A bag contains 100 cubes that are black, yellow, and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 9 black cubes, 4 yellow cubes, and 7 white cubes, which of the options below show a reasonable estimate for the total number of a certain cube in the bag? Select all that apply.
A) 45 black cubes
B) 20 yellow cubes
C) 70 white cubes
D) 90 black cubes
E) 35 white cubes

Answers

Answer 1

Answer:

The answer is..

A) 45 black cubes

B) 20 yellow cubes

E) 35 white cubes

Step-by-step explanation:

Answer 2

Final answer:

To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. The estimates for the total number of a certain cube in the bag are 45 black cubes and 20 yellow cubes.

Explanation:

To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. In this case, the proportion of black cubes to the total number of cubes is 9/20. So, if there are 100 cubes in total, we can estimate that there are approximately 45 black cubes in the bag. Similarly, the proportion of yellow cubes to the total number of cubes is 4/20, so we can estimate that there are approximately 20 yellow cubes in the bag. However, the proportion of white cubes to the total number of cubes is 7/20, which is less than the proportion of yellow cubes. Therefore, we cannot estimate that there are 70 white cubes in the bag. The estimates for the total number of a certain cube in the bag are A) 45 black cubes and B) 20 yellow cubes.


Related Questions

Nathan read 2 books in 10 months. What was his rate of reading in books per month

Answers

Answer:The rate of reading a book per month = [tex]\frac{1}{5}[/tex] = 20%

Step-by-step explanation:

Nathan read 2 books in 10 months.

The time taken to complete 1 book = [tex]\frac{10}{2}[/tex] = 5 months

To complete 1 book it takes 5 months.

The rate of reading a book per month = [tex]\frac{1}{5}[/tex] = 20%

PLZ IF ANY1 HELPS ME ON THIS ASAP GETS 25 POINTS

Answers

1 odd number

2 prime number

3 odd number and prime number

4 none (is out of the diagram)

5 odd number and prime number

Answer:

Ok here's the answer

Step-by-step explanation:

Odd numbers are whole numbers that cannot be divided exactly into pairs. Odd numbers, when divided by 2, leave a remainder of 1. 1, 3, 5, 7, 9, 11, 13, 15 … are sequential odd numbers. Odd numbers have the digits 1, 3, 5, 7 or 9 in their ones place.

Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,

so you need to put 1 in the odd number section

put 2 in the prime number section

put 3 in the middle section which is the similarities

don't put 4 anywhere because it's neither an odd number nor a prime number

put 5 in the middle section which is the similarities

4. Entomologists introduce 20 of one
variety of insect to a region and determine
that the population doubles every 6
hours.

part A Write an equation to model
this situation. Assume that the soulation
is continuously growing, and let t Represent
days.

part B What will the population be in 10 days?

part C How long will it take until the population reaches 100000?​

Answers

Answer:

This number can be found using the Rule of 70, which describes the formula dt = 70 / r, where dt is the doubling time, and r is the annual rate of growth.

Step-by-step explanation:

24/6 = 4

20 x 2 = 40 x 2 = 80 x 2 = 160 x 2 = 320

20 ---> 320 in the first day.

Keep doing this equation. Multiply each day's end result by 2 four times for 9 more days.

Express the square root 75 in
simplest radical form.

Answers

The square root of 75 is approximately 8.66025 or 5√3 in radical form.

The square root 75 in  simplest radical form will be [tex]5\sqrt{3}[/tex].

We have to Express the square root 75 in  simplest radical form.

We know that An expression that uses a root, such as a square root, cube root is known as a radical notation.

First find the factors of 75.

The factors of 75 will be,

[tex]3\times5\times5[/tex].

Now,

[tex]\sqrt{75} =\sqrt{3\times5\times5}[/tex]

since 5 is in pair under the root so it will come out from the root,

[tex]\sqrt{75}=5\sqrt{3}[/tex]

Thus the simplified radical form is [tex]5\sqrt{3}[/tex].

For more details on Radical form follow the link:

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A balloon is 23 feet below a tree limb. The balloon floats up 19 feet. What is it’s position relative to the tree limb

Answers

Answer:

It is 4 feet below the tree limb now

step by step

it starts at -23 or 23 below and rises 19 or adds 19 to the -23

so -23+19=-4. or 4 feet below the tree limb

Final answer:

After floating up 19 feet from its initial position of 23 feet below the tree limb, the balloon is 4 feet below the limb.

Explanation:

The student's question pertains to finding out the position of a balloon relative to a tree limb if the balloon starts 23 feet below the tree limb and then floats up 19 feet. We begin by acknowledging that the balloon's initial position is -23 feet (since it is below the limb, we consider this as negative). Upon floating up 19 feet, we perform the arithmetic operation of adding +19 feet to the initial position.

The calculation is as follows: -23 feet + 19 feet = -4 feet.

Therefore, the balloon's final position relative to the tree limb is 4 feet below it, since the result is still negative, indicating that the balloon did not reach or surpass the height of the limb.

which is a name for the angle shown? Select two answers

Answers

Answer:

I'm not sure how to answer is but i think its called   < CDE  or  < EDC  or it is an acute angle.

Step-by-step explanation:

The two ways of naming the given angle are:

1) D or ∠D2) EDC or ∠EDC

How to name an angle?

There are two general ways of naming an angle.

First, we just call the angle as the vertex. For example, in this case the vertex is D, then the name of the angle would be D or ∠D, where the symbol ∠ is used for angles.

Now, there are another way of naming an angle, and it depends on the arms of the angle (in cases where a point is a common vertex for many angles, we need to specify the arms).

So the name would be:

EDC or ∠EDC

Where the vertex goes always in the middle.

If you want to learn more about angles, you can read:

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help with properties of rhombus,rectangles and squares ​

Answers

Answer:

a = 3

b = 4

c = 5

Step-by-step explanation:

This is a rhombus. A property of a rhombus is that their diagonals perpendicularly bisect each other. In other words, if the point in the center is A, then HA = MA and EA = OA. So: 3 = a and 4 = b.

Since angle HAO forms a right angle, we can use the Pythagorean Theorem to say that HA^2 + AO^2 = OH^2: 3^2 + 4^2 = 9 + 16 = 25.

OH^2 = 25

OH = 5

Hope this helps!

Answer:

a = 3

b = 4

c = 5

Step-by-step explanation:

Rhombus has all sides equal

c = EH = sqrt(4² + 3²) = 5

Diagonals are Perpendicular bisectors of each other

b = 4

a = 3

To use the two sample t procedure to perform a significance test on the difference of two means, we assume: a) The populations' standard deviation are known. b) The samples from each population are independent. c) The sample sizes are large. d) The distributions are exactly normal in each population.

Answers

Answer:

The option which is an exception is;

c) The sample sizes are large

Step-by-step explanation:

Here the requirement to perform a two sample t procedure are as follows;

1. The two samples have equal variance, hence the variance should be known

2. The samples for which the two sample t procedure is performed must be independent

3. The data are in alignment with the normal distribution probability

4. The samples are random samples taken from the different respective population

Since the sample size is known, we do not assume that the sample size are large.

Therefore options a), b) and d) are all correct except option c).

In the early 1900's, the deer population of the Kaibab Plateau in Arizona increased rapidly because hunters had reduced the number of predators. However, the food supply was not great enough to support the increased population and the population eventually began to decline. The deer population for the years 1905 to 1930 can be approximated by the polynomial where x is the number of years from 1900. Evaluate the polynomial to find the deer population in 1920.

Answers

Answer:

The deer population in 1920 is 104000

Step-by-step explanation:

Here we have the deer population is given approximately by the following equation;

Population of deer = -0.125·x⁵ + 3.125·x⁴ + 4000

Where x = number of years from 1900

Therefore, in 1920, we have x = 20

Hence, the deer population in 1920 is then

-0.125·20⁵ + 3.125·20⁴ + 4000

Which gives

-400000 + 500000 + 4000 = 104000

The deer population in 1920 is therefore, 104000.

The sound intensity of rustling leaves is 100 times the reference intensity use your graph to determine the sound intensity of wrestling we use in the decibels

Answers

We can begin by noting a few things:

• dB represents the sound intensity in decibels

• I represents intensity

• I0 represents reference intensity

Assuming the reference intensity (I0) is the base level of hearing represented by the equation 1 • 10^(-12) watts per meter^2, we can incorporate 100 into the equation.

If the sound intensity of rustling leaves (I) is 100 times the reference intensity (I0), we can set up an equation to solve:

I = 100 • 10^(-12)

Now to calculate the intensity of rustling leaves in decibels:

dB = 10 • log10(100 • (1 • 10^(-12)) / (1 • 10^(-12)))

dB = 10 • log10(100) = 10 • 2 = 20 dB

Therefore, the sound intensity of rustling leaves is 20 decibels.

Distributive property for
14x+21y+7z

Answers

Answer:

7(2x+3y+z)

Step-by-step explanation:

Help me prove that sec(a-b) =seca*secb/1+tana*tanb​

Answers

Use:

[tex] sec a=\frac{1}{cos a}[/tex]

Answer:

See below.

Step-by-step explanation:

Write the sec's as 1 / cos  and the tan's as sin / cos

I will write sin as s and cos as c:

Left side  =  1 / ( cos)a - b)  =     1  / (ca cb + sa sb)

Right side =    1  /  (  ca cb ( 1 + sa sb / ca cb))

=  1 / ( ca cb *  ( ca cb + sa sb) / ca cb)

The 'ca cb' cancels out so

Right side = 1 / (ca cb + sa sb)  = left side..

If there are 2.2 pounds in 1 kilogram how many pounds are there in x kilograms?

Answers

Answer:

P=x/2.2

Step-by-step explanation:

We can create an equation to solve this.

Let the number of pounds be P

Let the number of kilograms be X

Now, we know that for 1 kilogram, there is 2.2 pounds.

Therefore if we have 1 kilogram (X) then we will have 2.2 pounds (P).

X=2.2P

All you have to do now is rearrange the equation to find the number of pounds in x kilograms. To do this divide both sides by 2.

Therefore you will get P=x/2.2

The number of pounds in X kilograms can be obtained by using the proportional relationship, Hence, the number of pounds in X kilograms is 2.2X pounds

Given the Parameters :

Number of pounds in 1 kilograms = 2.2 pounds

Creating the proportional expression thus :

1 kilogram = 2.2 pounds

X kilograms =?

Cross multiply :

Number of pounds = 2.2X

Therefore, there will be 2.2X pounds in 1 kilogram.

Learn more : https://brainly.com/question/18109354

The area of a rectangular garden is 18z+24 square feet. What are the possible dimensions of the garden?

Answers

Given:

The area of the rectangular garden is 18z+24 sq ft.

To find the possible dimensions of the garden.

Formula

The area of the rectangular garden is

[tex]A = lb[/tex]

where,

l be the length of the rectangle

b be the width.

Let us take l and b be the length and width of the given rectangular park respectively.

Now,

According to the problem,

[tex]lb = 18z+24[/tex]

or, [tex]lb = 6(3z+4)[/tex]

We can determine that,

l = 6 and b = 3z+4 or vice versa.

Hence,

The possible length and width of the rectangular garden is 6 and (3z+4) respectively.

6.7 is 10% of what number

Answers

Answer:

the answer is 67

Step-by-step explanation:

hope it's helpful

The answer is 67 , hope it helps !

When you start choose a pokemon starter in this game
there your choices are: Bulbasaur (green one), Squirtle
(blue one), & Charmander (red one). If you chose one
at random, what would be the probability of choosing
Squirtle?​

Answers

A 1 in 3 chance or 33.33%

Answer:

1/3 or 33.3%

Step-by-step explanation:

theres 3 total, and one squirtle so it's 1/3

A baby gains 11 pounds in its firat year of life. The baby gained 4 pounds during the first four months and
second four months. How much did the baby gain in the last four months?
3 1/4 pounds
3 1/2 pounds


4 pounds
5 pounds




Answers

Answer:

I think it's 3.5

Step-by-step explanation:

Is the following function exponential? *
3) y=7x-3

Answers

Answer:

Step-by-step explanation:

Both x and y have the exponent 1, and therefore this is a LINEAR equation.  NO, it is not an exponential function.

Final answer:

The function y=7x-3 is not an exponential function; it is a linear function with a slope of 7 and a y-intercept of -3.

Explanation:

The function given is y=7x-3. To determine whether this function is exponential, we should look at the form of the function. An exponential function has the form y = abˣ, where a is a constant, b is the base of the exponential (which is a positive real number other than 1), and x is the exponent. The given function, however, is a linear function because it can be rewritten in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m (the slope) is 7, and b (the y-intercept) is -3. Therefore, y=7x-3 is not an exponential function; it is linear.

Which is a perfect square? 5, 8, 44, 36

Answers

Answer:

The answer is 36.

Step-by-step explanation:

   36

    /\

6      6

/\      /\

3 2   3 2

Solve this system of equations using substitution
y = - 4
x + 2y = 10
Step 1: Substitute for y in the second equation. Which is
the resulting equation?

Answers

Answer:

x + 2(-4) = 10

x - 8 = 10

x = -18

y = -4

(-18, -4)

Step-by-step explanation:

Answer:

x + 2(-4) = 10

Step-by-step explanation:

Substituting -4 for y in the second equation results in x + 2(-4) = 10.  This simplifies to x - 8 = 10 and then x = 18.

Please, when the problem statement includes possible answer choices, share them.

If the area of a right triangle is 6.22 square inches and its base is 3.11 inches, write an equation that relates the area to the height, h, and the base. Solve the equation to determine the height.

Answers

Answer: (a) 12.44 - 3.11h = 0

(b) 4in²

Step-by-step explanation:

Area of a triangle = (1/2)bh, where b is the base and h is the height.

Now from the question, Area = 6.22in² and the base is 3.11inches.

Therefore, the equation that relates the area to the height and the base wiil be

Area = (3.11)h/2

6.22 x 2 = 3.11 x h

12.44 = 3.11h

12.44 - 3.11h = 0

(b) to find the value of h from the equation, make h the subject of the formula by solving for h

12.44 = 3.11h

h = 12.44/3.11

= 4in²

A tent originally sold for $260 and has been marked down to $208. What
is the percent of discount?

Answers

7% because I just needed to answer a question

The percent discount of the tent is 20%.

A discount reduces the price of an item. After a discount, the price of an item is reduced.

In order to determine the percent discount, the difference in price of the tents have to determined.

$260 - $208 = $52

The percent discount = ($52 / $260) x 100 = 20%

To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308

ms. smith bought a camera that cost $450 in addition she had to pay 4% sales tax how much did ms. smith pay for the camera

Answers

Answer:

$468

Step-by-step explanation:

450 + (450*0.04) = $468

Answer:

18

Step-by-step explanation:

​[related to solved problem ​#3​] suppose that andy sells basketballs in the perfectly competitive basketball market. his output per day and his costs are as​ follows: output per day total cost variable cost average total cost average variable cost marginal cost 0 ​$10.00 ​$0 ​-- ​-- ​-- 1 15.00 5 ​$15.00 ​$5.00 ​$5.00 2 17.50 7.50 8.75 3.75 2.50 3 22.50 12.50 7.50 4.17 5.00 4 30.00 20.00 7.50 5.00 7.50 5 40.00 30.00 8.00 6.00 10.00 6 52.50 42.50 8.75 7.08 12.50 7 67.50 57.50 9.64 8.21 15.00 8 85.00 75.00 10.63 9.38 17.50 9 105.00 95.00 11.67 10.56 20.00 suppose the equilibrium price of basketballs is​ $2.50. in the short​ run, how many basketballs will andy​ produce? 22 ​(enter a whole​ number).

Answers

Final answer:

In a perfectly competitive market, Andy will produce two basketballs in the short run, as this is the quantity at which the marginal cost equals the equilibrium price of $2.50.

Explanation:

In a perfectly competitive market, a firm like Andy's basketball business should continue to produce and sell its product as long as the marginal cost (MC) of producing an additional unit is less than or equal to the market price, and stop at the point where MC equals the market price. Given that the equilibrium price of basketballs is $2.50, and looking at the provided information where various costs are outlined, we can determine how many basketballs Andy should produce.

Andy should look at the marginal cost for each output level and compare it to the equilibrium price. He will produce up to the point where marginal cost equals the equilibrium price. The table shows the last unit he should produce at a marginal cost of $2.50 is the second basketball. Producing the third basketball would have a marginal cost of $5.00, which is higher than the equilibrium price, indicating that producing the third basketball would lead to a loss. Therefore, in the short run, Andy will produce two basketballs per day.

1. What is 26% written as a decimal?

Answers

Answer:

.26 = 26%     hope this helps!   :)

Step-by-step explanation:

.26

100 = 1.00

26 = .26

you just move the decimal point over 2

Answer:

26% = 0.26 in decimal form

Step-by-step explanation:

You just put a 0. in front of it,

take .26

Then 100 = 1.00

and 26 = .26

Hope This Helps:)

Would appreciate brainliest!!:)

Sarah saved $15 buying the dress
at a 20%-off sale. What was the
regular price of the dress?

Answers

Answer:

$18

Step-by-step explanation:

since she saved 20% you turn the percentage into a decimal which is .20 then multiply it by 15 because that's how much she saved and you get $3 which you add to $15 and you get the regular price which is $18

The price is $18 because you change the 20% to .20 and multiply it by 15 which gives you $3and then you add which gives you your answer.

emma will roll two number cubes labeled 1 through 6. She will record the sum of the two numbers after each roll. She will roll the two cubes 540 times. How many times should Emma expect the sum to equal 5?

Answers

Answer:

75 times

Step-by-step explanation:

First of all let's ook at the 36 possible outcomes and their sums.

2=1,1

3=1,2 2,1

4=1,3 ; 2,2 ; 3,1

5=1,4 ; 2,3 ; 3,2 ; 4,1

6=1,5 ; 2,4 ; 3,3 ; 4,2 ; 5,1

7=1,6 ; 2,5 ; 3,4 ; 4,3 ; 5,2 ; 6,1

8=2,6 ; 3,5 ; 4,4 ; 5,3 ; 6,2

9=3,6 ; 4,5 ; 5,4 ; 6,3

10=4,6 ; 5,5 ; 6,4

11=5,6 ; 6,5

12=6,6

Looking at the above, there are 4 sums equal to 5 out of a total of 36 sums.

Thus, probability of getting a sum equal to 5 is;

P(5) = 5/36

Now,since the cubes are rolled 540 times, number of times a sum equal to 5 will appear will be;

(5/36) x 540 = 75 times

NEED HELP ASAP!!
Which of the following is the correct expanded form for the series below?
a. 0 + 1 + 4 + 9 + 3
b. (0 + 3) +(1 + 3) + (4 + 3) + (9 + 3)
c. 1 + 3 + 9 + 27 + 3
d. (0 +3) + (2 + 3) + (4 + 3) + (6 + 3)

Answers

Answer: A

Step-by-step explanation:

The expanded form for the series is 0 + 1+ 4 + 9 +3

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

[tex]_3\\\sum{n^2}+3\\n=0[/tex]

⇒(0)² + (1)² + (2)² + (3)² +3

0 +1+ 4 + 9 +3

Learn more about Arithmetic operations here:

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#SPJ2

Plz HELP
.........../....

Answers

Answer:

The answer to your question is below

Step-by-step explanation:

Data

4 red marbles

3 blue marbles

3 yellow marbles

a) Total number of marbles = 4 + 3 + 3 = 10 marbles

b) Number of red marbles = 4 marbles

c) Number of blue marbles = 3 marbles

d) P(blue) = number of blue marbles/ total number = 3/10

e) P(red) = number of red marbles/total number = 4/10 = 2/5

the common ratio in a geometric series is 4 and the first term is 3 find the sum of the first 8 terms in the series

Answers

Answer:It’s b

Step-by-step explanation:

Girl it’s sum

Answer: 65535

Step-by-step explanation:

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The National Collegiate Athletic Association (NCAA) measures the Graduation Success Rate (GSR), which is the percentage of eligible athletes who graduate within six years of entering college. According to the NCAA, the GSR for all scholarship athletes in a particular division is 57%. The GSR for all students in this division is 62%. Suppose the NCAA report was based on a sample of 500 student-athletes, of which 285 graduated within six years. Is this sufficient information to conclude that the GSR for all scholarship athletes in this division differs from 62%? Carry out the test using a Type I error rate of 0.05. "The media doesnt influence me, but my sisters friends are clearly very much influenced. They always wear the latest fashions!" The common belief that we arent influenced by media messages but other people are is known as: Emporia Corporation is a lessee with a finance lease. The asset is recorded at $900,000 and has an economic life of 8 years. The lease term is 5 years. The asset is expected to have a fair value of $300,000 at the end of 5 years, and a fair value of $100,000 at the end of 8 years. The lease agreement provides for the transfer of title of the asset to the lessee at the end of the lease term. What amount of amortization expense would the lessee record for the first year of the lease How does Paine counter the arguments of Americas who still sought reconciliation with Great Britain A gas is at a pressure of 12.5 psi and a volume of 750 mL. What volume will the gas occupy at a pressure of 18 psi? A chemical reaction is carried out in a closed container. The energy absorbed by the chemical reaction is 150 kJ. How much energy moves inward from the air or the walls of the container? A. 75 kJB. 100 kJC. 150 kJD. 200 kJ What happens in "Eleven" during the falling action of the story?Mrs. Price puts the red sweater on Rachel's desk.Rachel describes the way she feels about turning eleven.Rachel moves the red sweater to the corner of her desk.Phyllis Lopez remembers that the sweater belongs to her. How did New Orleans leaders respond to the violence that broke out in their city over school integration? They declared martial law and called for federal troops to patrol the city. They closed the citys schools and bused students to rural communities. They encouraged the violent protests to stop public school integration. They pushed for acceptance of school desegregation to end the violence. Of the reactions below, which one is not a combination reaction?Immersive Reader (2 Points) 2N2 + 3H2 2NH3 2Mg + O2 2MgO 2CH4 + 4O2 2CO2 + 4H2O C + O2 CO2 CaO + H2O Ca(OH)2 Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size? a. A small mean difference and small sample variances b. A large mean difference and small sample variances c. A small mean difference and large sample variances d. A large mean difference and large sample variances Riverbed Company designated Jill Holland as petty cash custodian and established a petty cash fund of $236. The fund is reimbursed when the cash in the fund is at $31, which it is. Petty cash receipts indicate funds were disbursed for office supplies $94 and miscellaneous expense $89. 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Tams life worsened when a baby girl, Cam, was born. Tams father and stepmother showered Cam with everything she desired, leaving Tam to live a desolate, lonely life. She cleaned the house, cooked the food, hauled the trash, and collected the water. 2One day, Tams stepmother sent her and Cam to collect fish. Though they were half sisters, Tam and Cam had contrasting personalities. Tam fished continuously until her basket overflowed with fish, while Cam lazily lounged in the sun. Upon realizing that she had no fish to take home, Cam decided to steal Tams fish. When Tam wasnt looking, Cam poured Tams fish into her own basket, snickered, and fled home. 3Tam wept when she saw the empty basket because she knew that punishment awaited her; however, she stopped crying abruptly when a beautiful woman appeared. The woman grinned sweetly and told Tam not to weep.4Your misfortunes will be over soon, Tam. Inside your basket, you will find one fish. Take it home and care for it, said the woman.5Tam put the fish in the well behind her house. Each time Tam neared the well, the fish surfaced, which made Tam very happy. One day, because Tam's stepmother despised Tams happiness, she removed the fish from the well and returned it to the river. The next time Tam visited the well, the fish did not surface. Tam instantly knew what had occurred and wept. Once again, the beautiful woman appeared. She instructed Tam to visit the fish at the edge of the river whenever she needed help.6A few weeks later, the Autumn Festival began, and Tams town erupted with activity. Tam planned to attend the festival, but her stepmother wrote a list of many chores for her to complete. Saddened, Tam visited the water's edge and asked for help. In a moment, the beautiful woman appeared before Tam and instantly transformed Tam's shabby clothes into a stunning blue and silver dress.7Tam raced to festival, where she earned praise as the most beautiful woman in attendance. Tam shimmered like a star in the glowing gown, but having everyone's eyes on her made her self-conscious, and she ran away. In her haste, she lost a shoe on the staircase. 8Later, the Prince discovered Tams lost shoe. He had seen Tam at the festival and hoped to marry her. He traveled the kingdom seeking the woman whose foot fit the shoe. When the Prince arrived at Tams house, she tried on the shoe and it fit! The Prince was jubilant and asked Tam to marry him. Eventually, the Prince became King, and Tam became Queen. Though Tam never took revenge on her family members, they lived in agony knowing that if they had been kinder, they could have lived with Tam and the King.How does the author create a feeling of suspense or tension in this story?A) by creating sympathy for the abused and oppressed character, TamB) by characterizing one of the two young women as wicked and cruelC) by utilizing a natural creature, a fish, as a friend to poor, lonely, TamD) by having the beautiful woman appear several times to help Tam as her life worsens Assume that 0 < x < pi/2 and 0 < y < pi/2. Find the exact value of cos(x-y) if cos(x)=3/5 and cos(y)=4/5a. 25/24b. -25/24c. 24/25d. -24/25 Which theory states that living things change lower overtime in response to changes their environment