Forgot the formula for finding AREA of windows, etc. Problem: The area of a window measures 336 square inches. If the window is 16 inches wide, how long is the window? (4th grade)

The height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).

Let's assume the width of the rectangular box is represented by the variable 'w'. Given that the length of the box is twice the width, we can express the length as '2w'. The height of the box can be represented by the variable 'h'.

The volume of a rectangular box is given by the formula: V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.

We are given that the volume of the box is 8 ft³. Substituting the values into the formula, we have:

8 = (2w)(w)(h)

Simplifying, we get:

8 = 2w²h

Dividing both sides by 2w², we get:

4/w² = h

Therefore, the height of the box can be expressed as a function of the width, h = 4/w².

The domain of the height function is determined by the width. Since the width of a rectangular box cannot be zero or negative (as it represents a physical dimension), the domain of the height function is the set of positive real numbers, excluding zero. In interval notation, the domain can be expressed as (0, +∞).

In conclusion, the height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).

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Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The  95%  confidence interval is  \(0.2392 < p < 0.3108\)

No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

Step-by-step explanation:

From the question we are told that

  The total sample size is  \(n = 432 + 164 =596\)

   The  number of  offspring that is yellow peas is \(y = 432\)

   The  number of  offspring that is green peas   is \(g = 164\)

The sample proportion for offspring that are yellow peas is mathematically evaluated as

        \(\r p = \frac{ 164 }{596}\)

        \(\r p = 0.275\)

Given the the  confidence level is  95% then the level of significance is mathematically represented as

       \(\alpha = (100 - 95)\%\)

      \(\alpha = 5\% = 0.0 5\)

The  critical value of  \(\frac{\alpha }{2}\) from the normal distribution table is  

      \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically evaluated as

        \(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }\)

=>      \(E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }\)

=>      \(E = 0.0358\)

The  95%  confidence interval is mathematically represented as

      \(\r p - E < p < \r p + E\)

=>   \(0.275 - 0.0358 < p < 0.275 + 0.0358\)

=>   \(0.2392 < p < 0.3108\)

a) If w = I, then we can write w = 0 + I. This means that x = 0 and y = 1. Using the polar form of a complex number, we can write z = r cos theta + I r sin theta. Since x = 0 and y = 1, we can write z = r cos theta + I r sin theta = 0 + I. This means that r cos theta = 0 and r sin theta = 1. Since cos theta = 0, theta = pi/2. Therefore, z = r cos (pi/2) = I.

b) To prove that w = (x^3+2x+y^3+y) + I (x+2y+2)/ (x+2)^2+y^2, we can substitute the values of x and y from the equation w = x + I y into the equation and simplify.

w = (x^3+2x+y^3+y) + I (x+2y+2)/ (x+2)^2+y^2
= (x^3+2x+y^3+y) + I (x+2y+2)/ (x^2+4x+4+y^2)
= (x^3+2x+y^3+y) + I (x+2y+2)/ (x^2+4x+4+y^2)
= (x^3+2x+y^3+y) + I (x+2y+2)/ (x^2+4x+4+y^2)
= w

Therefore, the equation is true.

c) When Re(w) = 1, this means that the real part of w is equal to 1. Therefore, x^3+2x+y^3+y = 1. We can rearrange this equation to get y^3+y = 1-x^3-2x. Taking the derivative of both sides with respect to x, we get 3y^2 dy/dx + dy/dx = -3x^2-2. Solving for dy/dx, we get dy/dx = (-3x^2-2)/(3y^2+1). This is the gradient of the line l_1.

d) Given that arg(z) = arg(w) = pi/4, this means that the angle of both z and w is equal to pi/4. Using the polar form of a complex number, we can write z = r cos (pi/4) + I r sin (pi/4) and w = s cos (pi/4) + I s sin (pi/4). Since the angles are equal, this means that r cos (pi/4) = s cos (pi/4) and r sin (pi/4) = s sin (pi/4). Therefore, r = s and z = w.

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The values of x and y of the parallelogram PQRS are x = 2 and y = 11

We're given the dimensions of parallelogram PQRS as;

PT = y

TR = 5x + 1

QT = 2y

TS = 6x + 10

T is the intersection of the two diagonals PR and QS and so the diagonals bisect each other.

The diagonal PR is cut into PT and TR, both of which are congruent or equal. Thus, PT = TR.

Similarly, the other diagonal QS is split in half as well. The two equal pieces are QT and TS. So QT = TS.

PT = TR

y = 5x + 1

and

QT = TS

2y = 6x + 10

Plugging the values gives;

2y = 6x + 10

2(y) = 6x + 10

2(5x + 1) = 6x + 10

2*5x + 2*1 = 6x + 10

10x + 2 = 6x + 10

10x + 2 - 6x = 6x + 10 - 6x

4x + 2 = 10

4x + 2 - 2 = 10 - 2

4x = 8

4x/4 = 8/4

x = 2

If x = 2, then y is...

y = 5x+1

y = 5*x+1

y = 5*2+1

y = 10+1

y = 11

Thus, the values of x and y of the parallelogram PQRS are x = 2 and y = 11

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A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

Yes, the large-sample confidence interval will be valid.

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

A sample is considered large when n ≥ 30.

By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.

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Answer:

Step-by-step explanation:

I can't see the screenshot

so like yeah

Round to the nearest tenth for the right triangle, wouldn't it be 20 or am I wrong?

Answer:

1377.76x

Step-by-step explanation:

Simplify 1264*1.09

Answer:

1377.76x

(give the person above the crown)

The total number of different paths which we can have as calculated from the given data is 6.

To know the number of different three-step paths along the edges of a cube are there that take us from vertex a  to vertex b.

For the first path no of different ways = 3

For the second path no of different ways = 2

For the third path no of different ways = 1

Therefore , the total number of ways

= 3 x 2 x 1

= 6

The solid three-dimensional shape also known as a cube has six square faces, eight vertices, and twelve edges. A cube is also known as a hexahedron.

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Answer: k(8)=44

Step-by-step explanation:

We know that k(x)=17-3(-x-1) and we a trying to figure out what k(8) is

Sub 8 in for x and solve

k(8)=17-3(-(8)-1)

k(8)=17-3(-9)

k(8)=17-(-27)

k(8)=44

Answer: a, 9x10^9, largest number 900000000

Answer: greatest is A.

Step-by-step explanation:

Answer:

a and d

Step-by-step explanation:

v and w are parallel lines

R is the transversal

Alternate exterior means on the opposite sides of the transversal and outside of the parallel linea

a and d are alternate exterior angles

The number of subjects who participated in the study is 20.

To determine the number of subjects who participated in the study, we need to understand the relationship between the degrees of freedom (df) and the sample size in a t-test.

In a matched-subjects experiment, participants are typically matched based on certain characteristics or variables to create pairs or groups. Each pair or group is then exposed to different conditions or treatments, and the differences within each pair or group are analyzed.

This type of design is often used to minimize individual differences and increase the precision of the study.

In a matched-subjects t-test, the degrees of freedom are calculated based on the difference scores between the pairs or groups. The formula to calculate the degrees of freedom is:

df = n - 1

Where 'n' represents the number of pairs or groups.

In a matched-subjects design, each pair contributes one degree of freedom.

Given that the t statistic has a df of 19, we can set up the equation:

19 = n - 1

Solving for 'n', we add 1 to both sides:

19 + 1 = n - 1 + 1

20 = n

In summary, based on the given information, there were 20 subjects who participated in the matched-subjects experiment.

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Answer:

To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:

\(\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}\)

Using partial fractions, we can write:

\(\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}\)

Multiplying both sides by (x+i)(x-i), we get:

\(x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)\)

Substituting x=i, we get:

\(i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)\)

Simplifying, we get:

\(16 = 2Ci + 2B\)

Substituting x=-i, we get:

tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)\)

Simplifying, we get:

\(16 = 2Ai + 2D\)

Substituting x=0, we get:

\(0 = Bi + Di\)

Substituting x=1, we get:

\(0 = A+B+C+D\)

Solving these equations simultaneously, we get:

A = -22/7 + π

B = 0

C = 22/7 - π

D = -2/5

Therefore, the integral can be written as:

\(\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx\)

Integrating each term separately, we get:

\(\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)\)

\(\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)\)

\(\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)\)

Therefore, the correct options are:

A) \(\pi-\frac{22}{7}\)

B) \(\frac{2}{105}\)

C) 0

D) \(\frac{71}{15}-\frac{3\pi}{2}\)

The ending inventory amount is p68,000: (200 x 65) + (300 x 68) + (150 x 70) - (500 x 68) = 68,000.

1. Calculate the total cost of the beginning inventory: 200 units x p65 = p13,000

2. Calculate the total cost of the first purchase: 300 units x p68 = p20,400

3. Calculate the total cost of the second purchase: 150 units x p70 = p10,500

4. Calculate the total cost of the units sold: 500 units x p68 = p34,000

5. Calculate the total cost of the ending inventory amount : (13,000 + 20,400 + 10,500) - 34,000 = p68,000

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Answer:

-3/2 (x - 6)

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

Answer:1146.11111

500*200 = 100,000

100,000 / 90 = 1111.11111

1111.11111+35 = 1146.11111

Based on the given information, we know that the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. Since the arrival and service distributions are not known, we cannot use the m/m/1 formulas to calculate the average waiting time and total time spent in the system.

However, we can still use the Little's Law formula to relate the average number of customers in the system to the average waiting time. Little's Law states that the average number of customers in the system (N) is equal to the product of the arrival rate (λ) and the average time spent in the system (T), or N = λT.

Since we want to find the total time spent in the system, we can rearrange the formula to solve for T. Thus, T = N / λ.

We know from the given information that the average waiting time in the line is 18 minutes. Therefore, the average time spent in the system for a customer is T = 18 minutes + (1/14 hour), which is equal to 1.9 hours.

To calculate the total time spent in the system, we need to add the waiting time to the service time. Since the service rate is 14 customers per hour, the service time per customer is 1/14 hour or approximately 4.3 minutes. Thus, the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

In summary, the average time spent in the system for a customer is 1.9 hours, and the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

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1) The figure shows a translation.

2) It is translation because every point of the pre - image is moved the same distance in the same direction to form an image.

3) Point A from the pre - image corresponds with Point D on the image.

We have to given that,

There are transformation of triangles are shown.

Now, From figure all the coordinates are,

A = (- 5, 3)

B = (- 4, 7)

C = (- 1, 3)

D = (- 1, - 2)

E = (0, 1)

F = (3, - 2)

Hence, We get;

1) The figure shows a translation.

2) It is translation because every point of the pre - image is moved the same distance in the same direction to form an image.

3) Point A from the pre - image corresponds with Point D on the image.

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Answer:

24 miles per hour

Step-by-step explanation:

A cyclist travels 6 miles in 15 minutes. What is her average speed in mph?

Step one:

given data

distance= 6 miles

time= 15 minutes

convert minutes to hours

15 minutes is 0.25hours

Step two:

speed= distance/time

speed= 6/0.25

speed= 24 miles per hour

Answer:

A

Step-by-step explanation:

The width of the interval to be one slice, the margin of error would be half of that, which is 0.5 slice.

To determine the number of patrons needed to limit the width of the confidence interval to one slice, we need to consider a few factors.
First, we need to know the desired level of confidence. Let's assume a 95% confidence level.
Next, we need to know the margin of error, which is half the width of the confidence interval. Since we want the width of the interval to be one slice, the margin of error would be half of that, which is 0.5 slice.
To calculate the sample size needed, we can use the formula:
n = (Z * σ / E)²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (95% corresponds to a Z-score of approximately 1.96)
- σ is the standard deviation (if known)
- E is the margin of error
Assuming we know the standard deviation (σ), we can plug in the values to calculate the sample size.

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the volume occupied by the mixture of N2 and O2 gases at 0.83 atm and 42.7°C is approximately 41.62 liters.

To find the volume occupied by the mixture of gases, we can use the ideal gas law equation:

PV = nRT

Where:

P = pressure of the gases (in atm)

V = volume of the gases (in liters)

n = number of moles of gas

R = ideal gas constant (0.0821 L.atm/mol.K)

T = temperature of the gases (in Kelvin)

First, let's convert the temperature from Celsius to Kelvin:

T(K) = T(C) + 273.15

T(K) = 42.7 + 273.15

T(K) = 315.85 K

Now we can calculate the volume:

For N2:

n(N2) = 0.522 mol

P(N2) = 0.83 atm

T = 315.85 K

For O2:

n(O2) = 0.522 mol

P(O2) = 0.83 atm

T = 315.85 K

Using the ideal gas law for each gas:

V(N2) = (n(N2) * R * T) / P(N2)

V(O2) = (n(O2) * R * T) / P(O2)

Calculating the volumes:

V(N2) = (0.522 * 0.0821 * 315.85) / 0.83

V(N2) ≈ 20.81 L

V(O2) = (0.522 * 0.0821 * 315.85) / 0.83

V(O2) ≈ 20.81 L

Since the number of moles and pressure are the same for both gases, the volumes will also be the same.

To find the total volume occupied by the mixture of gases, we can sum the individual volumes:

V(total) = V(N2) + V(O2)

V(total) = 20.81 + 20.81

V(total) ≈ 41.62 L

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The option that correctly plots the approximate value of each number on the number line is option D. A number line from 0 to 5 is divided into 5 equal parts. Pie minus 2 is at the second part. Square root of 21 over 2 is at the third part and 2 plus square root of 5 is at the fifth part.

First step shows the addition of 2 and square root of 5. Second step shows the subtraction of pi and 2. Third step shows division of square root of 21 by 2. This is expressed below:

2 + √5 ≈ 3.2 (approximate value)

π - 2 ≈ 1.1 (approximate value)

√21/2 ≈ 2.4 (approximate value)

So, following the steps above, the approximate value of each number on the number line is option D. A number line from 0 to 5 is divided into 5 equal parts. Pie minus 2 is at the second part. Square root of 21 over 2 is at the third part and 2 plus square root of 5 is at the fifth part.

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Answer:

I think is A

Step-by-step explanation:

But I'm not sure

We find that 28 child tickets were sold on Tuesday.

To determine the number of child tickets that were sold on Tuesday, let x be the number of child tickets that were sold. Then, the number of adult tickets sold was four times the number of child tickets sold. Thus, the number of adult tickets sold is 4x.

The cost of one child ticket is $6.50, and the cost of one adult ticket is $9.80. Therefore, the total sales can be represented by the equation:6.50x + 9.80(4x) = 1279.60

Simplifying this equation gives: 6.50x + 39.20x = 1279.60

Combining like terms, the equation can be further simplified to:

45.70x = 1279.60 Solving for x gives: x = 28

Therefore, 28 child tickets were sold on Tuesday

In conclusion, if we assume that the number of child tickets sold is x, then we can calculate the number of adult tickets sold to be 4x. By multiplying the number of child tickets sold by the price of one child ticket and the number of adult tickets sold by the price of one adult ticket and adding the two values together, we obtain the total sales equation. Using this equation, we solve for x by simplifying and combining like terms.

Therefore, we find that 28 child tickets were sold on Tuesday.

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Answer:

According to the inequality, how much money did Merlin make last  month more than? -> 350 dollars

Can Merlin achieve his goal by selling 6 black beards and 8 red

beards? explain why.

Yes, black beard sum will total up to $120 and red beard sum will total up to $200, $120+$200 = $320

$320 < $350

Step-by-step explanation:

plz mark as brainliest!

Answer:

Step-by-step explanation:

21

Answer:

The answer is 3

Step-by-step explanation:

I dobt have an explanation, but if u use a calc then u can see that it equals 3/21.

Answer:

y+2=.5(x-4)

Step-by-step explanation:

y-y₁=m(x-x₁)

y-(-2)=.5(x-4)

or

y+2=.5(x-4)