B51 Find the number of ten-letter combinations (allowing repetition) from the set A, B,C that contain: (a) at least one of each letter; (b) at least two of each letter; (c) at least one A, two Bs, and three Cs; (d) any number of each letter; (e) at least one A and at least two Bs

There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.

To choose a president, a vice-president, and a secretary from a committee of 20 members,

We will use the formula for combinations,

which is: C(n, k) = n! / (k! (n - k)!)

where n is the total number of members and k is the number of members being chosen.

So, for n = 20 and k = 1, we have:

C(20, 1) = 20! / (1! (20 - 1)!) = 20

This gives us 20 choices for the president.

For the vice president,

We need to choose 1 member from the remaining 19 members.

So, for n = 19 and k = 1,

we have:

C(19, 1) = 19! / (1! (19 - 1)!) = 19

This gives us 19 choices for the vice president.

Finally, for the secretary,

We need to choose 1 member from the remaining 18 members.

So, for n = 18 and k = 1,

we have:

C(18, 1) = 18! / (1! (18 - 1)!) = 18

This gives us 18 choices for the secretary.

Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:

So, the required number of ways will be 20 * 19 * 18 = 6840

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The percentage of respondents said that cellular phones are "not at all annoying" is 9.52%

Now, According to the question:

Among the 1018 respondents, 97 said that cellular phones are "not at all annoying "

To find the percentage of respondents said that cellular phones are "not at all annoying"

Based on the given condition:

If we divide 97 divide by 1018, we get :

[tex]\frac{97}{1018}[/tex] ≈ 0.09528

If we want to express this number as a percentage, we need to multiply by 100. Then we get:

0.09528 x 100 = 9.52%

Hence, The percentage of respondents said that cellular phones are "not at all annoying" is 9.52%

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If the equation  y = 11x + 400 gives the cost of the field trip as a function of the number of students who attend , then the initial value of function is 400 , the rate of change is 11 , and the amount 400 represents cost of bus  and 11 represents per student ticket cost    .

Mr. Seda plans a field trip for his classes.

He rents one bus for whole class and purchases a museum ticket for each student.

the equation representing the situation is y = 11x + 400 ;

the value 400 is fix it does not change with "x" , that means ,

the initial value of the function is 400 and it denotes the cost of bus ,

the value 11x changes with the variable "x" , that means the cost of museum ticket is $11 per student .

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The inequality to compare it with the times others in the family skied without falling is 2f < 223.

In math the term inequality is defined as a relation which makes a non-equal comparison between two numbers or other mathematical expressions

Here we have given that Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family.

Here we have also given that his dad tells him that he can check by using the inequality.

Based on the given details we have identified that the inequality that compare it with the times others in the family skied without falling is written as

=> 2f < 223.

here the term f refers the time skied in seconds for each person.

Complete Question:

Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. The total amount of time spent on skied without falling 223. Then write the inequality to compare it with the times others in the family skied without falling.

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a) The current ages of his children are: 8 years, 15 years and 17 years

b) In the year when the ages of his three children have doubled, their ages also form a pythagorean triple.

Let x be the age of the youngest child, y represents the age of the middle child and z be the age of oldest child.

The oldest child is nine years older than the youngest.

so, we get an equation,

z = 9 + x

⇒ x = z - 9

and the middle child is two years younger than the oldest.

so, we get an equation,

y = z - 2

The age of his children now form a Pythagorean triple.

⇒ x² + y² = z²

substitute the values for x and y from above two equations.

⇒ (z - 9)² + (z - 2)² = z²

⇒ z² -18z + 81 + z² - 4z +4 = z²

⇒ 2z² -22z + 85 - z² = z² - z²

⇒ z² - 22z + 85 = 0

⇒ (z - 17)(z - 5) = 0

For z = 17:

x = 17 - 9

x = 8

and y = 17 - 2

y = 15

For z = 5, the value of x would be negative which is contradiction.

As is always greater than 0

For x = 8 , y = 15 and z = 17

Consider x² + y²

= 8² + 15²

= 64 + 225

= 289

= 17²

= z²

This means, (8, 15, 17) is a Pythagorean triple.

Thus, their current ages are: 8 years, 15 years and 17 years

If  the ages of his three children have doubled then:

x = 16 , y = 30 and z = 34

Consider x² + y²

= 16² + 30²

= 256 + 900

= 1156

= 34²

= z²

This means, (16, 30, 34) also form a Pythagorean triple.

In the year when the ages of his three children have doubled, their ages will form a pythagorean triple.

Thus, the man is correct.

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The total weight of the 4 heaviest pumpkins is given as follows:

D. 41 and 3/4 pounds.

The dot plot shows the number of times that each measure appears in the data-set.

Hence the weights of the four-heaviest pumpkins are given as follows:

Then the total weight of all these pumpkins is obtained as follows:

2 x (10.375 + 10.5) = 41.75.

The fraction equivalent to a decimal of 0.75 is given as follows:

3/4.

Which means that the correct option is given by option D.

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As per the given market value, the firm's P/E ratio for 20X2 is $2.85

The term P/E ratio is defined as measures a company's market price compared to its earnings and it shows what the market is willing to pay today for a stock based on a company's past or future earnings.

Here we have given that the market value of a share of common stock is 3. 3 times Book value (9. 42) for 20X2.

in the given values we have know that

Price of common stock = 3.3

Earning per share = 9.42

Then the value of P/E ratio is calculated as,

=> P/E ratio = 9.42/3.3

=> P/E Ratio = 2.85

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The expression |x-y| represents the distance of the subtraction of x by y to the number zero on the number line.

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

For example:

|-2| = |2| = 0.

The definition of the absolute value function is given as follows:7

Hence, for the difference between x and y, the absolute value is given as follows:

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The domain of the quadratic function is x ≥ -6.

The correct option is C.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Given:

The graph of quadratic function f is shown on the grid.

The domain of f(x) means,

all the values of x where function is defined.

From the graph,

the domain is, x ≥ -6.

Therefore, the domain is x ≥ -6.

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The graph of the exponential function y = 3(2)^x - 3 is given by the image presented at the end of the answer.

The parent function is given as follows:

y = 2^x.

Which has:

Then the transformations are given as follows:

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The inequality y ≤ -4 is NOT part of the system of inequalities that defines a polygonal convex set that includes a the interior of a square whose vertices are A(4, 4), B(4, -4), C(-4, -4) and D(4, -4).

As per the given data the interior of a square whose vertices are:

A(4, 4), B(4, -4), C(-4, -4) and D(4, -4)

Diagram attached at the end of solution.

The shaded portion is the polygonal convex set, which represents the interior of the square

Clearly for points inside the set,

x ≤ 4, x ≥ - 4, y ≤ 4 and y ≥ -4

Hence options

(a) The inequality y ≥ -4 represent points inside the set.

(b) The inequality x ≥ - 4 represent points inside the set.

(c) The inequality y ≤ -4 does not represent points inside the set.

(d) The inequality x ≤ 4 represent points inside the set.

Therefore option (c), the inequality y ≤ -4, does not represent points inside the set.

Thus (c) is the correct one.

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When the florist uses 10 white roses in a bouquet, the red roses that she uses will be 25.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, the ratio is given as 5:2. Therefore, when the florist uses 10 white roses in a bouquet, the red roses that she uses will be:

= 5/2 × 10

= 25

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A florist uses 5 red roses for every 2 white roses in her bouquets. If the florist uses 10 white roses in an arrangement, how many red roses does she use?

Answer:

A= 2000*(1+0.05)^t

Explanation: The equation represents the compound interest formula where A is the amount of money in the account, P is the principal amount (initial investment) which is $2,000, r is the interest rate (expressed as a decimal) which is 5% or 0.05, and t is the number of years. The formula shows that the account balance will increase by 5% each year, meaning the interest will be added to the principal and the new interest will be calculated on the new balance.

Step-by-step explanation:

The slope intercept form for D: y=0.5x+4

Slope-intercept form is a form of a linear equation, written as y = mx + b, where m is the slope, and b is the y-intercept.

This question is using the slope-intercept form of a linear equation, which is written as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation y=0.5x+4 is written in the slope-intercept form, with m = 0.5 and b = 4.

To solve this equation, we first need to identify the slope (m). In this case, the slope is 0.5. Then, we need to identify the y-intercept (b). In this case, the y-intercept is 4. Finally, we can use the slope and y-intercept to write the equation in the form of y = mx + b, which is y = 0.5x + 4.

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The correct answer is Number of science courses, discrete; time to complete homework, continuous.

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.

The number of science courses enrolled in is likely a whole number, making it a discrete random variable. On the other hand, the time it takes to complete homework could be any value within a continuous range, such as minutes or hours, so it is a continuous random variable.

Hence, the number of science courses is discrete and time to complete homework is continuous.

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The correct option that will make the inequality expression 2x - 3 > 11 - 5x true is when x is equal to 2.

We shall evaluate for the values of x to know that make the inequality expression true as follows;

2x - 3 > 11 - 5x

2x + 5x - 3 > 11 {add the 5x to both sides}

7x > 11 + 3 {add 3 to both sides}

7x > 14

x > 14/7 {divide through by 7}

x > 2

Therefore, the value for x that makes the inequality expression 2x - 3 > 11 - 5x true is 2.

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The variables are x = 1/2 and y = 5/3

From the figure, we have been told 21x = 5x + 8. So let's solve for x.

21x = 5x + 8

21x - 5x = 8

16x = 8

x = 8/16

x = 1/2 = 0.5

Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:

(20y-2)/(17y + 3) = (5x+8)/(21x)

Substitute x = 0.5 and solve for y:

(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))

(20y-2)/(17y + 3) = (10.5)/(10.5)

(20y-2)/(17y + 3) = 1

20y-2 = 17y + 3

20y - 17y = 3 + 2

3y = 5

y = 5/3

Thus, the variables are x = 1/2 and y = 5/3

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The difference in height of the trees in Bianca front yard is 2 3 / 4 metres.

Bianca has two trees in her front yard. One is 7 1 / 2 metres tall and the other tree is 4 3 / 4 metres tall.

Therefore, the difference in height of the trees can be calculated as follows:
Let's convert the height of the tree to improper fractions as follows:

7 1 / 2 = 15 / 2 metres

4 3 / 4 = 19 / 4 metres

Therefore,

difference in height of the trees = 15 / 2 - 19 / 4

difference in height of the trees =  30 - 19 / 4

difference in height of the trees = 11 / 4 metres = 2 3 / 4 metres.

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The solution to the inequality 7x + 9 ≤ 58 is given as follows:

x ≤ 7.

The inequality for this problem is defined as follows:

7x + 9 ≤ 58.

Isolating the variable x, we have that:

7x ≤ 58 - 9

7x ≤ 49

x ≤ 49/7

x ≤ 7.

Meaning that the inequality is solved similarly to an equality, with the difference that a range of values is obtained instead of a single value.

The problem asks for the solution to the inequality 7x + 9 ≤ 58.

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The following values are: 1) 9/10, 2) 1/10, 3) 24/100, 4) 21/100, 5) 1/10, 6) 15/100

There are a few steps for writing decimals in grids:

Step 1: Count how many grids are completely shaded. This will be the number for your one digit.

Step 2: In the grid that is partially shaded, count how many parts are shaded and how many total parts there are.

If the grid has 10 total parts, the number of shaded parts will be your tenth digit.

If the grid has 100 total parts, the number of shaded parts will end in the hundredth place.

Step 3: Combine your numbers from steps 1 and 2 to create the decimal that the grids represent.

As per the steps now we can calculate the decimal numbers:

0.9/100=0.9/10

0.1/100=1/10

0.24/1000=24/100

0.21/1000=21/100

0.15/1000=15/100.

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The values of x and y are 18,14 respectively.

What is Triangle  ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given ,

From the given figure ,

JK is a midsegment of triangle FGH.

And

FG = 28

FJ = x

JH = 10

JK = y

As, JK is midsegment of FG

So,

JK = FG / 2

y = 28 / 2

y = 14

So, the value of y could be 14.

And FG = 28

So,

FJ + JH = FG

10+x = 28

x = 28 - 10

x = 18

So, the value of x could be 18.

Hence, The values of x and y are 18,14 respectively.

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A control group is a group of individuals that is treated in exactly the same way as the experimental group in an experiment, except for the factor that is being manipulated.

This group is used as a comparison to measure the effects of the manipulated factor on the experimental group. The control group is key for determining the validity of the results of an experiment because it helps to ensure that any observed changes are actually due to the manipulated factor. A control group should be chosen at random from the same population as the experimental group and should be given the same conditions as the experimental group, except for the factor that is being manipulated. This helps to ensure that any observed differences in the experimental and control groups are due to the manipulation and not due to any other factor.

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No, because there is one x-value that corresponds to two y-values. Hence option D is the correct answer.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

We know that each input is connected to precisely one output in a function. In the graph given one 2 input value correspond to the same output value and hence, it does not form a function.

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The bee would be located at (-4, 3, 1) at time 7. The integral of a velocity vector over a certain time period represents the net displacement of an object.

In this case, the velocity vector is represented by r'(t) and the time period is from t=0 to t=7.

If the integral of the velocity vector over this time period is equal to 0, it means that the object's net displacement over the 7 seconds is 0. This implies that the object's final position is the same as its initial position.

As the bee started at (-4,3,1) at time t=0, it means the bee would have not moved from its initial position and would be located at (-4,3,1) at time t=7.

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=================================================

Work Shown:

P( (A u B u C)' ) = 0.33

P(A u B u C) = 1 - P( (A u B u C)' )

P(A u B u C) = 1 - 0.33

P(A u B u C) = 0.67

--------

P(AuBuC) = P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = P(C) + 0.37

P(C) = 0.67 - 0.37

P(C) = 0.30

For more information, search out "inclusion-exclusion principle". Also feel free to ask me if you have any questions.

The correlation between two variables is a measure of how strongly they are related to each other.

In order to calculate the correlation between two variables, one must calculate the covariance, which is the average of the product of the deviations of each variable from its mean. The formula for the covariance of two variables, X and Y, is cov(X,Y) = (1/n) Σ (x_i - mean_x)(y_i - mean_y).

The correlation matrix for the given data is as follows:

Number of Group Visits Attended  Fructosamine  Infant Birthweight (g)

Number of Group Visits Attended  1  -0.20  -0.10

Fructosamine  -0.20  1  0.83

Infant Birthweight (g)  -0.10  0.83  1

From the above correlation matrix, it can be seen that the two variables with a strong positive relationship are Fructosamine and Infant Birthweight, with a correlation of 0.83. This indicates that as Fructosamine increases, so does the Infant Birthweight.

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The maximum level of intensity for passion is when there is a feeling of intense desire and excitement.

The years in a relationship that this can occur varies depending on the couple and other factors.

The maximum level of intensity for passion in a romantic relationship can vary for different individuals and situations. Passion is a feeling of intense desire and excitement, and it can fluctuate over time. Some people may experience intense passion in the early stages of a relationship, while others may find that it grows stronger over time.

It is not possible to set a specific number for the maximum level of intensity for passion as it's subjective and can change over time.

Some people may feel intense passion in the early stages of a relationship, while others may experience it later on. Passion can also come and go in a relationship, and its intensity may fluctuate over time.

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The logarithmic form of the exponential expressions are;

1) log2 5 = x

2) log3 10 = y

3) logk 6 = 5

4) log2 32 = 5

5) log3 81 = 4

6) log 3 27 = 3

7) log10 100 = 2

8) logx y = 2

9) log10 x = 20

10) logp q = 10

11) logx y = 1/2

12) log9 3 = 1/2

We have to note that we can be able to write an exponential equation in the logarithmic form or in the exponential form. In the exponential form we we would have something like;

a^x = P

While in the logarithmic form we can be able to have something like;

logaP =x

These are the two forms that we can be able to write the equations that we have in the question.

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The debate over whether alcohol misuse is biologically determined or culturally influenced is most relevant to the issue of nature versus nurture.

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Answer: 181726.

Step-by-step explanation:Why?

X

Y

X+Y=!(***27652