In an electronic system, a sensor measures a crucial parameter and outputs a number, but there is random error in its measurement. The measurement error in a sensor output is known to be RV X with uniform distribution in (-0.05,0.05) and independent from one output to the next, that is, the errors are iid! During a run of the system, n = 1000 samples of the sensor output are recorded. (a) Find the numerical value of the mean ux and the variance oź for the uniform distribution described. (You can use results in the text by listing the theorem or formula.) Further processing of these n= 1000 samples adds them together, and we are concerned about the overall error in the sum resulting from adding 1000 iid errors. Let X, denote the error in the įth sample for 1 1." Show all the steps in how you compute this. (f) Are the answers in (d) and (e) in agreement? If they are different, explain how both can be correct.

Answer:

C(2010) = $1312 using linear approximation.

Step-by-step explanation:

The full complete question is attached to this solution.

The full table is given as

Year | 1970 | 1980 | 1990 | 2000

Cash |$180 |$262 |$564 | $938

we are told to use linear approximation to obtain C(2010)

Linear approximation, Mathematically, results in

C(2010) = C(2000) + C'(t) [t]

where t = years since 2010 = (Year - 2000)

Linear approximation gives C'(t) as the rate of change of C with time

C'(t) = (ΔC/Δt)

We will be using the latest year for this approximation.

ΔC = C(2000) - C(1990) = 938 - 564 = $374

Δt = 2000 - 1990 = 10

C'(t) = (374/10) = $37.4 per year.

C(2010) = C(2000) + C'(t) [t]

t = 2010 - 2000 = 10

C(2000) = $938

C'(t) = $37.4 per year

C(2010) = 938 + (37.4)(10) = $1312

Hope this Helps!!!

The amount, C(2010), of cash per capita in circulation in the year 2010 = $1312.

The full table is given as

Year | 1970 | 1980 | 1990 | 2000

Cash |$180 |$262 |$564 | $938

we are told to use linear approximation to obtain C(2010)

Linear approximation, Mathematically, results in

C(2010) = C(2000) + C'(t) [t]

where t = years since 2010 = (Year - 2000)

Linear approximation gives C'(t) as the rate of change of C with time

C'(t) = (ΔC/Δt)

We will be using the latest year for this approximation.

ΔC = C(2000) - C(1990) = 938 - 564 = $374

Δt = 2000 - 1990 = 10

C'(t) = (374/10) = $37.4 per year.

C(2010) = C(2000) + C'(t) [t]

t = 2010 - 2000 = 10

C(2000) = $938

C'(t) = $37.4 per year

C(2010) = 938 + (37.4)(10) = $1312.

Complete question:

Final answer:

The answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.

Explanation:

Can Segments Form a Triangle?

To determine if the segments with lengths of 1 and 8 can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have two sides that are each 8 units long, and one side that is 1 unit long.

Let's add the lengths of the two shorter segments: 1 + 8 = 9.

This sum is greater than the length of the other segment, which is 8. Now, we will check the sum of the other two possible pairs:

Since all combinations of the sums of two sides are greater than the third side, these segments can indeed form a triangle.

Thus, the answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.

Answer:

The correct answer is 161700.

Step-by-step explanation:

Total number of members of the senate of 107th congress is 100 in which there are 53 republicans, 42 democrats and 5 independents.

A new committee is to be formed from these 100 congressmen to study the benefits of arts in education.

Number of senators required to head the new committee is 3.

Therefore total number of ways 3 members are selected in the population of 100 congressmen is given by [tex]\left[\begin{array}{ccc}100\\3\end{array}\right][/tex] = 161700.

Thus there are 161700 ways one can select 3 senators to head a committee.

Step-by-step explanation:

By definition, the area of a rectangle is given by:

A = w * lA=w∗l

Where,

w: width of the rectangle

l: length of the rectangle

We then have the following expression for the area:

A = k ^ 2 + 19k + 60A=k

2

+19k+60

What we must do is factorize the expression following the following steps:

1) Find two numbers that are equal to 19

2) Find two multiplied numbers equal to 60

We have then:

A = (k + 15) (k + 4)A=(k+15)(k+4)

Therefore, the width of the rectangle is:

w = (k + 4)w=(k+4)

Answer:

Thats correct! The answer is B. (2nd option.) I took edge.

Step-by-step explanation:

Answer:

20 knives

Step-by-step explanation:

the ratio of fork to knives is [tex]\frac{4}{5}[/tex] and their are 16 forks, so we put the ratio of fork and knives equal to number of fork and knives so its:

[tex]\frac{4}{5}[/tex] = [tex]\frac{16}{x}[/tex]  We cross multiply

80 = 4x Divide both  side by 4

x = 20

we can check too

16/20 if we simplify, its give us 4/5

There are 20 knives in Isabella's kitchen.

The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5.

Given that there are 16 forks in the drawer, we can set up a proportion to find the number of knives:

4/5 = 16/X

Cross multiply to get: 4X = 80

Divide by 4 to find X = 20

Therefore, there are 20 knives in Isabella's kitchen drawer.

Answer:

d AND C

Step-by-step explanation:

Answer:the sum of the remote interior angles is 95 degrees.

measure of a:85

measure of B:95

Step-by-step explanation:

i just took this

Answer: 95

Step-by-step explanation:

Answer:Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

t = -2.69 , p = 0.0078

Step-by-step explanation:

We have the following data:

Sample Mean = x = 24.444

Sample Standard Deviation = s = 2.45

Sample size = n = 18

Josh wants to test that mean number is lesser than 26. So our test value is 26 i.e.

u = 26

Since Josh wants to test that mean would be fewer than 26, so this would be a left tailed test with a less than sign in Alternate Hypothesis. Therefore, the hypothesis would be:

[tex]H_{o}: u\geq 26\\H_{a}: u<26[/tex]

Since, we do not know the value of Population standard deviation, and we have the value of sample standard deviation, we will use One-Sample t-test for the population mean.

The formula to calculate the test-statistic would be:

[tex]t=\frac{x-u}{\frac{s}{\sqrt{n}}}[/tex]

Substituting the values in this formula gives us:

[tex]t=\frac{24.444-26}{\frac{2.45}{\sqrt{18}}}\\t=-2.69[/tex]

This means, the test statistic would be -2.69

Since, the sample size is 18, the degrees of freedom would be:

Degrees of freedom = df = n - 1 = 17

To find the p-value we need to check the p-value against test statistic of 2.69, with 17 degrees of freedom and One-tailed test. This value comes out to be:

p-value = 0.0078

Therefore, the correct answer would be:

t = -2.69 , p = 0.0078

Answer:

a) X is binomial with n = 10 and p = 0.3

Y is binomial with n = 10 and p = 0.7

b) The mean number of errors caught is 7.

The mean number of errors missed is 3.

c) The standard deviation of the number of errors caught is 1.4491.

The standard deviation of the number of errors missed is 1.4491.

Step-by-step explanation:

For each typing error, there are only two possible outcomes. Either it is caught, or it is not. The probability of a typing error being caught is independent of other errors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

10 word errors.

This means that [tex]n = 10[/tex]

(a) If X is the number of word errors missed, what is the distribution of X ?

Human proofreaders catch 70 % of word errors. This means that they miss 30% of errors.

So for X, p = 0.3.

The answer is:

X is binomial with n = 10 and p = 0.3.

If Y is the number of word errors caught, what is the distribution of Y ?

Human proofreaders catch 70 % of word errors.

So for Y, p = 0.7.

The answer is:

Y is binomial with n = 10 and p = 0.7

(b) What is the mean number of errors caught?

[tex]E(Y) = np = 10*0.7 = 7[/tex]

The mean number of errors caught is 7.

What is the mean number of errors missed?

[tex]E(X) = np = 10*0.3 = 3[/tex]

The mean number of errors missed is 3.

(c) What is the standard deviation of the number of errors caught?

[tex]\sqrt{V(Y)} = \sqrt{np(1-p)} = \sqrt{10*0.7*0.3} = 1.4491[/tex]

The standard deviation of the number of errors caught is 1.4491.

What is the standard deviation of the number of errors missed?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.3*0.7} = 1.4491[/tex]

The standard deviation of the number of errors missed is 1.4491.

(a). X follows a binomial distribution with n = 10 and p = 0.3, while Y follows a binomial distribution with n = 10 and p = 0.7.

(b) The mean number of errors caught is 7 and the mean number of errors missed is 3,

(c) Both with a standard deviation of approximately 1.4491.

Let's analyze the given problem step by step.

Part (a): Distribution of X and Y

X represents the number of word errors missed.

Since 70% of word errors are caught, 30% of word errors are missed.

Therefore, X follows a binomial distribution with n = 10 (total errors) and p = 0.3 (probability of missing an error).

Y represents the number of word errors caught.

Since 70% of word errors are caught, Y follows a binomial distribution with n = 10 and p = 0.7 (probability of catching an error).

Part (b): Mean Number of Errors Caught and Missed

Part (c): Standard Deviation of the Number of Errors Caught and Missed

Standard deviation of errors caught:

Thus, the standard deviation of the number of errors caught is approximately 1.4491.

Standard deviation of errors missed: For X (missed errors), σ = √(10 × 0.3 × 0.7) ≈ 1.4491. Thus, the standard deviation of the number of errors missed is approximately 1.4491.

Answer:

D. 144 cubic meters

Step-by-step explanation:

Volume of triangular prism(V)= Area of a triangle(A)×height of the prism(H)

That is,

V=AH

Where,

A=Area of a triangle

H=Height of the prism

Given,

A=1/2× base×height=16 square meters

Height=9 meters

Therefore,

Volume of triangular prism=16 square meters×9 meters

=144 cubic meters

Answer: D. 144 cubic meters

Step-by-step explanation:

A triangular prism consists of 2 triangular faces(base) and 3 rectangular faces.

The formula for determining the volume of a triangular prism is expressed as

Volume = area of the triangular base × height of the prism

Area of triangular base = 1/2 base × height

From the information given,

Height of prism = 9 meters

Area of triangular base = 16 square meters

Volume of the triangular prism = 16 × 9 = 144 cubic meters

Answer:

[tex]P(\bar X>215)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this: for the value of 215

[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]

Step-by-step explanation:

Let X the random variable that represent the ratings of applicants from a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200,50)[/tex]  

Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]

We select a sample size of n =40. We are interested on this probability

[tex]P(\bar X>215)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this: for the value of 215

[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]

Answer 39916800

Step-by-step explanation:

The probability that all hip-hop songs are played consecutively is 0.18%.

To calculate the probability that all hip-hop songs are played consecutively, to consider the total number of possible song arrangements and the number of arrangements where all hip-hop songs are consecutive.

The total number of song arrangements calculated using the concept of permutations. Since there are a total of 11 songs on the playlist, the number of possible arrangements is 11!.

Now, let's calculate the number of arrangements where all hip-hop songs are played consecutively treat the 6 hip-hop songs as a single unit or block. This means  6! ways to arrange the hip-hop songs within that block.

Since we have 5 rock songs remaining, we can arrange them in 5! ways.

Therefore, the total number of arrangements where all hip-hop songs are played consecutively is 6! ×5!.

To calculate the probability, we divide the number of favorable outcomes (where all hip-hop songs are played consecutively) by the total number of possible outcomes:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = (6! × 5!) / 11!

Calculating the numerical value:

Probability = (720 × 120) / 39,916,800

Probability ≈ 0.00180

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The relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is not irreflexive, asymmetric, or intransitive.

To determine whether the relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is irreflexive, asymmetric, or intransitive, we will analyze each property.

Therefore, the relation R2 is none of the given properties (irreflexive, asymmetric, or intransitive).

Answer:

The car's speed is 74.5444 mi/hr. It travels 298.2576 miles in 4 hours.

Step-by-step explanation:

If we want to know the speed in mi/hr, we must convert the km to mi. We can convert from kilometers to miles as follows.

mi = km * 0.62137

Then, if the car is moving at 120 km / hr, we have that the car is moving at

120*0.62137 mi /hr, which is 74.5644 mi/hr. If we want to know how many miles the car travels in four hours, we multiply the speed times the total time. Hence

total distance = 74.5444 mi/hr * 4 hr = 298.2576 miles.

High Risk because returns are not guaranteed, but time frames are set

—Speculation

Moderate Disk because expectations of returns are reasonable and average

—Growth

Low Risk because of steady Interest without fluctuation in value

—Savings

In investment terms, growth corresponds to high risk as returns aren't guaranteed, savings relate to low risk due to steady interest income, and speculation signifies moderate risk as it has reasonable return expectations.

The types of investment can be associated with different levels of risk as follows:

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Answer:

a. The percentage of adult men that will fit through the door without bending is 0.

b.  The percentage of adult women that will fit through the door without bending is 0.

c. No, it is not adequate. There must be another technical reasons to not use a larger door.

d. The doorway height that would allow 60% of men to fit without bending is 70.1 inches.

Step-by-step explanation:

a. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of men's height N(μ=69.5, σ=2.4).

We can calculate the z-score as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-69.5}{2.4}=\dfrac{-17.9}{2.4}=-7.4583[/tex]

[tex]P(X<51.6)=P(z<-7.4583)=0[/tex]

The percentage of adult men that will fit through the door without bending is 0.

b. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of women's height N(μ=63.8, σ=2.6).

We can calculate the z-score as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-63.8}{2.6}=\dfrac{-12.2}{2.6}=-4.6923[/tex]

[tex]P(X<51.6)=P(z<-4.6923)=0[/tex]

The percentage of adult women that will fit through the door without bending is 0.

c. No, it is not adequate. There must be another technical reasons to not use a larger door.

d. We can calculate this finding a z-value z1 for which P(z<z1)=0.60.

Looking in a standard normal distribution table, the value for z1 is z1=0.25335.

Then, transforming to our adult men's height distribution, we have:

[tex]X=\mu+z\sigma=69.5+0.25335*2.4=69.5+0.6=70.1[/tex]

The doorway height that would allow 60% of men to fit without bending is 70.1 inches.

Answer:

28.57℅

Step-by-step explanation:

If last year attendance was 860 and the attendance increases to 1204:

Attendance increment = 1204-860

= 344

%increase = increment/current attendance × 100%

% increase = 344/1204 × 100

℅ increase = 34400/1204

% increase = 28.57%

Therefore the percentage increase from last year is 28.57℅

Answer:

p = 0.574197

Step-by-step explanation:

There are 14000 ballots left.

The lead is 2174, so he needs to lead at least 2175 in these 14000 ballots.

He does so if he gets at least 8088 votes.

If P(x >= 8088) = 0.20, then the corresponding z score to this is, by table/technology,

z = 0.841621234

Now, as

z = (x - u) / s

and

u= n p

s = sqrt(n p(1-p))

Then

0.841621234 = (8088 - 14000*p) / sqrt(14000p(1-p))

Solving for p here,  

p = 0.574197

Answer:

y=1

Step-by-step explanation:

6=2(y+2)

Divide each side by 2

6/2=2/2(y+2)

3 = y+2

Subtract 2 from each side

3-2 = y+2-2

1 = y

Answer:

y = 1

Step-by-step explanation:

6 = 2 ( y + 2 )

6 = 2y + 4

subtract four from both sides

2 = 2y

divide by 2 on both sides

y = 1

Answer:

c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.

Step-by-step explanation:

1 quart : 0.95 litre

X quarts : ?

X/1 = ?/0.95

? = 0.95 × X

Final answer:

The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.

Explanation:

The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:

[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]

To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.

After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.

Answer:

The distribution of symmetrical to asymmetrical will change so that close to 100% of birds will have symmetrical wingspans.

Answer:

Refer below.

Step-by-step explanation:

The appropriation of symmetrical to asymmetrical will change so near 100% of flying creatures will have symmetrical wingspans.

Answer:

it would be a triangle

Step-by-step explanation:

Answer:

2500

Step-by-step explanation:

Find out how much 1 part is. Add all the parts together

1+2+3=6

find how much of 5000 is 1 part

5000/6=833.3 recurring

833.3 is 1 part

then multiple the parts

8.333.3 x 1

8.333.3 x 2

8.333.3 x 3

8.333.3 r : 1.666.6 r : 2500

The value of the greatest share is 2500.

Important information:

We need to find the greatest share.

Let 5000 is divided in three shares whose values are [tex]x, 2x[/tex] and [tex]3x[/tex].

[tex]x+2x+3x=5000[/tex]

[tex]6x=5000[/tex]

[tex]x=\dfrac{5000}{6}[/tex]

[tex]x=\dfrac{2500}{3}[/tex]

The value of greatest share is [tex]3x[/tex].

[tex]3x=3\times \dfrac{2500}{3}[/tex]

[tex]3x=2500[/tex]

Therefore, the value of greatest share is 2500.

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Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a)    10% of all adult Americans support the changes

Here, [tex]np>5\ and\ n(1-p)>5[/tex]

And , [tex]p=0.10[/tex]

So, consider the equality, to find the value of 'n'.

[tex]np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50[/tex]

So, there are [tex]50-35=15[/tex] more adult Americans needed.

(b)   15% of all adult Americans supports the changes

Here, [tex]p=0.15[/tex]

So, again we get that

[tex]np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34[/tex]

So, there are [tex]35-34=1[/tex] more adult Americans needed.

Hence, a) 15, b) 1.

Sample space for the experiment is {B, E, I, L , R , S, T }  .

Hence option D is correct.

Given, that the word IRRESISTIBLE .

An experiment consist of selecting a letter at random from the letters in the given word.

The number of distinct letters in the word is 7 i.e I is 3 times in the word but consider it as single letter.

Therefore the appropriate sample space for the experiment is {B, E, I, L , R , S, T } .

Thus the option D is correct.

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The sample space for an experiment consists of all possible outcomes or events that can occur. In this case, the experiment involves selecting a letter at random from the letters in the word "IRRESISTIBLE."

The appropriate sample space for this experiment would be the set of all individual letters that can be selected from the word. Therefore, the sample space is:

Sample space = {I, R, E, S, T, I, B, L}

Each element of the sample space represents a possible outcome of the experiment, which is selecting a specific letter from the word "IRRESISTIBLE."

It is important to note that the sample space only includes the individual letters as outcomes, and it does not consider the order or repetition of the letters in the word.

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Answer:

The median is 102

Step-by-step explanation:

Median = a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.

Therefore, the answer 102 is correct.

(I need to be granted one more brainliest to level up so if my answer helped, it would be very much appreciated to award that to me, no obligations though!)

complete question:

If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?

A parallelogram with a base of 10 centimetres and a height of 8 centimetres.

Answer:

area = 48 cm²

Step-by-step explanation:

A parallelogram is quadrilateral with 4 sides formed by 2 pair of parallel lines. The area of a parallelogram is represented as follows :

area of parallelogram =  B × H

where

B = breadth

H = height

According to the question the height and the base each reduced by 2 cm.

The new base = 10 - 2 = 8 cm

The new height = 8 - 2 = 6 cm

area = B × H

area = 8 × 6

area = 48 cm²

Given:

The length of a rectangle is 5 less than its width.

The area of the rectangle is 84 square feet.

We need to determine the quadratic equation in standard form that represents the area of the rectangle.

Dimensions of the rectangle:

Let l denote the length of the rectangle.

Let w denote the width of the rectangle.

Since, it is given that the length is 5 less than its width, it can be written as,

[tex]l=5-w[/tex] and [tex]w=w[/tex]

Area of the rectangle:

The area of the rectangle can be determined using the formula,

[tex]A=length \times width[/tex]

Substituting A = 84, [tex]l=5-w[/tex] and [tex]w=w[/tex], we get

[tex]84=(5-w)\times w[/tex]

[tex]84=5w-w^2[/tex]

Adding both sides of the equation by w², we have;

[tex]w^2+84=5w[/tex]

Subtracting by 5w on both sides, we get;

[tex]w^2-5w+84=0[/tex]

Thus, the quadratic equation in standard form for the area of the rectangle is [tex]w^2-5w+84=0[/tex]