Which of the following situations or activities involve permutation?
a. matching shirts and pants
b. forming different triangles out of 5 points on a plane, no three of which are collinear
c. assigning telephone numbers to subscribers
d. forming a committee from members of a club

Answer:15

Step-by-step explanation: 1st multiple what’s in the parenthesis (3*3= 9 & 4*4= 16

Next write it out 22+(9-16)

Then you subtract 9 from 16 since it’s in parenthesis So it’s 22+(-7) and since you are adding a negative and a positive together you will have to subtract and keep the sign of the larger number so the answer is 15 since u needed to subtract but 22 is the larger number making it positive answer

The intersection of two sets can be represented using a truth table that shows the input values and the resulting output value that represents the intersection of the two sets.

The purpose of truth tables is to help analyze logical statements and determine their truth values based on the different combinations of inputs or variables. Truth tables display all possible outcomes of a logical operation and allow for a clear visualization of the relationship between inputs and outputs.

Number systems, particularly those derived from binary, are closely related to truth tables because they involve the use of binary digits or bits (0 and 1) to represent numbers and perform logical operations. Truth tables can be used to determine the output of binary logical operations, such as AND, OR, and NOT, based on the input values.

Set theory, on the other hand, is related to truth tables in the sense that it deals with the study of sets, which can be represented using truth tables. Truth tables can be used to determine the membership of elements in a set and to evaluate logical statements involving sets. For example, the intersection of two sets can be represented using a truth table that shows the input values and the resulting output value that represents the intersection of the two sets.

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Answer: True

Step-by-step explanation:

True, if two points are in a plane, then the line joining the two points lies entirely in the plane.

Discussion:

For instance, if two points A and B lie in a plane x-y, We can conclude that the line AB also lies in the plane x-y.

This therefore means that; Irrespective of whether the points are in represented in 2 or 3 dimensions, the line joining them lies within the plane in discuss.

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The base salary per year is $66,200, and she only gets the target for medication A, the 70% of the annual bonus of $22,500

(22,500 * 70)/ 100 = 15,750

So the total of her compensation (salary plus bonus) is:

$66,200 + $15,750 = $81950

The answer to this question is c.The use of a correlation coefficient.

The use of a correlation coefficient would tell you that an association claim is being made in a research study. A correlation coefficient is a statistical measure that shows the strength and direction of a relationship between two variables. It ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect negative or positive relationship, respectively.

A scatterplot or bar graph may be used to visually display the relationship between two variables, but they do not necessarily indicate that an association claim is being made. The measurement of two variables is necessary for any type of research study, but it does not inherently imply that an association claim is being made.

Interrogation of internal validity is a process used to ensure that the study's results accurately reflect the relationship between the variables being studied. It is important for any research study but does not specifically indicate that an association claim is being made.

Therefore,the answer to this question is c.The use of a correlation coefficient.

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The known solutions to f(x) = g(x) are given as follow:

x = 1 and x = 9.

When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.

At these intersections point, the functions have the same numeric value, which are the points looked at to find the solution on a table.

Hence the solutions are given as follows:

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Answer:

8 hours

Step-by-step explanation:

70= 7x + 14

70 - 14 = 56

56/7= 8

X = 8

Check

7 x 8 + 14

56 + 14 = 70

Answer:

8 hours.

Step-by-step explanation:

Set the equation:

Dollars per hour x amount of hours + fixed fee = total cost.

Dollars per hour = 7

Fixed fee = 14

Total cost = 70

Total hours = x

Plug in the corresponding numbers and variables to the corresponding terms.

7x + 14 = 70

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 14 from both sides of the equation:

\(7x + 14 = 70\\7x + 14 (-14) = 70 (-14)\\7x = 70 - 14\\7x = 56\)

Next, divide 7 from both sides of the equation:

\(7x = 56\\\frac{7x}{7} = \frac{56}{7}\\ x = \frac{56}{7}\\ x = 8\)

8 hours is your answer.

~

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There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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In relation, the y values represents the range of the relation

The relation is defined as the relationship between set of ordered pairs. So generally we can say that the relation is defined as the relationship between x values and y values

We know the domain is the set of all inputs of the relation, that means the domain consist of the x values of the relations

Similarly, the range is the set of all outputs of the relation, that means the ranges consist of the y values of the relations

For example

The relation {(1, 2), (3, 4), (5, 6)}

Here x value = {1, 3, 5}

The y value = {2, 4, 6}

Therefore, the y values represents the range

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Answer:

The last year value of the house will be $230,000.

Step-by-step explanation:

GIVEN: Decrease in house price = 20%

            Current house price = $184,000

TO FIND: Value of the house last year

SOLUTION:

If the value of the house decreased by 20% during last year, this means the value of the house this year is 80% of last year's value.

Let the value of the house last year be 'x'.

If the value of the house today is  $184,000, then:

                           \(80/100 * x = 184,000\\\\0.8x = 184,000\\\\x = 184,000/0.8\\\\x = 230,000\)

Therefore, the last year value of the house will be $230,000.

The probability that the sum will be an even number on the toss of two dice is  5/9 .

In the question ,

it is given that ,

the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .

the probability of getting an odd number first is = 4/6 = 2/3,

the probability of getting an even number first is = 2/6 = 1/3,

To get an even, we must get either 2 odds or 2 evens.

The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .

The probability of getting 2 evens is 2/6 × 2/6 = 4/36.

If we add them together,

we get ,

= 16/36 + 4/36

= 20/36

= 10/18 = 5/9

Therefore , the required probability is 5/9  .

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Answer:          36x^3 +27x^2 = 9x^2\left(4x+3\right)

Step-by-step explanation: apply exponent rule rewrite factor out common term plz enjoy

Answer:

\(x = 0\; ,-\frac{3}{4}\)

Step-by-step explanation:

\(36x^3 + 27x^2 = 0\)

\(=> 9x^2(4x + 3) = 0\)

Here, x will have 2 values :-

1) \(9x^2(4x + 3) = 0\)

\(=> \frac{9x^2(4x + 3)}{(4x+3)} = \frac{0}{4x+3}\)

\(=> 9x^2 = 0\)

\(=> \frac{9x^2}{9x} = \frac{0}{9x}\)

\(=> x = 0\)

2) \(9x^2(4x + 3) = 0\)

\(=> \frac{9x^2(4x + 3)}{9x^2} = \frac{0}{9x^2}\)

\(=> 4x+3 = 0\)

\(=> 4x+3 -3 = 0 - 3\)

\(=> 4x=-3\)

\(=> \frac{4x}{4} = \frac{-3}{4}\)

\(=> x = -\frac{3}{4}\)

The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.

Let a, b, c, and d are the zeroes of the polynomial and k be the leading corefficient. Then the polynomial is given as,

⇒ k(x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

From the graph, the zeroes are -2, 1, and 1. Then the polynomial is given as,

y = a(x + 2)(x − 1)²

The curve passes through (0, 1), then we have

1 = a(0 + 2)(0 − 1)²

1 = 2a

a = 1/2

a = 0.5

Then the polynomial is given as,

y = 0.50 (x + 2)(x − 1)²

y = 0.50 (x + 2)(x² + 1 - 2x)

y = 0.50 (x³ + 2x² + x + 2 - 2x² - 4x)

y = 0.50 (x³ - 3x + 2)

y = 0.50x³ - 1.5x + 1

Compare with standard equation, then we have

a = 0.50

b = 0

c = - 1.5

d = 1

The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.

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The missing graph is attached below.

Answer:

The balance on the loan f(p) = $100 - $20 × p

Step-by-step explanation:

The parameters of the question are;

The loan amount = $100

The amount of monthly payment for the loan = $20

The function rule for the balance of the function f(p) where p is the number of payments is given as follows;

The balance on the loan, f(p) = The loan amount less the total amount paid

The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p

The total amount payment Jeania has made = $20 × p

∴ The balance on the loan, f(p) = $100 - $20 × p

Which gives;

f(p) = $100 - $20 × p.

The inverse of the coefficient matrix is \(\left[\begin{array}{cc}\frac {-3}{13}&\frac {2}{13}\\\frac {2}{13}&\frac {-3}{13}\end{array}\right]\)

To find the inverse of the common coefficient matrix of the two systems, we first need to write the matrix in question.

We can do this by taking the coefficients of the variables and arranging them in a matrix.

For the systems (a) and (b), the coefficient matrices are:

A =\(\left[\begin{array}{cc}-3&-2\\2&-3\end{array}\right]\)

To find the inverse of matrix A, we can use the formula:

\(A^-1 = (1/det(A)) * adj(A)\)

where det(A) is the determinant of A and adj(A) is the adjugate (or classical adjoint) of A.

First, let's find the determinant of A:

det(A) = (-3)(-3) - (2)(-2) = 9 - (-4) = 13

Next, we need to find the adjugate of A. To do this, we need to find the transpose of the matrix of cofactors of A. The matrix of cofactors of A is:

C =\(\left[\begin{array}{cc}-3&-2\\2&-3\end{array}\right]\)

Note that the cofactor of aij is \((-1)^{(i+j)}\) times the determinant of the matrix obtained by deleting row i and column j of A. Using this rule, we can find the matrix of cofactors C.

C =\(\left[\begin{array}{cc}-3&2\\2&-3\end{array}\right]\)

Now we need to find the transpose of C, which is:

\(C^T\) =\(\left[\begin{array}{cc}-3&2\\2&-3\end{array}\right]\)

Finally, we can find the inverse of A using the formula:

\(A^-1 = (1/det(A)) * adj(A)\)

\(A^-1 = (1/13) *\left[\begin{array}{cc}-3&2\\2&-3\end{array}\right]\)

\(A^-1 =\left[\begin{array}{cc}\frac {-3}{13}&\frac {2}{13}\\\frac {2}{13}&\frac {-3}{13}\end{array}\right]\)

Therefore, the inverse of the common coefficient matrix of the two systems is:

\(\left[\begin{array}{cc}\frac {-3}{13}&\frac {2}{13}\\\frac {2}{13}&\frac {-3}{13}\end{array}\right]\)

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Answer: 5

Step-by-step explanation:

 8+(-3)

=8-3 ⇔ you don't need to change signs when it is positive(+) outside the parenthesis

=5 ⇔ subtraction

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The clothing store should survey at least 306 customers to be 92% confident that the estimated proportion within 5 percentage points of the true population proportion.

A fraction or proportion of a whole number, typically expressed as a number out of 100, is referred to as a percentage. It is much of the time indicated by the image "%".

To determine the sample size needed for this study, we need to use the following formula:

\(n = (Z^2 *p * q) / E^2\)

where:

n = sample size

Z = the Z-score associated with the desired confidence level (in this case, 92% corresponds to a Z-score of 1.75)

p = the estimated proportion of customers who are over the age of forty (we don't have a specific estimate, so we can use 0.5 as a conservative estimate)

q = 1 - p

E = the desired margin of error (in this case, 5 percentage points or 0.05)

Plugging in the values, we get:

n = (1.75² × 0.5 × 0.5) / 0.05²

n = 306.25

Therefore, the clothing store should survey at least 306 customers to be 92% confident that the estimated proportion of customers over the age of forty is within 5 percentage points of the true population proportion.

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Answer:6/l per min??

Step-by-step explanation:

If the heart rate is 72 beats per minute and the stroke volume 81 mL per beat, then the cardiac output is 5.8 liters per minute, rounded to the tenths place.

Explanation:

Cardiac output (CO) is the volume of blood pumped by the heart per minute. It is the product of the heart rate (HR) and the stroke volume (SV).

HR (heart rate) is the number of heart beats per minute, and SV (Stroke volume) is the volume of blood pumped out by the heart with each beat. To calculate CO, we simply multiply HR by SV.

In this case, the given heart rate is 72 beats per minute, and the stroke volume is 81 mL per beat. To calculate the cardiac output, we need to convert the stroke volume from mL per beat to L per beat by dividing it by 1000 (since there are 1000 mL in a liter):

Stroke volume (SV) = 81 mL/beat ÷ 1000 mL/L = 0.081 L/beat

The cardiac output can be calculated by multiplying the heart rate by the stroke volume. Therefore, the cardiac output in this case would be:

Cardiac output (CO) = Heart rate (HR) x Stroke volume (SV)

= 72 beats/min x 0.081 L/beat

= 5.832 L/min

Therefore, the cardiac output is 5.8 liters per minute, rounded to the tenths place.

To summarize, we can calculate the cardiac output by multiplying the heart rate (HR) and the stroke volume (SV), where SV is the volume of blood pumped out by the heart with each beat, and HR is the number of heart beats per minute. In this case, the given HR is 72 beats per minute, and the stroke volume is 81 mL per beat, so we first convert the SV to L per beat and then multiply HR and SV to get the cardiac output, which is 5.8 liters per minute.

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Answer:

The answer is \(\frac{1}{6}a - \frac{1}{6}\) .

Step-by-step explanation:

Solve the following equation:

\(-\frac{2}{3}a + \frac{5}{6}a - \frac{1}{6}\)

Combine \(-\frac{2}{3} a\) and \(\frac{5}{6} a\) :

\(-\frac{2}{3}a + \frac{5}{6}a - \frac{1}{6}\)

\(\frac{1}{6}a - \frac{1}{6}\)

So, the answer is \(\frac{1}{6}a - \frac{1}{6}\) .

Answer:

1/6a-1/6

Step-by-step explanation:

Karnaugh map or K-map can be defined as the pictorial representation of the logic function.

Karnaugh map provides a pictorial representation of the binary function which is more easily minimized than a Boolean algebraic expression.

Now let us simplify the given Boolean function, using three-variable K-maps below:Three-variable K-maps:F(x, y, z) = (0, 2, 3, 4, 6)

By using Karnaugh map, we have:F(x, y, z) = xy + xz + yz.

The simplified boolean function is F(x, y, z) = xy + xz + yz, which contains 10 terms.Now, the answer is in 250 words.

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Answer:

4x y

Step-by-step explanation:

The phrases range, standard deviation, and mean are all very well-known, while skew is less well-known. The accompanying figure demonstrates how skewness affects mean, range, and standard deviation.

Here,

There are a number of benefits to utilizing the standard deviation instead of the interquartile range, including efficiency since the standard deviation takes the full distribution into account as opposed to the interquartile range, which only uses two data points.

What distinguishes IQR and range from each other?

If an extreme value exists, it may alter the value of a range. The first and second quartile boundaries, as well as the third and fourth quartile boundaries, are known as the IQR and Q3, respectively.

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complete question:

Which is more affected by skewness, the iqr or standard deviation?

Answer:

Factored?

x^2 + 8x +7

Step-by-step explanation:

x times x = x^2, with 7 times x = 7x and x times 1 = 1x. Add those two common terms together to get 8x. Then lastly 7 times 1 =7 so add that.

Simplify form of (x + 1)(x + 7) is equals to x² +8x +7.

"Simplification in mathematics means to write the given expression in such a way that it is easy to understand."

According to the question,

Simplify the given equation by opening the brackets we get,

  (x + 1)(x + 7)

=  x² + 1x +7x +7

= x² + 8x + 7

Hence, simplify form of (x + 1)(x + 7) is equals to x² +8x +7.

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Answer:

It is 3/4

Step-by-step explanation:

You take the 3/4 out of the 1 and are left with 1/4 and then add that to the 1/2 and you get 3/4

Answer:

p = ± q / 5r + 8; Option D

Step-by-step explanation:

We are given the following equation; q^2 / p^2 - 16p + 64 = 25r^2;

q^2 / p^2 - 16p + 64 = 25r^2 ⇒ Let us factor p^2 - 16p + 64, as such,

p^2 - 16p + 64,

( p )^2 - 2 * ( p ) * ( 8 ) + ( 8 )^2,

( p - 8 )^2 ⇒ Now let us substitute this into the equation q^2 / p^2 - 16p + 64 = 25r^2 in replacement of p^2 - 16p + 64,

q^2 / ( p - 8 )^2 = 25r^2 ⇒ multiply either side by ( p - 8 )^2,

q^2 = 25r^2 * ( ( p - 8 )^2 ) ⇒ divide either side by 25r^2,

q^2 / 25r^2 = ( p - 8 )^2 ⇒ Now apply square root on either side,

| p - 8 | = √( q^2 / 25r^2 ) ⇒ Simplify,

| p - 8 | = q / 5r,

| p | = q / 5r + 8,

Answer; p = ± q / 5r + 8; Option D

Answer:

A

Step-by-step explanation:

w = 12500p + 250

250 is a fixed number of words.

12500 is the slope

For each dollar the price increases, the number of words increases by 12,500.

Answer: A

Answer:

-24

Step-by-step explanation:

-3[-4(3-10)-12]/-2(-1)

-3[-4(-7)-12]/2

-3[28-12]/2

-3[16]/2

-48/2

-24

Hopes this helps

Answer:

3x+4y=-11

Step-by-step explanation: