how many terms are in the expansion of the expression $[(3x 2y)^2(3x-2y)^2]^3$ after it is simplified to lowest terms?

The graphical representation that would be the best for this data would be a circle graph. That is option C.

A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.

Now, the number of students that were surveyed = 100 students.

The number of subjects that are preferred by the students would be represented as x,y,z.

Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;

For subject x = Number of X/100 × 360/1

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Answer:

16/9

Step-by-step explanation:

(11/9) + (5/9) = 11/9 + 5/9 = 16/9

16/9 is already in simplest form, so the answer is 16/9

Answer: (11/9) + (5/9) = (11 + 5)/9 = 16/9

Step-by-step explanation:

We have to find a common denominator for the two fractions. Since both fractions have a denominator of 9, we can add the numerators directly.

Add the numerators of the two fractions: 11 + 5 = 16.

Write the sum over the common denominator: 16/9.

Simplify the fraction if possible. In this case, it is already in simplest form.

Therefore, (11/9) + (5/9) = 16/9.

Answer:

m = 6

Step-by-step explanation:

We have the proportion:

12/m = 18/9

To solve for m, we can cross-multiply the terms in the proportion:

12 × 9 = 18 × m

Simplifying both sides of the equation, we get:

108 = 18m

Dividing both sides by 18, we get:m = 6

Therefore, the solution to the proportion 12/m = 18/9 is m = 6.

Answer: m = 6

Step-by-step explanation:

First, we will rewrite this proportion:

     [tex]\displaystyle \frac{12}{m} =\frac{18}{9}[/tex]

Next, we will cross-multiply:

     12 * 9 = 18 * m

     108 = 18m

Lastly, we will divide both sides of the equation by 18:

     m = 6

We can also solve this proportion another way.

     We know that 18/9 = 2, so 12/m must equal 2 as well.

     12/6 = 2, so m = 6.

Answer:

  48

Step-by-step explanation:

You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.

The diameter of the can will be found from the volume formula:

  V = (π/4)d²h

  d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches

The cans are 4 inches in diameter.

The number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.

  Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high

  Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep

  Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long

A total of 2 × 2 × 12 = 48 cans will fit on the shelf.

__

Additional comment

There will be 2 inches of empty space in each direction.

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The general solution of the given higher-order differential equation is y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ.

The given higher-order differential equation is:

16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0

To find the general solution of this differential equation, we can assume that y(x) has the form:

y(x) = e[tex].^{rx}[/tex]

where r is a constant to be determined.

Differentiating y(x) four times with respect to x, we get:

d⁴y/dx⁴ = r⁴e[tex].^{rx}[/tex]

Differentiating y(x) two times with respect to x, we get:

d²y/dx² = r²e[tex].^{rx}[/tex]

Substituting these derivatives and y(x) into the differential equation, we get:

16(r⁴e[tex].^{rx}[/tex]) + 40(r²e[tex].^{rx}[/tex]) + 25e[tex].^{rx}[/tex] = 0

Simplifying this equation by dividing through by e[tex].^{rx}[/tex], we get:

16r⁴ + 40r² + 25 = 0

This is a quadratic equation in r². Solving for r² using the quadratic formula, we get:

r² = [-40 ± √(40² - 4(16)(25))] / 2(16)

r² = [-40 ± √(3600)] / 32

r² = [-40 ± 60] / 32

We get two possible values for r²:

r² = 5/4 or r² = 1

Taking the square root of each value, we get:

r = ±(1/2)i√5 or r = ±1

Thus, the general solution of the given higher-order differential equation is:

y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ

where c1, c2, c3, and c4 are constants determined by the initial or boundary conditions of the specific problem.

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The complete question is :

find the general solution of the given higher-order differential equation : 16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0

Answer:

Step-by-step explanation:

domain is -infinity to positive infinity range is -3 to infinity. Increasing from -3 to infinity and decreasing from - infinity to -3 and it’s minimum

The surface area of the actual ramp, including the underside, is approximately 15.38 yd².

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To find the surface area of the actual ramp, we need to first find the dimensions of the ramp.

We are given that the scale model of the ramp is a right triangular prism with legs of 8 in, 5 in, and 5 in, and a height of 3 in. We can use these dimensions to find the dimensions of the actual ramp.

Since the ramp is a scale model, the ratio of the dimensions of the model to the actual ramp is the same for all corresponding dimensions. The height of the triangular base in the actual ramp is given as 0.6 yards, which is equal to 21.6 inches. So, we have:

height of actual ramp / height of model = 21.6 in / 3 in = 7.2

We can use this ratio to find the dimensions of the actual ramp:

height of actual ramp = 7.2 * 3 in = 21.6 in

length of actual ramp = 7.2 * 8 in = 57.6 in

width of actual ramp = 7.2 * 5 in = 36 in

Now we can find the surface area of the actual ramp. The surface area of the top and bottom of the ramp is the area of the triangular base plus the area of the rectangle formed by the length and width of the ramp:

Area of triangular base = (1/2) * base * height = (1/2) * 5 in * 5 in = 12.5 in²

Area of rectangular top and bottom = length * width = 57.6 in * 36 in = 2073.6 in²

Total surface area of top and bottom = 2 * (Area of triangular base + Area of rectangular top and bottom) = 2 * (12.5 in² + 2073.6 in²) = 4153.2 in²

The surface area of the sides of the ramp is the area of the three rectangles formed by the height and width of the ramp:

Area of one side rectangle = height * width = 21.6 in * 36 in = 777.6 in²

Total surface area of sides = 3 * Area of one side rectangle = 3 * 777.6 in² = 2332.8 in²

Finally, we add the surface area of the top and bottom to the surface area of the sides to get the total surface area of the ramp:

Total surface area of ramp = Surface area of top and bottom + Surface area of sides = 4153.2 in² + 2332.8 in² = 6486 in²

Converting to yards and rounding to two decimal places, we get:

Total surface area of ramp = 6486 in² / (36 in/yd)² = 15.38 yd² (rounded to two decimal places)

Therefore, the surface area of the actual ramp, including the underside, is approximately 15.38 yd².

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a. The bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.

a. To find the scale factor for the large bagel that serves 25 people, we need to find the square root of the ratio of the number of people the large bagel serves to the number of people the small bagel serves.
Scale factor = [tex]\sqrt{(large_bagel_serving / small_bagel_serving)}[/tex]
Scale factor = [tex]\sqrt{(25 / 1)}[/tex]
Scale factor =[tex]\sqrt{ 25}[/tex]
Scale factor = 5
So, the bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. Since the bagels are in the same shape, the area of the large bagel will be the square of the scale factor times the area of the small bagel.

The cream cheese is spread over the area, so the ratio of the cream cheese needed for the large bagel to the small bagel will be the same as the ratio of their areas.
Ratio of cream cheese = [tex](scale factor)^2[/tex]
Ratio of cream cheese = [tex](5)^2[/tex]
Ratio of cream cheese = 25
So, 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.

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The dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.

a) To determine the scale factor for the dilated bagel, first, we need to find the ratio between the area of the large bagel and the area of a single serving bagel. Since the large bagel serves 25 people, the area ratio will be 25:1.

Area ratio = (scale factor)^2
25:1 = (scale factor)^2

To find the scale factor, take the square root of the area ratio:
scale factor = √25 = √(25/1) = 5

Therefore, the bagel will need to be dilated by a scale factor of 5 to serve 25 people.

b) Since the thickness of the cream cheese remains the same on both bagels, we only need to consider the difference in area between the two bagels. As calculated before, the area ratio is 25:1.

Thus, the dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.

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Jamal ought to utilize a histogram to display the information regarding the amount of steps he takes each day.

The complete set of people or things that we are interested in investigating is referred to as a population in statistics. We want to examine and draw conclusions from the entire set of facts. For instance, all adult women in a country would represent the population if we were interested in measuring the average height of adult women there.

In contrast, a sample is a smaller portion of the population that is chosen for analysis. When measuring the entire population is neither practicable or practical, this method is utilised.

Jamal ought to utilise a histogram to display the information regarding the amount of steps he takes each day. A histogram is a form of graph that shows how continuous data, such the number of steps, are distributed. It divides the data into intervals or "bins" and displays how frequently data points fall into each bin. Jamal may detect the usual or central trend of his daily step count as well as any fluctuation or outliers in the data by examining the shape of the histogram.

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The availability of this repairable product is approximately 0.762, or 76.2%.

In order to find the availability of a repairable product, we need to consider its failure rate and mean time to repair. The formula for availability (A) is:

A = MTBF / (MTBF + MTTR)

Where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair.

Since we have a constant failure rate (λ), we can calculate the MTBF as the inverse of the failure rate:

MTBF = 1 / λ

In this case, the failure rate (λ) is 0.0078 failures per hour. Let's calculate the MTBF:

MTBF = 1 / 0.0078 = 128.205 hours

Now, we know the MTTR is 40 hours. We can use the availability formula to find the answer:

A = MTBF / (MTBF + MTTR)
A = 128.205 / (128.205 + 40)
A = 128.205 / 168.205
A ≈ 0.762

So, the availability of this repairable product is approximately 0.762, or 76.2%.

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After performing long division on (x3+3x2-x+2)/(x-1) we get x² + 4x +3 leaving a remainder of 5.

Long division refers to the method of performing a division of two numbers or polynomials by hand. Furthermore, it involves several steps to evaluate in order to find a quotient and a remainder. It is considered an important and crucial form of practice in the branch of mathematics.                  

In the subject of dividing a polynomial, first, we divide the highest degree term of the dividend by the highest degree term of the divisor, and the remaining result is subtracted from the dividend. The calculation is as follows in the picture

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Answer:

Image

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

10

y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.

A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.

If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:

y = A sin (ωt + φ) + C

where: A is the amplitude of the wave, which is given as 12 meters

ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)

t is the time elapsed since the wave started passing the dock

φ is the phase angle, which we can assume to be 0 since we are not given any information about it

C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case

putting the given values into the equation,

y = 12 sin [(2π/20)t] + 8

Simplifying this equation,

y = 6 sin [(π/10)t] + 8

This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.

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The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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The minimum score required for an A grade is approximately 87 when the standard deviation is 7.4 and the mean is 77.1

The standard deviation is a measure of the amount of variation or dispersion in a set of data. It measures how much the individual data points deviate or differ from the mean or average of the data set.

Mathematically, the standard deviation is the square root of the variance, which is calculated by taking the average of the squared differences of each data point from the mean. The formula for the standard deviation is:

σ = sqrt(Σ(x - μ)^2 / n)

where σ is the standard deviation, x is a data point, μ is the mean, and n is the number of data points.

First, we need to find the z-score corresponding to a score that is at the 92nd percentile (the top 8%). We can use the inverse normal distribution function (also known as the probit function) to do this:

invNorm(0.92) ≈ 1.41

This means that a score at the 92nd percentile corresponds to a z-score of approximately 1.41.

Next, we need to convert this z-score to a raw score on the test. We can do this using the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Rearranging this formula to solve for x, we get:

x = z*σ + μ

Substituting the values we have, we get:

x = 1.41*7.4 + 77.1 ≈ 87.4

Therefore, the minimum score required for an A grade is approximately 87, rounded to the nearest whole number.

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If cosθ=-3/4 and tanθ is negative, then sinθ= √(7)/4.

Since cosθ = -3/4 and θ is an angle in the second quadrant where cosθ is negative, we know that sinθ must be positive.

The Pythagorean identity is a trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent

To find sinθ, we can use the Pythagorean identity

sin^2θ + cos^2θ = 1

Substituting the value of cosθ we get

sin^2θ + (-3/4)^2 = 1

Simplifying

sin^2θ + 9/16 = 1

sin^2θ = 7/16

Taking the square root of both sides, we get

sinθ = ±√(7)/4

Since we know that sinθ is positive in the second quadrant, we take the positive value

sinθ = √(7)/4

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The sample space for each experiment are as follow;

1. rolling a 12 sided fair die, the sample space is 12

2. flipping a coin, the sample space is 2

3. pulling a face card from a standard deck of cards is 12

4. A spin from the spinner, the sample space is 5

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

For example the sample space of getting an odd number from a 6 sided fair die is 3, because the odd numbers between 1-6 are 1,3,5.

1. The sample space of rolling a 12 sided fair die is 12, because it will have 12 faces.

2. A coin has two faces, therefore the sample space of flipping a coin is 2

3. There are 12 face cards in a standard deck, therefore, the sample space to pull a face card out of a standard deck is 12.

4. The spinner has 5faces, therefore the sample space for a spin is 5.

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Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:

A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.

This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.

Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.

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The 90% confidence interval for the probability of flipping a head with this coin is approximately b. [0.339, 0.501], which corresponds to option b). [0.339, 0.501].

Calculate the sample proportion (p-hat):

p-hat = number of heads / total flips = 42/100 = 0.42

Determine the confidence level, which is 90% in this case.

Find the corresponding z-score for the confidence level.

For a 90% confidence level, the z-score is approximately 1.645.

Calculate the standard error:

[tex]SE = \sqrt{(p-hat \times (1 - p-hat) / n)}  = \sqrt{ (0.42 \times 0.58 / 100)} = 0.0496[/tex]

Calculate the margin of error:

ME = z-score × SE = 1.645 × 0.0496 ≈ 0.0816

Determine the confidence interval:

CI = (p-hat - ME, p-hat + ME)

= (0.42 - 0.0816, 0.42 + 0.0816)

= (0.3384, 0.5016)

Therefore, option b.[0.339, 0.501] is correct.

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Answer:

a

Step-by-step explanation:

to find the missing side x , subtract the sum of the 5 given sides from the given perimeter.

x = 137 - (39 + 37 + 12 + 10 + 13) = 137 - 111 = 26 m

Answer:

Step-by-step explanation:

false

The coordinate vector of p(t) relative to the basis B is:

[ -1 ]
[  2 ]
[  2 ]

To find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2}, we need to express p(t) as a linear combination of the basis vectors and then write down the coefficients as a column vector.

We have:

p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2)

Expanding this out, we get:

p(t) = (a + c) + (b + 2c)t + (a + b + c)t2

Comparing coefficients with the polynomial 1 + 4t + 7t2, we get the following system of equations:

a + c = 1
b + 2c = 4
a + b + c = 7

Solving this system, we find:

a = -1
b = 2
c = 2

Therefore, the coordinate vector of p(t) relative to the basis B is:

[ -1 ]
[  2 ]
[  2 ]

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The value of the digit 5 in 24,513 is 1,000 times the value of the digit 5 in 357.

In the number 357, the digit 5 is in the ones area, which means that its value is just 5. We can write this number as 5 x 10^0, where 10 is the base of our number system, and the exponent 0 represents the ones area.

Now, to find out how many times the value of the digit 5 in 357 is compared to the value of the digit 5 in 24,513, we need to divide the value of the digit 5 in 24,513 by the value of the digit 5 in 357.

We have:

Value of 5 in 24,513 = 5 x 10³

Value of 5 in 357 = 5 x 10⁰

So,

Value of 5 in 24,513 ÷ Value of 5 in 357 = (5 x 10³) ÷ (5 x 10⁰)

We can simplify this expression by dividing 5 by 5, which gives us:

(5 x 10³) ÷ (5 x 10⁰) = 10³ = 1000

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The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).

The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.

It can be written as [tex]\frac{n_1+n_2+.....+n_a}{a}[/tex].

In the given question, the sum of the customer bill is given as $3,250.

And the number of customers served is given to be 200.

Therefore, the average size of a customer's bill is calculated by [tex]\frac{3250}{200}[/tex]

Which turns out to be $16.25.

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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.

To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:

1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.

Now, calculate the average bill size:

3. Divide the total daily earnings ($3,250) by the number of customers (200).

$3,250 ÷ 200 = $16.25

The average size of a customer's bill at the restaurant is $16.25.

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Answer:

a)

jenny - $160 + $50X = total

hong - $90X = total

b)

$160 + $50X = $90X

Step-by-step explanation:

a)

b)

Answer:

.40n = 80, so n = 200

.95 × 200 = 190

Answer:

190

Step-by-step explanation:

Testing is only one part of the overall assessment process.

What is evaluation in education?

Assessment is an ongoing process of gathering evidence of what each student actually knows, understands, and can do. A comprehensive evaluation approach includes a combination of formal and informal evaluation (formative, preliminary, and summative).

What is an assessment? Also what does it mean?

At the course level, assessments provide important data on the breadth and depth of student learning. Evaluation is more than scoring. It's about measuring student learning progress. Assessment is therefore defined as “the process of data gathering to better understand the strengths and weaknesses of a student's learning”. 

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