1
(Lesson 8.2) Which statement about the graph of the rational function given is true? (1/2 point)
4. f(x) = 3*-7
x+2
A. The graph has no asymptotes.
B.
The graph has a vertical asymptote at x = -2.
C. The graph has a horizontal asymptote at y =
+

Yes, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.

The slope ratio is the ratio of the vertical rise to the horizontal run of the ramp, and it is equivalent to the tangent of the angle of inclination of the ramp.

The tangent of 4.8 degrees is approximately 0.0084, which means that for every 1 unit of vertical rise, there is 0.0084 units of horizontal run. To convert this to a ratio, we can multiply both sides by 100 to get:

1 unit of rise : 100 x 0.0084 = 0.84 units of run

Simplifying this ratio by dividing both sides by 0.84, we get:

1 unit of rise : 1.19 units of run

which is equivalent to a slope ratio of 1:12 (since 12 = 1/0.084). Therefore, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.

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For a random sample of 155 observations results in 62 successes.

a) A 90% confidence interval for the population proportion of successes is equals to the (0.335 , 0.465).

b) A 90% confidence interval for the population proportion of failure is equals to the (0.535 , 0.665).

We have a random sample of 155 observations results in 62 successes. So,

Observed value, x = 62

Sample size,n = 155

Population Proportion, p = x/n

= 62/155

= 0.4

a) We have to determine 90% confidence interval for the population proportion of successes. Using the distribution table, for 90% confidence interval, z-score value is equals to 1.6. Consider Confidence interval formula with proportion, CI [tex]= p ± z×\sqrt\frac{p(1-p)}{n}[/tex]

substitute all known values in above formula, [tex]= 0.4 ± 1.64\sqrt\frac{0.4(1- 0.4)}{155}[/tex]

= 0.4 ± 0.0645

= (0.4 - 0.0645 , 0.4 + 0.0645)

= (0.335 , 0.465)

b) Now, we have to determine a 90% confidence interval for the population proportion of failures.

Now consider, here failure observed values, x = 155 - 62

= 93

proportion, p = x/n

= 93/155 = 0.6

Consider the confidence interval formula, CI [tex]= p ± z×\sqrt\frac{p(1-p)}{n}[/tex]

substitute values, [tex]= 0.6 ±1.64×\sqrt\frac{0.6(1-0.6)}{155}[/tex]

= 0.6 ± 0.0645

= (0.6 - 0.0645 , 0.6 + 0.0645)

= (0.535 , 0.665)

Hence, required value is (0.535 , 0.665).

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y < four-fifthsx - one-fifth

y < 2x + 6

The given system of inequalities can be represented in slope-intercept form as follows:

y < (4/5)x - 1/5

y < 2x + 6

To convert the given inequalities into slope-intercept form, we rearrange each equation to solve for y

In the first inequality, we add 5y to both sides and then divide by 4 to isolate y. This gives us:

4x - 5y < 1

-5y < -4x + 1

y > (4/5)x - 1/5

In the second inequality, we add x to both sides and then divide by -1/2 to isolate y. This gives us:

1/2y - x < 3

1/2y < x + 3

y > 2x + 6

Therefore, the given inequalities in slope-intercept form are:

y < (4/5)x - 1/5

y > 2x + 6

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The appropriate measures of center and variation are 13 and 4.

Measures of Center:

The appropriate measure of center for this data set is the median since there is no clear outlier present in the data. Hence, the value of median here is 13

Measures of Variation:

The appropriate measure of variation for this dataset is the range, which is the difference between the largest and smallest value in the dataset, Hence the value of range is 4

Since the data is small and there is no clear outlier present, the median is the appropriate measure of center. The range, which is the difference between the largest and smallest value in the dataset, is the appropriate measure of variation

Hence, the appropriate measures of center and variation are 13 and 4.

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we know that the spinner has an equal chance of landing on each section. Since there are a total of six sections on the spinner, we can assume that the probability of the arrow landing on any one section is 1/6 or approximately 0.1667.

Now, if the arrow is spun 72 times, we can use this probability to calculate the expected number of times the arrow will land on 4. To do this, we simply multiply the probability by the number of spins, as follows:

Expected number of times arrow lands on 4 = Probability of arrow landing on 4 x Number of spins
Expected number of times arrow lands on 4 = 0.1667 x 72
Expected number of times arrow lands on 4 = 12

So, we can expect the arrow to land on 4 approximately 12 times out of 72 spins. Of course, this is just an expected value, and the actual number of times the arrow lands on 4 may vary from this value due to random chance.

In summary, if we assume that the arrow on the spinner is equally likely to land on each section, and it is spun 72 times, we can expect the arrow to land on 4 approximately 12 times based on probability calculations.

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To evaluate the line integral JF.dr, where F = (-2 sin x, 2 cos y, 6zx) and C is the path given by r(t) = (3t^3, -3t^2, -3t) for 0 <= t <= 1, we first need to parameterize F and r in terms of t.

For F, we have:

F = (-2 sin x, 2 cos y, 6zx) = (-2 sin (3t^3), 2 cos (-3t^2), 6(3t^3)(-3t)) = (-2 sin (3t^3), 2 cos (3t^2), -54t^4)

For r, we already have the parameterization:

r(t) = (3t^3, -3t^2, -3t)

Now we can use the formula for the line integral:

JF.dr = ∫(F dot dr)

= ∫(-2 sin (3t^3) dx + 2 cos (3t^2) dy - 54t^4 dz)

= ∫(-18t^2 cos (3t^2) + 18t^2 cos (3t^2) - 54t^4) dt

= ∫(-54t^4) dt

= -9t^5 + C

Evaluating this expression for t = 1 and t = 0, we get:

JF.dr = (-9(1)^5 + C) - (-9(0)^5 + C)

= -9 + 9

= 0

Therefore, the line integral JF.dr evaluated along the path given by r(t) = (3t^3, -3t^2, -3t) for 0 <= t <= 1 is equal to 0.

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Answer:

(-1/5)x + 8 = -x + 4

(4/5)x + 8 = 4

(4/5)x = -4

x = -5, so y = 9

C. There is one unique solution (-5, 9).

The correct equation that represents Finley's annual salary, f(n), during the nth year is: [tex]f(n) = 56,000(1.06)^(n-1)[/tex] Thus, option D is correct.

What is an equation?

Finley's annual salary increases by 6% each year. This means that the salary for the second year is 6% more than the salary for the first year, the salary for the third year is 6% more than the salary for the second year, and so on.

To find an equation for Finley's annual salary during the nth year, we can use the initial salary of $[tex]56,000[/tex] and the fact that the salary increases by 6% each year. One way to write this equation is:

[tex]f(n) = 56,000(1.06)^(n-1)[/tex]

Here, the expression (1.06)^(n-1) represents the 6% increase in salary each year, starting from the second year (hence the (n-1) exponent). Multiplying this by the initial salary of $56,000 gives the salary for the nth year.

Therefore, the correct equation that represents Finley's annual salary, f(n), during the nth year is:[tex]f(n) = 56,000(1.06)^(n-1)[/tex]

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Answer: The answer is 5.

Step-by-step explanation:

You first set up the equation

10 + 7x = 45

You must put x because you don't know the number of hours he stays

You then subtract 10 from both sides of the numbers 10 and 45

That'll get you 7x = 35

To find out what x is you divide both sides by 7

7x divided by 7 is x

35 divided by 7 is 5

X = 5

Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.

To calculate the balance at the end of 3 years, we can use the simple interest formula for Victoria's account and the compound interest formula for Corbin's account.

For Victoria's account:

Simple interest = P * r * t

= 2000 * 0.05 * 3

= $300

Balance after 3 years = P + Simple interest

= 2000 + 300

= $2300

For Corbin's account:

Balance after 3 years = [tex]P * (1 + r)^t[/tex]

= 1800 * (1 + 0.09)³

= $2401.40

Therefore, the statement "Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.

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The number of horizontal rails for 10 sections is

The rule for the post is to multiply the number of section by 3

The rule for the rail is to multiply the post by 2

The rules is calculated using the unit value and comparing with other values

the rule for the number of post

1 section requires 3 posts hence multiplication by 3, comparing shows that multiplying by 3 gives the number of post

the rule for the number of rails

1 section requires 6 rails hence multiplication by 6, comparing shows that multiplying each section by 6 gives the correponding number of rails

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a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships.

A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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Answer:

Volume = 288695.6 in³

Step-by-step explanation:

Volume of a sphere is given by

v=4/3πr^3

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

v=4/3 x 41^3π

=275684/3 π

= 288695.6097

We have the final answer as

Volume = 288695.6 in³ to the nearest tenth

Volume = 288695.6 in³ to the nearest tenth

Hope this helps you

PLS MARK BRAINLIEST

The surface area of the similar cone is 415.8 in²

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.

The surface area of a cone is expressed as;

SA = πr( r+l) where r is the radius and l is the slant height.

The slant height of the original cone =

l= √h²+r²

l = √12²+3²

l = √144+9

l = √153

l = 12.4 in

SA= 3π( 3+12.4)

SA = 3 × 15.4

SA = 46.2 in²

The surface area of similar cone with radius 9 inches is calculated by;

(3/9)² = 46.2/x

= 9/81 = 46.2/x

x = 46.2 × 81/9

x = 415.8in²

Therefore the surface area of the similar cone is 415.8 in³

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The mZDPC is approximately 15 degrees.

We know that the length of an arc of a circle is given by the formula:

length of arc = (central angle / 360°) × 2πr

where r is the radius of the circle.

In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:

9.77 = (mZDPC / 360°) × 2π(8)

Simplifying this equation, we get:

mZDPC = (9.77 / (2π(8) / 360°))

mZDPC = (9.77 / 0.670206) degrees

mZDPC ≈ 14.58 degrees

Rounding to the nearest degree, we get:

mZDPC ≈ 15 degrees

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Answer:

Set your calculator to degree mode.

Using the Law of Sines:

7/sin(40°) = x/sin(81°)

x = 7sin(81°)/sin(40°) = 10.8

Answer:

10.8=x

Step-by-step explanation:

Using the Law of Sines, we can put together the fact that

[tex]\frac{sin A}{a} =\frac{sinB}{b}[/tex]

Substitute our given values from the triangle:

[tex]\frac{sin 81}{x} =\frac{sin40}{7}[/tex]

Turn the sines into a decimal:

[tex]\frac{0.9876}{x} =\frac{0.6427}{7}\\[/tex]

cross multiply using butterfly method

0.988·7=0.643x

solve for x

6.916=0.643x

divide both sides by 0.643

10.8=x (round to nearest tenth)

Hope this helps! :)

The two letters in which the new point lie include the following: C. between G and H.

In Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

This ultimately implies that, all number lines would primarily increase in numerical value (number) towards the right from zero (0) and decrease in numerical value (number) towards the left from zero (0).

From the number line shown in the image attached below, we can logically deduce the following point:

|J - E| = 45% of x

|J - E| = 0.45x

|J - E| = GH

In conclusion, 45% is almost half way or 50% between E and J, which makes the distance between the two letters G and H, the new point.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The average number of customers in the shop is 7.5

The average number of customers in the shop can be calculated using the M/M/2 queuing model. In this model, we assume that the arrivals follow a Poisson distribution, and the service times follow an exponential distribution.

The subscript "2" in M/M/2 refers to the fact that there are two servers or service channels available.

Using Little's Law, the average number of customers in a stable system is equal to the product of the arrival rate and the average time spent in the system.

Thus, to calculate the average number of customers in the shop, we need to find the average time spent in the system.

The average time spent in the system can be calculated as the sum of the average time spent waiting in the queue and the average time spent being served. Using the M/M/2 queuing model,

the average time spent waiting in the queue can be calculated as [tex](λ^2)/(2μ(μ-λ))[/tex], where λ is the arrival rate and μ is the service rate. In this case, λ=3 and μ=1/2 since there is one barber who can serve one customer at a time.

Thus, the average time spent waiting in the queue is [tex](3^2)/(21/2(1/2-3))[/tex] = 9/4 hours. The average time spent being served is the mean service time, which is 1/4 hour. Therefore, the average time spent in the system is 9/4 + 1/4 = 5/2 hours.

Finally, using Little's Law, the average number of customers in the shop is λ times the average time spent in the system, which is 3*(5/2) = 15/2 or 7.5 customers.

However, since the shop can only accommodate at most two customers at a time, the actual number of customers in the shop would be either one or two.

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The z-score is -1.2, rounded to the tenths place.

The center of the histogram would be around the population mean of 266 days.

The standard deviation of the histogram would be the standard error of the mean, which is the standard deviation of the population divided by the square root of the sample size. Thus, the standard deviation of the histogram would be 10 / sqrt(100) = 1 day.

To calculate the z-score for a sample mean of 264.8 days, we can use the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Substituting the given values, we get:

z = (264.8 - 266) / (10 / sqrt(100)) = -1.2

Therefore, the z-score is -1.2, rounded to the tenths place.

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The probability that a person either runs outside or joins a gym is 0.60 or 60%.

To find the probability that a person either runs outside or joins a gym, you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A is the event of running outside, B is the event of joining a gym, and "and" represents the intersection of both events.

Given:
P(running outside) = 0.45
P(joining a gym) = 0.40
P(both running outside and joining a gym) = 0.25

Plug these values into the formula:

P(either runs or joins a gym) = 0.45 + 0.40 - 0.25

Calculate the result:

P(either runs or joins a gym) = 0.60

Therefore, the 60% of person either runs outside or joins a gym

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The fish has located a horizontal distance of 7 meters away from the cliff.

How to find the distance between the bird and the fish?

To find the distance between the bird and the fish, we need to find the horizontal distance traveled by the bird during the dive. We can do this by finding the x-coordinate of the vertex of the parabolic curve, which represents the highest point of the dive.

The vertex of the parabolic curve of the given function f(x) = (x-7)^2 - 1 is at the point (7, -1). This means that the highest point of the bird's dive is reached at 7 seconds, and the bird is at a height of -1 meters at this point.

To find the distance traveled by the bird during the dive, we need to find the horizontal distance between the bird's starting point (the cliff) and the highest point of the dive (the vertex). The distance is given by the horizontal coordinate of the vertex, which is 7 seconds.

Therefore, the fish has located a horizontal distance of 7 meters away from the cliff, assuming that the bird started the dive from the edge of the cliff.

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The figure after changing the scale of the grid is added as an attachment

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

Old scale: 1 unit = 4 ft

New scale: 1 unit = 8 ft

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

Scale = Old scale/New Scale

Substitute the known values in the above equation, so, we have the following representation

Scale: (1 unit = 4 ft)/(1 unit = 8 ft)

Evaluate

Scale: 1/2

This means that the figure on the new grid will be half the side lengths of the old grid

Next, we draw the figure

See attachment for the new figure

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The solution of the quadratic equation is y = (x + 3)(x - 3).

The solution of the quadratic equation is calculated by applying difference of two squares as shown below;

y = x² - 9

y = x² - 3²

the difference of two square of x² - 3² = (x + 3)(x - 3)

The solution of the quadratic equation is calculated as;

y = (x + 3)(x - 3)

Thus, solution of the quadratic equation has been determined using  square root method.

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Answer:

no it is not possible

Step-by-step explanation:

We can use the formula for the area of a sector to find the area of sector $LMN$

The area of a sector with central angle $\theta$ in a circle with radius $r$ is given by:

$A = \frac{\theta}{360^\circ} \pi r^2$

In this case, we know that $m\angle LMN = 66^\circ$ and $LM = 19$ units, so the radius of circle M is half of the diagonal of the rectangle formed by $LM$ and $MN$. Using the Pythagorean theorem, we can find the length of $MN$:

$MN^2 = LM^2 + LN^2 = LM^2 + LM^2 = 2LM^2$

$MN = \sqrt{2} LM = \sqrt{2} \cdot 19$

So the radius of circle M is $r = \frac{1}{2}MN = \frac{1}{2}\sqrt{2} \cdot 19$

Now we can use the formula for the area of a sector to find the area of sector $LMN$:

$A = \frac{m\angle LMN}{360^\circ} \pi r^2 = \frac{66^\circ}{360^\circ} \pi \left(\frac{1}{2}\sqrt{2} \cdot 19\right)^2 \approx \boxed{90.89}$ square units (rounded to the nearest hundredth).

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Gabriela will use 1620 square inches of wood to build the open box.

The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.

The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:

Area of bottom = length x width = 18 in. x 15 in. = 270 in²

The area of each side is the product of the height and the length of the corresponding base, which is:

Area of each side = height x length = 15 in. x 18 in. = 270 in²

So the total surface area of the box is:

Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)

= 2 x 270 in² + 4 x 270 in²

= 1620 in²

Therefore, Gabriela will use 1620 square inches of wood to build the open box.

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The solution to the system of linear equations is x = 1, y = -3, and z = 8, which is option B: X=-1, y=-3, z=2.

To solve this system of linear equations, we can use Gaussian elimination, which involves adding and subtracting equations to eliminate variables. Here are the steps:

x - 3y - 2z = 6

2x - 4y - 3z = 8

-3x + 6y + 8z = -5

Step 1: Add twice the first equation to the second equation to eliminate x:

x - 3y - 2z = 6

4y + z = 20

-3x + 6y + 8z = -5

Step 2: Add three times the first equation to the third equation to eliminate x:

x - 3y - 2z = 6

4y + z = 20

9y + 2z = 13

Step 3: Solve for z in the second equation:

4y + z = 20

z = 20 - 4y

Step 4: Substitute z into the third equation and solve for y:

9y + 2z = 13

9y + 2(20 - 4y) = 13

y = -3

Step 5: Substitute y into the second equation and solve for z:

4y + z = 20

4(-3) + z = 20

z = 8

Step 6: Substitute y and z into the first equation and solve for x:

x - 3y - 2z = 6

x - 3(-3) - 2(8) = 6

x = 1

Therefore, the solution to the system of linear equations is x = 1, y = -3, and z = 8, which is option B: X=-1, y=-3, z=2.

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The text format of the question in the picture:

15. The solution the system of linear equation of

x-3y-2z = 6

2x-4y-3z = 8

(-3x+6y+8z = -5 is

A) X=-1,y=-3, z=-2 B) X=-1,y=-3, z=2 C) X=1,y=-3, z=2 D) X = 1, y = 3, z=-2

The combination of side lengths that would not form a triangle is C.XY = 11 mm, YZ = 14 mm, XZ = 21 mm.

We shall use the triangle inequality theorem to determine if a set of side lengths can form a triangle.

The triangle inequality theorem says that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We shall calculate each of the options:

For option A:

XY + YZ = 7 mm + 14 mm = 21 mm which is < XZ = 25 mm.

Therefore, option A does form a triangle.

For option B:

XY + YZ = 11 mm + 18 mm = 29 mm, which is > XZ = 21 mm.

YZ + XZ = 18 mm + 21 mm = 39 mm, which is > XY = 11 mm.

XY + XZ = 11 mm + 21 mm = 32 mm, which is > YZ = 18 mm.

Therefore, option B does form a triangle.

For option C:

XY + YZ = 11 mm + 14 mm = 25 mm, and is > XZ = 21 mm.

Therefore, option C does not form a triangle.

For option D:

XY + YZ = 7 mm + 14 mm = 21 mm, which is > XZ = 17 mm.

YZ + XZ = 14 mm + 17 mm = 31 mm, which is > XY = 7 mm.

XY + XZ = 7 mm + 17 mm = 24 mm, which is > YZ = 14 mm.

Therefore, option D does form a triangle.

Therefore, the combination of side lengths that would not form a triangle is XY = 11 mm, YZ = 14 mm, XZ = 21 mm.

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Answer:

Step-by-step explanation:

The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.

B. 200 is 1/20 the value of 2,000.

This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.

A family camping in a national forest used a 4-foot pole and a tarp to build a temporary shelter. One corner of the tarp was staked 5 feet from the bottom of the pole. The slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.

We can draw a right triangle with the pole being the height, the distance from the pole to the stake being the base, and the slope of the tarp being the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite to the right angle.

Using the Pythagorean theorem, we can find the length of the hypotenuse

hypotenuse² = height² + base²

hypotenuse² = 4² + 5²

hypotenuse² = 41

hypotenuse = √(41)

Therefore, the slope of the tarp is the ratio of the height to the base, which is

slope = height / base = 4 / 5 = 0.8

So the slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.

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