Suppose we want to choose 2 letter without replacement from the 3 letters a,b and c how many ways can this be done if the order of choice is taken into consideration and how many ways can this be done if the order of choices is not taken into consideration?

a) The number of families that were surveyed is given as follows: 17.

b) The percentage of families with exactly one children is given as follows: 29.4%.

A bar graph shows the output considering a given input.

In this problem, the input is the number of children, while the output is the number of families that have the given number of children.

Hence:

Hence, for item a, the total number of families is given as follows:

4 + 5 + 5 + 2 + 1 = 17.

Out of the 17 families, 5 have exactly one children, hence the percentage is given as follows:

5/17 x 100% = 29.4%.

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The proof that the value of x is 38° is shown below

From the question, we have the following parameters that can be used in our computation:

ABDE is a parallelogram.

The measure of the angle opposite the vertex x is

Angle = 180 - 68

Evaluate the like terms

So, we have

Angle = 112

Also, we have

B = 68

AB = AC

So, we have

y = 180 - 68 - 68

y = 44

Using the above as a guide, we have the following:

x + 44 = 82

So, we have

x = 82 - 44

Evaluate

x = 38

Hence, we have shown that the value of x is 38°

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Hello!

1 book => [tex]1^{\frac{3}{8} }[/tex]

14 books => [tex]14*1^{\frac{3}{8} }[/tex]

[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]

The answer is 14 inches thick.

The probability that a student takes a history class given that the student is taking a science class is 0.59 to the nearest hundredth.

The probability that a student takes a history class given that the student is taking a science class is a conditional probability.

Assuming;

P(H) = Probability of taking a history class

P(S) = Probability of taking a science class

P(H ∩ S) = Probability of taking both a history class and a science class

Given data:

P(H ∩ S) = 0.48

P(S) = 0.82

Solving for P(H | S) using the formula for conditional probability:

P(H | S) = P(H ∩ S) / P(S)

P(H | S) = 0.48 / 0.82

P(H | S) ≈ 0.59

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∠b and 76° are alternate angles. They are equal.

So, m∠b = 76

That's it :)

Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.

Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.

Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of options (15 colors) and r is the number of positions (4 rooms).

Using the formula, the number of color arrangements possible is:

P(15, 4) = 15! / (15 - 4)!

= 15! / 11!

= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)

= 32,760

1. The location of point A  and B in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of point A is 5.

3. The length of AB is 10.

4. B in polar form is 2√13 × (cos(146°) + i sin(146°))

5. The product of two complex numbers in rectangular form is  -36 - 2i

6. z1/z2 in polar form is z1/z2 = 4 cis (7π/6 - π/4)

1. The location of each point A and B are as follows  Arrow A is at (4, 3) and arrow B (-6, 4). therefore the location in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of a complex number (a + bi) is represented as √(a² + b²) ⇒ √(4² + 3²) = √(16 + 9) = √25 = 5.

3. We can calculate the length of vector AB with √(x₂-x₁)² + (y₂-y₁)²)

AB = √((-6 - 4)² + (4 - 3)²)

AB = √((-10)² + 1)

AB = √(100 + 1)

AB = √101 ⇒ 10

4. The modulus of B, r = √((-6)² + 4²) = √(36 + 16) = √52 = 2√13

θ = 180° - arctan(|4/-6|) = 180° - arctan(2/3)

θ = 180° - 33.69° = 146.31°

5. The product of the complex number can be see as follows

(4 + 3i) × (-6 + 4i) = (4×-6 - 34) + (4×4 + 3×-6)i

= (-24 - 12) + (16 - 18)i

= -36 - 2i.

6. (7π/6 - π/4) = (14π/12 - 3π/12) = 11π/12.

11π/12 × (180/π) = 165°.

In Polar form z1/z2 = 4 cis (7π/6 - π/4)

= 4 cis 165°.

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The diameter of the reservoir is:

Part (a): 112.86 m

part (b): 56. 44 m

The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height or depth

Part (a):

We have:

h = 10 cm = 0.1 m

V = 1000,000 litres = 1000 m³  (Remember: 1 litre = 1000 cubic metre)

V = πr²h

1000 = 3.14 * r² * 0.1

1000 = 0.314 r²

r² = 1000 / 0.314

r² = 3184.71

r = √3184.71

r = 56.43 m

Since diameter = 2 * r

diameter =  2 * 56.43

diameter = 112.86 m

part (b):

We have:

h = 10 cm = 0.1 m

V = 250,000 litres = 250 m³

V = πr²h

250 = 3.14 * r² * 0.1

250 = 0.314 r²

r² = 250 / 0.314

r² = 796.18

r = √796.18

r = 28.22 m

Since diameter = 2 * r

diameter =  2 * 28.22

diameter = 56. 44 m

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A. The greatest number of packages that can fit the truck is 24000

B. The volume of the part that is filled is 375 cubic feet

Given that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

Also, we have

Package = 1/4 foot cube

So, we have

Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)

Evaluate

Number of packages = 24000

This means that the greatest number of packages is 24000

Recall that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

So, we have

Volume = (8 * 6 1/4 * 7 1/2)

Evaluate

Volume = 375

Hence, the volume is 375 cubic feet

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The equation of the functions represented on the graph are (b)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following intervals:

When the intervals are represented as inequalities, we have the following:

Interval 1: x ≤ 1

Interval 2: x > 1

This means that the intervals of the graphs are x ≤ 1 and x > 1

From the list of options, we have the graph to be option (b

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The values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

The given quadratic equation is 2x² - 6x + 7 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

When we compare the given quadratic equation with standard form we get the values of a , b and c

a=2

b=-6

c=7

Hence, the values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

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Answer:

[tex]h(x) = 2 {x}^{2} + 5x - 3[/tex]

[tex]h(x) = (2x - 1)(x + 3)[/tex]

-The component functions must both be linear.

-The component functions must have y-intercepts with different signs.

The publisher must produce and sell approximately 4,857 books to break even.

Let's denote the number of books produced and sold as "x."

The total fixed cost is given as $51,000.

The variable cost per book is $1.50, and since x books are produced and sold, the total variable cost would be 1.50x.

The selling price per book is $12, and since x books are sold, the total revenue would be 12x.

To break even, the total revenue must equal the total cost:

Total Revenue = Total Cost

12x = 51,000 + 1.50x

Subtracting 1.50x from both sides:

12x - 1.50x = 51,000

10.50x = 51,000

Dividing both sides by 10.50:

x = 51,000 / 10.50

x ≈ 4,857

Therefore, the publisher must produce and sell approximately 4,857 books to break even.

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Answer:

23x+250 and that would equal your total cost

Answer:

B

Step-by-step explanation:

[tex]tan^{2}\alpha (sec^{2} \alpha + cosec^{2} \alpha )\\\frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2}\alpha}+\frac{1}{sin^{2}\alpha})\\ \frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2} \alpha . sin^{2}\alpha} )\\\frac{1}{cos^{4}\alpha}\\= sec^{4}\alpha[/tex]

The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).

The area of a rectangle is expressed as:

Area = length × width

Given that,  the length of the pen will be 2 feet longer than the width, so the width is x feet and the length can be expressed as (x + 2) feet.

Using area of rectangle:

Area = length × width

1680 = (x + 2) × x

Simplify

1680 = x² + 2x

x² + 2x - 1680 = 0

Solve for x:

Using factoring

(x + 42)(x - 40) = 0

Hence:

x + 42 = 0 or x - 40 = 0

x = -42 or x = 40

Since we are dealing with dimensions, we use the positive value:

The valid solution is x = 40.

This represents the width of the horse pen.

The length can be found by adding 2 to the width:

Length = x + 2

Plug in x = 40

= 40 + 2

= 42

Therefore, the length is 42 feets.

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Answer:

The area is 44

Step-by-step explanation:

If you add the numbers that across from each other you would get 12+12+2+2+8+8= 44

Answer:

14/33

Step-by-step explanation:

1/3

= 1/3 x 11/11

= (1 x 11)/(3 x 11)

= 11/33

2/11

= 2/11 x 3/3

= (2 x 3)/(11 x 3)

= 6/33

1/3 - 2/11 + 9/33

= 11/33 - 6/33 + 9/33

= (11 - 6 + 9)/33

= (5 + 9)/33

= 14/33

Answer: attached in image, look at both

Step-by-step explanation:

The percentage of the marbles that are red is 22%

From the question, we have the following parameters that can be used in our computation:

Red = 500

Green = 750

White = 1000

Using the above as a guide, we have the following:

Percentage of red =Red/Total * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage of red =500/(500 + 750 + 1000) * 100%

Evaluate

Percentage of red = 22%

Hence, the percentage of red is 22%

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Answer:

  302 m²

Step-by-step explanation:

You want the area of the figure composed of a triangle and rectangle.

The formulas for the areas of the parts are given in the problem statement.

The base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...

  A = 1/2bh

  A = 1/2(8 m)(8 m) = 32 m²

The area of the rectangle is ...

  A = LW

  A = (18 m)(15 m) = 270 m²

The area of the figure is the sum of the areas of its parts:

  A = (triangle area) + (rectangle area)

  A = 32 m² +270 m² = 302 m²

The area of the figure is 302 m².

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The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

From the question, we have the following parameters that can be used in our computation:

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

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Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.

The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

To find a formula for the nth term of the sequence 250, 100, 40, we need to first determine the pattern or rule that generates the sequence. If we divide each term by the previous term, we get the following ratios:

100/250 = 0.4

40/100 = 0.4

We can see that each term is obtained by multiplying the previous term by the common ratio of 0.4.

So, the formula for the nth term of the sequence is:

an = a1* r(n-1)

where a1= 250 is the first term, r = 0.4 is the common ratio, and n is the term number.

The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

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compplete question:

What is a formula for the nth term of the given sequence 250,100,40

After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1

In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a  polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2   0   -5.6   1
    |    -1    0.8  -0.5
    -------------------
          2   -1   -4.8  0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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The value of x which could replace the missing value in the table so that y is not a function of x is; 7.

It follows from the task content that the value of x which could make y not a function of is required to be determined.

Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.

On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.

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Explanation, step-by-step

You would need two angles to know the lines are parallel

Answer:

Option : A

Step-by-step explanation:

To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:

Equation 1: 2x + y = -4 (multiply by 3)

Equation 2: 5x + 3y = -6 (multiply by 1)

Multiplying equation 1 by 3 gives us:

6x + 3y = -12

Multiplying equation 2 by 1 gives us:

5x + 3y = -6

Now we can subtract equation 2 from equation 1 to eliminate y:

(6x + 3y) - (5x + 3y) = -12 - (-6)

6x + 3y - 5x - 3y = -12 + 6

x = -6

Therefore, the x-coordinate of the solution to the system of equations is x = -6.

The correct option is: Ox=-6.[tex][/tex]

Entertainment will comprise 90% of Ryan's total budget. He will allocate 90% of his monthly income towards entertainment expenses.

According to the given information:

Let's assume Ryan's take-home pay is P dollars.

Assuming that Ryan puts aside 10% of his net income for his retirement plan, he will accumulate savings of 0.10P dollars.

After setting aside funds for retirement, the remaining portion of his net earnings will constitute 90% of the original amount, equating to 0.90P dollars.

Assuming that Ryan puts the remaining amount of his income towards entertainment, it is possible to determine the proportion of his overall expenses that entertainment would represent.

Percentage of entertainment budget = (Entertainment budget / Total budget) * 100

Given an overall budget of P dollars, with 0.90P dollars allotted for entertainment expenses, the proportion of the total budget that will be spent on entertainment can be calculated as a percentage.

Percentage of entertainment budget = (0.90P / P) * 100

Percentage of entertainment budget = 90%

So, entertainment will comprise 90% of Ryan's total budget.

He will allocate a monthly entertainment budget of 0.90P dollars, equivalent to 90% of his salary after taxes.

As such, the overwhelming majority of Ryan's budget will be allocated towards Entertainment. Every month, the entertainment allowance will constitute 90% of his net income as per the allocated budget.

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