Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues.
She has 210 different combinations.
What is meant by combinatorial methods?A new wave of research methodology called the combinatorial approach to materials seeks to greatly speed up the discovery and development of novel substances.
The area of mathematics concerned with finding solutions to conundrums involving the selection and arrangement of parts of particular (often finite) sets in line with predetermined norms.
Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues. Candidate solutions are combinations of solution elements that could be found while trying to find a solution, but they don't have to meet all the requirements.
So, she has [tex]$C_1^4=\frac{A H}{A \frac{A}{4}}=\frac{10 \times 2 \times 8 \times 7}{1 \times 2 \times 3 \times 4}=210$[/tex]
So she has 210 different combinations.
[tex]$c_{1=}^4=\frac{4 \%}{A f}$[/tex]
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Tim buys a new computer for $1200. After four years, he sells the computer to a friend for $450.
Let y represent the current value of the computer, and x represent the number of years. Write a
linear equation in slope-intercept form to model the value of the computer over time. Find the value
of the computer after 6 years.
A linear equation in slope-intercept form for computer; y = -187.5(x) + 1200.
The value of the computer after 6 years will be $75.
What is defined as the slope-intercept form?An intercept is a y-axis point whereby the slope of a line passes. It is the y-coordinate of a point on the y-axis at which a straight line or a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c is really the y-intercept.Tim spends $1200 on a new computer.
He sells this same computer to that of a friend for $450 after four years.
Let y represent the computer's current value and x depict the number of years.
Create a linear equation in slope-intercept pattern to model the computer's value over time.
y = mx + b
y = 1200,
when x (time) is 0, thus b = 1200
when x = 4, y = 450,
Calculate the slope m.
4m + 1200 = 450
4m = 450 - 1200
m = -750/4
m = -187.5
Put the value of m in linear equation;
y = -187.5x + 1200
Noe, the value of computer after 6 years, put x = 6.
y = -187.5(6) + 1200
y = 75
Thus, the value of the computer after 6 years will be $75.
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Domain and Range, PLEASE HELP!!
The domain for the given graph would be [-5,10] and range for the graph would be [0.4,5.6]. in both the case whether increasing or decreasing graph.
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). The entire range of independent variable values is the domain of a function.
What is range?The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.
How to find the domain and range in graph?Graphs can also be used to determine the domain and range of functions. The domain of a graph consists of all the input values shown on the x-axis because the domain refers to the set of possible input values. The range represents the set of possible output values shown on the y-axis.
Here, The domain would be [-5,10] as the graph is depicting.
The range would be[0.4,5.6].
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Determine which integer will make the inequality x − 4 < 16 true.
S:{16}
S:{20}
S:{21}
S:{32}
Answer:
x-4<16
x<16+4
x<20
S:[20] TRUE
( Please help )
Answer the question in photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
twenty-seven percent of primary care doctors think their patients receive unnecessary medical care. if required, round your answer to four decimal places.
Incomplete question.No requirement of question
Garden Avenue Middle School has 23 boxes of math books delivered each box contains 12 books a group of four Math teachers divide the books of evenly amongst the cells for their students how many books did each math teacher receive
Step-by-step explanation:
this is very roughly converted from the original question, I bet. no punctuation marks and, and ...
what I understood of the important information is :
there are 23 boxes of books with 12 books in each.
there are 4 teachers dividing the books evenly among themselves for their cells (classes ?) of students.
so, we need to divide the books by 4 to distribute them evenly into 4 parts.
23×12/4 = 23×3 = 69
each teacher got 69 books.
If possible, use the Law of Detachment to make a conclusion. If not possible to make a conclusion, explain why.
If there is lighting, then it is not safe to be out in the open.
Marla sees lighting from the soccer field.
Using the Law of Detachment, the conclusion is that it is not safe to be out in the open, as the conclusion is true, since the conditional and the hypothesis are true.
What is the Law of Detachment?The Law of Detachment is a logic axiom which states that if a conditional and the hypothesis are true, then the conclusion is also true.
Supposing a conditional statement p -> q, we have that:
p is the hypothesis.q is the conclusion.For this problem, the sentence is:
"If there is lighting, then it is not safe to be out in the open."
Hence p and q are given as follows:
p: presence of lightning.q: it is not safe to be out in the open.Marla sees lighting from the soccer field, hence the statement p is correct, and we know that the conditional is true, hence the conclusion that it is not safe to be out in the open can be reached.
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What are the roots of the roots of the function f(x)=x^2+2x-1?
Answer:
Exact form: x= -1 ± √2
Decimal Form: x= 0.41421356..., -2.41421356...
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros) replace with 0 and solve for x.
||3x-1|+5|<1 pls solve
Answer: No Solution
Step-by-step explanation:
||3x - 1| + 5| <1 ⇒
[tex]\left \{ {{|3x - 1| + 5 < 1} \atop {|3x - 1| + 5 > -1 }} \right.[/tex] ⇒
[tex]\left \{ {{|3x - 1| < -4} \atop {|3x - 1| > -6} \right.[/tex] ⇒
The first equation does not make sense because absolute value and as it is a system of equations, the whole system does not have a solution.
The sum of two consecutive odd number is 72.
PLEASE ANSWER PLEASE PLEASE I NEEDTHE ANSWER FAST PLEASE
Which equation represents the scenario above.
Responses
A 2x + 3 = 72
B 2x + 2 = 72
C 2x + 1 = 72
D 2x = 70
Answer: B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
let the 2 consecutive odd numbers be x and x + 2 , then the sum is
x + x + 2 = 72 , that is
2x + 2 = 72 → B
subtract 2 from both sides
2x = 70 ( divide both sides by 2 )
x = 35
x + 2 = 35 + 2 = 37
the 2 consecutive odd numbers are 35 and 37
HELP PLEASE!!
Write the slope intercept form of the equation for each line
Answer:
y = -5/9x
Step-by-step explanation:
Two points on the line; (4,-2) & (-5,3)
Finding the slope (m):
m = (3-(-2))/(-5-4)
= 5/-9
= -5/9
y = -5/9x + c
Since it passes through the origin, c = 0.
Hence, y = -5/9x
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85 cubed in all three forms exponential form expanded form and you add evaluate
The cube of the number five is written in these following forms:
Exponential: 5³.Expanded form: 5 x 5 x 5.Evaluation: 125.How to calculate the cube of a number?The cube of a number n is equivalent to multiplying the number n by itself three times.
Hence, in expanded form, the cube of a number n is written as follows:
n x n x n.
In exponential form, the cube of a number n is written as follows:
n³.
In this problem, the number of interest is the number five, hence:
In exponential form, the cube of 5 is given by: 5³.In expanded form, the cube of 5 is given by: 5 x 5 x 5.The result of the expression, which is the evaluation, is given by:
5 x 5 x 5 = 25 x 5 = 125.
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prove that,
b) (a + b)2 = (−a − b)2
c) (a − b)2 = a2 − 2ab + b2
We will prove both of the identities by expanding the exponents, only in the first one we need to use a little trick that is multiplying by (-1)^2 = 1.
How to prove the identities?
Let's start with the first one:
(a + b)^2 = (- a - b)^2
We can start with the left side and write:
(a + b)^2 = (a + b)*(a + b)
Now, remember the rule of signs:
(-1)*(-1) = 1
So we can multiply by one the expression above and get:
(a + b)*(a + b) = (a + b)*(a + b)*1 = (a + b)*(a + b)*(-1)*(-1)
Now we can reorder the product to get:
(a + b)*(a + b)*(-1)*(-1) = (-1)*(a + b)*(-1)*(a + b) = (-a - b)*(-a - b) = (-a - b)^2
So we proved the first part, now the second one:
(a - b)^2
Let's just expand this:
(a - b)^2 = (a - b)*(a - b) = a*a + a*(-b) + (-b)*a + (-b)*(-b) = a^2 - 2ab - b^2
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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800. The law firm designated twice as many partners as associates to the case and was able to charge the client $17600 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.
EquationLet variable x =represent the number of associates, assigned to the case
Let variable y represent number of partners assigned to the case.
The system of equations re:
800 x + 1800 y = 17600
y = x + 2
Plug equation 2 in equation 1, we get,
800 x + 1800(x+ 2) = 17600
2600 x + 3600 = 17,600
Collect like terms
2400 x = 14,000
Divide both side by 2400x
x = 14,000 / 2400
x = 5.8
x = 6 (Approximately)
So,
y = x + 2
y = 5.8 +3
y = 7.8
y = 8 (Approximately)
Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.
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Select a month. Then select 2020 or 2025.
How many outcomes are there?
Answer:
September2020
13outcomes
Help me please with this math question
Answer:
40°
Step-by-step explanation:
By the exterior angle theorem, [tex]m\angle 1=100^{\circ}[/tex]. Applying the theorem again, we get [tex]m\angle 2=40^{\circ}[/tex]
Show all work to multiply: (3+sqrt(-16)(6-sqrt(-64)
Please only CORRECT ANSWERS. Don't answer if you don't know.
Answer:
50
Step-by-step explanation:
Complex numbers:i^2 = -1
First simplify the radicals. Then use FOIL method
[tex]\sf (3 + \sqrt{-16})(6-\sqrt{-64}) = (3 +\sqrt{i^2*4^2})(6-\sqrt{i^2*8^2})[/tex]
= ( 3 + 4i)(6 -8i)
= 3*6 - 3*8i + 4i*6 - 4i*8i
= 18 - 24i + 24i - 32i^2
= 18 - 24i + 24i - 32*(-1)
= 18 - 24i +24i + 32
= 18 + 32 - 24i + 24i
Combine like terms,
= 50
Craig has a job washing cars. He earns $28 for each car he washes. On Monday, he washed 7 cars. On Tuesday, he forgot to count how many cars he washed. He earned $448 for the two days. Josiah wants to find how many cars he washed on Tuesday.
Answer:
9.
he washes 9 cars on Tuesday.
Step-by-step explanation:
28 * 7 = 196.
448 - 196 = 252
252 / 28 = 9
On solving the linear equation 28x + 196 = 448, we get that Craig washed 9 cars on Tuesday.
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting , multiplying or dividing same number to both sides.
Given that Craig washes cars and earns $ 28 for each car . He washed 7 cars on Monday.
Let on Tuesday he washed x cars
Total money earned on Tuesday and Monday by Craig = $448
Money earned on Monday = $ 7× 28 = $ 196
Money earned on Tuesday = $ x×28 = $ 28x
⇒ 28x + 196 = 448
Subtracting 196 from both sides we get
⇒ 28x + 196 -196 = 448 - 196
⇒ 28 x = 252
Dividing both sides by 28
⇒ x = 252/28 = 9
Therefore, Craig washed 9 cars on Tuesday.
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write a paragraph proof for the following
Proved that ∠ 2 = 107° because these two angles are supplementary angles .
What are supplementary angles ?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. If the two additional angles are combined, they create a straight line and an angle.
However, it should be emphasized that the two complementary angles do not necessarily need to be close to one another. As a result, any two angles can be supplementary if their sum is 180 degrees. However, it should be emphasized that the two complementary angles do not necessarily need to be close to one another. So, if two angles are complementary, they can be any two angles.
Given : ∠ 1 and ∠ 2 are supplementary angles
that is ∠ 1 + ∠2 = 180 °
Given ∠ 1 = 73°
thus when we substitute this value in the equation we get ∠ 2 = 180 - 73
∠ 2 = 107 °
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The width of a rectangle is 3 more than half the length of the perimeter is 174 inches what is the length of the rectangle
(66 inches) because i don't know
but my answer is correct
Order from LEAST TO GREATEST
15%,14.8, 154/5 , 1450%
Answer:
assuming the percents are out of 100 the order is
14.8 then 15% then 154/5 then 1450%
if thats not the case let me know and i'll correct it
Step-by-step explanation:
15% of 100 = 15
154/5 = 30.8
1450% of 100 = 1450
If m/A = 3x – 15, find the values for x that would ensure is an acute angle
Answer: 5<x<35
Step-by-step explanation:
An acute angle ranges from 0 to 90 degrees.
[tex]0 < 3x-15 < 90\\\\15 < 3x < 105\\\\5 < x < 35[/tex]
Here is a data set:
1 2 3 3 4 4 4 4 5 5 6 7
A. For the data set with the value of 70, why would the median be a better choice for the measure of
center than the mean?
For the given data set, median is better choice for measure than mean because:
Median is usually a better measure of the center when there are extreme values as it is remains unaffected by the precise numerical value. The most common measure of the center is mean.
What is median and mean?Adding all numbers in the data and dividing it by the number of values in the set gives mean of a data. Whereas, median is the middle value in a data set, implying that 50% of data points can have a value smaller or equal to the median and 50% of data points can have a value higher or equal to the median.
For a small data set, firstly, count the number of data points and arrange them in increasing order. If the number of data is odd, then add 1 to the number and divide the result by 2 to obtain the rank of the data whose value is the median.
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The mean of 10,31,36,36,38,42,47,48,49,52
Step-by-step explanation:
Mean means the average
So to find the average, add all the numbers then divide by how many numbers there are.
Total=389
Divide by 10 = 38.9
5. Zach had a salary of $75,000 last year. He also received $4,500 in interest income from a CD he opened a few years ago. He contributed $4,000 to an IRA and had to move to another state for his new job. His moving expenses were $5,000. He is an unmarried man, with no dependents, and claims himself as an exemption. Standard deduction is $5700 for single, and exemption rate is $3,650 per exemption. What was Zach’s gross income?
Zach’s gross income was $79,500.
What is gross income?Gross income or gross pay for an individual is the total financial income that he or she earns before paying taxes or other deductions. Wages, dividends, capital gains, company revenue, retirement distributions, and other income are all included in your gross income. Salary, bonuses, tips, hourly pay, rental income, dividends from stocks and bonds, and savings account interest are all examples of earned income.Given:
Zach's salary = $75,000
His interest income from a CD = $4,500
Expenses = $5,000
Contribution to an IRA = $4,000
Standard deduction = $5700
Exemption rate = $3,650
Zach’s gross income = Salary + interest income
= $75,000 + $4,500
= $79,500
Therefore, Zach’s gross income was $79,500.
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WILL MARK BRAINLEIST!!
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
-4
-5
5
4
Answer:
k = 5
Step-by-step explanation:
f(x) = x + 4
g(x) = x + 9 = (x + 5) + 4 = f(x + 5)
So k = 5
b) The nearest-known exoplanet from earth is 4.25 light-years away. About how many miles is this? Give your answer in standard form. Please Help
4.25 light years is 2.4984x10¹³ miles
What is light years?
A light-year, sometimes spelt light year, is a huge measure of length used in astronomy that is comparable to approximately 9.46 trillion kilometers (9.461012 kph) or 5.88 trillion miles (5.881012 mi). A light-year, as defined by the International Astronomical Union (IAU), is the distance that light travels in a vacuum in one Julian year (365.25 days). The phrase light-year is frequently misconstrued as a unit of time since it contains the time-measurement word "year." The light-year is most commonly used in non-specialist contexts and popular scientific publications to indicate distances to stars and other cosmic distances.
1 light years is = 5.8786x10¹² miles
4.25 light years = 5.8786x10¹²x4.25 = 2.4984x10¹³ miles
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Rachel is making premade 3-inch by 5-inch tile rectangles for her driveway. If it takes her 6 minutes to position each rectangle, how many hours will it take her to create a 2-foot by 4-foot pattern drive? Write your answer as a decimal. (ASAP)
The time taken to create the driveway is 7 hours 42 minutes
The dimensions of the rectangle tile = 3 inch by 5 inches
The area of the rectangle tile = Length × width
= 3×5
= 15 square inches
Time taken to position each rectangle = 6 minutes
The dimensions of the driveway = 2 foot by 4 foot
Convert the dimensions to inches
2 foot by 4 foot = 2×12 inches by 4×12 inches
= 24 inches by 48 inches
The area = Length × Width
= 24×48
= 1152 square inches
Number of tiles needed = Area of the driveway/ Area of the tile
= 1152/15
= 76.8
≈77 tiles
Time taken to create the drive way = Number of tile× Time taken to position each rectangle
= 77×6
= 462 minutes
= 7 hours 42 minutes
Hence, the time taken to create the driveway is 7 hours 42 minutes.
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Picture below.
Help pls
x = 5 is the value of x in exterior angle.
Why is this term "exterior angle" used?
They are created on the polygon's exterior or exterior side. Since they both lie on the same straight line, the total of an inner angle and its matching outside angle is always 180 degrees. The exterior angles of the polygon in the figure are 1, 2, 3, 4, and 5.∠QRS is exterior angle .
apply exterior angle theorem in ΔPQR
So, ∠QRS = ∠PQR + ∠RPQ
8x - 9° = 3x + 12° + 3x - 11°
8x - 9 = 6x + 1
8x - 6x = 1 + 9
2x = 10
x = 10/2
x = 5
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Angela’s bedroom has an area of (2x2-7x-15) square feet. The length of the room is (2x+3) feet. What is the width of her bedroom?
The width of her bedroom is x - 5
How to determine the widthIt is important to note that the formula for area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the roomw is the width of the roomNow, let's substitute the values into the formula, we have;
2x²-7x-15 = (2x+3)w
Divide both sides by the coefficient of w
w = 2x²-7x-15/(2x+3)
Factorize the numerator
w = 2x²- 10x + 3x - 15/(2x+3)
Factor the common terms of the numerator
w = 2x(x - 10) + 3(x - 5)/(2x+3)
enclose the expressions
w = (2x + 3)(x-5)/(2x+3)
Divide the common terms
w = x - 5 feet
Hence, the value is x - 5
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