For each of the following, find the formula for an
exponential function that passes through the two points
given.
a. (-1,2) and (4,64)
f(x)=?
b. (-3,9) and (2,1)
g(x)=?

we can reject the null hypothesis

Null Hypothesis (H₀): μ ≥ 50

Alternative Hypothesis (H₁): μ < 50

Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05

Critical-value approach:

First, calculate the test statistic using the formula:

Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

= (41.3 - 50) / (12.2 / √20)

= -2.6

Then, compare this test statistic to the critical-value.

The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.

Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.

p-value approach:

Calculate the p-value using the formula:

p-value = 1 - CDF(test statistic)

Where CDF is the cumulative distribution function.

= 1 - CDF(-2.6)

= 0.004

Since 0.004 is less than 0.05, we reject the null hypothesis.

In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.

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1.3567% is the average percent change in population in California from 2000-2009.

The term "population" is frequently used to describe the total number of people living in a particular location. To estimate the number of the residents within a certain territory, governments conduct censuses.

Population is referred to a group of people who share some established characteristics, such as region, race, culture, nationality, or religion, in sociology or population geography. The social science of demography involves the statistical analysis of populations.

average percent change in population =1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9

= 1.3567%

Therefore, 1.3567% is the average percent change in population in California from 2000-2009.

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The supremum of the first subset does not exist, and the supremum of the second subset is 1.

The supremum of a subset of a set is the smallest element in the set that is greater than or equal to all elements in the subset. In other words, it is the least upper bound of the subset.

For the first subset {x^2+11 : x∈R}, the supremum does not exist. This is because the function x^2+11 is always increasing as x increases, so there is no smallest element that is greater than or equal to all elements in the subset.

For the second subset {cosx : x∈R}, the supremum is 1. This is because the cosine function has a range of [-1, 1], meaning that the largest value it can take on is 1. Therefore, the smallest element in the set R that is greater than or equal to all elements in the subset {cosx : x∈R} is 1.

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The probability that a person from the survey who has a tablet also has a laptop is 5.8%.

To calculate this, we can use conditional probability. We know that 62% of respondents have a tablet, and 12% of the respondents who have a laptop also have a tablet. So, the probability that a respondent has a laptop given that they have a tablet can be calculated as follows:

We know that P(laptop and tablet) = 0.12 (since 12% of laptop owners also have a tablet), and P(table) = 0.62 (since 62% of respondents have a tablet). So, plugging these values into the formula gives:

However, this is the probability that a person who has a tablet also has a laptop. The question asks for the probability that a person from the survey who has a tablet also has a laptop, which means we need to consider the overall probability of having a laptop, regardless of whether or not they have a tablet. This can be calculated as follows:

P(laptop) = 0.3

So, the probability that a person from the survey who has a tablet also has a laptop, given that they have a laptop, is:

P(laptop|tablet and laptop) = P(laptop and tablet) / P(laptop) = 0.12 / 0.3 = 0.4 or 5.8%

Therefore, the correct answer is 5.8%.

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The value of the missing side of the triangles are;

1. 10in

2. 12 mi

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the square of the other two sides.

This is written as;

a² = b² + c²

For the first triangle, we have that;

a² = 6² + 8²

find the squares

a² = 36 + 64

Add the values

a² = 100

Find the square root

a = 10in

For the second triangle

x² = 13² - 5²

find the squares

x² = 169 - 25

Subtract the values

x² = 144

Find the square root

x = 12 mi

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Answer:

9/10

Step-by-step explanation:

Find a common denominator

4/5 × 2 = 8/10

8/10 + 1/10 = 9/10

Hey there!

4/5 + 1/10

= 4 × 2 / 5 × 2 + 1/10

= 8/10 + 1/10

= 8 + 1 / 10 + 0

= 9/10

Therefore, your answer should be:

9/10

Good luck on your assignment \& enjoy your day!

~Amphitrite1040:)

Yolanda can rent his boat for upto 6hrs and spend his money correctly.This can be solved by inequalities.

What is discount?

The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price.

let's think about how to set up inequality.

Amount Spent ≤ 39

we have to find what the amount spent is.

It would be $7 times the number of hours he rents the boat for (X), minus $3. So the equation will be:

                               7X - 3 ≤ 39

By solving   this:           7X ≤ 42

                                      X ≤ 6

So, Yolanda can rent the boat for up to 6 hours to spend at most $39.

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Answer:9

Step-by-step explanation:

6/2(1+2)

3(1+2)

3(1)+3(2)

3+6

9

Answer:

9

Step-by-step explanation:

brackets will get a priority and will be solved at first

6 / 2 ( 1 + 2)

6 / 2 (3)

18 / 2

9

let's convert all mixed fractions to improper fractions, let's add all berries and then see how many times 1/2 go into that sum or namely division.

[tex]\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} ~\hfill \stackrel{mixed}{4\frac{1}{2}} \implies \cfrac{4\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ strawberries }{\cfrac{13}{4}}~~ + ~~\stackrel{ blueberries }{\cfrac{9}{2}}\implies \cfrac{(1)13~~ + ~~(2)9}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{13+18}{4}\implies \cfrac{31}{4} \\\\\\ \stackrel{\textit{now let's divide that sum by }\frac{1}{2}}{\cfrac{31}{4}\div \cfrac{1}{2}}\implies \cfrac{31}{4}\cdot \cfrac{2}{1}\implies \cfrac{31}{2}\implies {\Large \begin{array}{llll} 15\frac{1}{2} \end{array}}[/tex]

Answer:

C(4) is less

Step-by-step explanation:

Let C(x) represent Rule C and let D(x) represent Rule D.

C(x) = 10x + 15

D(x) = 80x

C(4) = 10(4) + 15 = 40 + 15 = 55

D(4) = 80(4) = 320

Thus, C(4) is less.

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The solution to the equation [tex](x+2)^{(1)/(2)}=x-4[/tex] is x = 2.

To solve this equation, we need to square both sides to eliminate the radical. This gives us [tex]x+2 = (x-4)^2[/tex]. Expanding the right side of the equation and simplifying, we get [tex]x^2 - 11x + 20 = 0[/tex]. Factoring this quadratic equation, we get [tex](x-1)(x-20) = 0[/tex], so the solutions are x=1 and x=20.

However, we must check if these solutions are extraneous, meaning they do not satisfy the original equation. Checking x=1, we get [tex](1+2)^{(1)/(2)}=1-4[/tex], which simplifies to [tex]3^{(1)/(2)}=-3[/tex], a contradiction since the square root of a positive number cannot be negative. Therefore, x=1 is an extraneous solution.

Checking x=20, we get [tex](20+2)^{(1)/(2)}=20-4[/tex], which simplifies to [tex]22^{(1)/(2)}=16[/tex], or [tex]22 = 16^2[/tex], which is true. Therefore, x=20 is a valid solution.

In conclusion, the only solution to the equation is x=2, and the solution x=1 is extraneous.

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The midpoint is   [(Yx + Fx)/2, (Yy + Fy)/2]

The distance between 2 points in the map is √[(FVx - CSx)^2 + (FVy - CSy)^2]

To determine the distance between two points on a map, we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]

In this case, we are trying to find the distance between Clear Springs (x1, y1) and Finger Valley (x2, y2). Plug in the coordinates for each point into the formula and solve for d.
d = √[(x2 - x1)^2 + (y2 - y1)^2]

= √[(Finger Valley x - Clear Springs x)^2 + (Finger Valley y - Clear Springs y)^2]
= √[(FVx - CSx)^2 + (FVy - CSy)^2]
Round the answer to one decimal place to get the distance between the two points.

To find the coordinates of the meeting point between you and your friends, we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

In this case, we are trying to find the midpoint between your location (x1, y1) and your friends' location (x2, y2). Plug in the coordinates for each point into the formula and solve for the midpoint.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
= [(Your x + Friends' x)/2, (Your y + Friends' y)/2]
= [(Yx + Fx)/2, (Yy + Fy)/2]
Round the coordinates to one decimal place to get the midpoint, which is the meeting point between you and your friends.'

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The  answer is b^((-3)/(8))*a^(-1)

The expression (b^((3)/(2))*a^(4))^(-(1)/(4)) can be simplified by using the properties of exponents. First, we can distribute the exponent -(1/4) to each of the terms inside the parenthesis:

b^((3)/(2))^(-(1)/(4))*a^(4)^(-(1)/(4))

Next, we can simplify the exponents by multiplying them:

b^((-3)/(8))*a^((-4)/(4))

Finally, we can simplify the exponents further:

b^((-3)/(8))*a^(-1)

So, the final answer is b^((-3)/(8))*a^(-1). This is the simplified form of the expression without any assumptions about the values of the variables.

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Accοrding tο similarity οf triangles, the length οf CF is 8/3.

Similarity οf triangles is a cοncept in geοmetry that describes the relatiοnship between twο triangles that have the same shape but may be different in size. Twο triangles are cοnsidered similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.

Since FG is parallel tο CD, we can use similar triangles tο find the length οf CF. Let's call the length οf CF x. Then we have:

FE/FG = CD/CF

Substituting the given values, we have:

5/(x-1) = 8/x

Crοss-multiplying, we get:

5x = 8(x-1)

Expanding the brackets, we get:

5x = 8x - 8

Subtracting 5x frοm bοth sides, we get:

3x = 8

Dividing bοth sides by 3, we get:

x = 8/3

Therefοre, the length οf CF is 8/3.

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Complete question:

Answer:

3

Step-by-step explanation:

7.2<x+4.2

3<x
x>3
the graph would be

The repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.

The product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.xxxx. To find x, we can multiply the two decimals together.

First, let's convert the repeating decimals to fractions:

0.3333 = 1/3

0.6666 = 2/3

Now, we can multiply the two fractions together:

(1/3) * (2/3) = 2/9

To convert the fraction back to a decimal, we can divide 2 by 9:

2/9 = 0.2222

So, the repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.

Therefore, the product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.2222.

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When a power is raised to an exponent, the power is multiplied by the exponent twice. Applying this rule to the given expression, we are able to simplify it down to a single value: 1.

To simplify the expression, we use the property of exponents that states that the exponent of a power to a power is equal to the product of the two exponents. Applying this to our expression, we get:

((y-3)-6y-3) / (y-6)-1 = (y(-3)×(-6)y-3) / (y(-6)×(-1))

Simplifying, we get: y18 / y6 = y12

In summary, when a power is raised to an exponent, the power is multiplied by the exponent twice. Applying this rule to the given expression, we are able to simplify it down to a single value: 1.

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Answer:

Yes

Step-by-step explanation:

The congruent triangles are given as follows:

DEC and BEA.

Congruent triangles are two or more triangles that have the same size and shape. More specifically, two triangles are said to be congruent if all three corresponding sides and all three corresponding angles are equal in measure.

When two triangles are congruent, it means that one can be superimposed exactly onto the other by rotating, reflecting, or translating.

In the context of this problem, we have that triangle BEA is constructed rotating triangle DEC over vertex A, hence the two triangles are congruent.

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The name of the formula is a polynomial of degree 25 and is expressed as y = ax25 + bx24 + cx23 + dx22 + ex21 + fx20 + gx19 + hx18 + ix17 + jx16 + kx15 + lx14 + mx13 + nx12 + ox11 + px10 + qx9 + rx8 + sx7 + tx6 + ux5 + vx4 + wx3 + xx2 + yx + z

The formula you have provided is called a polynomial equation. It is a type of algebraic equation that consists of a sum of several terms, each term consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. In this case, the variable is x and the coefficients are a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z. The highest power of the variable in this equation is 25, which means it is a 25th degree polynomial equation.

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Answer:

Step-by-step explanation:

Ratio of corresponding sides are equal.

[tex]\tt \cfrac{BD}{FD} =\cfrac{AC}{EC}[/tex]

[tex]\tt \cfrac{BC}{30} =\cfrac{16}{40}[/tex]

[tex]\tt BD=30\left(\frac{2}{5}\right)[/tex]

[tex]\tt BC=6\cdot \:2[/tex]

[tex]\tt BD =12[/tex]

Therefore, the length of BD is 12.

___________________________

Hope this helps! :)

(a) (i) The function f(x) - g(x) is  √(1-x).

    (ii) The function f(x) - g(x) is -x -1   The domain for f-g is all real numbers.
(b) (i) The function  (f-g)(1) = -2

    (ii) The function (f-g)(2) = √(-1). Therefore, (1/2)g(f(2)) is undefined.

(a)

(i) The function f(x) is already given as f(x) = √(1-x). The domain of f is all real numbers for which 1-x is non-negative. Therefore, the domain of f is x ≤ 1.

(ii) The function f-g can be found by subtracting g from f, which gives: f-g = (V1 - x) - (2 + x) = -x - 1. The domain of f-g is the same as the domain of f, which is x ≤ 1.

(b)

(i) To evaluate (f-g)(1), we substitute x = 1 into the expression for f-g, which gives: (f-g)(1) = -(1) - 1 = -2.

(ii) To evaluate (1/2)g(f(2)), we first find f(2) by substituting x = 2 into the expression for f: f(2) = √(1-2) = √(-1). Since the square root of a negative number is not a real number, f(2) is undefined. Therefore, (1/2)g(f(2)) is also undefined.

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The greatest number is 3,600, since it is larger than all the other numbers when expressed in standard notation. Option D is correct.

Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format using powers of ten. In scientific notation, a number is expressed as the product of a coefficient and a power of ten. The coefficient is a number between 1 and 10, and the power of ten indicates how many places the decimal point should be moved.

Standard notation, also known as decimal notation, is a way of expressing numbers using a sequence of digits, where each digit represents a different power of ten. In standard notation, the digits to the left of the decimal point represent the whole part of the number, and the digits to the right of the decimal point represent the fractional part of the number.

To compare these numbers, we need to express them in the same units. We can do this by converting the numbers in scientific notation to standard notation: 2.3 x 10 = 23,

8.6 x 10 = 86

1.2 x 10 = 12

3,600 = 3,600

Hence, D. 3,600 is the correct option.

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Answer:

Okay this is the bi-modal distribution histogram

Answer:

Step-by-step explanation:

4.  16 players enter the tournament.  f(0) = 16(1/2)° = 16

This is the value of y when x=0

5.  After 4 rounds, 1 player is left.  f(4) = 16(1/2)⁴ = 1

6.  Rate of change = Δy/Δx = (4-8) / (2-1) = -4

f(1) = 16(1/2)¹ = 8

f(2) = 16(1/2)² = 4

The average rate of change between rounds 1 and 2 is 4, meaning 4 players are eliminated.

The second column of matrix B can be calculated by solving the equation where A and B are matrices of size (2,3). The second column of B is
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

First, we must transpose both A and B:
[tex]A^t[/tex]= [tex][a_11, a_12, a_13][a_21, a_22, a_23][/tex]

[tex]B^t[/tex] = [tex][b_11, b_21][b_12, b_22][b_13, b_23][/tex]
The second column of B.

[tex]B^tA^t[/tex] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
[1, -2] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]


Since we have two equations and two unknowns, we can solve for the elements of the second column of B.
Solving for [tex]b_21[/tex]:
[tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Solving for [tex]b_22[/tex]:
[tex]-2 = a_11b_12 + a_12b_22 + a_13b_32b_22 = (-2 - a_11b_12 - a_13b_32)/a_12[/tex]

Therefore, the second column of B is:
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

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The rate of change of the radius when the height of the cylinder is 8 feet and the volume is 583 cubic feet is approximately 1.854 feet per second.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as;

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

dh/dt = -4 ft/s and dV/dt = 476 ft^3/s. We need to find dr/dt when h = 8 ft and V = 583 ft^3.

Now,

We can start by differentiating the volume formula with respect to time t, using the product rule:

dV/dt = d/dt (πr^2h)

= πh d/dt (r^2) + πr^2 d/dt (h)

= 2πrh (dr/dt) + πr^2 (dh/dt)

We can use the given values of h and V to find the value of r using the formula for the volume of a cylinder:

V = πr^2h

583 = πr^2(8)

r^2 = 583/(8π)

r ≈ 3.031

Now we can substitute the values we have into the formula for dV/dt and solve for dr/dt:

476 = 2π(8)(3.031)(dr/dt) + π(3.031)^2(-4)

dr/dt = (476 + 36π(3.031)^2) / (16π(3.031))

dr/dt ≈ 1.854

Therefore, by the given volume the answer will be 1.854 feet per second.

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If today it was sunny in the morning and raining in the afternoon, and Laura traveled a total of 24 km in 40 minutes, then she is calculated to have rode the electric scooter for  24 minutes in the afternoon.

Let's assume that Laura rode her scooter for x minutes in the morning and for (40 - x) minutes in the afternoon.

In the morning, she traveled a distance of 45 × (x/60) km.

In the afternoon, she traveled a distance of 30 × ((40-x)/60) km.

The total distance traveled is 24 km, so we can set up the equation:

45 × (x/60) + 30 × ((40-x)/60) = 24

Multiplying both sides by 60, we get:

45x + 30(40-x) = 1440

Simplifying and solving for x, we get:

15x + 1200 = 1440

15x = 240

x = 16

Therefore, Laura rode her scooter for (40-16) = 24 minutes in the afternoon.

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The question is :

Laura rides an electric scooter at 45 km/h when it is not raining and at 30 km/h when it is raining. Today it was sunny in the morning and raining in the afternoon, and she traveled a total of 24 km in 40 minutes. How many minutes did she ride in the afternoon?

The value of the height function h(-2) is 0.

The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1

To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1

Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2

The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:

For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0

For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1

To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1

Since h1'(0) is negative, h1 has a local maximum at u=0.

The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0

Therefore, the value of the height function h(-2) is 0.

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To find all zeros for the function f(x) = x3 - 12x? - 13x + 24.

To find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros.

The Rational Root Theorem states that if a polynomial f(x) = anxn + an-1xn-1 + ... + a1x + a0 has integer coefficients, then any rational zero of f(x) must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

In this case, the constant term is 24 and the leading coefficient is 1. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 1 are 1. Therefore, the possible rational zeros are:

±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±8/1, ±12/1, ±24/1

Simplifying these fractions gives us the list of possible rational zeros:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Now, we can use synthetic division to test each of these possible zeros until we find one that gives us a remainder of 0. Once we find a zero, we can factor it out of the polynomial and continue the process with the remaining polynomial until we have found all the zeros.

For example, if we test the possible zero 2, we get:

2 | 1 -12 -13 24
| 2 -20 -66
-----------------
1 -10 -33 -42

Since the remainder is not 0, 2 is not a zero of the function. We can continue testing the other possible zeros until we find all the zeros of the function.

Once we have found all the zeros, we can write them as a list. For example, if the zeros are 3, -2, and 4, we would write:

The zeros of the function are 3, -2, and 4.

Therefore, to find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros, and then use synthetic division to test each possible zero until we find all the zeros of the function.

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