Write out the form of the partial fraction decomposition of the function x3 x2 1 x(x 2 + x + l)(2 1)3 SOLUTION x3 +x2 +1 x(x 1(r2 + x + )(2)

Answer: B, non response bias, and sampling bias

Step-by-step explanation:

Non response bias is when there is a huge difference between people that responded or took part in the polls and people that didn't respond, since we are told the response rate was 24% and sampling bias because it is said that most people using telephones belong to the party of candidate A, so using a telephone poll makes the sampling biased

The incorrect prediction occurred due to non-response bias, where not all opinions were represented due to a low response rate, and sampling bias, where the sampling method resulted in an under-representation of the whole population.

In this election prediction scenario, two types of biases influenced the incorrect prediction. The first is a non-response bias. Only 24% of people responded to the poll which means the opinions of the remaining 76% of people are not represented in the survey results. This can cause a distortion in the data and result in an inaccurate prediction. Secondly, there was a sampling bias present. The poll was conducted via telephone directories, and at the time, most telephone households were supportive of Candidate A's party. This means that the sample frame does not accurately represent the target population, leading to an 'undercoverage' issue. As a result of these biases, the newspaper predicted that Candidate A would win, but in fact, Candidate B won with about 62% of the popular vote.

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Answer: A two-way table

Explanation:

A two-way table, also known as a contingency table, is used in statistics to present results of an investigation that contain two variables to analyze. The table shows the relationship between the two variables to be able to represent two sets of data under different categories.

The table is composed of two columns and two rows of data, and two columns of labels at the top, and two rows of labels on the left.

In this case, A two-way table would present the two variables to be analyzed; television violence, and domestic abuse.

I hope this information can help you.

In this exercise we have to use the knowledge of plots to write the correct alternative that best matches, thus we can say that:

Number 3

A two-way table exist one habit to display commonness for two different type calm from a single group of human beings. One classification is depicted for one rows and the other happen depicted by the line.

A two-way table, as known or named at another time or place a possibility table, happen secondhand in enumeration to present results of an thorough check that hold two variables to resolve. The table shows the connection middle from two points two together variables expected able to show two sets of information in visible form secondary various classification.

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Answer:

a.  -i.

Step-by-step explanation:

i^2 = -1 so

i^3 = i^2 * i

= -1 * i

= -i.

Answer:

Denominator

x = 12

Step-by-step explanation:

Let x be the denominator of the fraction at point y.

Given:

Point X is at 2/3 on a number line from 0.

On the same line, point y is the same point from 0.

Numerator of the fraction at point y is 8.

We need to find the denominator of the fraction at point y.

Solution:

From the above statement the distance from 0 to point X and 0 to point Y is same, so point X is equal to Y.

[tex]\frac{2}{3} =\frac{8}{x}[/tex]

By cross multiplication.

[tex]x=\frac{8\times 3}{2}[/tex]

[tex]x= \frac{24}{2}[/tex]

[tex]x = 12[/tex]

Therefore, the denominator of the fraction at point y is 12.

Answer:

[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line

Find the slope

we have

(0,0.2) and (3,2.2)

[tex]m=(2.2-0.2)/(3-0)=\frac{2}{3}[/tex]

The y intercept b is equal to

[tex]b=0.2=\frac{2}{10}=\frac{1}{5}[/tex]

so

the equation of the solid line  in slope intercept form is equal to

[tex]y=\frac{2}{3}x+\frac{1}{5}[/tex]

step 2

Find the equation of the inequality

we know that

The solution of the inequality is the shaded area below the solid line

therefore

[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]

Answer:

c,y>2/3x-1/5

Step-by-step explanation:

Answer:

  a) 22π cm/s; on the odd half-second (t=0.5, 1.5, 2.5, 3.5, 4.5); at the rest position; zero

  b) 22 cm from the rest position; zero

Step-by-step explanation:

Undamped simple harmonic motion is not complicated. Acceleration is a maximum where the applied force is a maximum, at the extremes of position. Since the position is extreme, the velocity is zero at those points. All of the energy is potential energy.

The speed is a maximum when the object is at the rest position, There is no applied force at that point, and no acceleration. All of the energy has been transformed to kinetic energy.

Part A:

The cart's velocity is given by the derivative of the position:

  s'(t) = -22π·sin(πt)

This has a maximum magnitude (speed) of 22π ≈ 69.1 cm/s, as you have noted.

The speed is a maximum at the rest position. The cart is there on each odd quarter-period, at t=0.5, 1.5, 2.5, 3.5, 4.5 seconds.

The cart's acceleration is given by the derivative of the velocity:

  s'' = -22π²·cos(πt)

On the odd quarter-period, the acceleration is zero.

Part B:

Acceleration is greatest when position is greatest (both are cosine functions). The speed of the cart is zero then (it is a sine function). The sine is at an extreme when the cosine is zero, and vice versa.

_____

The attached graph shows position, velocity, and acceleration (color coded).

To solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. This can be done by finding the derivative of the acceleration function and setting it equal to zero. The value of t that satisfies this equation can then be used to find the position and speed of the cart.

In order to solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. We can do this by finding the derivative of the acceleration function and setting it equal to zero. The derivative of the acceleration function is given by: a'(t) = -22πsin(πt). Setting this equal to zero gives: -22πsin(πt) = 0. Solving for t, we find that t = 1/2.

Now that we have the value of t, we can plug it back into the position function to find the position of the cart when the magnitude of the acceleration is greatest. The position function is given by: s(t) = 22cos(πt). Plugging in t = 1/2, we get: s(1/2) = 22cos(π/2) = 0.

To find the cart's speed when the magnitude of the acceleration is greatest, we can plug t = 1/2 into the velocity function. The velocity function is the derivative of the position function, which is given by: v(t) = -22πsin(πt). Plugging in t = 1/2, we get: v(1/2) = -22πsin(π/2) = 22π.

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Answer:

Trisha made 2 pans of brownies.

Step-by-step explanation:

Let the number of pans of brownies made by Trisha be 'x'.

Given:

Number of pans contributed by Rachel = 5

Number of squares in each pan = 12

Total number of squares (S) = 84

Total number of pans (N) = Number of pans by Trisha (x) + Number of pans by Rachel

So, [tex]N=x+5[/tex] -------- (1)

Total number of squares (S) = Number of squares in each pan × Number of pans (N).

[tex]S = 12N\\84=12N---- (2)[/tex]

Plug in the value of 'N' from equation (1) in equation (2). This gives,

[tex]84=12(x+5)[/tex]

Solve for 'x'.

[tex]12(x+5)=84\\\\x+5=\frac{84}{12}\\\\x+5=7\\\\x=7-5=2[/tex]

Therefore, Trisha made 2 pans of brownies.

Answer:

slope is 5

Step-by-step explanation:

the slope represents the cost of the kayak for as many hours as the person rents it for. the y intersect is 20 because that is the cost just to rent the boat before using it.

Answer:

Water level in the reservoir is falling at the rate of 0.398 ft per minute.

Step-by-step explanation:

From the figure attached,

Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.

Let the level of water in the reservoir after time t is h where radius of the water level becomes r.

ΔABE and ΔCDE are similar.

Therefore, their corresponding sides will be in the same ratio.

[tex]\frac{r}{h}=\frac{4}{10}[/tex]

[tex]r=\frac{2}{5}h[/tex] --------(1)

Now volume of the water V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

From equation (1),

V = [tex]\frac{1}{3}\pi (\frac{2}{5}h)^{2} h[/tex]

V = [tex]\frac{4\pi h^{2}\times h}{75}[/tex]

[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})[/tex]

[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}[/tex]

[tex]\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}[/tex]

Since [tex]\frac{dV}{dt}=5[/tex] feet³ per minute and h = 5 feet

[tex]5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}[/tex]

[tex]5=4\pi \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}=\frac{5}{4\pi}[/tex]

[tex]\frac{dh}{dt}=0.398[/tex] feet per minute

Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.

Answer: Cluster Sampling

Step-by-step explanation:

In cluster sampling, researcher divides the population into groups ,which are called clusters. Then random sample of clusters are chosen ,and researcher conduct study to collect data about the population.

Here each bus is considered a cluster ,because busses are selected at random ,this sampling would be an example of cluster type of sampling.

Answer:

Step-by-step explanation:

mean=(5.9+5.7+5.5+5.4+5.7+5.5+5.6+6.2+6.1+5.5)/10=57.1/10=5.71

we assume mean=5.7

x    mean  |x-mean| (x-mean)^2

5.9   5.7      0.2         0.04

5.7   5.7         0            0

5.5   5.7      0.2         0.04

5.4   5.7      0.3         0.09

5.7   5.7         0             0

5.5   5.7      0.2         0.04

5.6   5.7      0.1          0.01

6.2   5.7      0.5         0.25

6.1    5.7      0.4         0.16

5.5   5.7      0.2         0.04

                                --------

                                0.63

standard deviation=√((0.63)/10)=√(0.063)≈0.251

so c

Final answer:

By finding the range of the office workers' heights and applying the range rule of thumb (estimating the standard deviation as approximately one-fourth the range), the calculated standard deviation is rounded to 0.2 feet, matching answer choice (c).

Explanation:

To estimate the standard deviation of the office workers' heights using the range rule of thumb, we first find the range, which is the difference between the maximum and minimum values in the data set. The maximum height is 6.2 feet and the minimum is 5.4 feet, so the range is 6.2 - 5.4 = 0.8 feet.

The range rule of thumb states that the standard deviation can be estimated as approximately one-fourth of the range. Therefore, the estimated standard deviation is 0.8 / 4 = 0.2 feet. When rounded to the nearest tenth, the standard deviation is 0.2 feet, which corresponds to answer choice (c).

Answer: 197,443,926,105,102,399,225,573,693

Step-by-step explanation:

Here we use combination which is the selection of all or part of a set of objects or items without considering the order of selection.

Mathematically, The number of 'r' combinations from 'n' elements is given as :

nCr = n!÷((n-r)!r!)

From the question above :

n=99 r=66

99C66 = 99!÷((99-66)!66!)

99!÷(33!66!) = 197,443,926,105,102,399,225,573,693

There are 197,443,926,105,102,399,225,573,693 different possible routes.

Answer: 19 paddle boards were rented.

Step-by-step explanation:

Let x represent the number of surfboards that were rented.

Let y represent the number of paddleboards that were rented.

A total of 44 surfboards and paddleboards were rented. It means that

x + y = 44

For a two day rental at the surf shop, it cost $45 to rent a surfboard and $60 to rent a paddleboard.

The total cost of surfboards and paddleboards rented was $2265. This means that

45x + 60y = 2265 - - - - - - - - - 1

Substituting x = 44 - y into equation 1, it becomes

45(44 - y) + 60y = 2265

1980 - 45y + 60y = 2265

- 45y + 60y = 2265 - 1980

15y = 285

y = 285/15 = 19

x = 44 - y = 44 - 19

x = 25

Answer:Marcel flew 4060 miles for Valentine's Day.

Step-by-step explanation:

For Christmas, Marcel flew 6090 miles from New York to Japan.

For Valentine's Day, Marcel flew from New York to England. The distance from New York to England's is 2/3 of the distance from New York to Japan. This means that the number of miles that Marcel flew for Valentine's Day would be

2/3 × 6090 = 4060 miles

Final answer:

To determine the distance from New York to England, one must multiply the distance from New York to Japan (6090 miles) by 2/3, resulting in 4060 miles. This represents the distance Marcel flew for Valentine's Day.

Explanation:

Marcel's vacation air travel distances involve a mathematical proportion problem. Marcel flew 6090 miles from New York to Japan for Christmas. The question states that the distance from New York to England is 2/3 of the distance from New York to Japan. To find the distance flown for Valentine's Day from New York to England, we multiply the distance from New York to Japan by 2/3.

So, the calculation is: 6090 miles × (2/3). When we perform this multiplication, we find that Marcel flew 4060 miles from New York to England for Valentine's Day.

Answer:

The answer to your question is 2i

Step-by-step explanation:

                                             [tex]\sqrt[4]{-16}[/tex]

- Get the prime factors of -16

                                                  - 16   2

                                                   -  8  2

                                                   -  4  2

                                                   -  2  2

                                                       1

                                   16 = 2⁴

- Express the -16 as a power

                          [tex]\sqrt[4]{-2^{4}}  or   \sqrt[4]{2^{4}i^{2}}[/tex]

Remember that -1 = i²

- Get the fourth root of -16

                                         2i

Answer: 0.1064

Step-by-step explanation:

D= Both Alzheimer's are less than 80years old.

E= Two of 3 people who have Alzheimer's.

P(D | E ) = P ( D ∩ E)

P ( E )

= P ( A ∩ B ∩ C )

P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C )

= Pa * Pb * (1 - Pc ) Pa * Pb * (1 - Pc ) + (1 - Pa ) * Pb * Pc + Pa * (1 - Pb ) * Pc

= 0.0017

=0.0010+0.0017+0.0037

=0.1064

The conditional probability that two individuals with Alzheimer's are both under 80 cannot be precisely calculated without more information about the general probabilities of each condition. However, the general formula for calculating conditional probability is P(A and B) = P(A) * P(B|A).

This is essentially a question about conditional probability. In order to calculate the conditional probability suggested by the question – that is, the probability that both individuals with Alzheimer's disease are younger than 80, given that we know that two people have the disease – we'd need more information about the overall probabilities of having Alzheimer's disease and being under 80. However, if we had this information the formula for conditional probability is P(A and B) = P(A) * P(B|A). In this equation, P(A) would be the probability that a randomly selected individual has Alzheimer's, P(B|A) would be the probability that a known Alzheimer's patient is under 80, and P(A and B) is the conditional probability we're trying to figure out. So, we'd need to multiply P(A) by P(B|A) to get P(A and B)

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The percentage of correct answers out of the total question is 25%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

The number of incorrect questions = is 42

The number of Correct questions = 14

So, the total number of questions is,

42 + 14 = 56

Let the percentage of correct questions be x.

x = 14/56 × 100

x = 1400/56

x = 25%  

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ANSWER:

Carl could divide the circle into a larger even number of congruent sectors. Then each sector would be smaller, and the approximation of the circle’s area will be closer to the actual area of the circle.

STEP BY STEP EXPLANATION :

Area of a Circle by Cutting into Sectors:

1. Cut a circle into equal sectors and the more we divided the circle up, the closer we get to being exactly right.

2.Rearrange the sectors, which resembles a parallelogram.

What are the (approximate) height and width of the parallelogram?

The height is the circle's radius.

The width (actually one "bumpy" edge) is half of the curved parts around the circle. In other words it is about half the circumference of the circle.

We know that:

Circumference = 2 × π × radius

And so the width is about:

Half the Circumference = π × radius

ow we just multply the width by the height to find the area of the rectangle:

Area = (π × radius) × (radius)

= π × radius2

Conclusion

Area of Circle = π r2

Answer:

1. 20-15/0-8= -5/8

2. In a positive slope the Y value increases as the X value increases (as the line moves towards the right it gets higher). In a negative slope the Y value decreases as the X value increases (as the line moves towards the right it gets lower). (Question 3 is in here)

4. It depends on the amount of time she's been driving

Answer:

8.4 cm

Step-by-step explanation:

The longest side of an acute isosceles triangle is 12 centimeters.

Let x be the length of the smallest side

Isosceles triangle has one longest side and two smallest sides

so its acute triangle

[tex]c^2<a^2 +b^2[/tex]

where c is the longest side

a  and b are two shortest sides 'x'

[tex]c^2<x^2 +x^2[/tex]

[tex]12^2<x^2 +x^2[/tex]

[tex]144<2x^2[/tex]

divide both sides by 2

[tex]72<x^2[/tex]take square root on both sides

[tex]8.4<x[/tex]

So 8.4 cm

Answer:

a) (n²-n+m²-m)÷((n+m)×(n+m-1))

b)(n²+m²)÷(n+m)

c) part b is larger ,check below.

Step-by-step explanation:

a)If there are n white and m black balls ,total will be n+m balls. Let's find the probability of choosing two balls white.

First ball as white n÷(n+m)  second ball to be white again is n-1÷(n+m-1) the reason why we take away 1 is because we already chose one white ball in the beginning .So the probability will be product of these to get the both balls white.

Let's find the the probability of choosing both black.Same strategy ,first ball black  is m÷(n+m),second ball black is m-1÷(n+m-1).So the probability will be product of these to get the both balls black. We should add the final products and simplify

b)Because this time they are replacing the ball ,we will not take away 1.So to get both white probability is n÷(n+m) times n÷(n+m) .The probability of both black is m÷(n+m) times m÷(n+m).Add the products .

c) b will be always larger,We should compare the final products.

In b  (n²+m²) is divided by (n+m)

In a (n²-n+m²-m)÷((n+m)×(n+m-1))  less amount divided by a bigger value ,so it will result always with a smaller quotient

Answer: y = 12x + 50

Step-by-step explanation:

Let y represent the cost of having the party.

Let x represent the number of people who would attend the party.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given

y2 = 590

y1 = 290

x2 = 45

x1 = 20

Slope,m = (590 - 290)/(45 - 20) = 300/25 = 12

To determine the intercept, we would substitute x = 20, y = 290 and m= 12 into y = mx + c. It becomes

290 = 12 × 20 + c = 240 + c

c = 290 - 240 = 50

The equation becomes

y = 12x + 50

Answer:

h=2A/b

Step-by-step explanation:

A=1/2bh

Isolate h by moving 1/2 and b to the other side of the equation.

Divide each side by 1/2,which is multiplying by 2, which gives you 2A=bh.Now divide each side by b, which gives you 2A/b=h. Turn it around.

2A/b=h becomes h=2A/b

Answer:

h=2A/b

Step-by-step explanation:

The perimeter of Kayla's garden including the walkway can be calculated using the formula P = 2(4 + 2w) + 2(3 + 2w), where w is the width of the walkway. This can also be rearranged as P = 2*(4 + 3 + 2w + 2w).

The perimeter of a rectangle, like the garden in question, is usually calculated by adding up the lengths of all its sides. In this case, however, the garden is bordered by a walkway of width w. Thus, to calculate the total perimeter, including the walkway, we need to account for this additional width on all four sides of the garden.

The original dimensions of the garden are 4 feet by 3 feet. With the walkway, the new dimensions become (4+2w) feet by (3+2w) feet, because the width of the walkway is added on both sides of the lengths.

Therefore, the two equivalent expressions for the perimeter, P, of Kayla's garden, including the walkway, are P = 2(4 + 2w) + 2(3 + 2w) or simply rearranged as P = 2*(4 + 3 + 2w + 2w). In these expressions, w is the width of the walkway.

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Answer:

  x = π

Step-by-step explanation:

The circumference of the circle is given by ...

  C = 2πr = 2π(2) = 4π

The perimeter of a square of side length x is given by ...

  P = 4x

You want the perimeter equal to the circumference, so ...

  4π = 4x

  π = x . . . . . . . divide by 4

The value of x is π.

The side length x of the square is the same as the radius of the circle, which is π units, because the perimeter of the square, 4x units, is set equal to the circumference of the circle, 4π units.

It is asked to determine the side length x of a square when its perimeter is equal to the circumference of a circle with radius 2 units.

To find the perimeter of a square, you multiply the side length by 4, since a square has four equal sides. Thus, the perimeter of the square is 4x units.

The formula for the circumference of a circle is [tex]C = 2\pi r,[/tex] where r is the radius of the circle.

Given that the radius is 2 units, the circumference of the circle would be [tex]2\pi (2) = 4\pi[/tex]units.

By setting the two equal to each other:

[tex]4x = 4\pi[/tex]

Divide both sides by 4 to isolate x:

[tex]x = \pi[/tex]

Therefore, the side length x of the square is π units.

Answer:

$111

Step-by-step explanation:

37x3 = 111

111/3 =37

The total restaurant bill that Joan, Melanie, and Sam paid, multiply the amount each person paid ($37) by the number of people (3), resulting in a total of $111.

Joan, Melanie, and Sam have decided to divide the restaurant bill evenly. If each person paid $37, we can determine the total bill by multiplying the amount each person paid by the number of people. Since there are three people, we calculate the total as follows:

Identify the amount each person paid: $37.

Count the number of people: 3 (Joan, Melanie, and Sam).

Multiply the amount paid by each person by the total number of people: $37 x 3 = $111.

Therefore, The total bill at the restaurant was $111.

Answer:

24

Step-by-step explanation:

The can will hold 75.36 inch³ of soup.

The volume of a cylinder with base radius 'r' and height 'h' is,

V = πr²h. If its base diameter is d, then we have d = r/2.

Given:

Radius = 2 inches

Height = 6 inches

So, Volume of Cylinder = πr²h

Now, put r= 2 inches and h= 6 inches

Then, Volume of cylinder = 3.14 x 2 x 2 x 6

Volume of Cylinder = 3.14 x 24

Volume of Cylinder = 75.6 inch³

Hence, the can hold 75.36 inch³.

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Answer:

[tex]\displaystyle g(x) = 2^{x - 3}[/tex]

Explanation:

See above graph

The exponent gives you the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL.

I am joyous to assist you anytime.

Answer:

[tex]a=29000 -1.28*2400=25928[/tex]

Tires that wear out by 25928 miles will be replaces free of charge

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(29000,2400)[/tex]  

Where [tex]\mu=29000[/tex] and [tex]\sigma=2400[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

He wants to give a guarantee for free replacement of tires that don't wear weel so then we need to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

Because we are interested in the lower tail.

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(z>-1.28)=0.90

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.1[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.1[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-1.28=<\frac{a-29000}{2400}[/tex]

And if we solve for a we got

[tex]a=29000 -1.28*2400=25928[/tex]

So the value of height that separates the bottom 10% of data from the top 90% is 25928 mi.  

Tires that wear out by 25928 miles will be replaces free of charge

Answer:

The first graph

Step-by-step explanation:

From the definition of [tex]h[/tex] we can see that:

                                 [tex]h(2)=-3\cdot 2+2 = -6+2=-4[/tex]

So, we can eliminate the third answer.

Now we can take for example [tex]x=4[/tex]:

From the definition of [tex]h[/tex] we can see that:

                                   [tex]h(4)=\frac{1}{2}\cdot 4-4 = 2-4=-2[/tex]

If we take a look at the two remanining graphs we can see that at the first graph indeed it is h(4)=-2,and on the second graph it is h(4)=-6

So, the correct answer is the first graph