On the school playground, the slide is 7 feet due west of the tire swing and 7 feet due south of the monkey bars. What is the distance between the tire swing and the monkey bars?

Answers

Answer 1

Answer:

Step-by-step explanation:

According to the question, a slide is 7 feet due west of a tire swing and 7 feet due right of the monkey bars and we were asked the calculated the distance between them.

If you look at it carefully, since the slide is due west of the tire swing and 7 feet due south of the monkey bars, you'll notice a shaped form, the shape formed is an inverted right-angled triangle.

Right-angled Triangles can be solved using pythagoras' theorem which says [tex]a^{2} + b^{2} = c^{2}[/tex].

a= 7, b=7, c=??

[tex]c^{2} = 7^{2} + 7^{2}[/tex]

[tex]c =\sqrt{98}[/tex]

c = 9.9 feet

Answer 2

Final answer:

The distance between the tire swing and the monkey bars is found using the Pythagorean theorem, which gives approximately 9.90 feet.

Explanation:

To find the distance between the tire swing and the monkey bars, we can model the situation using a right triangle. The slide being 7 feet due west of the tire swing and 7 feet due south of the monkey bars forms a right-angled triangle with the slide as the vertex where the right angle is, the tire swing and monkey bars forming the other two vertices.

Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b), we can find the distance (hypotenuse) between the tire swing and the monkey bars.

In other words, we have:

a² + b² = c²

Given:

a = 7 feet (distance from slide to tire swing)

b = 7 feet (distance from slide to monkey bars)

We can calculate:

c² = 72 + 72 = 49 + 49 = 98

The distance (c) is the square root of 98, which is approximately 9.90 feet.

Therefore, the distance between the tire swing and the monkey bars is approximately 9.90 feet.


Related Questions

The painting by itself is a rectangle with length 20 cm and width 16 cm. The painting and frame together form a larger rectangle with length 25 cm and width 20 cm Find the area of the frame.

Answers

Answer:

The area of frame is 180 square meters.

Step-by-step explanation:

We are given the following in the question:

Dimension of rectangular painting:

Length, l = 20 cm

Width, w = 16 cm

Dimension of frame:

Length, L = 25 cm

Width, W = 20 cm

We have to find the area of frame.

Area of rectangle =

[tex]A = l\times w[/tex]

Area of frame =

[tex]A-a\\=(L\times W)-(l\times w)\\=(25\times 20)-(20\times 16)\\=180\text{ square meters}[/tex]

Thus, the area of frame is 180 square meters.

You are throwing darts at a dart board. You have a chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?

Answers

Answer:

Correct answers is

[tex] \frac{1}{216} [/tex]

Step-by-step explanation:

Given: The chances of striking the bull's-eye each time of throw =\frac{1}{6}

Since, if we throe dart on dart board , each event will be independent of the other.

Then, If we throw 3 times, what is the probability that we will strike the bull's-eye all 3 times is given by :-

[tex]p(strike \: bulls \: eye \: ) = \frac{1}{6} x \frac{1}{6} x \frac{1}{6} = \frac{1}{216} [/tex]

Hence, the probability that we will strike the bull's-eye all 3 times is 1/216

Answer:

1/216

Step-by-step explanation:

Leigh drive 1470 km from smith falls ON to thunder bay ON she stopped 370 km from smith falls About what percent of her trip has she completed when she stopped

Answers

Answer:

75%

Step-by-step explanation:

Here, we are asked to calculate the percentage of a trip that has been completed by Leigh.

Firstly, we identify the total length of the trip, this is 1470km. She stopped 370km from her destination. The length of the distance traveled is 1470km - 370km = 1100km

Now we proceed to calculate what percentage of the journey is this.

We calculate this by placing it over the total length multiplied by 100%

That would be

1100/1470 * 100 = 74.82 approximately 75%

How do you simplify numbers with exponents

Answers

You write it out then you’ll get the exponent

kira has a rope that is 5 meters long. she cuts a piece that is 1.51 meters long. how long is the remaining piece of rope

Answers

Answer:

3.49

Step-by-step explanation:

5-1.51=3.49

Answer:

3.49 meters long

Step-by-step explanation:

5-1.51 = 3.49

- If you need this further explained please let me know. I would be glad to help.

Tony needs 16-inch pieces of gold chain to make each of 3 necklaces. He has a piece of chain that is 4 1/2 feet long. How much chain will he have left after making the necklaces?

Answers

Final answer:

After converting the chain length from feet to inches, Tony will have 6 inches of gold chain left after making three necklaces, each requiring 16-inch pieces.

Explanation:

Tony needs to determine how much gold chain he will have left after making three necklaces, each requiring 16-inch pieces. First, we need to convert the total chain length from feet to inches. Since 1 foot equals 12 inches, 4.5 feet would be 4.5 × 12 inches, which equals 54 inches. Now, we can calculate the total length of chain needed for the necklaces by multiplying the length of one necklace (16 inches) by the number of necklaces (3), which is 16 × 3 = 48 inches.

Subtracting the total chain used for the necklaces (48 inches) from the total length of chain available (54 inches) gives us the remaining length of chain. So, 54 inches - 48 inches = 6 inches of chain leftover after making the three necklaces.

3/4 of the students at Timber Elementary play sports. Of those students, 1/5 of them play soccer. What fraction of the students at Timber Elementary play soccer?

Answers

Answer:

3/20 of the students play soccer

Step-by-step explanation:

1. Divide the amount of students that play sports, 3/4 by the amount of those that play soccer, 1/5

2. 3/4 divided by 1/5= 3/20

Answer:

3/20

Step-by-step explanation:

Find the area of the shaded region. Round to the nearest hundredth where necessary. Remember: you are subtracting the areas.

Answers

Given:

The base of the given figure = 23.8 ft

Height of the parallelogram = 15 ft

To find the area of the shaded region.

Formula

[tex]A = A_{1} -A_{2}[/tex]

where, [tex]A[/tex] be the area of the shaded region

[tex]A_{1}[/tex] be the area of the parallelogram.

[tex]A_{2}[/tex] be the area of the triangular part.

The area of triangle [tex]A_{2} = \frac{1}{2} bh[/tex] where, b be the base and h be the height.The area of the parallelogram [tex]A_{1} =( base)(height)[/tex]By Pythagoras theorem, [tex]hypotenuse^{2} = base^{2}+height^{2}[/tex]

Now,

Putting, Base = 21, Hypotenuse = 23.8 we get,

[tex]Height^{2} = 23.8^{2}-21^{2}[/tex]

or, [tex]Height = \sqrt{566.44-441}[/tex]

or, [tex]Height = 11.2[/tex]

Therefore,

Area of the parallelogram [tex]A_{1} = (23.8)(15)[/tex] sq ft = 357 sq ft

Area of the triangle [tex]A_{2}[/tex] = [tex]\frac{1}{2}(11.2)(21)[/tex] sq ft = 117.6 sq ft

So,

The area of the shaded part = (357-117.6) sq ft = 239.4 sq ft

Hence,

The area of the shaded part is 239.4 sq ft.

You are given the exponential function g(x) = 3 x . Which option below gives the formula for a new function h created by stretching g by a factor of 3 along the y-axis?


h(x) = 3x+1

h(x) = 3x-1

h(x) = x · 3x+1

h(x) = x · 3x-1

Answers

Answer:

A. [tex]h(x) = 3^{x+1}[/tex]

Step-by-step explanation:

Stretching means that original function is multiplied by a constant, which is equal to 3 in this case:

[tex]h(x) = 3 \cdot g (x)[/tex]

[tex]h(x) = 3\cdot 3^{x}[/tex]

[tex]h(x) = 3^{x+1}[/tex]

The answer is A.

Answer:

A

Step-by-step explanation:

I need to know the lengths of MN, NP, and PM

Answers

Answer:

MN = 12 units

NP = 16 units

PM = 20 units

Step-by-step explanation:

You can find MN and NP by counting on the graph. To find PM you will need to use the formula a^2 + b^2 = c^2 ( ^ stands for exponent)

MN and NP will be a and b.

Example: 12^2 + 16^2 = c^2

Simplify.

Example:

144 + 256 = c^2

144 + 256 = 400

Then find the square root of 400 which is 20.

To check your work put all of the sides into the formula and it should be true.

A ball is hit into the air with an initial velocity of 100 ft/s. Its height, h(t), after t seconds is given by the function h(t) = -16t² + 100t + 5. What is the ball's maximum height?

Answers

at maximum. dt/dh=0

if you differentiate you will get

-32t=-100

t=3.125

Solve the system of equations 7x - y = -13 and -3x - y = -3 by combining the equations

Answers

Answer:

The answer to your question is (-1, 6)

Step-by-step explanation:

Data

                       7x - y = -13               Equation l

                      -3x - y = -3                Equation ll

-Solve equation l for y

                       y = 7x + 13                Equation lll

-Substitute equation lll in equation ll

                      -3x - (7x + 13) = -3

-Solve for x

                     -3x - 7x - 13 = -3

                     -10x = 13 - 3

                     -10x = 10

                          x = 10/-10

                          x = -1

-Substitute x in equation lll

                        y = 7(-1) + 13

                        y = -7 + 13

                        y = 6

3 3/4 divided by 5/7

Answers

Answer:

  5 1/4

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by its inverse.

  (3 3/4)/(5/7) = (15/4)/(5/7) = (15/4)·(7/5) = 21/4 = 5 1/4

_____

Many graphing calculators (and some scientific calculators) will do this mixed-number arithmetic for you.

3x + 10 = 22
Solve for x

Answers

Answer:

x=4

Step-by-step explanation:

Step 1: Subtract 10 from both sides.

3x+10−10=22−10

3x=12

Step 2: Divide both sides by 3.

3x/3=12/3

x=4

if i can get brainliest that would be great

3x+10=22
-10 -10

3x=12
3/3 = 12/3
X=4

Mason is having new tires put on his wheel chair. The tires are regularly 56, but this weekend, they are on sale for 25% off. Mason wants to know the sale price for the tires

Answers

Answer:

the tires are 42 dolars

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

25% × 56 =

(25 ÷ 100) × 56 =

(25 × 56) ÷ 100 =

1,400 ÷ 100 =

14

If 30% of a number is 45, what is 4/5 of the number?

Answers

Answer: 4/5 of 45 is 36

Step-by-step explanation: If you were to divide 45 by 5 you would get 9. 9 is 1/5 of 45 so if you multiplied it by 4 you would 4/5 of 45 which is 36.

The ( 4/5 )th of the number is 120 and the equation is ( 30 / 100 ) N = 45 , where N is the number and N = 150

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as N

A = 30% of a number is 45

Substituting the values in the equation , we get

( 30/100 ) N = 45   be equation (1)

Multiply by 100 on both sides of the equation , we get

30 N = 4500

Divide by 30 on both sides of the equation , we get

N = 4500 / 30

N = 150

Therefore , the value of N is 150

Now , ( 4/5 )th of the number be calculated as

Let the ( 4/5 ) of the number be = B

So , the equation will be

B = ( 4/5 ) x 150

B = 4 x 30

B = 120

Hence , the number is 150 and ( 4/5 ) th of the number is 120

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A plane has an airspeed of 134 km divided by h. It is flying on a bearing of 78 degrees while there is a 21 km divided by h wind out of the northeast​ (bearing 225 degrees​). What are the ground speed and the bearing of the​ plane?

Answers

The ground speed of the plane is approximately 116.88 km/h, and its bearing is about 83.44°, given an airspeed of 134 km/h on a 78° bearing and a 21 km/h wind from 225°.

The plane's ground speed is approximately 116.88 km/h, and its bearing is roughly 83.44°. This calculation incorporates the plane's airspeed of 134 km/h at a bearing of 78° and a wind speed of 21 km/h from a bearing of 225°.

First, we decompose the velocities into horizontal and vertical components. For the plane's airspeed, the horizontal component is about 27.81 km/h, and the vertical component is around 131.04 km/h. Similarly, for the wind, the horizontal and vertical components are approximately -14.85 km/h each. By adding the horizontal components of the airspeed and wind, we get 12.96 km/h. Likewise, adding the vertical components yields 116.19 km/h.

Using these components, we calculate the resultant velocity vector's magnitude, approximately 116.88 km/h, using the Pythagorean theorem. The direction, or bearing, is computed to be approximately 83.44° using the inverse tangent function.

Therefore, the plane moves at a speed of about 116.88 km/h, slightly northeast of east, due to the combined effect of its airspeed and the wind.

What is the relative minimum of the function?

Enter your answer in the box.


Answers

Answer:

-5

Step-by-step explanation:

The minimum is at the vertex.  This is at (1, -5)

The minimum value is -5

The circumference of a circle is 16 pi ft.
What's the radius

Answers

Answer:

2.54648 ft

Step-by-step explanation:

r = 8/π (ft.) Therefore, the radius of the circle when its circumference is 16 feet is r ≈ 2.54648 ft. C = 2 (3.14159) (2.54648) ft :)

Rashid solved a fraction division problem using the rule "multiply by the reciprocal." His work is shown below. Three-fourths divided by 9. Three-fourths times StartFraction 1 Over 9 EndFraction = StartFraction 3 Over 36 EndFraction or StartFraction 1 Over 12 EndFraction

Answers

Answer:

A. Rashid solved the problem correctly.

Step-by-step explanation:

The missing option is given as:

Which is the most accurate description of Rashid’s work?

A. Rashid solved the problem correctly.

B. Rashid multiplied the dividend by the divisor instead of finding the reciprocal.

C. Rashid multiplied the denominators instead of finding a common denominator.

D. Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Rashid solve the problem correctly as he gave the answer in lowest form.

[tex]\frac{3}{4}[/tex] ÷ [tex]9[/tex]

[tex]\frac{3}{4} *\frac{1}{9} \\\frac{3 * 1}{4 * 9} \\\frac{3}{36} =\frac{1}{12}[/tex]

So, Rashid final answer is correct 3/36 or 1/12

Answer:

Rashid Missed This Step: [tex]\dfrac{3}{4 X 9}[/tex]

Step-by-step explanation:

Rashid solved a fraction division problem using the rule "multiply by the reciprocal."

[tex]\dfrac{3}{4} \div 9\\ =\dfrac{3}{4} X \dfrac{1}{9}\\=\dfrac{3}{36}\\=\dfrac{1}{12}[/tex]

Rashid misses a step which will now be shown below:

[tex]\dfrac{3}{4} \div 9 =\dfrac{3}{4} X \dfrac{1}{9}\\=\dfrac{3}{4 X 9}\\=\dfrac{3}{36}\\=\dfrac{1}{12}[/tex]

A study was conducted looking at the association between the number of polyps in the colon and mean grams of fiber consumed per day based on a standard food frequency questionnaire. The Pearson correlation coefficient was 0.9 with a p-value of 0.003 and the Spearman correlation coefficient was 0.28 with a p-value of 0.049. Which form of correlation would be more appropriate to report and why?

Answers

Answer:

C) The Spearman correlation results should be reported because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.

Explanation:

The following multiple choice responses are provided to complete the question:

A) The Pearson correlation results should be reported because it shows a stronger correlation with a smaller p-value (more significant).

B) The Pearson correlation results should be reported because the two variables are normally distributed.

C) The Spearman correlation results should be reported because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.

D) The Spearman correlation results should be reported because the p-value is closer to 0.0556.

Further Explanation:

A count variable is discrete because it consists of non-negative integers. The number of polyps variable is therefore a count variable and will most likely not be normally distributed.  Normality of variables is one of the assumptions required to use Pearson correlation, however, Spearman's correlation does not rest upon an assumption of normality. Therefore, the Spearman correlation would be more appropriate to report because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.

Find the solutions of the quadratic equation 14x^2+9x+10=0

Answers

Answer:

No real Solution

Step-by-step explanation:

Plug a=14, b=9, and c=10 into the quadratic formula, and you'll get

[tex]x=(-(9)±\sqrt{-479})/ 28[/tex]

since -479 is negative, you'll get an imaginary number.

There are 16 tables set up for a banquet, of which 4 have red tablecloths.
What is the probability that a randomly selected table will have a red tablecloth?
Write your answer as a fraction or whole number.

Answers

Final answer:

The probability that a randomly selected table will have a red tablecloth is 1/4, since there are 4 red tablecloths out of 16 tables.

Explanation:

The question asks for the probability that a randomly selected table will have a red tablecloth given that there are 16 tables and 4 have red tablecloths. To find the probability, we use the formula:

Probability (P) of choosing a red tablecloth = (Number of red tablecloths) / (Total number of tables)

Substituting the given numbers:

P(red tablecloth) = 4 / 16 = 1 / 4

Therefore, the probability is 1/4 or 0.25 when expressed as a decimal.

It is important to round answers to relative frequency and probability problems to four decimal places when required, but in this case, the fraction 1/4 is already as simple as it can be.

How many batches of cookies can you make if you have 8 cups of flour and recipe calls for 3/4 per batch?

Answers

Answer:

10 batches i think, sorry if im wrong

Step-by-step explanation:

Final answer:

To determine the number of batches of cookies you can make with 8 cups of flour and a recipe that calls for 3/4 cup per batch, you would divide 8 by 3/4.

Explanation:

To determine the number of batches of cookies you can make with 8 cups of flour and a recipe that calls for 3/4 cup per batch, you need to divide the total amount of flour by the required amount for each batch. So, you would divide 8 cups by 3/4 cup:

8 cups ÷ 3/4 cup = 8 ÷ 3/4 = 10 2/3 batches of cookies

Therefore, you can make approximately 10 and 2/3 batches of cookies.

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Suppose a coffee cup has a diameter of 8cm and a height of 9cm. What is the volume of the cup ? (to the nearest whole number)
A) 81 cm^3
B) 226 cm^3
C) 452 cm^3
D) 1018 cm^3

Answers

Answer:

452 cm^3

Step-by-step explanation:

The volume of a cilinder is [tex]\pi (radius^{2})(height)[/tex]

The diameter of the cup is 8cm, the formula of the radius is [tex]\frac{diameter}{2}[/tex]

So the radius would be [tex]\frac{8}{2}[/tex] = 4cm

We change variables in the formula of the volume [tex]\pi(4^{2})(9)[/tex] = 144[tex]\pi[/tex] = 452cm^3

Answer:

i needed the same thing woa

Which simplified fraction is equal to 0.1ModifyingAbove 7 with bar?
StartFraction 9 Over 17 EndFraction
StartFraction 8 Over 45 EndFraction
StartFraction 17 Over 9 EndFraction
StartFraction 16 Over 90 EndFraction

Answers

Answer:

8/45

Step-by-step explanation:

The simplified fraction is equal to 0.1ModifyingAbove 7 with bar is StartFraction 17 Over 9 EndFraction, the correct option is C.

How to interpret the fraction?

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

[tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

[tex]\dfrac{a}{b}[/tex] = a parts out of b parts of a thing.

We are given that;

The fraction; 0.1ModifyingAbove 7 with bar

Now,

The number 0.1 is a repeating decimal, which means it has a repeating pattern of digits after the decimal point. To convert this decimal to a fraction, we can use the fact that:

0.1= 0.111= 1/9

So the simplified fraction that is equal to 0.1 is;

StartFraction 1 Over 9 EndFraction

StartFraction 9 Over 17 EndFraction can't be simplified further.

StartFraction 8 Over 45 EndFraction can be simplified to StartFraction 16 Over 90 EndFraction.

StartFraction 17 Over 9 EndFraction can't be simplified further.

StartFraction 16 Over 90 EndFraction can be simplified to StartFraction 8 Over 45 EndFraction.

Therefore, by fraction the answer will be StartFraction 17 Over 9 EndFraction.

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Sarah used her calculator to work out the value of a number y .

The answer on her calculator display began.

7.8

Complete the error interval for y.

[......] ≤ y < [......]

Answers

Final answer:

The error interval for y is 7.8 ≤ y < 7.9.

Explanation:

The error interval is determined by the decimal digits that will determine the value of y. Since the calculator display shows 7.8, y will be between 7.8 and the next smallest number, which will be 7.9. Therefore, the error interval for y is:



7.8 ≤ y < 7.9

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Final answer:

The error interval for y is [7.8, 7.9).

Explanation:

To find the error interval for y, we need to consider the decimal place immediately after the given value on Sarah's calculator display. Since the given value is 7.8, we look at the digit after the decimal point, which is 0. If this digit is 5 or greater, we round up the previous digit. In this case, 0 is not greater than 5, so we do not round up. Therefore, the error interval for y is [7.8, 7.9).

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Your math professor gives you a set of 10 problems and tells you that the final exam will consist of a random selection of 5 of them. If you figured out how to do 7 of the problems, what is the probability that you answer correctly (a) all 5 problems (b) at least 4 of the problems

Answers

Answer:

hi

Step-by-step explanation:

sue your math professor that professor is evil

Martin has collected 18 U.S. stamps and 12 international stamps. He wants to display them in identical groups of U.S. and international stamps, with no stamps left over. What is the greatest number of groups Martin can display them in?

Answers

12 groups of two stamps

True or False
Interior Angle - Angle formed by 3 adjacent sides inside the polygon.
Select the appropriate response:

True

False

Answers

Answer:

False.

Step-by-step explanation:

it is an angle formed by 2 adjacent sides inside the polygon.

Answer:

False

Step-by-step explanation:

Interior angle is formed by 2 adjacent sides

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Skater X Center of MassZero Zero An experiment that claimed to show that meditation reduces anxiety proceeded as follows. The experimenter interviewed the subjects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how to meditate and they meditated daily for a month. The other group was simply told to relax more. At the end of the month, the experimenter interviewed all the subjects again and rated their anxiety level. The meditation group now had less anxiety. What property of good experiments is missing from the study? control group randomization using enough subjects blinding What declaration did President Lincoln make about secession?A) it was illegal B) It was unlikely C) It was avoidable D) It was understandable In order to avoid any confusion, one should _____________the answer to a multiple choice question before reading the possible answers.a.Predictc.Spellb.Ignored.Hide Interpreting Significance What was the significance of Washington declining to serve a third term? If My home is searched with out a warrant and they find a gun and I get arrested can I sue the police department for illegal search? HELPP!!!!Estimate a 15% tip on a dinner bill of $38.43 by first rounding the bill amount to the nearest ten dollars. Which activist organized a grape boycott?OA. Rosa ParksOOOB. Cesar ChavezC. Malcolm XD. Elijah Muhammad After being marked up 40%, the sale price of a tennis racket is $87.50What was the original price of the tennis racket? One angle of an isosceles triangle measures 50. Which other angles could be in thatisosceles triangle? Choose all that apply.Answer:50 , 80, 65 Archie Hamilton is 45 years old and single. Archie had wage income of $55,000. He also had gambling winnings of $1,000. He is not sure if he should itemize or take the standard deduction. Archie paid the following: $5,200 qualifying home mortgage interest. $9,507 for real estate taxes. $5,040 for state income taxes withheld in 2019. Unreimbursed doctor and dentist bills in the amount of $7,000. Unreimbursed prescription drugs for $14. Vitamins for $120. A statement received from his church showing donations made throughout the year totaling $1,200. Receipts for donations of furniture and clothing in good, used condition to Goodwill. The total estimated fair market value is $100. Tax preparation fee of $315 for his 2018 tax return. $50 paid in 2019 on his 2018 balance due state income tax return. $45 investment expense $250 in gambling losses 11. What is the total amount of state income and real estate taxes deductible on Archie's Form 1040, Schedule A The variety and variability of organisms is called?My Options:Symbiotic relationshipsBiodiversity Ecological succession Population ecology I need help ASAP please What function is money serving when you take it on a trip and keep it in your wallet or purse in caseyou need it?a. a flow of funds b. a unit of account c. a store of value d. a medium of exchange