solve real-world problems involving multiple unknowns. They are a fundamental concept in algebra and linear algebra.

Using this information, we can set up a system of equations to find the cost of a milkshake and the cost of an ice cream sundae. Let's use x to represent the cost of a milkshake and y to represent the cost of an ice cream sundae.

From the first sentence, we can write the equation:

\(4x + 2y = 23.5\)

From the second sentence, we can write the equation:

\(8x + 6y = 56.5\)

Now we can solve for x and y using any method of solving systems of equations, such as substitution or elimination.

Let's use elimination. Multiplying the first equation by -3 and adding it to the second equation, we get:

\(-12x - 6y = -70.5\)

\(8x + 6y = 56.5\)

\(-4x = -14\)

Dividing both sides by -4, we get:

\(x = 3.5\)

Now we can substitute x = 3.5 into one of the original equations to solve for y. Let's use the first equation:

\(4x + 2y = 23.5\)

\(4(3.5) + 2y = 23.5\)

\(14 + 2y = 23.5\)

\(2y = 9.5\)

\(y = 4.75\)

Therefore, a milkshake costs $3.50 and an ice cream sundae costs $4.75.

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Answer:

Step-by-step explanation:

I really don’t know but I think you have to find the hypothenuse first then you can do the rest

Answer:

Step-by-step explanation:

"SAS" is when we know two sides and the angle between them. use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

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Answer:

\(m=-1\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in 2 coordinates into the slope formula to find slope m:

\(m=\frac{0-(-2)}{-2-0}\)

\(m=\frac{0+2}{-2}\)

\(m=\frac{2}{-2}\)

\(m=-1\)

Answer:

Slope is negative 1

Step-by-step explanation:

You can either find it in 2 ways. (1) pick 2 coordinates and find the slope by solving for y1-y2 divided by x1-x2. way number 2 is (2) by counting the spaces. slope is rise over run, so we can see the the coordinate went down 1, which is negative one. and it went 1 space to the right. so by setting up the equation, it would be -1/1, which equals negative 1. message me if u have a problem, kinda hard to explain it in words.

Answer:

81

Step-by-step explanation:

First find the amount decrease

90 * 10 %

90 * .10

9

90 decreased by 9

90 -9

81

Answer:

81

Step-by-step explanation:

Turn into decimal.

10% = 0.1

Multiply

90 * 0.1 = 9

Subtract

90 - 9 = 81

Best of Luck!

If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.

However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.

Substituting the given values, we get:

m = 10 N / 12 m/s²

m = 0.83 kg

So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

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Complete Question:

A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?

Answer:

The answer for the Perimeter of the semi circle is 15.71cm

Step-by-step explanation:

Perimeter of semi circle =perimeter of circle/2

P=2pir/2

P=pir

r=d/2=10/2

r=5cm

P=pir

P=5pi

P=5×3.142

P=15.71cm

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer: y=5x+7

Step-by-step explanation:

Since we are given the slope, all we have to do is plug in the given point and solve for the y-intercept.

-3=5(-2)+b             [multiply]

-3=-10+b                [add both sides by 10]

b=7

Now, we know the equation is y=5x+7.

Answer:

no lol

Step-by-step explanation:

Answer:

m DE=60°

Step-by-step explanation:

OR≅OS

in Δ STW,

SW=TW

TS=SW=TW

m∠TSW=60°

m DE= 60°

༄❁༄❁༄❁༄❁༄

hope it helps...

have a great day ! ! !

The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256.

a. To get exactly 6 heads, we need to choose 6 out of the 8 flips to be heads, and the remaining 2 flips to be tails. The number of ways to choose 6 out of 8 is given by the binomial coefficient (8 choose 6) = 28. Therefore, there are 28 possible outcomes with exactly 6 heads.

b. To get at least 3 heads, we need to count the number of outcomes with 3, 4, 5, 6, 7, or 8 heads. Using the same logic as part (a), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at least 3 heads.

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Number of outcomes with 7 heads: (8 choose 7) = 8

Number of outcomes with 8 heads: (8 choose 8) = 1

Total number of outcomes with at least 3 heads = 56 + 70 + 56 + 28 + 8 + 1 = 219.

c. To get at most 6 heads, we need to count the number of outcomes with 0, 1, 2, 3, 4, 5, or 6 heads. Using the same logic as part (b), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 6 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Total number of outcomes with at most 6 heads = 1 + 8 + 28 + 56 + 70 + 56 + 28 = 247.

d. To get at most 2 heads, we need to count the number of outcomes with 0, 1, or 2 heads. Using the same logic as parts (b) and (c), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 2 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Total number of outcomes with at most 2 heads = 1 + 8 + 28 = 37.

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Answer:

r = 10.72 cm

Step-by-step explanation:

h = 6 cm

Volume of cone = 722 cubic cm

\(\frac{1}{3}\pi r^{2}h=722\\\\\frac{1}{3}*3.14*r^{2}*6=722\\\\r^{2}=\frac{722*3}{3.14*6}\\\\r^{2}=114.97\\\\r = \sqrt{114.97}\\\\r = 10.72\)

Answer:

4x+6y = 46

Step-by-step explanation:

you just add by column

2x+2x

y+5y

9+37

Answer:

\( 3x + y = 2 \)

Step-by-step explanation:

\( y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) \)

\( y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1)) \)

\( y - 5 = \dfrac{-12}{4}(x + 1) \)

\( y - 5 = -3(x + 1) \)

\( y - 5 = -3x - 3 \)

\( 3x + y = 2 \)

Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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Given an initial value problem: y (1) = −sin(t) + cos(t); y³) (0)=7, y" (0) = y'(0) = -1, y(0) = 0Solution:Let us consider the initial value problem y (1) = −sin(t) + cos(t) -(1)y³) (0)=7y" (0) = y'(0) = -1y(0) = 0.

Integrating equation (1) we gety = -cos(t) - sin(t) + cWhere c is the constant of integration Now, we have to find the value of c using the initial condition y(0) = 0y(0) = 0 = -cos(0) - sin(0) + cc = 1.

y = -cos(t) - sin(t) + 1Therefore the solution of the initial value problem:y = -cos(t) - sin(t) + 1

We are given an initial value problem and we need to find the solution of this initial value problem. We can do this by integrating the given differential equation and then we need to find the value of the constant of integration using the given initial condition. Then we can substitute the value of the constant of integration in the obtained general solution to get the particular solution.

The general solution obtained from integrating the given differential equation is:

y = -cos(t) - sin(t) + c Where c is the constant of integration. Now we need to find the value of c using the initial condition y(0) = 0y(0) = 0 = -cos(0) - sin(0) + cc = 1.

Therefore the particular solution obtained from the general solution is:y = -cos(t) - sin(t) + 1Hence the solution of the initial value problem:y = -cos(t) - sin(t) + 1.

Therefore, the solution of the initial value problem: y (1) = −sin(t) + cos(t); y³) (0)=7, y" (0) = y'(0) = -1, y(0) = 0 is given by y = -cos(t) - sin(t) + 1.

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Answer: 880

Step-by-step explanation:

Answer:

450 kilo watt hour of electricity was used

Step-by-step explanation:

Here, we are interested in calculating the kilowatt-hour of electricity used.

From the question, we are told that the bill is $67.50 and the cost of 1 kilo watt hour is $0.15

So to know the amount of kilowatt hours of electricity used, we will simply divide the bill by the charge per 1 kwh

Mathematically that would be 67.5/0.15 = 450

Answer:

x(-5,0) ,y(0,5)

Step-by-step explanation:

Answer:

The slope is - 5,0

Step-by-step explanation:

U just draw a line from where the - 5 cut the line n from there to zero too

Answer:

16.5

Step-by-step explanation:

264 / 16 = 16.5

Answer:

16.5 or you can round it to 17

Step-by-step explanation:

If you divide 264 by 16, the answer is 16.5, but I don't know if you can have 16.5 bags depending on the situation. So, you might have to round to 17.

Answer:

y=1152

Step-by-step explanation:

18 x 64 hope I was helpfull

Answer:

By proportion :-

x/2.8 = 3/2.4

x = 3(2.8)/ 2.4

x= 3.5

Answer: C) 3.5

《OAmalOHopeO》

Step-by-step explanation:

all the functions with the "exponent" -1 mean inverse function (and not 1/function).

the inverse function gets a y value as input and delivers the corresponding x value as result.

so,

\(g { }^{ - 1} (0)\)

gets 0 as input y value. now, what was the x value in g(x) that delivered 0 ?

4

that x value delivering 0 as y was 4.

so,

\(g {}^{ - 1} (0) = 4\)

the inverse function for a general, continuous function get get by transforming the original functional equation, so that x is calculated out of y :

h(x) = y = 4x + 13

y - 13 = 4x

x = (y - 13)/4

and now we rename x to y and y to x to make this a "normal" function :

y = (x - 13)/4

so,

\(h {}^{ - 1} (x) = (x - 13) \div 4\)

a combined function (f○g)(x) means that we first calculate g(x) and then use that result as input value for f(x). and that result is then the final result.

formally, we simply use the functional expression of g(x) and put it into every occurrence of x in f(x).

so, we have here

4x + 13

that we use in the inverse function

((4x + 13) - 13)/4 = (4x + 13 - 13)/4 = 4x/4 = x

the combination of a function with its inverse function always delivers the input value x unchanged.

so,

(inverse function ○ function) (-3) = -3

Answer:

\(\text{g}^{-1}(0) =\boxed{4}\)

\(h^{-1}(x)=\boxed{\dfrac{x-13}{4}}\)

\(\left(h^{-1} \circ h\right)(-3)=\boxed{-3}\)

Step-by-step explanation:

The inverse of a one-to-one function is obtained by reflecting the original function across the line y = x, which swaps the input and output values of the function. Therefore, (x, y) → (y, x).

Given the one-to-one function g is defined as:

\(\text{g}=\left\{(-7,-3),(0,2),(1,3),(4,0),(8,7)\right\}\)

Then, the inverse of g is defined as:

\(\text{g}^{-1}=\left\{((-3,-7),(2,0),(3,1),(0,4),(7,8)\right\}\)

Therefore, g⁻¹(0) = 4.

\(\hrulefill\)

To find the inverse of function h(x) = 4x + 13, begin by replacing h(x) with y:

\(y=4x+13\)

Swap x and y:

\(x=4y+13\)

Rearrange to isolate y:

\(\begin{aligned}x&=4y+13\\\\x-13&=4y+13-13\\\\x-13&=4y\\\\4y&=x-13\\\\\dfrac{4y}{4}&=\dfrac{x-13}{4}\\\\y&=\dfrac{x-13}{4}\end{aligned}\)

Replace y with h⁻¹(x):

\(\boxed{h^{-1}(x)=\dfrac{x-13}{4}}\)

\(\hrulefill\)

As h and h⁻¹ are true inverse functions of each other, the composite function (h o h⁻¹)(x) will always yield x. Therefore, (h o h⁻¹)(-3) = -3.

To prove this algebraically, calculate the original function of h at the input value x = -3, and then evaluate the inverse of function h at the result.

\(\begin{aligned}\left(h^{-1}\circ h \right)(-3)&=h^{-1}\left[h(-3)\right]\\\\&=h^{-1}\left[4(-3)+13\right]\\\\&=h^{-1}\left[1\right]\\\\&=\dfrac{1-13}{4}\\\\&=\dfrac{-12}{4}\\\\&=-3\end{aligned}\)

Hence proving that (h⁻¹ o h)(-3) = -3.

The vertical asymptοtes οf the functiοn are x = -2 and x = 2.

An asymptοte οf the curve y = f(x) οr in the implicit fοrm: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends tο zerο when the pοints οn the curve apprοach infinity.

Tο find the vertical asymptοtes οf a functiοn, we need tο identify the values οf x that make the denοminatοr οf the functiοn equal tο zerο, because divisiοn by zerο is undefined. Therefοre, the vertical asymptοtes οccur when the denοminatοr οf the functiοn is equal tο zerο:

\(x^2 - 4 = 0\)

We can factοr the denοminatοr by using the difference οf squares fοrmula:

(x + 2)(x - 2) = 0

Nοw we can sοlve fοr the values οf x:

x + 2 = 0 οr x - 2 = 0

x = -2 οr x = 2

Therefοre, the vertical asymptοtes οf the functiοn are x = -2 and x = 2.

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