When not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.
How to determine in how many ways can this be done if the order of choices is not taken into considerationWhen choosing 2 letters without replacement from the 3 letters a, b, and c, the number of ways can be calculated considering the order of choice and without considering the order of choice.
1. Considering the order of choice:
In this case, the order in which the letters are chosen matters. We can think of this as a permutation problem.
To calculate the number of ways when order matters, we use the formula for permutations:
[tex]nPr = n! / (n - r)![/tex]
where n is the total number of items and r is the number of items chosen.
In this case, we have 3 letters and we want to choose 2, so n = 3 and r = 2.
Using the formula, we get:
[tex]3P2 = 3! / (3 - 2)![/tex]
[tex]= 3! / 1![/tex]
= 3
Therefore, when considering the order of choice, there are 3 ways to choose 2 letters from a, b, and c.
2. Without considering the order of choice:
In this case, the order in which the letters are chosen does not matter. We can think of this as a combination problem.
To calculate the number of ways when order does not matter, we use the formula for combinations:
[tex]nCr = n! / (r!(n - r)!)[/tex]
Using the same values of n = 3 and r = 2, we get:
[tex]3C2 = 3! / (2!(3 - 2)!)[/tex]
= [tex]3! / (2! * 1!)[/tex]
= 3
Therefore, when not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.
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I WILL GIVE BRAINLYEST
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
A group of adults were asked how many children they have in their families. The bar graph below
shows the number of adults who indicated each number of children.
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%.
What does a bar graph show?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:
4 families have zero children.5 families have one children.5 families have two children.2 families have three children.One family has five children.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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Find the measure of Zb.
←
Zb=
Blank 1:
76 a
104/b
∠b and 76° are alternate angles. They are equal.
So, m∠b = 76
That's it :)
Which of the following functions is graphed below? HELP
The equation of the functions represented on the graph are (b)
Which of the functions is represented on the graph?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:
Interval 1: Closed circle that stops at 1Interval 2: Open circle that starts at 1When 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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What is a formula for the nth term of the given sequence?
Select Explicit Formula for Sequence
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
If h(x) is a function created by combining two functions by multiplication and h(x) = 2x² + 5x-3, which could be true
of the two component functions?
The component functions must both be linear.
O The component functions must both be quadratic.
The component functions must have y-intercepts with different signs.
The component functions must have increasing or accelerating rates of change.
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.
Pls show how you found the answer.
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]
For the quadratic equation 2x² - 6x + 7 = 0, enter the correct values of a, b, and c.
X =
-b ± √√b² - 4ac
2a
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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Samantha wants to enclose 1680 ft² for a rectangular horse pen. The length will be 2 ft longer than the width. Find the dimensions of the pen. (Hint: A = lw)
The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).
What are the dimensions of the rectangular horse pen?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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help me ASAP pleaseee
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)
How do we solve for the complex (a + bi) form?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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find the area of the figure 8m, 5m 5m, 15m, 18m A= [?] m^2
Answer:
302 m²
Step-by-step explanation:
You want the area of the figure composed of a triangle and rectangle.
AreaThe formulas for the areas of the parts are given in the problem statement.
TriangleThe 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
RectangleThe area of the rectangle is ...
A = LW
A = (18 m)(15 m) = 270 m²
FigureThe 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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A bag of marbles is being sold in a store. The box says that there are 500 red marbles, 750 green marbles, and 1,000 blue marbles inside. What percent of the marbles are red? Round the percentage to the nearest whole number
The percentage of the marbles that are red is 22%
Calculating the percentage of the marbles are red?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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Will Give Brainliest Please Help!
Question 11
Explanation, step-by-step
You would need two angles to know the lines are parallel
What is one value of x that could replace the missing value in the table
The value of x which could replace the missing value in the table so that y is not a function of x is; 7.
What is the missing value of x that could make y not a function?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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Which value is a solution of the equation c + 14 = -20? A: -34 B: -6 C: 6 D: 34
ABDE is a parallelogram.
AB=AC
B
Show that x = 38°
A
C
82°
D
68%
E
Not drawn
accurately
[3 marks]
The proof that the value of x is 38° is shown below
How to show that the value of x is 38°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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factorise P(x)=2x*3-5.6x+1
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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At a high school, the probability that a student takes a science class and a history class is 0.48. The probability that a student takes a science class is 0.82, and the probability that the student takes a history class is 0.64. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?
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.
What is the probability?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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Deepak stacked 14 copies of the same book. each book is 1 3/8 inches thick. How high is the stack?
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 bedroom, garage, office, and bathroom of a house will be painted, each with a different color. There are 15 colors to choose from. This means that there are ________ color arrangements possible.
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
Can someone please help me? I need this fast and it’s really important that I get it right. Graph the function shown in the image.
Answer: attached in image, look at both
Step-by-step explanation:
Assume that ryan does save 10% for retirement if he allocate the remainder of his take-home pay to entertainment then what percent of the total budget will entertainment compromise how much money will the budget towards entertainment in each month
Entertainment will comprise 90% of Ryan's total budget. He will allocate 90% of his monthly income towards entertainment expenses.
How to solveAccording 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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A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $51,000, and variable costs (printing, paper, binding, shipping) at $1.50 for each book produced. If the book is sold to distributors for $12 each, how many must be produced and sold for the publisher to break even?
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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Find the quotient and remainder using synthetic division.
x^4
-
3
x^3
+
9
x
+
6/
x
+
1
The quotient is
The remainder is
The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1 using synthetic division is x³ + 2x² - 2x + 7 and the remainder is 13
Finding the quotient and remainder using synthetic divisionFrom 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.
What is 1/3-2/11+9/33?
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
A reservoir for storing water is in the shape of a large cylinder on a circular base and is 10cm in depth when it holds a million litres of water. (a) Find the diameter to the nearest metre. (b) what will be the diameter if it hold only 250,000litre(take 1litre=1000cm)
The diameter of the reservoir is:
Part (a): 112.86 m
part (b): 56. 44 m
How to find the diameter of the reservoir?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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.
What is the x-coordinate of the solution to the following system of equations?
2x + y = -4
5x + 3y = -6
Ox=-6¹
Ox=6
Ox = -8
Ox=8.
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]
I need the answer to the problem
Need help on this!!!!!!!!
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
A. How to determine the greatest number of packagesGiven 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
B. How to determine the volume of the part that is filledRecall 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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bryan’s hockey team is purchasing jerseys the company charges 250$ for a one time set up fee and 23$ for each printed jersey which expression represents the total cost of x number of jerseys for the yeam
Answer:
23x+250 and that would equal your total cost
