what is 24 + p = 54?
what is w − 16 = 28?
what is 18 = t + 2?

The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Order Of Operation — Also known as BODMAS says to solve Bracket first then Roots or Exponents, Divide, Multiply, Add and finally Subtract.

However, while solving an equation we need to multiply before subtraction isn't always necessary.

For Example :-

Here we need to solve the brackets first and in order to solve the brackets we need to subtract before multiplying.

As we know (12 - 6 = 6) so,

➔ 3 + 2 × 6

➔ 3 + 12

➔ 15

In the equation above, we subtracted 6 from 12 before multiplying 2 with it that was because (12 - 6) were inside brackets.

Taking Another Example :-

Solving Brackets first, (1 + 2 = 3)

➔ 10 - 6 ÷ 3

➔ 10 - 2

➔ 8

In the second example, we added 1 & 2 before dividing 6 by it that was because (1 + 2) were inside brackets.

Thus,

Following Order Of Operation (BODMAS) doesn't always means to multiply before subtraction, we can Subtract first if the number to be subtracted is inside Brackets.

\(\begin{gathered}\begin{gathered}\: \begin{gathered}\begin{gathered} \footnotesize{\boxed{\boxed{\begin{array}{cc} \\ \\ \bf{ \: \: \: B = Bracket \: \: \: } \\ \\ \bf{ \: \: \: O = Order \: \: \: } \\ \\ \bf{ \: \: \: D = Divide \: \: \: } \\ \\ \bf{ \: \: \: M = Multiply \: \: \: } \\ \\ \bf{ \: \: \: A = Add \: \: \: } \\ \\ \bf{ \: \: \: S = Subtract \: \: \: } \\ \\ \: \end{array}}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)

\(\bf{\pmb{\underline{\rule{170pt}{5pt}}}}\)

Answer:

23 years old

Step-by-step explanation:

Given the following question:
Ricky is 5 years older than Ciara...
6 years their ages will equal 53 years of age.

So, we have to remember that in six years their ages will equal 53 and one is five years older than the other.

\(23+6=29\)
\(18+6=24\)
\(29-5=24\)
\(29+24=53\)
\(29-6=23\)
\(=23\)

Which means Ricky as of right now is "23 years of age" and Ciara as of right now is "18 years of age".

Hope this helps.

The product of two rational numbers is a rational number.

In any field containing integers, rational numbers, along with addition and multiplication, produce a field that also contains the integers. In other words, a field only has characteristic zero if and only if it contains the field of rational numbers as a subfield. The field of rational numbers is a prime field.

"A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator 'p' and a non-zero denominator 'q'."

Therefore, when we are multiplying two rational numbers, their product must be a rational number.

This is because, numerators of both rational numbers are integers and denominators of both the numbers are non-zero integers.

Hence, the product is a rational number.

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Answer:

\(f^{-1} (x)\)=\(\frac{4}{1+x}\)

Step-by-step explanation:

The first step is to switch y for x and x for y so the equation will look like

x=\(\frac{4-y}{y}\)

the next thing you do is isolate y so you have to multiply y to both sides to get

\(xy=4-y\) now you got to add y to both sides which would get you

xy+y=4

since xy and y share a y value you have to try and factor out y which would get you

y(x+1)=4

the final step is to divide x+1 on both sides

y\(\frac{(x+1)}{x+1}\)=\(\frac{4}{x+1}\)

which since x+1 and x+1 crosses each other out we are left with

y=\(\frac{4}{1+x}\)

Answer:

  a.  $110,700

Step-by-step explanation:

You want to know the value of a $141,000 house after 15 years, if it declines in value 1.6% each year.

The value multiplier each year is ...

  1 - 1.6% = 1 -0.016 = 0.984

When the house value is multiplied by this factor 15 times, it becomes ...

  $141,000×0.984^15 ≈ $110,700

Russell's house is worth about $110,700.

Answer:

7m^4-52m^3-28m^2+67m+42

Answer:

Step-by-step explanation:

Answer:

276 unit^2.

Step-by-step explanation:

This area  is the sum of the area of 2 rectangles

= 12 * 13 + 8 * 15

= 156 + 120

= 276.

Answer:

299

Step-by-step explanation:

The solution to the expression is A = 299

Given data ,

Let the expression be represented as A

Now , the value of A is

Let the first number be represented as p

The value of p = 23

Let the second number be represented as q

The value of q = 13

So, A = pq

On simplifying the equation , we get

A = p multiplied by the value of q

And , A = 23 x 13

A = 299

Therefore , the value of A is 299

Hence , the expression is A = 299

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(c)There is a weak negative linear association between the explanatory variable and the response variable (c).

Look at the scatterplot and examine the general pattern of the points.Notice that as the explanatory variable (x-axis) increases, the response variable (y-axis) generally decreases.

However, the points are not tightly clustered around a straight line, indicating a weak association.Additionally, the negative slope suggests that as one variable increases, the other tends to decrease.

Therefore, the correct answer is a weak negative linear association between the explanatory variable and the response variable.

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The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.

You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

Now according to the question,

Possible letter combinations

Choose any letter and make it a repeat letter = 26 ways

But, there are ⁴C₂ = 6 spots available for the identical letters.

And there are (25)×(24) other methods for selecting the other two letters.

The total amount of "words" equals ⁴C₂ × 26 × 25 × 24 = 93600.

Furthermore, because the numerals cannot be repeated = 10 × 9 = 90

So, the total number of choices = 93600 × 90 = 8,424,000

Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.

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Step-by-step explanation:

.............,.,.,.,.,.,.,.,

Answer:

3x +7x +11=10x+11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Group like terms:

=3x+7x+11

Add similar elements: 3x+7x=10x

=10x+11

don't know if this is actually the answers but:

1.) V=4/3pi r^3

3V= 4pi r^3

3V/4pi = r^3

3√3V/4 pi = 3√r^3

Answer: r = 3√3V/4pi

2.) Answer: 1/4V - 532 = 4/3pi 22^3

The sphere is a three-dimensional figure where the volume is given as

= 4/3 x πr³

4/3 x πr³ = 5575

The radius of the current gumball is ∛(117075/88) inches

5575 = (1/4)V - 532

The volume of the giant gumball is 24428 cubic inches.

It is a three-dimensional figure where the volume is given as

= 4/3 x πr³

We have,

Current gumball machine.

Diameter = 22 inches

Radius = 22/2 = 11 inches

Volume = 5,575 cubic inches

The volume can be written as,

4/3 x πr³ = 5575

4/3 x 22/7 x r³ = 5575

r³ = (5575 x 3 x 7) / (4 x 22)

r = ∛(117075/88) inches

Giant gumball machine.

Volume = V

5575 = (1/4)V - 532

(5575 + 532) x 4 = V

V = 24428 cubic inches.

Thus,

The radius of the current gumball is ∛(117075/88) inches

The volume of the giant gumball is 24428 cubic inches.

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The learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047. The time required to build the first house (T1) can be calculated using the learning curve formula. If the learning-curve percentage is changed to 76%, starting from the Nth house, the time for construction per house would be less than half the construction time for the third house. The value of N can be determined by solving the equation.

he learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047.

The learning curve follows a mathematical relationship where the time required to complete a task decreases as more units are produced. The formula for the learning curve is T = T1 * \((N^b)\), where T is the time required for N units, T1 is the time required for the first unit, N is the cumulative number of units, and b is the learning-curve exponent.

To find the learning-curve exponent (b), we can use the given information that the construction team spent 18% less time building the seventh house compared to the third house. This can be expressed as:

T7 = T3 * \((7^b)\) - 0.18 * T3

Since we know that T7 is 0.82 times T3, we can substitute these values into the equation:

0.82 * T3 = T3 * \((7^b)\) - 0.18 * T3

Simplifying the equation, we get:

0.82 =\(7^b\) - 0.18

Solving for b, we find that b is approximately 0.291.

To calculate the learning-curve rate (R), we can use the formula R = \(2^(^1^-^b^)\). Plugging in the value of b, we get R is approximately 1.047.

If the last house built required 2,500 manual labor hours, we can use the learning curve formula to calculate the time required to build the first house (T1). We know that N = 18 and T = 2,500. Rearranging the formula, we have:

T1 = T / (N^b)

Plugging in the values, we get:

T1 = 2,500 / (18^0.291)

Calculating T1, we find that the time required to build the first house is approximately 2,808.

To determine the value of N when the learning-curve percentage is changed to 76% starting from the Nth house, where the time for construction per house would be less than half the construction time for the third house, we can use the learning curve formula again. In this case, the time required for the Nth house would be 0.5 times the time required for the third house:

T3 * (N^b) * 0.76 = 0.5 * T3

Simplifying the equation, we get:

N^b = 0.5 / 0.76

Taking the logarithm of both sides of the equation, we can solve for N:

b * log(N) = log(0.5 / 0.76)

log(N) = log(0.5 / 0.76) / b

N = 10^(log(0.5 / 0.76) / b)

Calculating N using the given values of b, we find that N is approximately 12.

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Answer:

\(0.186\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Suppose\ getting\ head\ is\ a\ success\ and\ getting\ tail\ is\ a\ failure.}\\\mathrm{Now,}\\\mathrm{Probability\ of\ success(p)=0.45}\\\mathrm{Probability\ of\ failure(q)=1-p=1-0.45=0.55}\\\mathrm{Number\ of\ times\ experiment\ is\ done(n)=6}\\\mathrm{Number\ of\ success\ desired(r)=4}\\\mathrm{We\ use\ the\ formula,}\\\mathrm{P(r)=nCr\times p^r\times q^{n-r}}\\\mathrm{P(4)=6C4\times 0.45^4\times 0.55^{6-4}}=0.186}\)

\(\mathrm{So,\ the\ required\ probability\ is\ 0.186.}\)

Step 1: Calculate the total cost for the first hour. The total cost for the first hour is $2,000.

Step 2: Calculate the cost for each additional hour. The cost for each additional hour is $1,000.

Step 3: Calculate the total cost. To calculate the total cost, add the cost for the first hour ($2,000) to the cost for each additional hour ($1,000) multiplied by the number of additional hours (n). This gives us a total of P = 2,000 + 1,000(n + 1).

Therefore, the correct expression for the total cost is P = 2,000 + 1,000(n + 1).

C(x)=F+V is the generic form of the cost function formula (x) C(x) = F + V(x), where x is the number of units, V(x) is the total variable cost, and C(x) is the overall cost of production.

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Answer:

0.026

Step-by-step explanation:

6 out of 10 steps between 0.02 and 0.03.

The average American student spends about 5 hours and 20 minutes in school each day.

To convert the average time spent in school from minutes to hours, we will divide the total minutes by 60 (since there are 60 minutes in an hour).

320 minutes ÷ 60 minutes per hour = 5.33 hours (rounded to two decimal places)

Therefore, American students spend about 5 hours and 20 minutes in school each day, based on the statistic given.

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The hotel makes a random purchase of 3 flat screen high definition television sets out of the 7 available. We need to determine the number of defective sets purchased by the hotel, represented by the variable x.

Since there are 2 defective sets out of the total 7, we can use combinations to calculate the probability. The number of ways to choose x defective sets out of 2 is given by \(C(2, x).\)

Similarly, the number of ways to choose (3 - x) non-defective sets out of the remaining (7 - 2) non-defective sets is given by \(C(5, 3 - x).\)

To find the probability, we divide the number of favorable outcomes (x defective sets and 3 - x non-defective sets) by the total number of possible outcomes (choosing any 3 sets out of 7).

Therefore, the probability of the hotel purchasing x defective sets out of the 3 purchased sets is given by the formula \(P(x) = (C(2, x) * C(5, 3 - x)) / C(7, 3).\)

To find the probability of the hotel purchasing at least 1 defective set, we calculate \(P(x = 1) + P(x = 2).\)

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No, this is not an accurate predictor because angie is not representative of the population in the algebra test.

Here,

Angie, a student in an advanced statistics course, was given an algebra test and she scored 80%.

We have to find is this an accurate predictor.

What is Accurate predictor?

Accurate predictor describes whether the predicted values match the actual values of the target field within the incertitude due to statistical fluctuations and noise in the input data values.

Here,

Angie is the student of an  advanced statistics course but she gives the algebra test and scored 80%.

We know that the advanced statistics is the higher level of math so it is not an accurate predictor.

Because, An accurate predictor should be applied when the person is 100% confirmed to the related thing. So in the given situation, the student is not 100% confirm.

Hence,  this is not an accurate predictor because Angie is not representative of the population in the algebra test.

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Answer:

37/50

Step-by-step explanation:

Step 1) Multiply 7/10 by 5/5 to get 35/50

Step 2) Add 3/50 and 35/50

Step 3) 3/50+ 35/50= 37/50

The average distance of a point in a solid ball of radius r is π r^4.

To find the average distance of a point in a solid ball of radius r, we need to calculate the average value of the distance function over the volume of the ball.

The distance function from a point in the ball to the center is given by d(r) \(= √(x^2 + y^2 + z^2), where (x, y, z)\) are the coordinates of a point in the ball.

To find the average distance, we need to integrate the distance function over the volume of the ball and divide it by the volume.

Let's consider the ball of radius r centered at the origin. The volume of the ball can be calculated using the formula for the volume of a sphere:

\(v = (4/3)πr^3\)

Now, we can calculate the integral of the distance function over the ball:

\(∫∫∫(d(r)) dV\)

Since the ball is spherically symmetric, we can use spherical coordinates to simplify the integral. The distance function can be expressed in spherical coordinates as d(r) = r. The volume element in spherical coordinates is given by \(dV = r^2 sin(φ) dr dθ dϕ.\)

The limits of integration for the spherical coordinates are as follows:

\(r: 0 to rθ: 0 to 2πφ: 0 to π\)

Now, we can set up the integral:

\(∫∫∫(r)(r^2 sin(φ)) dr dθ dϕ\)

Integrating with respect to r:

\(∫∫(1/4)(r^4 sin(φ)) dr dθ dϕ= (1/4) ∫∫(r^4 sin(φ)) dr dθ dϕ\)

Integrating with respect to θ:

\((1/4) ∫(0 to r^4 sin(φ)) ∫(0 to 2π) dθ dϕ= (1/4) (r^4 sin(φ)) (2π)\)

Integrating with respect to φ:

\((1/4) (r^4) (-cos(φ)) (2π)= (1/2)π r^4 (1 - cos(φ))\)

Now, we need to evaluate this expression over the limits of φ: 0 to π.

Average distance = (1/2)π r^4 (1 - cos(π))

\(= (1/2)π r^4 (1 + 1)= π r^4\)

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Answer:

\(14 \: 26 \: 6.5\)

14

26

6.5

Answer:

it is C the 4

Step-by-step explanation:

-6 to pos 4

Answer

The answer is -43.

Explanation

The question wants us to evaluate the expression using the given variables

-k² - (2k - 5n) + 3n

if k = -3, n = -5

So, to solve this, we would just substitute the given values for k and n

-k² - (2k - 5n) + 3n

= -(-3)² - [(2 × -3) - (5 × -5)] + (3 × -5)

= -(9) - [-6 - (-25)] - 15

= -9 - (-6 + 25) - 15

= -9 - (19) - 15

= -9 - 19 - 15

= -43

Hope this Helps!!!

Answer:

0.83

Step-by-step explanation:

10.5-9.67 the answer is 0.83

Answer:The answer is 0.83

Step-by-step explanation:Please give brainliest if right.I hope this helps.

Given matrices are,i) [2, 0], [5, -1]ii) [22, 4], [5, -1]iii) [1, 2], [0, -4]iv) [0, 2], [-4, 1]Now, to compute the exponentials of these matrices, we can use the following formulae:

For any matrix A, we can define its exponential e^A as the following power series:e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ... (1)where I is the identity matrix, and ! denotes the factorial of a number.

To evaluate the right-hand side of this formula, we need to calculate the matrix powers A^n for all n.

We can use the following recursive definition for this purpose:A^0 = I (2)A^n = A * A^(n-1) (n > 0) (3)

Using these formulae, we can compute the exponentials of the given matrices as follows:i) [2, 0], [5, -1]

First, we calculate the powers of A: A^2 = [4, 0], [10, -3] A^3 = [8, 0], [23, -11]

Next, we substitute these powers into equation (1) to get:e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ... = [3.1945, 1.4794], [4.8971, 2.8062]

ii) [22, 4], [5, -1]

First, we calculate the powers of A: A^2 = [484, 88], [110, 21] A^3 = [10648, 2048], [2420, 461]

Next, we substitute these powers into equation (1) to get:e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ... = [5300.7458, 1075.9062], [1198.7273, 242.9790]

iii) [1, 2], [0, -4] First, we calculate the powers of A: A^2 = [1, -6], [0, 16] A^3 = [1, -22], [0, -64]

Next, we substitute these powers into equation (1) to get: e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ... = [1.8701, 5.4937], [0, 0.6065]

iv) [0, 2], [-4, 1]

First, we calculate the powers of A: A^2 = [-8, 2], [-16, -6] A^3 = [28, -8], [64, 24]

Next, we substitute these powers into equation (1) to get: e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ... = [1.0806, 0.7568], [-0.7568, 1.0806].

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