Find the tables with unit rates greater than the unit rate in the graph. Then arrange these tables in order from least to greatest unit rate. x y 7 13 14 26 x y 5 9 10 18 x y 9 17 18 34 x y 11 21 22 42 x y 10 19 20 38 x y 13 25 26 50 x y 12 23 24 4

Find The Tables With Unit Rates Greater Than The Unit Rate In The Graph. Then Arrange These Tables In

Answers

Answer 1

Except table 2, all tables have greater unit rate than the graph.

The required arrangements of tables is  Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rate of graph is

m=20-0/11=20/11=1.818

Similarly, we need to calculate the unit rate for each table.

m1=26-13/14-7=1.81

m2=18-9/10-5=9/5=1.81

m3=34-7/18-9=1.88

m4=42-21/22-11=21/11=1.90

m5=38-19/20-10=1.9

m6=50-25/26-13=25/13=1.923

m7=46-23/24-12=23/12=1.9166

Hence, Except table 2, all tables have greater unit rate than the graph.

The required arrangement of tables is  Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6

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Related Questions

Madion went out to eat and pent $13. Thi wa 3/5 of the amount that he received. How much money did he receive?

Answers

The total money received by madison was $ 21.6 from which she spent $13 when she went out.

We are given that -

Madison spent $13 in all when she went out.

Also, this was 3/5 of the amount that she had received.

Now let us find the total money she received as follows -

Money spent by madison = 3/5 of the total money received by madison

                              i.e.    13 = 3/5 x (total money received by madison)

or we can say that total money received by madison = (5/3) x 13

                                                                                        =  65/3

                                                                                        = 21.6

Hence, the total money received by madison was $ 21.6

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12. Juan is a programmer going to school at
night to earn a higher degree. He starts the
month with $500 in his savings account. His
income is $4750. Each month he currently
spends $750 on food; $400 on clothes; $530
on video games and movies. His classes cost
$500 each month. His essential expenses
(rent, medical costs, insurance, tax) total
$2800. How much does Juan have for his Net
Cash Flow and Ending Cash at the end of the
month?

[A]Net Cash Flow: -$230
Ending Cash: $730
[B] Net Cash Flow: $2,570
Ending Cash: $3,070
[C] Net Cash Flow: -$230
Ending Cash: $270

[D] Net Cash Flow:-$270
Ending Cash: $230

[E] Net Cash Flow: $270
Ending Cash: -$770

Answers

Juan's Net Cash Flow at the end of the month is -$230 and his Ending Cash is $270.

To calculate Juan's Net Cash Flow and Ending Cash, you need to subtract his expenses from his income.

Juan's income is $4750 per month. His essential expenses, including rent, medical costs, insurance, and tax, total $2800 per month. He also spends $750 on food, $400 on clothes, and $530 on video games and movies, for a total of $2680 in non-essential expenses.

Therefore, his total expenses are $2800 + $2680 = $5480.

His Net Cash Flow is his income minus his expenses, which is $4750 - $5480 = -$730.

His Ending Cash is his Net Cash Flow plus his starting balance of $500, which is -$730 + $500 = $270.

Therefore, the correct answer is option C: Net Cash Flow: -$230, Ending Cash: $270.

9/2 * -(8/3) pls answer fast!...step by step explanation plss

Answers

Answer:

9 * -8

____   =-72/6

2  * 3

Write an equation in the form of y= mx for the proportional relationhip that pae through the point (2, -5) and (6, -45)

Answers

y=-10x+15 is the equation passing through the point which is in the form of y=mx+b

The equation of a line y = mx+b is called a straight line.

Where:

m is the slope, and b is the y-intercept.

given points are (2,-5) and (6,-45) consider these points as (x1,y1) and (x2,y2)

we have to find m: the slope of the line...

                            [tex]m=\frac{y2-y1}{x2-x1}[/tex]------------(1)

Now, plug the values into the formula of equation(1):

                             [tex]m=\frac{-45-(-5)}{6-2} \\\\m=\frac{-40}{4}[/tex]

                           m=-10

y=mx+b will become y=-10x+b

To find the b values:

for point(2,-5) consider x as 2,y as -5 and substitute in y=mx+b

-5=-10*2+b

b=15

for point(6,-45) consider x as 6,y as -45 and substitute in y=mx+b

-45=-10*6+b

b=15

so the final equation is y=-10x+15

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Mustafa walks 15 km east and then 10 km south. How far is Mustafa from the starting point? Is in which direction

Answers

Answer:

25 kilometres West direction

A rectangular aquarium is 12 inches tall. The perimeter of the base is 80 inches. The length of the base is 4 times the width of the base. Enter the volume, in cubic inches, of the aquarium.

Answers

Let's call the width of the base "w" and the length of the base "l". Since the perimeter of the base is 80 inches, this means that 2w + 2l = 80. We are also told that the length is 4 times the width, so l = 4w. We can substitute this second equation into the first equation to get 2w + 2(4w) = 80, which simplifies to 10w = 80. Dividing both sides by 10, we find that w = 8 inches. The width of the base is 8 inches, so the length of the base is 4 * 8 inches = 32 inches. The volume of the rectangular aquarium is the product of the base's area and the height of the aquarium, so it is (32 inches * 8 inches) * 12 inches = 3072 cubic inches. Therefore, the volume of the aquarium is 3072 cubic inches.

Answer:

Step-by-step explanation:

Okay so you have to multiple 12 x 80 which gives you 960, then you  mulitply 960 x 4 to get your final answer which is 3840 cubic inches

The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.
C(x) = 5x²-1500x + 125,000
a. Find the number of bicycles that must be manufactured to minimize the cost.
b. Find the minimum cost.
a. How many bicycles must be manufactured to minimize the cost?
bicycles

Answers

Given function:

C(x) = 5x² - 1500x + 125000

It has a positive leading coefficient, hence the parabola opens up. It means it has the minimum point at vertex.

The x-coordinate of the vertex is:

x = - b/(2a) = - (-1500)/(2*5) = 150

The minimum cost is:

C(150) = 5(150)² - 1500(150) + 125000 = 12500

Answer:

a) The minimum number of bicycles is the x-coordinate of the vertex, 150,b) The minimum cost is the value of C when x is 150, this is $12500.

Vivian and her friends are planning a superhero movie marathon. Vivian is in charge of the

popcorn, so she buys a 2-pound jar of unpopped kernels. The jar's label says that 1 ounce of

kernels will make 1 quart of popcorn. How many cups of popcorn will her jar make?

Answers

If the jar level says that 1 ounce of kernels will make 1 quart of popcorn then 128 cups of popcorns will her jar make the popcorns.

The term ounce is a unit of measurement used in the Imperial system. It is mostly used in the United States. Ounces can be used to measure either liquid or dried goods. There are 32 ounces in one quart using the Imperial System of measurement. There are 4 cups in one quart. 1 quart is same as 32 ounces. Vivian and her friends are planning a superhero movie marathon. if Vivian buys 2 pound jar of unpropped kernels. then it will make 128 cups of popcorn. we know that 1 pound is equal to the 16 ounces so Vivian will make 32 ounces in 2 pound. A quart represented is a measuring unit used in the Imperial system and United States to measure liquids and dried goods. As per the leveling of the jar it will make 32 ounces in 32 quartz. then in 32 quartz it will make 128 cups of popcorn.

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two planes flying at the same altitude are heading toward jwd airport. the paths of these planes form a right triangle. the jet is flying due east toward jwd at 450 mph. the turboprop is approaching jwd from the south at 275 mph. when each is 100 miles from the airport how fast is the distance between the planes changing?

Answers

The speed of the distance between the two planes is increasing at 325 mph as they approach JWD Airport.

The two planes form a right triangle, with the jet flying due east at 450 mph and the turboprop approaching from the south at 275 mph. The hypotenuse of the triangle is the distance between the planes, and the length of the hypotenuse is changing as the planes approach the airport. The rate of change of the length of the hypotenuse is equal to the sum of the rates of change of the two sides of the triangle, which are the speeds of the jet and the turboprop. As they are both 100 miles from the airport, the speed of the distance between the two planes is equal to the sum of the two speeds, or 450 mph + 275 mph = 325 mph. Therefore, the distance between the two planes is changing at a rate of 325 mph.

Rate of change of distance between the planes = Rate of change of jet + Rate of change of turboprop

= 450 mph + 275 mph

= 325 mph.

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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.

What conclusion can they reach based on the above output when they set the significance level to be 0.10?

a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.

b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.

c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.

d.Two of the above are correct.

e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out

Answers

There is no statistical support in the data for the claim that seeded clouds typically cover more than 300 acres per foot by average acrefeet.

Since the significance level is set at 0.10, the meteorologists can conclude that the data does not provide statistical evidence that the average acrefeet from seeded clouds is more than 300.

This is because the calculated p-value is greater than the significance level. This means that there is not sufficient evidence to reject the null hypothesis, which states that the average acrefeet from seeded clouds is no greater than 300.

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pls help me in this homework id really appreciate it <3

Answers

I would but I’m not sure if I can put multiple picture at once but here is this first 5

Find the value of x for {(-2/5)^2}^x*(-5/2)^-1=-8/125

Answers

Answer: x=1

Step-by-step explanation:

[tex][(-\frac{2}{5})^2] ^x*(-\frac{5}{2}) ^{-1}=-\frac{8}{125} \\\\(-\frac{2}{5})^{2*x}*(-\frac{2}{5})^1 =-\frac{2^3}{5^3} \\\\(-\frac{2}{5} )^{2x+1}=(-\frac{2}{5})^3 \\\\Hence,\\\\2x+1=3\\\\2x+1-1=3-1\\\\2x=2[/tex]

Divide both parts of the equation by 2:

[tex]x=1[/tex]


Describe all the
positive integers that would make (32)x greater than 39. Explain your reasoning

Answers

The positive integers that will make (32)x greater than 39 must be greater than 39/32

How to find positive integers that will make (32)x greater than 39

A whole number that is greater than zero is what is meant by the term "positive integer."

All counting numbers are included in the set of positive integers (that is, the natural numbers)

In the problem, the given expression is (32)x greater than 39 rewriting gives

(32)x > 39

solving for x

x > 39/32

the integer must be greater than 39/32

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Given: AB = CD
Prove: AC = BD
What reason can be used to justify statement 3 in the proof above?
the addition property the subtraction property the division property the substitution property

Answers

To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.

Solve for x. Round to the nearest tenth.
X= type your answer...
X
28
32

Answers

The value x is 28. By using Pythagorean theorem on the given triangle.

What is the meaning of the nearest tenth?

To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.

Given that,

DC = 28

BC = 32

Assume that, AB = a and AD = b

Applying Pythagorean theorem on △BCD:

BC² = DC² + DB²

Putting BC = 32 and DC = 28 in the above equation:

32² = 28² + DB²

DB² = 32² - 28²

DB² = 32² - 28²

DB² = 240

The length of AC is CD + DA = 28 + b.

Now applying Pythagorean theorem on △ABC:

BC² = AB² + AC²

32² = a² + (28 + b)²

a² = 32² - (28 + b)²   .....(i)

Now applying Pythagorean theorem on △ABD:

AB² = AD² + BD²

a² = b² + 240  ....(ii)

Now comparing equation (i) and equation (ii)

32² - (28 + b)² = b² + 240

1024 - (28² + 56b + b²) = b² + 240

1024 - 784 - 56b - b² = b² + 240

b² + 240 - 1024 + 784 + 56b + b² = 0

2b² + 56b = 0

2b(b + 28) = 0

Either,

2b = 0,  b + 28 =0

b = 0, b = -28

Since the value of b can't be negative. Thus b = 0.

The length of AC is CD + DA = 28 + b = 28.

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The catter plot how the number of people at a fair baed on the outide temperature. How many fewer people would be predicted to be at the fair on a 100 f day then on a 75 f

Answers

The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.The answer will depend on the specific data from the catter plot.

1. Look at the catter plot and identify the points that correspond to the temperatures of 75°F and 100°F.

2. Note the number of people at the fair for each temperature.

3. Subtract the number of people at the fair in the 75°F point from the number of people at the fair in the 100°F point.

The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.

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Check for Reasonableness What is a good estimate for 380% of 60? Explain.

Answers

Pls look at the analysis in the attachment below

i need help desperately please don’t ignore!! :(
LN= 5x-8
NM= 12
m find the value of x

Answers

The value of the missing part which is x is; x = 8

How to find the missing part of a triangle?

From the given triangle, we are told that;

LN = 5x - 8

NM = 12

KNL = (13x - 14)°

Now, since KN is an altitude in ΔKLM, it means that KN is perpendicular to LM and as such KNL is a right angle which is 90 degrees. Thus;

(13x - 14)° = 90

1x = 90 + 14

13x = 104

x = 104/13

x = 8

This is the value of the missing value

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Simplify this expression
Distribute first in the box below
2 (3x − 6) (2x + 1)

Answers

Answer: [tex]12x^{2} -18x-12[/tex]

Step-by-step explanation:

(6x-12)(2x+1)

Foil method

6x*2x

6x*1

-12*2x

-12*1

add them up

[tex]12x^{2} -18x-12[/tex]

In a series of transformations, which transformation would make two figures similar as opposed to congruent?a. dilationb. reflectionc. rotationd. translation

Answers

In a series of transformations, dilation would make two figures similar as opposed to congruent.

Rotation, reflection and translation are known as rigid transformations.

This means they do not change the size or shape of a figure, they simply move it.

These rigid transformations preserve congruence.

Dilation, however, are not rigid transformation, since they change the size of  a shape.

Dilation would not change the shape, just the size: the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.

This would give us a similar, but not congruent.

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Write the expression using exponents.

5.2 x y x y x y
The ( X ) stands for multiplication. So 5.2 times Y times Y times Y.

Answers

The expression using exponents is 5.2^3

There are no results for an airplane can carry a maximum of 36600 pound of cargo,passenger and luggage.On on the plane's next flight,it will carry 7,320 pounds of cargo.If each passenger with luggage weighs 220 pounds,what is the greatest number of passengers the plane can carry on its next fligh a 33 passenger b 133passenger c 166 passengers d 199 passengers

Answers

Answer:

b. 133 passengers

Step-by-step explanation:

The anount of weight taken by the passengers can be up to [tex]36600-7320=29280[/tex] lbs.

Dividing this by [tex]220[/tex] lb per passenger, we get there can be up to [tex]\lfloor 29280/220 \rfloor=133[/tex]

part of a regression output is provided below. some of the information has been omitted. source of variation ss df ms f regression 3177.17 2 1588.6 residual 17 17.717 total 3478.36 19 the ss (residual) is a. 3177.17. b. 301.19. c. impossible to determine. d. 17.71.

Answers

The SS(residual) is - 301.19. Option (b) is the correct answer.

Given the table :

Source of Variation - - SS - - - df - - - MS - - - - F

Regression - - - - - -3177.17 - - -2 - - 1588.6

Residual - - - - - - - - ______ --17 - - -17.717

Total - - - - - - - - - - 3478.36 - - 19

Calculate the SSR, the Sum of the Square residual.

The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR), and Degree of Freedom RESIDUAL (DFR) are related by the formula :

MSR = SSR / DFR

Hence,

SSR = MSR × DFR

For the table ;

MSR = 17.717 ; DFR = 17

SSR = (17.717 × 17)

SSR = 301.19

So, the SS(residual) is - 301.19.

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If
m

=
21
6

m
UPE

=216

and
m

=
5
8

m
LS

=58

, find
m

L
B
S
m∠LBS.

Answers

Answer:

use the way I told u down

Step-by-step explanation:

Angle ABC is a straight angle.

Angles ABD and DBC are right angles.

Angles CBE and DBE are acute angles.

Angle ABE is an obtuse angle.

Angles

The sum of the three angles in any triangle is always 180°.

a + b + c = 180°

Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.

Angles

In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?

a + b + c = 180°

Since b is a right angle, b = 90°.

The problem states that c = 40°.

Therefore, a + 90° + 40° = 180°

a + 130° = 180°

a + 130° − 130° = 180° − 130°

a = 50°

Angle a measures 50°.

Angles

Click on the figure that matches this description.

An obtuse angle

Question 1 of 8

This is an acute angle. It measures less than 90°. Try again

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°.

One of these figures is an obtuse angle. Try again.

An obtuse angle is larger then a right angle and smaller then a straight angle.

Angles

Click on the figure that matches this description.

An acute angle

Question 2 of 8

This is an acute angle. It measures less than 90°.

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°. Try again.

One of these figures is an acute angle. Try again.

An acute angle is smaller then a right angle.

Angles

Click on the figure that matches this description.

A right angle

Question 3 of 8

This is an acute angle. It measures less than 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.

This is an acute angle. It measures less than 90°. Try again.

A right angle looks like a square corner and measures 90°.

A right angle measures 90°.

Angles

There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.

Angles

Click on the correct answer.

Angle ABC is a right angle. If angle n is 40°, how large is angle m?

50°

140°

90°

60°

None of these

Question 4 of 8

90° − 40° = 50°

Angle m is 50°.

Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.

Angle ABC is 90°, and angle m is only part of this right angle. Try again.

Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.

One of these is size of angle m. Try again.

Since angle ABC is a straight angle, angle m + angle n = 90°.

Consider the function below. (If an answer does not exist, enter DNE.)h(x) = 5x3 − 3x5(a) Find the interval of increase. (Enter your answer using interval notation.)(−1,0)∪(0,1)

Answers

The interval in which the function h(x) = 5x³ - 3x^5 is increasing is given as follows:

(−1,0)∪(0,1).

How to obtain the intervals in which the function is increasing?

The function in this problem is defined as follows:

h(x) = 5x³ - 3x^5.

To obtain the intervals for increase of decrease, the critical points of the function need to be obtained, which are the values of x for which the derivative is of zero.

The derivative of the function in this problem is given as follows:

h'(x) = 15x² - 15x^4.

Hence the critical points of the function are given as follows:

15x² - 15x^4 = 0

15x²(1 - x²) = 0.

Hence:

15x² = 0 -> x = 0.1 - x² = 0 -> x² = 1 -> x = -1, x = 1.

Then the signals of the derivative in each interval is given as follows:

x less than -1: negative, as (1 - x²) < 0.x between -1 and 0: positive, as (1 - x²) > 0.x between 0 and 1: positive, as (1 - x²) > 0.x greater than 1: negative, as (1 - x²) < 0.

The function is increasing when the derivative is positive, hence the interval is given as follows:

(−1,0)∪(0,1).

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Draw a line l, and take two point A and B on it. Through A and B, draw line L2 and L3 perpendicular to L1. On L2, mark a point C at a ditance 4cm from L1 and draw a line L4 parrallel to L1 through C. If L4 interect L3 at D , what type of quadrilateral i ABDC? ​

Answers

ABDC is a quadrilateral with two non-parallel sides. It has two pairs of opposite sides which are parallel. It is also known as a trapezoid.

ABDC is a four-sided figure with two pairs of opposite sides that are parallel. This type of quadrilateral is also known as a trapezoid. A trapezoid has two non-parallel sides, while the other two sides are parallel to each other. In this case, the two parallel lines are L1 and L4, while L2 and L3 are the two non-parallel sides. We can see that the point C on L2 is a distance of 4cm from L1, and L4 is a line that is parallel to L1 and passes through C. Finally, L4 intersects L3 at the point D, which completes the trapezoid ABDC.

The length of AB can be determined by using the Pythagorean Theorem. We know that the length of L1 is 8 cm, so the length of AB is 3 cm.

example

AB = √(8^2 - 4^2) = √64 - 16 = √48 = 6 cm

The length of BD can also be determined by using the Pythagorean Theorem. We know that the length of L2 is 4 cm, so the length of BD is 3 cm.

BD = √(4^2 - 4^2) = √16 - 16 = 0 cm

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The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x – h| is solid.



Use the slider to change the value of h. How does changing the value of h affect the vertex?



Positive values of h shift the graph
.

Negative values of h shift the graph
.

Answers

Answer:

Step-by-step explanation:

The graph of the parent function f(x) = |x|

transformed function g(x) = |x – h|

To Find : How does changing the value of h affect the vertex?

Positive values of h shift the graph

Negative values of h shift the graph

Solution:

f(x) = |x|

is f(x) = x  for  x ≥ 0

 f(x) = -x   for  x < 0

g(x) = |x – h|

Positive values of h shift the graph  to the right  

f(x)  = x  - h   for x  ≥ 0

f(x)  = h - x   for x  < h

As values of h increase graph keep shifting to right

Vertex is ( h , 0)   Vertex keep shifting to right with increases value of h

g(x) = |x – h|

Negative value of h shift the graph  to the left

f(x)  = x  - h   for x  ≥ 0

f(x)  = h - x   for x  < h

Vertex is ( h , 0)   Vertex keep shifting to left with increases magnitude of negative h

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The linear functions f(x) and g(x) are represented on the graph ...

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The linear functions f(x) and g(x) are represented on the graph ...

suppose that a box contains 6 cameras and that 5 of them are defective. a sample of 2 cameras is selected at random ( without replacement). define the random variable x as the number of defective cameras in the sample. write the probability distribution for x .write your answer in fraction form or round to 3 decimal places.

Answers

If x is the number of defective cameras in the 2-size sample, that means that:

P(x = 0) = 0 (since there are no 2 cameras that can be selected without replacement that are not defective)

P(x = 1) = 5/15 = 1/3 (since there are 15 total ways to select a distinct sample and only 5 of these would have the non-defective one in them)

P(x = 2) = 10/15 = 2/3 (since there are 15 total ways to select a distinct sample and 10 of these would NOT have the non-defective one in them)

Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0. 80. 80, point, 8 probability of staying in the alternative time for more than an hour. During the first year of testing, shota uses his machine 202020 times. Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour? round your answer to the nearest hundredth. P(\text{at least one} < 1\text{ hour})=.

Answers

The Probability that at least one trip will last less than one hour =7/8

What is probability?

It refers to the ratio of favorable outcome to the total possible outcome.

The possibility of happening an event is probability.

How to calculate probability of the given question?

Probability of staying in the alternative time for more than an hour is 8

each trip is likely to last for more than one hour so probability of at least one trip will last more than an hour =1/8

Now, probability of at least one trip will last less than one hour = 1-1/8

                                                                                                    7/8

hence, the result is 7/8

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Calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1

Answers

The value of the double integral  ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is  11.77

In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1

i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]

First we integrate the function (8x)/(1 + xy)  as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy

G(x) = 8 ln(8x + 1)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, 1] G(x) dx

= ∫_[0, 1] [8 ln(8x + 1)] dx

= 9 ln(9) - 8

= 11.77

Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77

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