As of a certain​ date, there had been a total of 14,404 performances of two shows on​ Broadway, with 2384 more performances of Show A than Show B. How many performances were there of each​ show?

Answer:she had $63.75 at first.

Step-by-step explanation:

Let x represent the amount of money that she had at first.

kathy spent 3 fifths of her money on a necklace. This means that the amount of money that she spent on the necklace is

3/5 × x = 3x/5

The amount of money remaining would be

x - 3x/5 = 2x/5

She used 2 thirds of the remainder on a bracelet. This means that the amount of money that she spent on the bracelet is 2/3 × 2x/5 = 4x/15

If the bracelet costs $17.00, then

4x/15 = 17

4x = 15 × 17

4x = 255

x = 225/4

x = 63.75

Final answer:

Kathy had $63.75 at first. We determined this by dividing the cost of the bracelet by 2 to find 1/3 of the remainder, then multiplying by 3 to find the full remainder, and finally calculating the total by multiplying by 5.

Explanation:

To solve the problem of how much money Kathy had at first, we need to work backwards from the cost of the bracelet. Kathy spent 2 thirds of the remainder of her money on a bracelet that costs $17.00. If 2/3 of the remainder equals $17, then 1/3 of the remainder would be $17 / 2 = $8.50. This means the full remainder (3/3) would be 3 times $8.50, which is $25.50. This remainder represents the 2/5 of her original amount, as she spent 3/5 on the necklace.

To find out the full amount of money Kathy had, we need to figure out what number 2/5 of it is $25.50. So, if 2/5 equals $25.50, then 1/5 equals $25.50 / 2 = $12.75. Finally, to find the total amount Kathy had at first, we multiply $12.75 by 5 (since her total money is 5/5), giving us $63.75 as the total amount of money Kathy had originally.

Answer:

um in the first place why the hell did they steal a car? and paint the dmn car?

Step-by-step explanation:

Answer:

F=3

Step-by-step explanation:

Due to the difficulty of visualizing the graph of the function in degrees (graph 1), we will graph it in radians (graph 2)

f(x)=−sin(3x)−1 ≡ y=−sin(3x)−1

To graph y=−sin(3x)−1

y=a.sin(bx+c)+d, where

a=-1, b=3, c=0, d=-1 and the period (T) of the function  is:

[tex]T=\frac{2\pi }{b}=\frac{2\pi }{3}[/tex]

On the graph 2 we place the original function y=sin(x) to compare

We watch that y=−sin(3x)−1 moves 1 down (-), but amplitud is the same (1)

Frequency is the number of repetitions (3x) of a function in a given interval, so

F=3

The frequency of the function f(x) = -sin(3x) - 1 is 3/(2π), determined by the coefficient of x inside the sine function.

The frequency of the function f(x) = -sin(3x) - 1 can be determined by examining the coefficient of x within the sine function. The standard form for a sine function is f(x) = sin(Bx), and the frequency f is given by f = B/(2π). In this case, the coefficient B is 3, so the frequency of the function is 3/(2π), which is already in simplest fraction form.

Answer:

(a)∴A=$6753.71.

(b)∴A=$1480.24

(c) ∴P=$7424.70

(d)∴P=$49759.62

(e)∴P=$5040.99

(f) ∴P=$2496.11

Step-by-step explanation:

We use the following formula

[tex]A=P(1+\frac rn)^{nt}[/tex]

A=amount in dollar

P=principal

r=rate of interest

(a)

P=$2,500, r=5%=0.05,t =20 years , n= 4

[tex]A=\$2500(1+\frac{0.05}{4})^{(20\times 4)[/tex]

   =$6753.71

∴A=$6753.71.

(b)

P=$1,000, r=8% =0.08,t =5 years , n= 2

[tex]A=\$1000(1+\frac{0.08}{2})^{(5\times 2)[/tex]

   =$1480.24

∴A=$1480.24

(c)

A=$10,000, r=6% =0.06,t =5 years , n= 4

[tex]10000=P(1+\frac{0.06}{4})^{(5\times 4)}[/tex]

[tex]\Rightarrow P=\frac{10000}{(1+0.015)^{20}}[/tex]

[tex]\Rightarrow P=7424.70[/tex]

∴P=$7424.70

(d)

A=$100,000, r=6% =0.06,t =10 years , n= 12

[tex]100000=P(1+\frac{0.07}{12})^{(10\times 12)}[/tex]

[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.07}{12})^{120}}[/tex]

[tex]\Rightarrow P=49759.62[/tex]

∴P=$49759.62

(e)

A=$100,000, r=10% =0.10,t =30 years , n= 12

[tex]100000=P(1+\frac{0.10}{12})^{(30\times 12)}[/tex]

[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.10}{12})^{360}}[/tex]

[tex]\Rightarrow P=5040.99[/tex]

∴P=$5040.99

(f)

A=$100,000, r=7% =0.07,t =20 years , n= 4

[tex]100000=P(1+\frac{0.07}{4})^{(20\times 4)}[/tex]

[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.07}{4})^{80}}[/tex]

[tex]\Rightarrow P=2496.11[/tex]

∴P=$2496.11

To find the balance A, we use the formula A = P(1 + r/n)^(nt). To find the principal P, we rearrange the formula to P = A / ((1 + r/n)^(nt)).

(a) To find the balance A, we can use the formula A = P(1 + r/n)^(nt). Plugging in the given values, we have:

A = $2,500(1 + 0.05/4)^(4*20) = $2,500(1.0125)^80 ≈ $9,005.29

(b) Using the same formula, we can calculate:

A = $1,000(1 + 0.08/2)^(2*5) = $1,000(1.04)^10 ≈ $1,483.11

(c) To find the principal P, we rearrange the formula: P = A / ((1 + r/n)^(nt)). Plugging in the given values, we get:

P = $10,000 / ((1 + 0.06/4)^(4*5)) ≈ $7,772.22

(d) Using the rearranged formula, we can calculate:

P = $50,000 / ((1 + 0.07/12)^(12*10)) ≈ $23,022.34

(e) Since the compounding is monthly, we need to calculate the value of r/n first: r/n = 0.10/12 ≈ 0.0083. Plugging in the values, we have:

P = $100,000 / ((1 + 0.0083)^(12*30)) ≈ $3,791.61

(f) Similarly, we calculate:

P = $100,000 / ((1 + 0.07/4)^(4*20)) ≈ $24,084.48

Answer:

y=2x+7

Step-by-step explanation:

2x−y+4=0

y=2x+4

m=2

Line are parallel, so their slope is the same.

A(-1,5)... x1 =-1,y1 =5

y-y1 =m(x-x1)

y1 - 5=2(x-(-1))

y1 - 5=2(x+1)

y1-5=2x+2

y=2x+2+5

y=2x+7

Answer: y = 2x + 7

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c represents y intercept

m represents the slope of the line.

The equation of the given line is

2x - y + 4 = 0

y = 2x + 4

Comparing with the slope intercept form, slope = 2

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 1, 5) is 2

To determine the y intercept, we would substitute m = 2, x = - 1 and y = 5 into y = mx + c. It becomes

5 = 2 × - 1 + c

5 = - 2 + c

c = 5 + 2 = 7

The equation becomes

y = 2x + 7

Answer: Xn = n(n+1)/2

Step-by-step explanation:

Firstly, you work with asingle dot for each and let n= 1,2,3,4....

Now if you double the dots, it will form a rectangle and it is easier to work with many dots i.e just multiple n by n+1

Dots in rectangle= n(n+1)

But remember the number of dots were doubled therefore,

Dots in triangle = n(n+1)/2.

Answer:

subtract 2 from both sides of the equation

Step-by-step explanation:

The first step in solving the equation 5 = 2 + ? is to subtract 2 from both sides of the equation.

The first step in solving the equation 5 = 2 + ? is to subtract 2 from both sides of the equation. This helps to isolate the variable and find its value. By subtracting 2 from both sides, the equation becomes: 5 - 2 = 2 + ? - 2. Simplifying further, we get: 3 = ?.

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Answer:

F(x)=-1/5x-7

Step-by-step explanation:

You have to switch signs and flip the orgininal slope to get a perpendicular one.

5 will become - 5

Then it will become -1/5 because 5 on its own is equivalent to -5/1

Answer: the slope is - 1/5

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form which is expressed as

y = mx + c

Where

m represents the slope

c represents the y intercept

Comparing with the given equation,

Slope, m = 5

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Therefore, the slope of the line perpendicular to

F(x)=5x-7 is - 1/5

See the attached picture:

Answer:

  see below

Step-by-step explanation:

Rotation problems can be worked fairly easily if you have tracing paper or a transparency. Overlay the (semi-)transparent material on the given graph and trace the axes and figure. Then rotate the material according to the directions and copy the new position back to the graph.

(I find this much easier than trying to figure the coordinates.)

Step-by-step explanation:

Let us assume the two needed vehicles are A and Q.

Let P(A) be the probability of the vehicle A available when needed.

And, P(Q) be the probability of the vehicle Q available when needed.

Now, P(A) = 90 % = 0.90

⇒ P (not A) =  1 - P(A)  

                    =  1- 0.9 =  0.1

⇒ P (not A) = 0.1

Similarly,  P(Q) = 90 % = 0.90

⇒ P (not Q) =  1 - P(Q)  

                    =  1- 0.9 =  0.1

⇒ P (not Q) = 0.1

So, the probability that both the vehicles are NOT available when needed  

= P(not A) x P(not Q)  

= 0.1 x 0.1 = 0.01

Hence, the probability that neither vehicle is available at a given time is 0.01

Option B:

The relationship between angle j and angle k is j° + k° = 180°.

Solution:

Given JKLM is a parallelogram.

angle J and angle K are consecutive angles.

To find the relationship between angle j and angle k:

In parallelogram, the sum of the consecutive angles is 180°.

⇒ m∠J + m∠K = 180°

⇒ j° + k° = 180°

Hence the relationship between angle j and angle k is j° + k° = 180°.

Option B is the correct answer.

In parallelogram JKLM, angle J and angle K are congruent or have the same measure.

In parallelogram JKLM, angle J and angle K are congruent. This means that they have the same measure.

A parallelogram is a quadrilateral with opposite sides that are parallel. Since the opposite sides of a parallelogram are parallel, the opposite angles are also congruent.

Therefore, angle J and angle K in parallelogram JKLM have the same measure.

Answer:

Both apply

Step-by-step explanation:

SSS can be used because sides are already known to be equal

SAS can also be used because when you have the 3 sides, you can use the cosine law to find any angle

Answer:

B.

Step-by-step explanation:

The line is going up 1 and over 2, making the slope 1/2 and the y-intercept is 1. Hope this helped!

Answer: a) [tex]\frac{x^{2} }{2352.25 }[/tex] + [tex]\frac{y^{2} }{529}[/tex] = 1

b) The distance of two foci is 85.4 feet

c) Area = 3502.67 square feet

Step-by-step explanation: a) An ellipse has the equation in the form of:

[tex]\frac{x^{2} }{a^{2} }[/tex]+[tex]\frac{y^{2} }{b^{2} }[/tex] = 1, where a is the horizontal axis and b is the vertical axis.

For the Statuary Hall, a = [tex]\frac{97}{2}[/tex] = 48.5 and b = [tex]\frac{46}{2}[/tex] = 23, so the equation will be

[tex]\frac{x^{2} }{2352.25 }[/tex] + [tex]\frac{y^{2} }{529}[/tex] = 1.

b) To determine the distance of the foci, we have to calculate 2c, where c is the distance between one focus and the center of the ellipse. To find c, as a, b and c create a triangle with a as hypotenuse:

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

[tex]c^{2} = a^{2} - b^{2}[/tex]

c = [tex]\sqrt{48.5^{2} - 23^{2} }[/tex]

c = 42.7

The distance is 2c, so 2·42.7 = 85.4 feet.

The two foci are 85.4 feet apart.

c)The area of an ellipse is given by:

A = a.b.π

A = 48.5 · 23 · 3.14

A = 3502.67 ft²

The area of the floor room is 3502.67ft².

Answer:

a) For Bella, x has to be a positive even values

For Tito, x has to be a negative even values

b) For Bella, x = 4

For Tito, x = -4

Answer:

(option C/3) 12^3 + 6x^2

Step-by-step explanation:

Took test and got it right.

The product of 2x^2 and (6x + 3) is calculated using the distributive property of multiplication over addition, resulting in 12x^3 + 6x^2.

The question requires us to find the product of the polynomial 2x^2 with the binomial (6x + 3). We use the distributive property of multiplication over addition to multiply 2x^2 by each term in the binomial.

Step 1: Multiply 2x^2 by 6x: 2x^2 * 6x = 12x^3

Step 2: Multiply 2x^2 by 3: 2x^2 * 3 = 6x^2

Thus, the product of 2x^2(6x + 3) = 12x^3 + 6x^2. So the correct answer is D. 12x^3 + 6x^2.

Learn more about Polynomial multiplication here:

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*100% CORRECT ANSWERS

Question 1

Alan is writing out the steps using the "shortest Route Algorithm". On the second step, he just circled the route ABD as the shortest route from A to D. What should he cross out next?  

AD; 6  

Question 2

Beth is writing out the steps using the "Shortest Route Algorithm". She just finished writing out all the routes for the third step. What route should she circle next?  

ACE; 6  

Question 3

If you start at vertex A and use the "shortest route" algorithm, what would be the second path to be selected/highlighted?  

ACF  

(SEE ATTACHMENTS BELOW)

Answer: ACF

Step-by-step explanation: Starting at vertex A and using shortest routes algorithm the secondary route to be selected would be ACF = 1+2 = 3

The first route would be AC = 1. A vertex is a point where two straight lines meet or join, they are usually found in angles.

Answer: she bought 5 greeting cards at $2.50 each.

Step-by-step explanation:

Let x represent the number of greeting cards that she bought at $2.50 each.

Let y represent the number of greeting cards that she bought at $4 each.

She buys some greeting cards that cost $2.50 each and some greeting cards that cost $4 each. She buys 12 cards. This means that

x + y = 12

The total amount that she spent in buying the greeting cards is $40.50. It means that

2.5x + 4y = 40.5- - - - - - - - - - 1

Substituting x = 12 - y into equation 1, it becomes

2.5(12 - y) + 4y = 40.5

30 - 2.5y + 4y = 40.5

- 2.5y + 4y = 40.5 - 30

1.5y = 10.5

y = 10.5/1.5

y = 7

x = 12 - y = 12 - 7

x = 5

Maya bought 5 greeting cards that cost $2.50 each.

Step 1

Let's denote the number of greeting cards that cost $2.50 as x, and the number of greeting cards that cost $4 as y . We know two things from the problem statement:

1. Maya buys a total of 12 cards: x + y = 12 .

2. The total cost of the cards is $40.50: 2.50x + 4y = 40.50.

Now, we'll solve these equations simultaneously to find x .

From equation (1):

x + y = 12

y = 12 - x

Step 2

Substitute y = 12 - x into equation (2):

[tex]\[ 2.50x + 4(12 - x) = 40.50 \][/tex]

Expand and simplify:

[tex]\[ 2.50x + 48 - 4x = 40.50 \][/tex]

[tex]\[ -1.50x + 48 = 40.50 \][/tex]

Subtract 48 from both sides:

[tex]\[ -1.50x = 40.50 - 48 \][/tex]

[tex]\[ -1.50x = -7.50 \][/tex]

Step 3

Divide both sides by -1.50 to solve for x :

[tex]\[ x = \frac{-7.50}{-1.50} \][/tex]

[tex]\[ x = 5 \][/tex]

So, Maya bought x = 5 greeting cards that cost $2.50 each.

Verification:

Now, substitute x = 5 back into the equation y = 12 - x  to find y :

y = 12 - 5

y = 7

Check the total cost:

[tex]\[ 2.50 \cdot 5 + 4 \cdot 7 = 12.50 + 28 = 40.50 \][/tex]

Everything checks out correctly. Therefore, Maya bought 5 greeting cards that cost $2.50 each.

Answer:

It'll take the robot 8 minutes to complete one task

7.5 tasks will be completed in one hour

Step-by-step explanation:

Total time to complete 5 tasks is 2/3hr (40 minutes)

Time it takes to complete one task = 40 ÷ 5 = 8 minutes

Since the robot completes one task in 8 minutes, x tasks will be completed in 60 minutes.

x = 60 ÷ 8 =  7.5 tasks

Answer:

A. 8 minutes; B. 7.5 tasks in one hour; C. It takes the robot about [tex] \\ \frac{2}{15}\;hour[/tex] or about 0.1333 hour to complete one task or 13.33% of one hour.

Step-by-step explanation:

Part A

Two thirds hours is

[tex] \\ \frac{2}{3}*60 = 40\;min[/tex]  

We know that each task takes the same amount of time. So, 40min can be divided by 5:

[tex] \\ \frac{40}{5} = 8\;min[/tex]

Thus, each task takes 8 min to be completed. Then, it takes the robot 8 minutes to complete one task.

Part B

The robot can complete 5 tasks in 40 minutes, how many tasks can the robot complete in 60 minutes or one hour?

There are 20 minutes ahead to complete one hour. In the next 8 minutes, the robot can complete one task. There are still 12 minutes ahead. In the next 8 minutes, the robot completes another task. There is still 4 minutes ahead to complete the hour, but in 4 minutes the robot can complete half of the task because it takes 8 minutes for a complete task. Therefore, the robot can complete 5 tasks + 2 tasks + 0.5 task = 7.5 tasks in one hour or 60 minutes.

We can obtain the same answer using proportions. That is, if 5 tasks are completed in 40 minutes, how many of them will be completed in one hour or 60 minutes.  

Then

[tex] \\ \frac{5\;tasks}{40\;min} = \frac{x}{60\;min}[/tex]

[tex] \\ \frac{5\;tasks}{40\;min}*60\;min = x[/tex]

[tex] \\ x = \frac{5\;tasks*60\;min}{40\;min}[/tex]

[tex] \\ x = \frac{300\;tasks}{40} = 7.5\;tasks[/tex]

Part C (A)

From part A, we already know that the robot can complete a task in 8 minutes, which is a fraction of one hour. What is this fraction? In one hour we have 60 minutes, then

[tex] \\ 8\;min*\frac{1\;hour}{60\;min} = 1\;hour*\frac{8}{60} = 1\;hour*\frac{4}{30} = 1\;hour*\frac{2}{15} = 0.1333333....\;hours \approx 0.1333\;hours[/tex].

Therefore, it takes the robot about [tex] \\ \frac{2}{15}\;hour[/tex] or 0.1333 hour to complete one task (rounding to four decimal places) or 13.33% of one hour.

Answer:

After 12 years height of both the trees would be same.

Step-by-step explanation:

Given,

Height of tree type A = 5 ft

Height of tree type B = 8 ft

We need to find after how many years both the trees will be of same height.

Solution,

Firstly we will convert the height of both plants into inches.

Since we know that 1 feet is equal to 12 inches.

So height of tree type A =[tex]5\ ft=5\times12=60\ in[/tex]

Similarly, height of tree type B =[tex]8\ ft=8\times12=96\ in[/tex]

Also given that;

Rate of growth of tree type A = 9 in/year

and rate of growth of tree type A = 6 in/year

Let the number of years be 'x'.

So according to question after 'x' years the height of both trees type A and type B will be same.

Now we can frame the equation as;

[tex]60+9x=96+6x[/tex]

Combining the like terms, we get;

[tex]9x-6x=96-60\\\\3x=36[/tex]

On dividing both side by '3' using division property, we get;

[tex]\frac{3x}{3}=\frac{36}{3}\\\\x=12[/tex]

Hence after 12 years height of both the trees would be same.

Answer:

[tex] x^{\frac{3}{5}} [/tex]

Step-by-step explanation:

[tex] \dfrac{\sqrt[3]{x^3}}{\sqrt[5]{x^2}} = [/tex]

[tex] = \dfrac{x^\frac{3}{3}}{x^\frac{2}{5}} [/tex]

[tex] = \dfrac{x^1}{x^\frac{2}{5}} [/tex]

[tex] = x^{\frac{1}{1} - \frac{2}{5}} [/tex]

[tex] = x^{\frac{5}{5} - \frac{2}{5}} [/tex]

[tex] = x^{\frac{3}{5}} [/tex]

Answer:

The third fret is 64.390mm from the first fret

Step-by-step explanation:

Distance between first and second fret is 33.641mm

Distance between second and third fret is 31.749mm

Hence distance between third and first fret will be = 33.641 + 31.749 = 64.390mm

Answer65.

Step-by-step explanation:

In this question, we are asked to state the distance between third and first frets.

Now, to consider this distance, just visualize. From the particulars in the question we can see that to get the distance, we need to add the two numbers together.

Mathematically, to calculate the distance, we need to make addition. This is represented by 31.749 + 33.641 = 65.39mm

The distance between the first fret and the second fret is 65.39mm

Answer:

4457400

Step-by-step explanation:

25C14 = 4457400

Not practical, these are too many

Answer:

4,457,400  combinations.

Step-by-step explanation:

The number of combinations of 14 from 25 is a very large number :

25C14 =   25! / 14! 11!

=  4,457,400.

With so many possible combinations it would not be practical to make a Cd for all these possibilities.

Answer:

The answer to your question is 17.5 units

Step-by-step explanation:

Data

A (-10, 12)

B (5, 3)

Formula

dAB = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

x1 = -10   y1 = 12  x2 = 5  y2 = 3

- Substitution

dAB = [tex]\sqrt{(5 + 10)^{2} + (3 - 12)^{2}}[/tex]

- Simplification

dAB = [tex]\sqrt{15^{2}+ (-9)^{2}}[/tex]

dAB = [tex]\sqrt{225 + 81}[/tex]

dAB = [tex]\sqrt{306}[/tex]

Result

dAB = 17.49 units

The answer is the first choice

Answer:

2 chocolate balls with 1 coconut for chocolate

3 chocolate balls with 4 of coconut for coconut

Step-by-step explanation:

In this case, what should be done to know when it will taste more chocolate or coconut, is to get the percentage of each one with respect to the total there is. Analyzing each case would be:

2 chocolate balls with 1 coconut, total 3 balls.

% chocolate = (2/3) * 100% = 66.6%; % coconut = (1/3) * 100% = 33.3%

3 chocolate balls with 2 coconut, total 5 balls

% chocolate = (3/5) * 100% = 60%; % coconut = (2/5) * 100% = 40%

4 chocolate balls with 3 coconut, total 7 balls

% chocolate = (4/7) * 100% = 57.14%; % coconut = (3/7) * 100% = 42.86%

3 chocolate balls with 4 coconut, total 7 balls

% chocolate = (3/7) * 100% = 42.86%; % coco = (4/7) * 100% = 57.14%

6 chocolate balls with 4 coconut, in total 10 balls

% chocolate = (6/10) * 100% = 60%; % coconut = (4/10) * 100% = 40%

3 chocolate balls with 3 coconut, in total 6 balls

% chocolate = (3/6) * 100% = 50%; % coconut = (3/6) * 100% = 50%

When it tastes more like chocolate it is in the case of 2 chocolate balls with 1 coconut, which contains 66.6% chocolate, therefore it is when it tastes more like chocolate.

When it tastes more like coconut it is in the case of 3 chocolate balls with 4 of coconut, a total of 7 balls, which contains 57.14% chocolate, therefore it is when it tastes more like coconut.

Answer:

Step-by-step explanation:

it is 11423 ft3

Final answer:

The difference in volume of the weather balloon from launch to burst is calculated using the formula for the volume of a sphere, considering the change in diameters from 5 ft to 28 ft. The resulting difference is approximately 11,428.89 cubic feet.

Explanation:

The question asks for the difference in volume of a weather balloon when it burst compared to at launch. To solve this, we use the formula for the volume of a sphere, which is V = \(\frac{4}{3}\)\(\pi\)r^3, where r is the radius of the sphere. Given that the diameter at launch was 5 ft and at burst was 28 ft, the radiuses would be 2.5 ft and 14 ft, respectively.

Volume at launch: V1 = \(\frac{4}{3}\)\(\pi\)(2.5)^3 \approx 65.45 cubic feet. Volume at burst: V2 = \(\frac{4}{3}\)\(\pi\)(14)^3 \approx 11,494.34 cubic feet. The difference in volume: V2 - V1 \approx 11,494.34 - 65.45 \approx 11,428.89 cubic feet.

Therefore, the difference in volume of the balloon when it burst compared to at launch is approximately 11,428.89 cubic feet.

The quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled is h = -2/15*(d-15)² + 30 with the maximum point at (15, 30) and passing through the origin.

The problem here can be diagnosed using concepts of

quadratic functions

and

vertex form

. In a real world scenario, the motion of a projectile like the flea jumping can be modeled using a downward opening parabola represented by a quadratic function. In this case, we are asked to find the quadratic function in vertex form, which is given by

h = a(d - h1)² + k

where (h1,k) is the vertex of the parabola. In the given scenario, the maximum height attained by the flea is 30 cm which is at a horizontal distance of 15 cm from the starting point, thus the vertex of the parabola is (15, 30). From the information given, we know that the flea starts from the ground, so at the origin, height h = 0. Substituting these values, we get the equation of the parabola as

h = -a(d-15)^2 + 30

.

To find the value of 'a'

, we can use the information that the parabola passes through the origin (0,0). Substituting these values in the equation, we get a = -30/225 = -2/15. Therefore, the quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled becomes

h = -2/15*(d-15)² + 30

.

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Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: number of 18-20-year-olds that consume alcoholic beverages in a sample of 50.

The proportion of underage people that drinks are known to be p= 0.697

This variable is discrete. This experiment has two possible outcomes success or failure, we will call "success" each time we encounter an underage individual that consumes alcohol and "failure" will be counting an underage that does not consume alcohol. The number of repetitions of the trial is fixed n= 50. All randomly selected underage individuals are independent and the probability of success is constant trough the whole experiment p=0.697.

Then we can say that this variable has a binomial distribution and we will use that distribution to do the calculations.

a. Under a binomial distribution, the expected value is calculated as:

E(X)= n*p= 50*0.697= 34.85.

The variance of a binomial distribution is:

V(X)= n*p*(1-p)= 50*0.697*0.303= 10.55955

And the standard deviation is the square root of the variance:

√V(X)= 3.2495 ≅ 3.25

b. To know how rare the value 45, you have to see how distant it is concerning the expected value. For this you have to subtract the expected value and divide it by the standard deviation:

[X-E(X)]/√V(X)

(45-34.85)/3.25= 3.12

The value X=45 is 3.12 standard deviations above the mean, which means that it would be rare to find 45 people or more than consumed alcohol.

c. P(X≥45) = 1 - P(X<45)= 1 - P(X≤44)= 1 - 0.9994= 0.0006

I hope it helps!

The required values are:

a) Expect to have consumed alcoholic beverages[tex]=np=34.85[/tex]

and, Standard Deviation [tex]\sigma =3.25[/tex]

b) yes, 45 is more than two standard deviations above the expected value(mean)

C) Probability[tex]=0.0015[/tex]

a)

[tex]n=50\\p=0.6970[/tex]

They expect to have consumed alcoholic beverages,

[tex]=n \times p\\=50 \times 0.6970\\=34.85[/tex]

Standard Deviation,

[tex]\sigma =\sqrt{\left ( np\left ( 1-p \right ) \right )} \\ =\sqrt{\left (34.85 \right )(1-0.6970)} \\ =3.25[/tex]

b) Yes, 45 is more than 2 standard deviations above the expected value (mean)

C) Probability,

[tex]P=\left ( x > 44.5 \right ) \\ P=\frac{( Z > 44.5-34.85)}{3.25} \\ P=\left ( Z > 2.97 \right ) \\ P=1-P\left ( Z < 2.97 \right ) \\ P=1-0.9985 \\ P=0.0015[/tex]

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Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 denotes the number you get for rolling 1st die.

- Random Variable X_2 denotes the number you get for rolling 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

- First we will develop a probability distribution of X such that it is defined by the difference of second and first roll of die.

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                  ( X = -2 ):  { X_2 = 1 , X_1 = 3 }

                  P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )

                                 :  ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 1 / 9 )

                  ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                 P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 2 / 9 )

       ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

       P ( X = -1 ):P ( X_2 = 1 )*P ( X_1 = 1 )+P( X_2 = 2 )*P ( X_1 = 2)+P( X_2 = 3 )*P ( X_1 = 3)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 3 / 9 ) = ( 1 / 3 )

                    ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

                 P ( X = 1 ):  P ( X_2 = 2 ) * P ( X_1 = 1 ) + P ( X_2 = 3 ) * P ( X_1 = 2)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 2 / 9 )

                    ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                  P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )

                                    :  ( 1 / 3 ) * ( 1 / 3 )

                                    : ( 1 / 9 )                  

- The distribution Y = X_2,

                          P(Y=0) = 0

                          P(Y=1) =  1/3

                          P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

Answer:

Adding a constant to every score increases the mean by the same constant amount. Thus, μ

= 50+10= 60.

Adding a constant to every score has no effect on the standard deviation. σ = 5

Step-by-step explanation:

If a constant value is added to every score in a distribution, the same constant will be added to the mean. similarly, if you subtract a constant from every score, the same constant will be subtracted from the mean.

A;so recall the definition of standard deviation, it measures how each observation is far from its center on average, so if you shift your data by A then, also every observation is shifted by A and then standard deviations stays the same. also think standard deviation as measure of spread not a measure of scale.

When 10 points are added to every score in a population with a mean of 50 and standard deviation of 5, the new mean will be 60 but the standard deviation does not change and remains 5.

In the given scenario, the population has a mean of 50 (µ = 50) and a standard deviation of 5 (σ = 5). When you add 10 points to every score in the population, the mean of the population, which is the average of all scores, will increase by 10, resulting in a new mean of 60.

The standard deviation, which measures the dispersion or spread of scores from the mean, will not change. This happens because adding a constant to every score only shifts the entire distribution of scores, but does not increase or decrease the spread, or 'standard deviation,' among them. In other words, the new value of the standard deviation will remain as 5.

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