Solve for b.
ab + c = d
Ob = a + c/d
b = a/(c-d)
b = (d - c)/a

Please attached a diagram drawn with MS Word based on the question parameters, and from a diagram from a similar question.

The length of the rectangle that contains 10 identical squares and has a width of 15 centimeters is 21 centimeters

A square is a quadrilateral that has four sides of the same length and the the four interior angles are each equal to 90°.

Some parts of the question appear missing, please find attached the design of a rectangle based on a similar GCSE question online. The width of the rectangle = 15 cm

The number of squares = 10

The number of squares that make up the width from the drawing = 5

The side length of the square is therefore; 15 cm ÷ 5 = 3 cm

The number of squares that make up the length of the rectangle = 7

The length of the rectangle is therefore, L = 7 × 3 cm = 21 cm

The length of the rectangle = 21 centimeters

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Answer:

4.95+0.10x=120

Step-by-step explanation:

Hope this helps

Three different recursive definitions of a set W, which is described as a string made by concatenating copies of "." (dot), are discussed in the question. A definition that uses itself is known as a recursive definition. In this instance, an empty string (wº) serves as the base case for all three definitions. The question asks which of the various definitions' recursive rules is correct.

The correct recursive definition for the set W is:

Base case: the empty string, w₀ ∈ W.

Recursive rule: w' = w + . + w, where w ∈ W.

This means that the empty string and any string that can be created by joining one or more copies of a string present in W, each separated by a single period, make up the set W. For instance, the string. is in W because it can be created by joining two copies of the empty string together with a period. The string .. is also in W because it can be created by concatenating two copies of the empty string, a period, and one copy of the character.

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Answer:

this expression is not factorable luv :)

Step-by-step explanation:

The true or false statements, given the function, would include:

True:

False :

The point of symmetry is the vertex of the given function f(x). The vertex of f(x) is (3, 6), so the point of symmetry on ƒ-¹(x) will be the inverse of the vertex, which is (6, 3).

The statement is incorrect because the correct representation of the domain of ƒ-¹(x) is (-∞, ∞). The cubic function f(x) is a one-to-one function, and its range is all real numbers.

The given function f(x) is a one-to-one function because it is a cubic function with a unique output for each input. The inverse of a one-to-one function is also a function.  

The domain of the given function f(x) is all real numbers, and since it is a one-to-one function, its range will be the domain of its inverse function, which is (-∞, 6).

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Answer:WAIT HE IS TELLING THE TIME

Step-by-step explanation:

Answer:

1 1/12 has part of a whole number but 3/4 doesn't have a whole number.

Step-by-step explanation:

1 1/12 is also greater than 3/4

Answer:

3/4 is the difference

Step-by-step explanation:

Answer:

Laila read 210 pages of her 300 page book is correct

Explanation:

From the question given ,we are to chosse which one is true if Laila read 70% of her book.

According to option C, if Laila read 210 pages of her 300 page book, then;

the percentage she read is exppressed as;

210/300 * 100

= 21/30 * 100

= 21/3 *10

= 210/3

= 70%

Since the percent tallies with that in question, hence Laila read 210 pages of her 300 page book is correct

9514 1404 393

Answer:

  3 grams of helium are used

Step-by-step explanation:

Solving the given equation for H, we have ...

  5.6H +0.56A = 22.4

  5.6H = 22.4 -0.56A

  H = (22.4 -0.56A)/5.6

  H = 4 -0.1A

Using A=10, we find ...

  H = 4 -0.1·10 = 3

3 grams of helium are used.

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

b

Step-by-step explanation:

The value of the inequality is x ≥ - 5.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is an inequality 6 (x/2+4) ≥ 9 we need to find the value of the inequality,

6(x/2 + 4) ≥ 9

x/2 + 4 ≥ 9/6

x/2 + 4 ≥ 3/2

x/2 ≥ 3/2 - 4

2*(x/2) ≥ 2*(3/2 - 4)

x ≥ 3 - 8

x ≥ - 5

Hence the value of the inequality is x ≥ - 5.

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Answer:The number of text messages sent by his sister=162

Step-by-step explanation:

Step 1

The ratio of number of text messages sent by Lucas to the number of text messages sent by his sister =4 to 9= 4:9

Number of text messages sent by Lucas =72

Total ratio is given as 4+ 9= 13

Step 2

such that the total number of messages sent by Lucas and by his sister will be calculated as

Ratio of text messages sent by Lucas/  total ratio x Total messages  = Number of text messages sent by Lucas . Let X = Total number of messages  

4/13 x X = 72

X=72  x 13 / 4 =234

Therefore, The number of text messages sent by his sister= ratio of  text messages sent by his sister/ Total ratio x Total number of messages  =

9/13  X 234= 162 messages

The sign of displacement is negative.

Displacement: It is defined as the change in the position of an object. It is a vector quantity, means it has both direction and magnitude. It is the shortest distance between two position of an object.

It is the difference between final and the initial position of an object.

Initial position, \(x_i\) = 5m

Final position, \(x_f\) = 3m

Displacement, \(d = x_f - x_i\)  = (3 - 5)m

= -2m

negative sign shows that the direction of the an object is towards negative x-axis.

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It can be shown that PSL(2,7) has order 168, which is equal to 2^3 * 3 * 7. Since 7 is a prime and 2 and 3 are coprime to 7, it follows that PSL(2,7) is a simple group of order 168.

By Sylow's theorems, we know that there exist Sylow p-subgroup, Sylow q-subgroup, and Sylow r-subgroup in G. Let P, Q, and R be the respective Sylow p, q, and r-subgroups. Then by the Sylow's theorems, we have:

|P| = p^a for some positive integer a and p^a divides qr

|Q| = q^b for some positive integer b and q^b divides pr

|R| = r^c for some positive integer c and r^c divides pq

Since p, q, and r are distinct primes, it follows that p, q, and r are pairwise coprime. Therefore, we have:

p^a divides qr

q^b divides pr

r^c divides pq

Since p, q, and r are primes, it follows that p^a, q^b, and r^c are all prime powers. Therefore, we have:

p^a = q^b = r^c = 1 (mod pqr)

By the Chinese remainder theorem, it follows that there exists an element g in G such that:

g = 1 (mod P)

g = 1 (mod Q)

g = 1 (mod R)

By Lagrange's theorem, we have |P| = p^a divides |G| = pqr. Similarly, we have |Q| = q^b divides |G| and |R| = r^c divides |G|. Therefore, we have:

|P|, |Q|, |R| divide |G| and |P|, |Q|, |R| < |G|

Since |G| = pqr, it follows that |P|, |Q|, |R| are all equal to p, q, or r. Without loss of generality, assume that |P| = p. Then |G : P| = |G|/|P| = qr. Since qr is not a prime, it follows that there exists a nontrivial normal subgroup of G by the corollary of Lagrange's theorem. Therefore, G is not a simple group.

An example of a simple group of order pqr where p, q, and r are distinct primes is the projective special linear group PSL(2,7). It can be shown that PSL(2,7) has order 168, which is equal to 2^3 * 3 * 7. Since 7 is a prime and 2 and 3 are coprime to 7, it follows that PSL(2,7) is a simple group of order 168.

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Answer:

7/3 is x take 7/6 divided by 1/2

Answer:

x = 7/3

Step-by-step explanation:

1/2x=7/6

Multiply each side by 2

1/2x*2 = 7/6*2

x = 14/6

x = 7/3

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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This cannot be written in associative property as this deals with subtraction where the associative property is for addition and multiplication.

The associative property of addition states that the way numbers are grouped in an addition operation doesn't change the result. This means that for any numbers a, b, and c, (a + b) + c is the same as a + (b + c).

Applying the associative property to your equation :

= 3 - ( - 4 - 5)

= 3 - (-9)

= 3 + 9

= 12

And :

= (3 - 4) - 5

= -1 - 5

= - 6

Therefore, this is not an example of the associative property, as the expressions are not the same.

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Yes, the relationship holds true for all rectangles, regardless of the dimensions of the rectangle.

The opposite sides of a rectangle are equal in length and parallel to each other. Therefore, if we let the length of the rectangle be l and the width be w, then the opposite sides of the rectangle will have lengths of l and w, respectively. This can be written as the rule:

l = opposite side of the rectangle

w = adjacent side of the rectangle

Therefore, the opposite sides of a rectangle can be expressed as l = 2w, or w = 0.5l. This relationship holds true for all rectangles because by definition, a rectangle has four right angles and opposite sides that are equal in length. As a result, manipulating the sides of the rectangle will not change this relationship.

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To express (3x)2 in radical form, we start by understanding that raising a number to the power of 2 means multiplying the number by itself. In this case, we have (3x)2, which means we need to multiply 3x by itself.

Step 1: Multiply 3x by itself: (3x) * (3x) = 9x²

So, (3x)2 can be expressed in radical form as √(9x²).

The expression 29x10 cannot be expressed in radical form because there is no power or exponent involved. Radical form is used to represent expressions with roots or exponents.

To express W13 in radical form, we need to understand that the expression 7^(1/9) represents the ninth root of 7.

Step 1: Take the ninth root of 7: ∛7

So, W13 can be expressed in radical form as ∛7.

(3x)2 can be expressed in radical form as √(9x²).
29x10 cannot be expressed in radical form because there is no power or exponent involved.
W13 can be expressed in radical form as ∛7.
To express an expression in radical form, we need to understand the power or exponent involved and apply the appropriate radical operation.

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The two supporting reasons that are missing from this two-column proof include the following:

Statements                                             Reasons_______________

∠5 ≅ ∠1                                  Alternate Interior Angles Theorem

m∠6 + m∠5 = 180°                 Linear Pair Postulate

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

The Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal.

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The probability that a message transmitted using a Hamming code of length 25 and that corrects 2 errors will be correctly received is 0.6384.

Hamming codes use parity bits to detect and correct errors in the data. In this case, a code of length 25 with 2 error corrections can detect up to two errors and can correct up to one error.

Since the probability of a correct transmission of an individual symbol is 0.75, the probability of a correct transmission of the entire message is calculated by multiplying 0.75 by itself 25 times, giving a probability of 0.6384.

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In context of "group-diversity", a contributor is "data-driven", supplies the "necessary-information", and adheres to the high "performance-standards".

They actively contribute to the group's goals and objectives, bringing their expertise, skills, and knowledge to the table. A contributor may provide valuable insights and data-driven analysis regarding diversity-related matters, helping the group make informed decisions and take appropriate actions.

They are committed to achieving high performance standards and consistently deliver quality work. In the context of diversity, a contributor may actively participate in promoting inclusivity, supporting diverse perspectives, and advocating for equal opportunities within the group or organization.

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Answer:

This problem has been solved! See the answer Show transcribed image text Expert Answer Transcribed image text: Decide whether or not the functions are inverses of each other. f (x) = 2x + 4, g (x) = x – 2 no yes The function fis one-to-one.

Step-by-step explanation:

For a single alveolus requires the surface area of 0.133 square meters for gas exchange.

In this question, we have been given each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters.

we need to find  the approximate surface area of a single alveolus.

By unitary method the required surface area would be,

A = 40/300

A = 10/75

A = 0.133 square meters

Therefore, the approximate surface area of a single alveolus = 0.133 square meters

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The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

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To determine if a die is balanced, we can perform a chi-square goodness-of-fit test. In this case, a die is tossed 180 times, and the observed frequencies for each face are given as 28, 36, 36, 30, 27, and 23 for faces 1, 2, 3, 4, 5, and 6, respectively.

To test if the die is balanced, we will conduct a chi-square goodness-of-fit test. The null hypothesis, H0, states that the die is fair and follows an equal distribution for all faces. The alternative hypothesis, Ha, suggests that the die is biased or unbalanced.

We will calculate the expected frequencies assuming a fair die by dividing the total number of tosses (180) by the number of faces on the die (6). Each face would be expected to appear 180/6 = 30 times if the die is fair.

Next, we calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies. This test statistic follows a chi-square distribution with (number of categories - 1) degrees of freedom.

Finally, we compare the calculated chi-square test statistic with the critical chi-square value at the given significance level (0.01). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis and conclude that the die is not balanced.

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Range is R={n^2: n is natural number} U {n(n+1) : n is natural number}

The expression ⌈y⌉⋅⌊y⌋ represents the product of the ceiling and floor functions of y.

To find the range of all possible values of y, we need to consider the possible values of the ceiling and floor functions individually.

1. Ceiling function (⌈y⌉): This function rounds y up to the nearest integer. Since y is greater than 0, the ceiling of y will always be greater than or equal to y.

2. Floor function (⌊y⌋): This function rounds y down to the nearest integer. Again, since y is greater than 0, the floor of y will always be less than or equal to y.

Now, let's consider the product of the ceiling and floor functions, ⌈y⌉⋅⌊y⌋.

The product ⌈y⌉⋅⌊y⌋ will always be greater than or equal to 0 since y > 0 and this can take only integral values.

Therefore, the range of all possible values of y such that ⌈y⌉⋅⌊y⌋ is the set R={n^2: n is natural number} U {n(n+1): n is natural number}

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