Mr. Molesky and Mr. Liberty are avid video game golfers. Both like to compare times to complete a
110 minutes and standard deviation of 10 minutes. Mr. Liberty's times are Normally distributed with
particular course on their favorite game. Mr. Molesky's times are Normally distributed with a mean of
mean 100 minutes and standard deviation 8 minutes.

a) Find the mean and standard deviation of the difference of their times (Molesky - Liberty). Assume
their times are independent.

b) Find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day.

Answer:

HI = 9

Step-by-step explanation:

      HJ = HI + IJ

2x + 10 = x + 9 + 1

 2x - x = 10 - 10

      ∴ x = 0

∴ HI = x + 9

       = 0 + 9

       = 9

The path may be Quadratic in nature.

The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches its maximum height and then starts dropping back to the ground at increasing speeds due to positive acceleration exerted by the force of gravity.

The flight path of the parabola can thus be modeled by height as a function of elapsed time

h = f(t) where f(t) is a quadratic equation in t with the general form being

a · t² +b · t  + c

We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever

The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However, we know from observation that the firework has the highest speed at the moment of launch

Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.

Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.

Indeed the actual path of the firework is a reflection of the graph about the x-axis. so that it is a downward-facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.

The height would be the y-axis and the time t the x-axis.

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An algebraic equation which represents this word description "Seven more than the quotient of a number b and 45 is greater than 5" is b > -90.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let the variable b represent the unknown number.

Translating the word problem into an algebraic equation, we have the following;

7 + b/45 > 5

By collecting like terms, we have the following:

b/45 > 5 - 7

b/45 > -2

By cross-multiplying, we have the following:

b > -2 × 45

b > -90

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If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet  .

le the side length of the big square board be = "x" ft ;

the side length of smaller square is = 17 ft ;

So , the area of the smaller square is = (side length) × (side length)

= 17 × 17

= 289 ft² .

and , the area of the larger square is = (x) × (x) ;

= x²  .

So , the approximate area of the remaining board is calculated as :

= x² - 289  ;

Therefore , area of remaining board is "x² - 289" .

The given question is incomplete , the complete question is

A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?

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It is right to receive a change of 19.50 if Juan gave php 100.00 to the fruit vendor

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating how many Juan spend we have:

Total cost = mango + pineapple

Total cost = 45.50 + 35.00

Total cost = 80.5

Calculating how much Juan should receive in change:

Change = Amount given - Total cost

Change = 100 - 80.5

Change = 19.5

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Correctly written question:

Juan bought a kilo of mango at 45.50 and pineapple at 35.00 is it right to receive a change of 19.50 if he gave php 100.00 to the fruit vendor?

The median of the trapezoids is given by QR = 23.5 and VW = 15.2

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the first trapezoid be represented as A

Let the second trapezoid be represented as B

Now , the median of the trapezoid M = ( 1/2 ) ( sum of longer base and shorter base )

Substituting the values in the equation , we get

a)

The length of longer base = 35.6

The length of shorter base = 11.4

So , the median of A is QR = ( 1/2 ) ( 35.6 + 11.4 )

On simplifying the equation , we get

The median of trapezoid QR = ( 1/2 ) 47

The median of trapezoid QR = 23.5

b)

The length of longer base = 19.1

The length of shorter base = 11.3

So , the median of B is VW = ( 1/2 ) ( 19.1 + 11.3 )

On simplifying the equation , we get

The median of trapezoid VW = ( 1/2 ) 30.4

The median of trapezoid VW = 15.2

Hence , the median of trapezoid is solved

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The probability that at least two of the balls have the same number is 27.40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes

No. of ways to succeed = 90P8

No. of possible outcomes = 90^8

No. of ways to succeed =

nPr = n! / (n-r)!

90P8 = 90! / (90-8)!

90P8 = 90! / (82)!

90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!

90P8 = 90*89*88*87*86*85*84*83

90P8 = 3.13x10^15

P(no 2 have same number) = 3.13x10^15 / 90^8

P(no 2 have same number) = 0.73

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(at least 2 have same number) = 1 - 0.73

P(at least 2 have same number) = 0.2740 = 27.40%

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Absolute value function f(x) = | x + 3 | written in piece wise function includes the piece  given by option B . x + 3, x > -3.

Function f(x) is represented as absolute value function:

f(x) = | x + 3 |

Absolute function is always positive when the included variable is greater than zero.

| x + 3 |  > 0

⇒ ( x + 3 ) > 0

Subtract three from both the sides we get,

⇒ x + 3 - 3 > 0 - 3

⇒ x > -3

Here piecewise function incudes the piece :

x + 3,  x > -3.

Therefore, the absolute function f(x) = | x + 3 | includes the piece after written in piecewise function form is equal to option B. x + 3,  x > -3.

The above question is incomplete , the complete question is:

Select the correct answer.

Consider this absolute value function.

f(x) = | x + 3 |

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

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Answer: It's the third down. (-1/-2) - PLEASE TAKE THIS WITH A GRAIN OF SALT. I'm not very good at this type of math.

Step-by-step explanation:

The probability that at least one of the next five dogs he sees is a German shepherd is 0.75.

We have from the question.

0,1, and 2: retrievers

3 and 4: terriers

5 and 6: German shepherds

7,8 and 9: other dogs

In these results, 5 and 6 represent a german shepherd "at least one of the next five dogs he sees is a German shepherd." this means that at least one of the five numbers is 5 or 6.

There are a total of 20 results among them; 12 results include at least one 5 or 6.

∴P = 12/20 = 0.75

Hence, the correct option is B.

--The given question is incomplete; the complete question is

"Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers, and 20% are German shepherds. He designs a simulation.  Let 0,1 and 2 represent retrievers. Let 3 and 4 represent terriers. Let 5 and 6 represent German shepherds. Let 7,8, and 9 represent other dogs. The table shows the simulation results. According to this simulation, what is the probability that at least one of the next five dogs he sees is a German shepherd?

A. 0.70

B. 0.75

C. 0.65

D. 0.60"--

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Answer:

$8

Step-by-step explanation:

Answer:

12/5 = 2.4 miles

2.4 x (15/16) = 2.25 miles.

2.25, or 9/4 miles

Answer:

X = 4

Step-by-step explanation:

We have to add like variables, so all the x variables will be added together. We get this:
-x + 35 = 31

Get x by itself.
-x = -4

Get rid of the negatives since what you do on one side you do to both sides.

x = 4

I hope this was able to help you out :D

16 (-x +x ) +19 + x = 31

16+19+x = 31

35+x = 31

x= -4

hey buddy i hope uh got an answer

Answer:

the answer is 0= -5/3x + c

Answer: non

as a wordf 2 b geven

Using the created proportion for each set of similar triangles, the missing side lengths are 3√29 units and 24 units respectively

Similar triangles are triangles that have the same shape, but not necessarily the same size. Two triangles are similar if and only if they have the same shape, meaning they have the same angle measures.

For the 1st triangles, we can write the proportion as follows:

proportion = (√29)/5

(√29)/5 = x/15

x = 15 × (√29)/5

x = 3√29 units

Thus, the missing side length is 3√29 units

For the 2nd triangles, we can write the proportion as follows:

proportion = 12/13

12/13 = x/26

x = 26 × (12/13)

x = 24 units

Thus, the missing side length is 24units

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Answer:

See below

Step-by-step explanation:

North, 50

West, 28

South, 71

Answer: i got North, 50

West, 28

South, 71

but have a good day

Step-by-step explanation:

Calvin representation of 108% as 10.8 is incorrect

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

Percentage increase = 108%

Express the percentage as a fraction

So, we have the following representation

Percentage increase = 108/100

Evaluate the quotient

This gives

Percentage increase = 1.08

Hence, the expression is 1.08 and Calvin is wrong

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Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.

Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.

This is represented as follows:

t = k(l/p)

Where, k is the proportionality constant.

Given that, it takes 10 hours to paint 400 feet of fence with six workers.

Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:

10 = k (400 / 6)

10 = k (66.66)

k = 10 / 66.66

k = 0.15

Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:

t = (0.15) (1000 / 10

t = (0.15) (100)

t = 15

Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

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Answer:

[tex]20x^{2} + 12x[/tex]

Step-by-step explanation:

We can expand this equation:

(4x * 5x) + (4x * 3)

= [tex]20x^{2} + 12x[/tex]

If simplified/factored further, we can take out the common variable, x, as well as 4, which is a common number shared between 20 and 12:

4x(5x + 3)

It should be emphasized that this suggests that we are 90% certain that the mean GPA for all students at the institution is between 3.14 and 3.52

Sampling

If the confidence level were raised to 99%, something would happen to the interval's length, increasing it.

The difference between a 90% confidence interval based on a 200-person sample and the original 90% interval is that the latter is narrower.

Last but not least, having the students say their grades aloud could have introduced bias into Ellery's study, which is not taken into account by the margin of error. Some of them with lesser grades will start to lie as a result.

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The area of an isosceles trapezoid is 45 square ft.

We have to evaluate the area of trapezoid.

The perimeter of an isosceles trapezoid is 40 ft.

The bases of the trapezoid are 11 ft and 19 ft.

The perimeter of an isosceles trapezoid = a + b + c + d

a, b, c and d all are sides of an isosceles trapezoid.

a + b + c + d = 40

According to question, c = d

11 + 19 + c + c = 40

30 + 2c = 40

Subtract 30 on both side, we get

2c = 10

Divide by 2 on both side, we get

c = 5 = d

The formula of area of an isosceles trapezoid is

A = [tex]\frac{1}{2}[/tex](a+b)h, where a and b are bases and h is the height.

We can see on the diagram that we can use Pythagorean theorem to find the height.

According to theorem;

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

[tex](5)^2 = h^2+(4)^2[/tex]

25 = [tex]h^2[/tex] + 16

Subtract 16 on both side, we get

[tex]h^2[/tex] = 9

Taking square root on both side, we get

h = 3

The height of an isosceles trapezoid is 3 ft.

Now, the area of an isosceles trapezoid is

A = [tex]\frac{1}{2}[/tex](11+19)×3

A = [tex]\frac{1}{2}[/tex] × 30 × 3

A = 15 × 3

A = 45 square ft

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Answer:

28.26 [tex]in^{2}[/tex]

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = 3.14([tex]3^{2}[/tex])

a = 3.14(9)

a = 28.26

The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

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Answer: No Solution is the answer

Step-by-step explanation:

Have a photo attached with the work

The perimeter of a rectangle measuring 4.1263cm long and 2.8315cm is 13.9 cm

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

Length = 4.1263 cm

Width = 2.8315 cm

The perimeter of a rectangle can be calculated using tge following equation

Perimeter = 2 x (Length + Width)

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

Perimeter = 2 x (4.1263 + 2.8315)

Evaluate

Perimeter = 13.9156

Approximate

Perimeter = 13.9 to 3 significant figures

Perimeter = 13.916 to 3 decimal places

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Expression 1: 4t - (4t x 0.25) = 4t - (t) = 3t

Expression 2: 4 x (t - (t x 0.25)) = 4 x (t x 0.75) = 3t

where 't' is the cost of one T-shirt.

In expression 1, the original cost of the four T-shirts (4t) is multiplied by 25% (0.25) which is the given discount percent, and then subtracted from the original cost.

In expression 2, the original cost of one T-shirt (t) is multiplied by 25% (0.25) and subtracted from the original cost, and then the resulting cost (t x 0.75) is multiplied by four to represent the cost of four T-shirts.

Both expressions represent the cost of the four T-shirts after a 25% discount has been applied. they both yield the same result of 3t, which represents the final cost of the four T-shirts after the discount has been applied.

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Answer:

Step-by-step explanation:

D

The number of people that attended the school play is given as follows:

The situation is modeled by a system of equations, for which the variables are given as follows:

There was a total of 937 people, hence:

a + s = 937.

s = 937 - a.

The total sales were of $1,109, hence:

2a + 0.75s = 1109.

Replacing s = 937 - a in the second equation, the number of adults is obtained as follows:

2a + 0.75(937 - a) = 1109

1.25a = 406.25

a = 406.25/1.25

a = 325.

Then the number of students is obtained as follows:

s = 937 - a

s = 937 - 325

s = 612.

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