A kangaroo chae a rabbit that tart 150 feet ahead of the kangaroo. For every 12-foot leap of the kangaroo, the rabbit leap 7 feet. How many leap would the kangaroo have to make to catch up to the rabbit?

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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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:

-5=-10*2+b

b=15

-45=-10*6+b

b=15

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

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Answer:

y = 2x-3

Step-by-step explanation:

Find slope from the two points (which is 2)

and then plug in one of the points (either (3,3) or (1,-1)) to find b in y=mx+b.

Combine everything, and there's your equation

Answer:

9 * -8

____   =-72/6

2  * 3

Given function:

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:

The minimum cost is:

Answer:

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

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]

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.

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)

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

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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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.

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

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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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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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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Answer:

27cm

Step-by-step explanation:

[tex]s + s + s = p \\3x + x + x = 45 \\ 5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]

That's the length of one of its legs

The length of the base = 3x

= 3 x 9

= 45cm

The time taken to traveled the van and the tornado before they  meet as per the speed of the van and the tornado is equal to 2.6 minutes.

As given in the question,

Speed of the van along the straight road = 94 kilometers per hour

After travelling distance of 7 kilometers

Speed of the tornado along the same road = 69 km/hour

Total relative speed of van and tornado = 94 + 69

                                                                  = 163km/hour

Distance travelled between two different speed = 7km

Time used to traveled before they meet = distance / speed

                                                                   = 7 / 163

                                                                   = 0.043 hours

                                                                   = 2.58minutes

                                                                   = 2.6minutes

Therefore, the time required to traveled the van and the tornado before they   meet is equal to 2.6 minutes.

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Answer:                                                                                                                                                      

Step-by-step explanation:

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

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

The possibility of happening an event is probability.

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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32 minutes and 2 seconds - 12 minutes and 15 seconds

 0 days 0 hours 32 minutes 2 seconds

- 0 days 0 hours 12 minutes 15 seconds

_________________________________

= 0 days 0 hours 19 minutes 47 seconds

[tex]=\fbox{19 minutes and 47 seconds or 19.783333 minutes}[/tex]

Answer:

25 kilometres West direction

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 ...

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

(−1,0)∪(0,1).

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:

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

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

(−1,0)∪(0,1).

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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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