There are 22 students, from which 6 people will be selected to be on a panel. If Allen and Joe are 2 of the 22 students, then what is the probability that neither will be selected to be on the panel?

Round your answer to three decimal places.

Answers

Answer 1
Answer:  0.519

==========================================

Explanation:

Let's start off counting the number of ways to form the panel that doesn't have Allen or Joe on it. In other words, both are not on the panel.

There are 22 students, but we want to exclude 2 of them (Allen and Joe) from the panel. So in reality, we only have 20 students to pick from. There are 6 slots to fill.

The first slot has 20 choices

The second slot has 19 choices

The third has 18 choices

And so on. We count our way down until all six slots are filled. We'll have this sequence of six values: 20, 19, 18, 17, 16, 15

They multiply out to 20*19*18*17*16*15 = 27,907,200

This is the number of permutations where we choose 6 from a pool of 20.

With permutations, order matters; however, order doesn't matter on this panel. All we care about is the group overall.

So we must divide by 6! = 6*5*4*3*2*1 = 720 and we get

(27,907,200)/(720) = 38,760

There are 38,760 different combinations, so there are 38,760 different panels where neither Allen nor Joe are selected.

We'll use this later later, so let A = 38,760

------------------------------------------------------

Now onto the next part. We need to count the total number of possible panels, and this time we're including Allen and Joe.

We have our original total of 22 students. There are still 6 seats to fill.

We could follow the same steps as the prior section, but I'll use a different route.

Let n = 22 and r = 6. Plug these values into the nCr combination formula below

[tex]_n C_r = \frac{n!}{r!*(n-r)!}\\\\_{22} C_6 = \frac{22!}{6!*(22-6)!}\\\\_{22} C_6 = \frac{22!}{6!*16!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17*16!}{6!*16!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17}{6!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17}{6*5*4*3*2*1}\\\\_{22} C_6 = \frac{53721360}{720}\\\\_{22} C_6 = 74613\\\\[/tex]

There are exactly 74,613 ways to form a committee of 6 people from a pool of 22 total.

Let B = 74,613

------------------------------------------------------

To find the probability of neither Allen or Joe are on the committee, we divide the values of A and B found earlier

A/B = (38,760)/(74,613) = 0.5194805

This value is approximate.

Rounding to three decimal places, or rounding to the nearest thousandth, leads to the final answer 0.519

There's roughly a 51.9% chance of forming a panel where neither Allen nor Joe are members.


Related Questions

Question #3: Can you add the following terms? Why or why not?
3V2 + 2V2

Answers

Yes, it’s because they are like terms. They both have the same variable and exponent. (v^2) Only the coefficients are added together.

So when they’re added, it becomes 5v^2.

what do expressions (3^3) and (3^4) have in common?​

Answers

Answer:

they are both 3 with different powers

Step-by-step explanation:

The sum of the 112th term of the geometric series is 256 and the common ratio is 3/4. Find the first term of the first geometric series.

Answers

Answer:

First term = 64

Step-by-step explanation:

We are given the formula for the nth term of a geometric series to be;

S_n = (a1(1 - rⁿ))/(1 - r)

Where:

S_n is the sum of n terms

A1 is first term

r is common ratio

We are given;

S_112 = 256

r = ¾

Thus;

256 = a1(1 - ¾^(112))/(1 - ¾)

256 = a1(4)

a1 = 256/4

a1 = 64

499 to the nearest hundred

Answers

Answer:

the correct answer would be 500

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

hope this helps

James ran 25/100 of a mile yesterday. His friend, Natasha, ran 4/10 of a mile. Who ran farther and how do you know?

Answers

Answer:

James ran faster

Step-by-step explanation:

Rewrite 14/32 in simplest form.​

Answers

Answer:

7/16

Step-by-step explanation:

Answer:

14/32 = 7/16

Step-by-step explanation:

You divide each number by two

I need your knowledge.

Answers

Answer:

det(2*3) also det(6)

Step-by-step explanation:

this is just filler so I can send it

Solve for y
3(7y + 4) = 15y + 6y +4+8

Answers

Answer: the are no values of y that make it true

Step-by-step explanation: no solution

Answer:

-4/7

Step-by-step explanation:

33. The distance d in miles that a car travels in t
hours at a rate of 58 miles per hour is given by
the equation d = 581. What is the best estimate
of how far a car travels in 7 hours?

Answers

Answer:

406 miles

Step-by-step explanation:

You would simply multiply 7 by 58.

Hope this helps...... Hisoka

Determine the range of the function graphed above.
OA. (-4, 0]
OB. [0, 4]
Oc. (-00, 4]
OD. [4, 00)

Answers

Answer:

Step-by-step explanation:

the range are the y values so must be [4,-∞) because if you look at the y-axis the highest value is 4 and the lowest goes to -∞

In the diagram below, BC is an altitude of AABD. To the nearest whole unit, what is the length of CD? ​

Answers

Answer:

C

Step-by-step explanation:

Using the Pythagorean theorem, find BA: [tex]\sqrt{37^{2}+53^{2} } = \sqrt{4178}[/tex]

Making BC = x, find the lenth of BD: [tex]\sqrt{x^{2} +37^{2} }[/tex]

Since DBA is a right triangle, this follows: [tex]DA^{2}=BD^{2}+BA^{2}[/tex]

Substitute: [tex](x+53)^{2} =\sqrt{4178} ^{2} +\sqrt{x^2+37^2} ^{2}[/tex]

Expand: [tex]x^{2} +106x+2809=x^{2} +5547[/tex]

Solve: 106x = 2736

Finally: x ≈ 25.8 ≈ 26

Therefore: C

Help me please please

Answers

Answer:

Hold a sec I got this

Evaluate the given integral by making an appropriate change of variables.

Answers

The integrand and given boundary for R suggests we should use

u = x - 4y

v = 5x - y

with 0 ≤ u ≤ 3 and 6 ≤ v ≤ 9.

Then

x = (4v - u)/19

y = (v - 5u)/19

and the Jacobian for this transformation is

[tex]J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac1{19}\begin{bmatrix}-1&4\\-5&1\end{bmatrix}\implies|\det J|=\left|\dfrac1{19}\right|=\dfrac1{19}[/tex]

The integral is then

[tex]\displaystyle\iint_R 2\frac{x-4y}{5x-y}\,\mathrm dA = \frac1{19} \int_6^9 \int_0^3 \frac{2u}v\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle \frac2{19} \int_6^9 \frac{3^2-0^2}{2v}\,\mathrm dv[/tex]

[tex]=\displaystyle \frac9{19} \int_6^9 \frac{\mathrm dv}v[/tex]

[tex]=\dfrac9{19}(\ln9-\ln6)=\dfrac9{19}\ln\dfrac96=\boxed{\dfrac9{19}\ln\dfrac32}[/tex]

Malcolm and Theo's families are both traveling to the same vacation resort.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours.

The graph below shows the relationship between the distance and the amount of time that Theo's family traveled.

How much faster did Malcolm's family travel than Theo's family

10 miles per hour


15 miles per hour


30 miles per hour


65 miles per hour

Answers

Graph is missing, so i have attached it.

Answer:

15 miles per hour

Step-by-step explanation:

We are given that d = 65t models the distance, d, that Malcolm's family travels after t hours.

Since we are comparing speed of both families, then we will find the speed here.

Formula for speed is;. Speed = distance/time

d = 65t and we know that d is distance and t is time. Thus, d/t = 65 m/hr = speed.

For Theo's family, looking at the image attached;

At a distance of 50 miles, time spent is 1 hr

At a distance of 100 miles, time spent is 2 hrs

At a distance of 150 miles, time spent is 3 hrs

At a distance of 200 miles, time spent is 4 hrs

Thus, speed = 200/4 or 150/3 or 100/2 or 50/1.

They all give a constant value of 50 m/hr.

Thus, speed of Theo's family = 50 mi/hr

Comparing this to that of Malcolm's family,we can see that Malcolm's family were faster by 65 - 50 = 15 mi/hr

Answer:

15

Step-by-step explanation:

Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

x
y
1
7
2
5
3
3
4
1

What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18

Answers

Answer:

C

Step-by-step explanation:

y = mx + c

m = (y2 - y1 )/ (x2 - x1)

using (1 , 7) & (2,5)

y2 = 5 y1 = 7 so y2 -y1 = -2

x2 = 2 x1 = 1 so x2 - x1 = 1

m - -2/1 = -2

y = -2x + c

when x =1 y = 7

so 7 = -2 + c

=> c =9

y = -2x + 9

if ordered pairs (2, 5) and (4, 1) used

m = (1-5)/(4-2)

=> m = -4/2

=> m = -2

y = -2x + c

for x =2 y =5

5 = -2*2 + c

=> c = 9

y = -2x + 9

she would have got same equation

Answer:

The person above is correct !  :))

Step-by-step explanation:

This is an confirmation :))

James determined that these two expressions were equivalent expressions using the values of x - 4 and x - .6
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x = 2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x = 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x = 8.

Answers

Answer:2 4 and 5

Step-by-step explanation:

-6p + 4p > 12
( please look at picture instead )

Answers

Answer:

the asnwer is p is less than or equal to -6.

Step-by-step explanation:

The reasonfro that is becuase when u have a negative variable you have to divide both sides by a negative, which will flip the symbol making it less than in this case rather than greater than. Hope this works mark as brainliest pls

that what i got but check the sign well

x + 8x + 15 help me out with this plz

Answers

Answer:

3(3x + 5)

Step-by-step explanation:

x + 8x + 15              Combine liked terms

9x + 15

GCF: 3

3(3x +5)                   Factor

Billy and Joe go to McDonalds for lunch. They order 2 burgers, 3 fries, and 2 sodas. The mom
bugers cost $3.50 each. The sodas cost $1.00 each. If the total was $16.29 how much was
each fry. Write and solve an equation to represent this situation. Round your answer to
the nearest tenth

Answers

Answer:

2.43 and rounded it is 2 dollars

Step-by-step explanation:

2 burger-$7.00

3 Fries-

2 Sodas- $2.00

7+2=9

$16.29-9.00=7.29

$7.29/3=2.43

Carmine and Hiram are solving the following word problem.

Gina is training for a marathon. She ran 6.75 miles on Saturday. On Sunday, she ran 7.20 miles. How far did she run on Saturday and Sunday combined?

Carmine sets up his problem as 6.75 + 7.20

Hiram sets up his problem as 7.20 + 6.75

Who is correct? Carmine, Hiram, or both

Answers

Answer:

Both is the anwser.

Step-by-step explanation:

Look it this way its simple 7.20 plus 6.75 equals 13.95

6.75 plus 7.20 is 13.95 theres no decimals changing in this problem meaning that both of them are correct.

Kira skied at a steady speed in a 2 mile cross country ski race her finished time was 5/12 hour Kira wants to know her speed miles per hour

Answers

Answer: The purpose of this task is to give students experience in reasoning with equivalent ratios and unit rates from both sides of the ratio. This prepares for studying proportional relationships in Grade 7, and in Grade 8 for understanding that a proportional relationship can be viewed as a function in two different ways, depending on which variable is regarded as the input variable and which as the output variable. The values in column B were found by dividing both values in column A by 10. The values in column C were found by dividing both values in column B by 2. The other columns contain multiples of the values in column B.

If we look in column E, we can see that it would take her 45 minutes to run 6 miles.

If we look in column B, we can see that she could run 2 miles in 15 minutes.

If we look in column F, we can see that she is running 8 miles every 60 minutes (which is 1 hour), so she is running 8 miles per hour.

If we look in column C, we can see that her pace is 7.5 minutes per mile.

If we divide 150 by 20, we get the unit rate for the ratio 150 minutes for every 20 miles.

150÷20=7.5

So the runner is running 7.5 minutes per mile. We can multiply this unit rate by the number of miles:

7.5minute mile×6 miles=45 minutes

Thus it will take her 45 minutes to run 6 miles at this pace.

If it takes her 45 minutes to run 6 miles, it will take her 45÷3=15 minutes to run 6÷3=2 miles at the same pace.

If it takes her 15 minutes to run 2 miles, it will take her 4×15=60 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.

We found her pace in minutes per miles in part (a).

Using the speed - distance relationship, kira's speed in miles per hour would be 4.8 miles per hour.

Given the Parameters :

Speed = 5/12 hours = 0.416666 hour Distance = 2 miles

Speed = distance / time

Hence,

Speed = (2 ÷ 0.416666) = 4.8 miles per hour.

Therefore, Kira's speed is 4.8 miles per hour.

Learn more : https://brainly.com/question/13816092

A loaf of sandwich bread contains 24 slices. Which of these tables correctly shows the ratios of different numbers of loaves of bread to the numbers of total slices they contain?

Answers

Answer:

which table?

Step-by-step explanation:

im assuming it would look like this

1   24

2  48

3  72

4  96

5  120

6  144

7  168

8  192

9  216

10  240

just multiply the number of loaves to 24

Hope this helped :)

whats the rate if 13 inches of snow in 7 hours

Answers

Answer:

1.86 (rounded to nearest hundredth) inches of snow in 1 hour

Step-by-step explanation:

Divide 13 inches of snow by 7 hours

The answer is 1.8571428571428571428571428571429

Round to the nearest hundredth

1.86

Hope this helped :)

[tex]\textsf{Hey there!}[/tex]

[tex]\textsf{What's the rate of 13 inches of snow in 7 hours?}[/tex]

[tex]\mathsf{\dfrac{13\leftarrow \bf{inches}}{7\leftarrow{hours}}} \\\\\mathsf{\dfrac{13\div7\leftarrow inches}{7\div7\leftarrow hours}}\\\\\mathsf{7\div7=1}\\\\\mathsf{\dfrac{13\div7\leftarrow\underline{ inches}}{1\leftarrow \underline{hour(s)}}}\\\\\mathsf{13\div7=1.857143}\\\\\mathsf{\dfrac{1.857143\leftarrow \frak{inches}}{1\leftarrow\frak{hour(s)}}}}}}\\\\\mathsf{1.85714\div1=\bf{ANSWER}}\\\\\textsf{Solve above and you have your answer.}[/tex]

[tex]\lhuge\text{Note: We're rounding our answer because the actual answer will take some time}[/tex]

[tex]\boxed{\boxed{\textsf{Thus, your answer is: \boxed{\boxed{\large\textsf{\bf1.86 inches per hour}}}}}}\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst}[/tex]

How far does the tip of the minute hand of a clock move in 20 minutes if the hand is 10 inches long?

Answers

Answer:

20.95 inches

Step-by-step explanation:

The complete revolution of the minute hand forms a circle in 60 minutes.

circumference of a circle = 2[tex]\pi[/tex] radius

i.e C = 2[tex]\pi[/tex]r

But from the question, r = length of the minute hand = 10 inches

⇒ C = 2[tex]\pi[/tex] x 10

  = 20[tex]\pi[/tex]

C = 20[tex]\pi[/tex] inches

Also, 20 minutes = [tex]\frac{20 minutes}{60 minutes}[/tex] = [tex]\frac{1}{3}[/tex] of the circumference.

So that,

the distance of the tip of the minute hand = [tex]\frac{1}{3}[/tex] x C

                                                                     = [tex]\frac{1}{3}[/tex] x 20[tex]\pi[/tex]

                                                                     = [tex]\frac{1}{3}[/tex] x 20 x [tex]\frac{22}{7}[/tex]

                                                                     = 20.9524

                                                                     = 20.95 inches

Thus, the distance of the tip of the minute hand is 20.95 inches

What is the distance between 0.6 and 0

Answers

the answer would most likely be .6

Answer:

on the number its between 0 and 1

Step-by-step explanation:

if you jump from 0 to 6 you would have 6 jumps, so it would be 6.

0.6 equals 0.60 so it could ALSO be 60 jumps. (incase u needed that)

Classify the equation 5 (2x + 3) = 3(3x + 12) as having one solution, no solution, or infinitely many solutions.

Answers

Answer: one solution I believe

Step-by-step explanation: I got 21 as my answer and that is one solution

Can someone please help me it's slope

Answers

Answer:

-0.04

Step-by-step explanation:

The slope looks like it’s -1

Farmers market Sells grapefruit strawberries and avocado they each have a different cost and are price per box Alyssa Buys two boxes of strawberries and three boxes of avocados and spent $23 London by three boxes of grapefruit and four boxes of strawberries in Spain $19 Tina by seven boxes of grapefruit and five boxes of avocados in Spencer $51 find the missing quantity below

Answers

Answer:

The cost of grapefruits per box is $3, The cost of strawberries per box is $2.5

The cost of avocados per box is $6

Step-by-step explanation:

Let us represent the price of Grapefruits per box = g

Strawberries per box = s

Avocados per box = a

Alyssa buys two boxes of strawberries and three boxes of avocados and spent $23

2s + 3a = 23 ....... Equation 1

a = 23 - 2s

London buys three boxes of grapefruit and four boxes of strawberries in Spain $19

3g + 4s = 19 ....... Equation 2

Tina buys seven boxes of grapefruit and five boxes of avocados in Spencer $51

7g + 5a = 51..... Equation 3

2s + 3a = 23 ....... Equation 1

3g + 4s = 19 ....... Equation 2

7g + 5a = 51..... Equation 3

Substituting 3a = 23 - 2s in Equation 3

a = 23 - 2s/3

7g + 5(23 - 2s/3) = 51

7g +( 115 - 10s/3) = 51

Multiply through by 3

7g × 3 + ( 115 - 10s/3) × 3 = 51 × 3

21g + 115 - 10s = 153

21g -10s = 38 ........ Equation 4

Combining Equation 2 and 4

3g + 4s = 19 ....... Equation 2 × 10

21g -10s = 38 ........ Equation 4 × 4

30 + 40s = 190.. Equation 5

84g - 40s = 152 .... Equation 6

We Add Equation 5 and Equation 6 to eliminate s

114g = 342

g = 342/114

g = $3

To find s, cost 0f straw berries

g = $3

3g + 4s = 19 ....... Equation 2

3(3) + 4s = 19

9 + 4s = 19

4s = 19 -9

4s = 10

s = 10/4

s = $2.5

For find a, the cost of avocados.

7g + 5a = 51..... Equation 3

g = $3

7(3) + 5a = 51

21 + 5a = 51

5a = 51 - 21

5a = 30

a = 30/5

a = $6

g =$ 3, s =$ 2.5 and a = $6.

Therefore:

The cost of grapefruits per box is $3.

The cost of strawberries per box is $2.5 and

The cost of avocados per box is $6

Help please and thank you

Answers

Answer:

1. 22

2. 8

3. 31

4. 20

5. 38

6. 22

7. 26

8. 16

9. 14

10. 28

Step-by-step explanation:

USE PEMDAS

P: Parantheses

E: exponents

D: division

A: addition

S: subtraction

and ywww

You are redecorating your room and the only thing left to paint is your door. You’re only going to paint the side that faces the inside of your room. The door is 6 feet 8 inches tall and 30 inches wide. You need to know the surface area of the side of the door to determine how much paint to buy. The hardware store sells paint by how much covers a square foot. What is the surface area you should report to the hardware store? (Hint: First find the number of square inches in 1 square foot.)

Answers

Answer: Then the surface area that you should report to the hardware store is 15 ft^2.

Step-by-step explanation:

Remember that the area of a rectangle of length L and width W is

A = L*W

In this case, we can think in the door as a rectangle, where:

L = 6ft + 8in

W = 30in

Now, we know that in the hardware store they sell paint by how much covers a square foot, then we must calculate the area of the door in square feet.

Then the first step would be to replace all the units by ft.

We know that:

1ft = 12in.

Then we have that:

(1ft/12in) = 1

Then we have that:

8in = 8in*1 = (8in/12in)*1ft = 0.6... ft

(the 3 dots means that the 6 repeats infinitely)

And;

30in = 30in*1 = 30in*(1ft/12in) = 2.5ft

Then the measures of the door are:

L = 6ft + 0.6...ft = 6.6...ft

W = 2.5ft

The area will be:

A = L*W = 6.6...ft*2.5ft = 15 ft^2

Then the surface area that you should report to the hardware store is 15 ft^2.

Other Questions
Peyton is collecting data on the lunch habits of students at Hyattsville Middle School. In one class, 14 students bring lunch from home, and 20 buy a school lunch. Hyattsville Middle School has 1700 students. From the data collected, how many students would Peyton predict would buy a school lunch? * Lucys ranch has 1,718 acres and Pauls ranch has 2,484 acres. What is the difference in size between the two ranches A. filtration B. sieving C. using a magnet D. decantationE. evaporationDirections: Choose the best technique that can be used to separate the substances ormaterials in each mixture. Write the letter of your answer on the space before the nu1. Cornstarch and water2. Iron and sulfur3. Rice grains and stones4. Pebbles and soil5. Muddy water6. Ground pepper and water7. Flour and coarsely ground corn8. Needles in a box of beads9. Sesame seeds in soy sauce10. Pebbles and iron nails11. Fine sand from rocks12. Sand from water13. Gravel and sand14. Salt and iron filings15. Pins from assorted buttons16. Coconut oil from coconut milk17. Sand and pebbles18. Pasta from water19. Sand and thumb tacks20. Salt solution What side is congruent to side AC? I NEED HELP ASAP!!!111Read the quote about Charlemagne.The man who led the Franks to victory and so created modern Europe was Charles the Great. . . . [W]ithout Charles and the legend of Charles Europe would have had a different history and a different character.Which of Charlemagnes accomplishments might this writer have had in mind in crediting Charlemagne with the creation of modern Europe? Select the two correct answers. A. He established a peace that lasted for centuries. B. He blocked the power of the popes. C. He helped spread Christianity. D. He encouraged the creation of schools. Egyptian writing was written from left to right like the English language. How many grams of Ag2CO3 will precipitate when excess Na2CO3 solution is added to 40.0 mL of 0.679 M AgNO3 solution PLZ HELP ME1. A stone is thrown horizontally from a cliff 30m high with an initial speed of 20m/s. How far from the cliff does the stone strike the ground? 2. A ball rolls off the edge of a table 1.44m above the floor and strikes the floor at a point 2m horizontally from the edge of the table. A) What is the time the ball was in the air? B) What is the initial velocity of the ball? 3. A golfer hits a ball and gives it an initial velocity of 40 m/s, at an angle of 30 above the horizontal.A) How long does the ball stay in the air? B) How far horizontally (the range) does the ball travel before hitting the ground? Help plzzz will give brainliest 5. Read the following excerptrticle."Beneath the dark canopy of leaves and smoke the fire laid hold on the forest and began tognaw."William Golding personifies which inanimate object in this quote?A. The CanopyB. The LeavesC. The SmokeD. The Fire Perioddddddd poohhhh Will give brainlist to who finds this out! What is An equivalent fraction to 1/6 What led New York and Virginia to ratify the constitution? Whats your claim of the Civil War The ______freed all enslaved people inrebel or Confederate territory.A. Compromise of 1850B. Emancipation ProclamationC. Missouri Compromise I need help!!!Will give brainly If your gonna spam dumb stuff then leavee Sandy sold 22 tickets, which was at least 6 more than twice the number of tickets that Teresa sold. This can be represented by this inequality, where t represents the number of tickets Teresa sold.Which could be a number of tickets that Teresa sold?1711714 20 pts, please write in JAVA. need this ASAPIn the Lesson Slides for this activity, we developed a method findChar for figuring out if a character was in a String.The implementation was:public boolean findChar(String string, String key) { for(int index = 0; index < string.length(); index++) { String character = string.substring(index,index+1); if(character.equals(key)) { return true; } } return false; }However, there is a much more efficient and simple algorithm that we can use to determine if a character is in a String. Using the method signature public boolean findChar(String string, String key), figure out a more efficient method with a lower exection count.Hint: Weve learned a couple of methods that can tell us what index a character is at - can we use those to determine if the character is in a String? The sales tax rate in New Mexico is 8% You buy an Anime coloring book that is $18. What is the final price of the Anime coloring book? Justify how you determined the final price.