simplify the expression ^3√27x^12y^16

Answer:

I D K

Step-by-step explanation:

In the given problem, solving the problem systematically, the greatest number of groups the teacher can make is 6.

To form groups with the same combination of sopranos and altos, we need to find the greatest common divisor (GCD) of the numbers of sopranos and altos. Then, we can divide the total number of singers by the GCD to find the maximum number of groups.

The GCD of 36 and 30 is 6 (you can find it by listing the factors and finding the greatest one that they have in common: 36=2x2x3x3 and 30=2x3x5, so GCD=2x3=6).

So, we can form groups of 6 sopranos and 5 altos. Each group would have 6 + 5 = 11 singers.

To find the maximum number of groups, we divide the total number of singers by the number of singers per group:

(36 + 30) / 11 = 66 / 11 = 6

Therefore, the greatest number of groups the teacher can make is 6.

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Answer: d=10

Step-by-step explanation:

Answer:

6xy^2 + 9(xy)^2.dy/dx

Step-by-step explanation:

d/dx(3x^2.y^3)=

3y^2.d/dx(x^2) + 3x^2.d/dx(y^3)      [Using uv rule, d/dx(uv)=u.dv/dx +v.du/dx]

= 3y^2.2x + 3x^2.3y^2.dy/dx

= 6xy^2 + 9(xy)^2.dy/dx

Answer:

14,348,903

Step-by-step explanation:

3×3 15 times

A. The probability that none of the seven adult friends have done a one-time fling is approximately 0.314. B. The probability that at least one of the seven adult friends has done a one-time fling is approximately 0.686. C. The probability that no more than two of the seven adult friends have done a one-time fling is approximately 0.793.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

The probability of an adult doing a one-time fling is 0.15.

A. To find the probability that none of the seven adult friends have done a one-time fling, we can use the following formula:

P(none) = (1 - 0.15)⁷

P(none) ≈ 0.314

So the probability that none of the seven adult friends have done a one-time fling is approximately 0.314.

B. To find the probability that at least one of the seven adult friends has done a one-time fling, we can use the complement rule:

P(at least one) = 1 - P(none)

P(at least one) ≈ 1 - 0.314 ≈ 0.686

So the probability that at least one of the seven adult friends has done a one-time fling is approximately 0.686.

C. To find the probability that no more than two of the seven adult friends have done a one-time fling, we can use the binomial distribution with n = 7 and p = 0.15, and add up the probabilities of having 0, 1, or 2 friends who have done a one-time fling:

P(no more than two) = P(0) + P(1) + P(2)

P(no more than two) = C(7,0)(0.15)⁰(1-0.15)⁷ + C(7,1)(0.15)¹(1-0.15)⁶ + C(7,2)(0.15)²(1-0.15)⁵

P(no more than two) ≈ 0.793

So the probability that no more than two of the seven adult friends have done a one-time fling is approximately 0.793.

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We are adjusting the original rectangular solid and here is what we have:

(a) The lateral area is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:

2(24) + 2(30) = 48 + 60 = 108 square units

(b) The total area is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:

2(80) + 2(24) + 2(30) = 160 + 48 + 60 = 268 square units

(c) The volume is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:

10 x 8 x 3 = 240 cubic units

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Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

The height is 3 units.

We have,

l = 4 and b= 3

Using Pythagoras theorem

d² = l² + b²

d² = 4² + 3²

d² = 16 + 9

d² = 25

d= 5 unit

let h be the height.

Again, using Pythagoras theorem

34 = 25 + h²

h² = 9

h= 3 unit

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Answer:

thats 4th grade math... 0_0               but the answer is 414 ft².

Step-by-step explanation:

So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo

Answer: y = 932 (1.02)^x

Step-by-step explanation:

Answer:

y = 163 since vertical angles are congruent.

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to gather data from a sample or population and to draw conclusions or make predictions based on that data.

There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of summarizing and presenting data in a meaningful way, such as by calculating measures of central tendency (e.g. mean, median, mode), variability (e.g. range, variance, standard deviation), and correlation. Inferential statistics involves using probability theory to make inferences about a larger population based on a sample of data.

Statistics is used in a wide variety of fields, including business, economics, psychology, social sciences, medicine, and engineering. It is often used to test hypotheses, identify trends, and make predictions based on data. The field of statistics has evolved over time, with the development of new techniques and technologies for collecting and analyzing data.

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying. Surveying a larger group of fifth grade students or every teacher at the school would not be as effective since it would include girls and boys who are not in the fifth grade, and teachers who may not have as much knowledge about the specific video game preferences of fifth grade boys. Surveying every boy who will pass to fifth grade next year would also not be as effective since they are not currently in the fifth grade and their preferences may change by the time they reach that grade. Therefore, surveying the 25 fifth grade boys would provide the most relevant and accurate data for Ryan's study.

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The complete question is:

Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be BEST for Ryan to survey? 25 fifth grade boys 25 fifth grade students every teacher at his school every boy who will pass to fifth grade next year

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So 3/10 divided by 5/8 is equal to (3/10) * (8/5) which simplifies to 24/50 or 12/25 in its simplest form12. Therefore, 3/10 divided by 5/8 is equal to 0.48 when rounded to four decimal points

Hope this helps fellow friend!

The required answer is (3/10) ÷ (5/8) equals 12/25. in other words, the quotient fraction obtained is 12/25

To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions together. Let's solve the division problem (3/10) ÷ (5/8) step by step:

Step 1: Take the reciprocal of the second fraction. The reciprocal of 5/8 is 8/5.

Step 2: Multiply the first fraction by the reciprocal of the second fraction:

(3/10) * (8/5)

Step 3: Multiply the numerators together:

3 x 8 = 24

Step 4: Multiply the denominators together:

10 x 5 = 50

Step 5: Write the result as a fraction:

24/50

Step 6: Simplify the fraction, if possible:

Both the numerator and the denominator have a common factor of 2:

24 ÷ 2 = 12

50 ÷ 2 = 25

The simplified fraction is 12/25.

Therefore, (3/10) ÷ (5/8) equals 12/25.

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

The expression that can be used to determine the reference angle for an angle, x, measuring 150° is A) 180 - X.

The reference angle is the acute angle between the terminal side of an angle and the x-axis in standard position. To find the reference angle for an angle greater than 90 degrees, we subtract the angle from 180 degrees.

In this case, the angle is x = 150 degrees. So, the reference angle would be:

180 - x = 180 - 150 = 30 degrees.

Therefore, the reference angle for an angle measuring 150 degrees is 30 degrees.

The integer that represents the change in temperature from morning to afternoon is 18.

The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.

To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:

9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F

Therefore, the integer that represents the change in temperature from morning to afternoon is 18.

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Step-by-step explanation:

Pick two convenient points to calculate the slope, m  

I'll use    (2.5,80) and (5.5, 95)

m = slope = (y1-y2)/(x1-x2) =   (80 - 95) / ( 2.5 - 5.5 ) = -15 / -3 = 5

Slope intercept form of a line is  y = mx = b

          y = 5x + b      Use one of the points to calculate 'b'

          95 = 5 (5.5) + b    shows b = 67.5

Line equation is then:

y = 5x + 67.5

Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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For the given expression a)(f◦g)(4) = 1. b)(g◦f)(2) = -29. c)(f◦f)(1) = 1. d)(g◦g)(0) = -17.5.

An expression refers to a combination of numbers, symbols, and/or operators that represents a mathematical value or relationship. It can be a single term, such as a number or a variable, or a combination of terms connected by operators, such as addition, subtraction, multiplication, division, exponentiation, etc.

A function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain), such that each input is associated with exactly one output.

According to the given information:

(a) To find (f◦g)(4), we need to first substitute g(4) into f(x) in the given expression, and then evaluate f(g(4)).

Given:

f(x) = 3x² - 2

g(x) = 7 - (1/2)x²

Substituting g(4) into f(x):

g(4) = 7 - (1/2)(4²) = 7 - 8 = -1

Now, substituting -1 into f(x):

f(-1) = 3(-1)² - 2 = 3 - 2 = 1

So, (f◦g)(4) = 1.

(b) To find (g◦f)(2), we need to first substitute f(2) into g(x), and then evaluate g(f(2)).

Substituting f(2) into g(x):

f(2) = 3(2)² - 2 = 12

Now, substituting 12 into g(x):

g(12) = 7 - (1/2)(12)^2 = 7 - 36 = -29

So, (g◦f)(2) = -29.

(c) To find function (f◦f)(1), we need to first substitute f(1) into f(x), and then evaluate f(f(1)).

Substituting f(1) into f(x):

f(1) = 3(1)²- 2 = 1

Now, substituting 1 into f(x):

f(1) = 3(1)² - 2 = 1

So, (f◦f)(1) = 1.

(d) To find (g◦g)(0), we need to first substitute g(0) into g(x), and then evaluate g(g(0)).

Substituting g(0) into g(x):

g(0) = 7 - (1/2)(0)² = 7

Now, substituting 7 into g(x):

g(7) = 7 - (1/2)(7)² = 7 - 24.5 = -17.5

So, (g◦g)(0) = -17.5.

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Step-by-step explanation:

to find the interest she needs to pay back every month, we need to use this formula:

I = PRT/12

in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:

I = (300,000)(7)(1)/12 = $17,500 in interest every month

to find her yearly income from rent, we have to multiply the monthly rent by 12

1500 × 12 = $18,000

to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000

she said that she hopes the property's value will increase to cover the loss she made.

to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as

Percentage increase = (difference in increase/Original price) × 100

so

percentage increase = (15000/300000) × 100 = 5%

so the property needs to increase in value by at least 5% per year to cover the loss.

The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

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After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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The equation which shows how many cases c you can buy is $250 = $15.50 * c.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation represents a relationship between quantities, and it is often used to describe or model real-world situations or problems.

According to the given information:

Let's denote the number of cases of assorted candy snacks as "c". The price of one case of assorted candy snacks is $15.50. The goal is to sell $250 worth of candy per week.

The total cost of buying "c" cases of assorted candy snacks can be calculated by multiplying the price per case ($15.50) by the number of cases (c):

Total Cost = Price per case * Number of cases = $15.50 * c

The goal is to sell $250 worth of candy per week. So, we can set up an equation to represent this goal:

$250 = $15.50 * c

This equation shows the relationship between the number of cases of candy snacks (c) that you can buy and the total cost of buying those cases, which is equal to $250, your goal for weekly candy sales.

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Answer:

88

Step-by-step explanation:

To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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The difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

Assume that the data is n-sized as follows:

x1, x2, x3 .....xn

Let the mean of this data be: x'

The mean of the absolute differences between the observations and the mean of the data to which they belong, then, is the mean absolute deviation of such a data.

It is determined by:

M.A.D = ∑ |xi - x'| / n  (i = 1 ....n)

Hence, mean absolute deviation is the average deviation of the data values, regardless of whether it is above or below the mean.

Due to the fact that:

The mean absolute deviation of the monthly temperatures in New Orleans is 43.5°F, which implies that on average, the temperature deviates 43.5°F from the average monthly temperature.

where mean displays New Orleans, Louisiana's typical monthly temperature.

Thus, the difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

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