Therefore, there are 21 possible selections of two individuals from a group of seven people.
What is combination?In mathematics, a combination is a way of selecting a subset of objects from a larger set, where the order of selection does not matter. Combinations are also known as unordered selections or combinations without repetition. The number of combinations of k objects that can be selected from a set of n distinct objects is denoted by "n choose k" and is given by the formula: n choose k = n! / (k! (n - k)!) where n! is the factorial of n, defined as the product of all positive integers up to and including n, and k! and (n-k)! are the factorials of k and n-k, respectively. In words, this formula says that the number of combinations of k objects that can be selected from a set of n objects is equal to the number of ways to arrange k objects out of n, divided by the number of ways to arrange the remaining n-k objects.
Here,
To determine the number of possible selections of two individuals from a group of seven people, we can use the formula for combinations:
nCk = n! / (k! (n - k)!)
where n is the total number of individuals in the group, and k is the number of individuals to be selected. In this case, we want to select 2 individuals from a group of 7, so we have:
n = 7
k = 2
Substituting these values into the formula, we get:
7C2 = 7! / (2! (7 - 2)!)
= 7! / (2! 5!)
= (7 x 6 x 5!) / (2 x 1 x 5!)
= (7 x 6) / (2 x 1)
= 21
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Arrange 5/9,2/3 and 8/21 in ascending order of magnitude
Answer:
2/3/5/8/9/21 I hope it is able to help you
50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
Answer:
20
Step-by-step explanation:
If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines
Please check my answers and give explanation of why it is wrong if it is wrong 20 points!
The solution is, the correct option is, A.) tan 37 = x/12.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
now, from the given figure we get,
tan 37 = x/12
Hence, The solution is, the correct option is, A.) tan 37 = x/12.
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What is the conversion of 65f to c ?
65 °F is equal to 18.3333 °C.
A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).
Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.
To convert a temperature from Fahrenheit (°F) to Celsius (°C),
We can use the following formula:
°C = (°F - 32) x 5/9
Where °C is the temperature in Celsius
°F is the temperature in Fahrenheit.
Substituting 65 for °F,
We get:
°C = (65 - 32) x 5/9
Simplifying the expression:
°C = 33 x 5/9
°C = 18.3333333333
Therefore, 65 degrees Fahrenheit is equal to nearly 18.3333 degrees Celsius (rounded to four decimal places).
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scatter plot that shows a positive association that is not linear.
Yes, it is possible to have a scatter plot that shows a positive association that is not linear.
What is the scatter plot?
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
In a scatter plot, a positive association means that as the values of one variable increase, the values of the other variable tend to increase as well.
However, the relationship between the variables does not have to be linear.
In other words, the pattern of points on the plot does not have to form a straight line.
For example, the relationship between two variables could be curved, such as a quadratic relationship where the increase in one variable initially leads to larger increases in the other variable, but at higher levels of the first variable, the increase in the second variable begins to level off.
Alternatively, the relationship could be exponential, where the increase in one variable leads to an exponential increase in the other variable.
In both cases, the pattern of points on the scatter plot would show a positive association, but not a linear one.
Therefore, it is true that scatter plot that shows a positive association is not linear.
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Turn the (a) Are they taking the test? (b) Write a letter. a lette (c) Don't make a noise. (d) Please bring some noodles. (e) Let him complete his work. (f) Does she compose poems? (g) Has she composed a song? (h) Did he To following sentences into passive voice. Opleted Linder
I need help ASAP
what is the domain of y=-16x^2+1700
The domain of the equation y = -16x^2 + 1700 is the set of all real numbers.
Explanation:
To find the domain of the equation y = -16x^2 + 1700, we need to determine the set of all real numbers for which the equation is defined.
Since the equation is a quadratic equation, it is defined for all real values of x. There are no restrictions on the values of x that can be plugged into the equation.
Therefore, the domain of the equation y = -16x^2 + 1700 is the set of all the real numbers.
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What are the coefficients of the product
(5y-3)^2 ?
A: -30
B: -6
C: 9
D: 10
E: 25
The value of the coefficient of the product is equal to - 30. (Correct choice: A)
How to determine the value of coefficient in a quadratic equation
The expanded form of a quadratic equation includes three real coefficients, whose definition is shown below:
(a · x + b)² = a · x² + 2 · a · b · x + b · x²
The coefficient of the product is the element 2 · a · b of the expanded form. If we know that a = 5 and b = - 3, then the coefficient of thre product is:
2 · a · b = 2 · 5 · (- 3)
2 · a · b = - 30
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Kaylee conducted a scientific experiment. For a certain time, the temperature of a compound rose 1 1/2 every 3/5 of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose?
The rate, in degrees per hour, that the temperature of the compound rose was 5/2
In Kaylee's scientific experiment, she is interested in the rate at which the temperature of a compound is rising. To answer this question, we need to use mathematics to determine the rate, in degrees per hour, that the temperature of the compound rose.
Using the information provided, we can set up a proportion to solve this problem.
We can represent the rate of temperature rise during a certain time period as a/b, where a is the temperature rise and b is the time period.
We can then set this equal to the rate of temperature rise per hour, c/1. Therefore, we have a/b = c/1.
We are told that the temperature rose 1 1/2 every 3/5 of an hour, so a = 1 1/2 and b = 3/5.
Therefore, we can solve for c to get c = 5/2.
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Which of the following people is/are legally required to file a tax return?
Amanda, who can be claimed as a dependent and earned $850 last year,
Greg, who can be claimed as a dependent and earned $12,650 last year.
Jason, who cannot be claimed as a dependent and earned $1,500
lEst earo cannot be claimed as a dependent and carned $1,000
last year.
Greg and Jason are the people who are legally required to file a tax return.
What is Tax?An amount of money that a government requires people to pay according to their income
Amanda, who can be claimed as a dependent and earned $850 last year, is not required to file a tax return.
The minimum income requirement for filing taxes for dependents is $1,100 for 2022.
Greg, who can be claimed as a dependent and earned $12,650 last year, is required to file a tax return if his earned income (such as wages or salary) exceeds $12,400 in 2022.
However, if his earned income is less than $12,400 but he had any taxes withheld, he may want to file a tax return in order to claim a refund.
Jason, who cannot be claimed as a dependent and earned $1,500 last year, is required to file a tax return if his gross income exceeds $12,950 in 2022.
Lester, who cannot be claimed as a dependent and earned $1,000 last year, is not required to file a tax return.
The minimum income requirement for filing taxes for single taxpayers under age 65 is $12,950 for 2022.
Hence, Greg and Jason are the people who are legally required to file a tax return.
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Which of these fractions are terminating decimals
9/20
1/35
14/35
1/16
Out of the given fractions, 9/20, 14/35, and 1/16 are terminating decimals, while 1/35 is a non-terminating decimal.A terminating decimal is a decimal number that ends or terminates after a finite number of digits.
In other words, the decimal representation of the fraction does not go on forever.
To determine if a fraction is a terminating decimal, we need to convert it into a decimal by dividing the numerator by the denominator. If the result is a finite decimal, then the fraction is a terminating decimal; otherwise, it is a non-terminating decimal.
Now, let's apply this method to the fractions given in the question:
9/20: To convert 9/20 into a decimal, we divide 9 by 20, which gives 0.45. Since the decimal terminates after two digits, 9/20 is a terminating decimal.
1/35: To convert 1/35 into a decimal, we divide 1 by 35, which gives 0.02857142857... The decimal goes on forever, so 1/35 is a non-terminating decimal.
14/35: To convert 14/35 into a decimal, we divide 14 by 35, which gives 0.4. Since the decimal terminates after one digit, 14/35 is a terminating decimal.
1/16: To convert 1/16 into a decimal, we divide 1 by 16, which gives 0.0625. Since the decimal terminates after four digits, 1/16 is a terminating decimal.
In summary, out of the given fractions, 9/20, 14/35, and 1/16 are terminating decimals, while 1/35 is a non-terminating decimal.
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What is the equivalent fraction for the following fraction using 5 as the multiplier?
Will give brainlest!!!
3/8
Answer:
Step-by-step explanation:
The answer is 15/40
Because 3 times 5 is 15 and 8 times 5 is 40
Answer:
15/40
Step-by-step explanation:
the equivalent fraction for 3/8 using 5 as a multiplier is :
3 x 5 / 8 x 5
= 15 / 40
A dish has an area of 400 square inches. What is the length of the radius rounded to the nearest tenth of an inch?
Answer:
11.3 inches
4th option
Step-by-step explanation:
Area of a circular object = πr² where r = radius
Given area = 400 square inches,
πr² = 400 square inches
r² = 400/π
r = √(400/π)
r = 20/√π
= 11.3 inches rounded to one decimal place(tenth)
-0.75, -3, -12, -48... Find the 9th term
Answer:
-49,152
Step-by-step explanation:
if you multiply -0.75, times 4 it equals -3 so do that until you get the ninth term. (Multiply each term by 4).
how to convert 50 mph to kmh?
The speed of 50 mph is equivalent to 80.47 km/h.
Mph is an abbreviation for miles per hour, and it is a unit of measurement commonly used in the United States. On the other hand, km/h stands for kilometers per hour, and it is a unit of measurement commonly used in most other countries.
To convert 50 mph to km/h, we need to use a conversion factor that relates the two units.
The conversion factor we need to use in this case is 1 mile = 1.60934 kilometers. This means that for every mile covered, there are 1.60934 kilometers covered. To convert 50 mph to km/h, we simply need to multiply 50 by the conversion factor, as shown below:
50 mph x 1.60934 km/mi = 80.47 km/h
Therefore, 50 mph is equivalent to 80.47 km/h. This means that if you were driving at 50 mph in the United States, you would be traveling at a speed of 80.47 km/h if you were to convert to km/h in another country.
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Yoni drove a total of 9/24 of a mile on Tuesday and Wednesday. She drove 1/6 of a mile on Tuesday.
How far did Yoni drive on Wednesday?
9/24mile
1/6 mile
5/24mile
24 miles
As per the total distance, the distance that Yoni drive on Wednesday is option (c) 5/24 miles.
To find out how far Yoni drove on Wednesday, we must first determine the total distance she drove over the two days.
Tuesday, Yoni drove 1/6 of a mile, which can be expressed as 6/24 of a mile. Wednesday, she drove an additional 9/24 of a mile.
This means that, in total, she drove 15/24 of a mile.
Since we already know that Yoni drove 6/24 of a mile on Tuesday, we can subtract this amount from the total distance she drove over the two days to find out how far she drove on Wednesday.
Subtracting 6/24 of a mile from 15/24 of a mile, we get 9/24 of a mile, which is the distance Yoni drove on Wednesday.
Therefore, Yoni drove 5/24 of a mile on Wednesday
Then the correct option is (c).
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Triangle XYZ has verticals eggs one negative one why 34 in Z bar negative one Nico rotated the trailer 90° counterclockwise about the origin what is the correct side of image points for the triangle XYZ
The image of vertex Z after a 90 degree counterclockwise rotation about the origin is (-34, -1). To find the coordinates of the image points for X and Y, we would need to know their coordinates as well.
How to calculate the the correct side of image points?Although the question is a little challenging to understand as worded, I'll do my best to respond.
Here is what I believe you are asking, assuming "verticals eggs" is a typo and you meant "vertex angles" and "Z bar" is a typo and you meant "Z = (-1, 34)":
Triangle XYZ has vertex angles at X and Y and vertices at X, Y, and Z. Pointed at is Vertex Z (-1, 34). What are the coordinates of the picture points for the triangle XYZ if the triangle is rotated 90 degrees anticlockwise about the origin?
We can use the following rotation matrix to rotate the origin 90 degrees anticlockwise:
R = [sin(90); cos(90); cos(90)-cos(90)]
R = [0 -1; 1 0]
We may represent the coordinates of each point in the triangle as a column vector and then multiply by the rotation matrix to apply this matrix to each point in the triangle:
[X'; Y'] = R * [X; Y]
[Z'] = R * [Z; 1]
(Notice that we make the Z coordinate a homogeneous coordinate by adding a third component of 1 to it.)
We are unable to provide the precise coordinates of the image points without knowing the X and Y coordinates. However, we can multiply matrices using the Z coordinate that is provided:
[Z'] = R * [-1; 34; 1]
[Z'] = [(-1) * 0 + 34 * (-1) + 1 * 0; (-1) * 1 + 34 * 0 + 1 * 0; (-1) * 0 + 34 * 0 + 1 * 1]
[Z'] = [-34; -1; 1]
Hence, vertex Z's image following a 90° anticlockwise rotation of the origin is (-34, -1). We would also need to know their coordinates in order to determine the coordinates of the image points for X and Y.
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What is the Value of G?
The value of g in the intersected lines is 28 degrees.
How to find angles?When lines intersect, angle relationships are formed such as linear angles, adjacent angle, vertically opposite angles. Therefore, let's find the angle g in the intersected lines as follows:
Therefore,
g + 43 = 71
subtract 43 from both sides of the equation'
g + 43 - 43 = 71 - 43
g = 28
Therefore,
g = 28 degrees
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A lightbulb consumes 600 watts per day. How long does it take to consume 3450 watt hours
5.75 hours long to consume 33450 watt hours
The time it takes for a lightbulb to consume 3450 watt hours can be calculated using the formula: time = energy/power. In this case, the energy is 3450 watt hours and the power is 600 watts.
To find the time, we can plug the values into the formula:
time = 3450 watt hours / 600 watts
time = 5.75 hours
Therefore, it takes 5.75 hours for the lightbulb to consume 3450 watt hours.
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Express 4 + ln 2 - ln 4 as a single natural logarithm. a. ln 2 b. ln 4 c. ln 64
The single natural logarithm expression is ln(2). Therefore, correct answer is (a)
Logarithmic Equations:The expression in the form [tex]e^a=b[/tex] can also be written as In b = a which is called as logarithmic expression.
Properties of Logarithms:
1. In (mn) = In m + In n
2. In [tex]a^m =[/tex] m In a
3. In [tex]e^a[/tex] = a.
How to express as a single natural logarithm?The natural logarithm expression is:
4 + ln 2 - ln 4
Apply the product and quotient rule of natural logarithm:
4 + ln 2 - ln 4 = In (4 × 2/4)
Evaluate the quotient:
4 + ln 2 - ln 4 = In (2)
Hence, the single natural logarithm expression is ln(2).
The correct option is (a)
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Answer:
B: ln 4.
Step-by-step explanation:
Calculate the amount that will be in the bank after 5 years if R4 700 is invested at 5% simple interest
Answer:
R4700×5% = 235
total: R4700+235 = 4935
invest:R235 per month or year
Step-by-step explanation:
interest simple is increase your amount to addition increase from rate 5%
I use format a calculate that answer
area is determined by what type of measurement?
Area is calculated using length measurements, specifically measurements of two dimensions of a flat or planar shape, such as length and width. The resulting value represents the amount of space occupied by the shape on a flat surface.
Area is commonly measured in square units such as square metres ([tex]m^{2}[/tex]), square feet ([tex]ft^{2}[/tex]), square inches ([tex]in^{2}[/tex]), and so on.
To calculate the area of a flat shape, multiply its length and width by the appropriate unit of measurement.
Area = Length x Width
Similarly, to find the area of a circular surface, we would use the formula for the area of a circle:
Area = π x (Radius)^2
[tex]Area = \pi . (r)^2[/tex]
where π is the mathematical constant pi, and the radius is half the diameter:
So, area is a measure of the amount of space occupied by a flat or planar shape and is calculated using length measurements.
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how much is 120 euros to dollars
By using the current currency exchange rate , the value of 120 Euros is equivalent to $128.4 .
The "Euro" is the official currency of the European Union, which includes 19 of its member states. and The "US dollar", is official currency of the United States.
The Currency Exchange Rate between euros and dollars can vary depending on market conditions, but
The current exchange rate is approximately 1 euro = 1.07 US dollars.
By using this exchange rate, we can calculate that 120 euros is equal to ;
⇒ 120 euros × 1.07 US dollars/euro = 128.4 US dollars .
Therefore, 120 euros is equivalent to 128.4 US dollars at the current exchange rate.
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Use <,>, or =
1.9 ? 1.90
0.05 ? 0.2
3.88 ? 6.38
The comparision between decimal number are 1.9 = 1.90, 0.05 < 0.2, 3.88 < 6.38
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system.
Therefore, one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Here we can see that
1.9 = 1.90
0.05 < 0.2
3.88 < 6.38
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The system of equations below represents the amount in dollars that Brianna paid for 5 paint brushes and 3 art canvases and Ahmed paid for 10 paint brushes and 6 art canvases. {5x+3y=4710x+6y=94 Did Brianna and Ahmed pay the same price for the items?
There is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
What is the system of equations?
A system of equations is a set of one or more equations that are to be solved simultaneously. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.
In this case, the system of equations represents the amount that Brianna and Ahmed paid for 5 paintbrushes and 3 art canvases, and 10 paintbrushes and 6 art canvases, respectively. The system of equations is:
5x + 3y = 47 (Brianna's purchase)
10x + 6y = 94 (Ahmed's purchase)
To determine whether Brianna and Ahmed paid the same price for the items, we can compare the value of x and y that satisfy both equations. To do this, we can solve the system of equations using any method we prefer, such as elimination or substitution. Here, we'll use the method of substitution:
From the first equation, we can solve for y in terms of x:
5x + 3y = 47
3y = 47 - 5x
y = (47 - 5x)/3
Substituting this expression for y into the second equation, we get:
10x + 6y = 94
10x + 6((47 - 5x)/3) = 94
Simplifying, we get:
10x + 94 - 10x = 94
94 = 94
This equation is always true, regardless of the value of x.
Therefore, there is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
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On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
The true statement about Graphed Function is:
f(x) > 0 over the interval (–∞, –4)
What is Interval in graph?A graph is referred to be an interval graph if each of its vertices can be connected to a real line interval in such a way that two vertices are only connected if and only if the connected intervals have a nonempty intersection.
Given:
Our curve has a minimum at (-2.5, -12)
Our curve has a maximum at (0, - 3)
We know that the curve crosses the x-axis at (-4, 0) and y-axis at (0, -3)
At the value x = -2.5 > (-4) the function is negative.
So, f(-2.5) = -12
f(-4) = 0
As a result, it is clear that the function is negative after f(x) crosses the x-axis at x = -4.
This implies that the function must be positive prior to that point.
Thus, the function > 0 for x values less than -4.
f(x) > 0 if x < -4
From this, we can conclude that in the range (-∞, –4), the function is above the x-axis.
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solving systems of equations by substitution examples 3x + y = 13. 5x -2y = 7.
Answer:
x = 3, y = 4
Step-by-step explanation:
3x + y = 13
5x - 2y = 7
To solve by substitution, you solve one of the equations for a variable, and then plug it into the other equation.
I'm going to choose to solve the first equation for y, as that will be the easiest.
y = -3x + 13 (subtract 3x from both sides)
Now we plug this equation into the y in the second equation and solve for x.
5x - 2(-3x + 13) = 7 (distribute)
5x + 6x - 26 = 7 (combine like terms)
11x - 26 = 7 (add 26 to both sides)
11x = 33
x = 3
Now that we know x is 3, we can plug it in a solve either equation for y.
y = -3(3) + 13
y = -9 + 13
y = 4
In the number 2,222.222, what is the difference between the 2 in the hundreds place and the 2 in the place to its left
1800
200 is the hundreds place value
2000 is the value to its left
2000-200 is 1800
What is the measure of arc e b c? 40° 90° 140° 220°
The measure of the arc is option (c) 140°
In geometry, an arc is a curved line that is a part of a circle's circumference. The measure of an arc can be calculated using the angle of the arc, which is measured in degrees.
In the case of EBC, the measure of the arc is 140°. This is because we can use the Angle-Side-Angle (ASA) congruence theorem, which states that two triangles are congruent if and only if two angles and the included side are equal.
In the case of EBC, we know that angle A equals 40° and angle C equals 90° so the only variable left is the measure of the arc, which is equal to 140°.
Therefore, the measure of EBC is 140°. This can be verified by drawing the triangle and measuring the arc with a protractor.
Therefore, option (c) is the right one.
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Complete Question:
What is the measure of arc EBC when the values of Angle a nd c are 90 and 40 degree respectively.
a) 40°
b) 90°
c) 140°
d) 220°
show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation. what are the equivalence classes of f and of t?
we have seen that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection.
What's more, the equivalence classes of F,T are :
[tex][F]_{R}[/tex] = Set, all things considered,
[tex][T]_{R}[/tex] = Set of all redundancies .
We have been given :
A= Set of every single compound suggestion
R= Logical equivalence of compound propositions .
We need to show that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection i.e.R is an equivalence connection .
Then, at that point, we have find the equivalence classes of F and T .
To show that R is an equivalence connection, we need to demonstrate that the connection R is reflexive, transitive and symmetric .
Reflexive
We will let a ∈ A.
As, a compound suggestion is in every case logically comparable to itself .
In this manner, a ≡ a, which suggests that (a,a) ∈ R.
Thus,R is reflexive .
Symmetric
We will let(a,b) ∈ R.
This implies that a ≡ b.
On the off chance that an and b have a similar truth table, b and a have a similar truth table .
Thus, by the evenness of logical equivalences, we get : b ≡ a
which suggests (b, a) ∈ R.
In this way, R is symmetric.
Transitive
We will let (a,b) ∈ R and (b,c) ∈ R.
This infers that :
a ≡ b
b ≡ c .
If an and b have a similar truth table and in the event that b and c have a similar truth table then,a and c
have a similar truth table.
Thus, by transitivity of logical equivalences, we get: a ≡ c
which suggests that (a,c) ∈ R.
Along these lines, R is transitive.
Presently, we can infer that R is an equivalence connection.
Presently, we need to find the equivalence classes of Fand T.
The equivalence class of F has every one of the logical equivalences that are misleading. Also, such logical equivalences are contradictions.
Accordingly,
[tex][F]_{R}[/tex] = Set, everything being equal.
The equivalence class of T have every one of the logical equivalences that are valid. Furthermore, such logical equivalences are redundancies .
Hence,
[tex][T]_{R}[/tex] = Set, all things considered.
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