In Class 12, to find the domain and range of a function, you can use the following steps:
Domain: The domain of a function is the set of all input values for which the function is defined. To find the domain of a function, you need to look at the function and identify any values of x that would make the function output undefined. These values of x are not in the domain of the function.For example, if the function is f(x) = 1/x, the domain of the function is all real numbers except 0, because dividing by 0 is undefined. In this case, the domain of the function is (-∞,0) U (0,+∞)
Range: The range of a function is the set of all possible output values of the function. To find the range, you can look at the function and identify any restrictions on the output values.For example, if the function is f(x) = √x, the domain of the function is all non-negative real numbers, because √x is only defined for non-negative values of x. In this case, the range of the function is [0,+∞)
Note that some functions may have more complex expressions, in such cases, you may have to use algebraic methods to find the domain and range.
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In an algebra class, there are 10 less than twice as many boys as girls. If the total number of students is 38, how many boys and girls are there in class?
Answer: 16 girls and 22 boys
Step-by-step explanation:
This can be solved with simple algebra.
Let's say that the number of girls is x.
Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)
The total number of students is 38. Adding the girls, the equation is now 3x-10=38.
3x=48
x=16.
2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.
To check our work, add 16+22. This equals 38.
a 10 foot ramp must make an angle of 30° with the ground if it is to reach a certain window. what angle must a 15 foot ramp make with the ground to reach the same window
The 15 foot ramp must make an angle 19.45° with the ground to reach the same window.
What angle must be made with the ground by the 15 foot ramp?Since the height of the window above ground remains constant in both cases, it follows that by means of trigonometric identity sine; we have;
10sin30° = 15sinx
sinx = 5/15 = 0.333
x = sin-¹(0.333)
x = 19.45°.
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A gambling game pays 10 to 1 and there is 1 chance in 12 for me to win. suppose i play this game 150 times, betting $20 each time. assume that the plays are independent of each other.
The amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.
What is a fractional game?A fractional betting or game allows the gambler to calculate the winning from their betting when it is compared with their stake.
The number on the left-side represents the winning, while the number on the right side of the fractional odds represents the stake (investment).
When the gambler wins, they receive 10x their stake. The expected amount to be won is computed as the total stakes, multiplied by the winning probability and the fractional odds.
Data and Calculations:Fractional odds of winning = 10/1
Chance of winning = 1/12
Number of independent games played = 150 times
Bet each time = $20
Total bets = $3,000 ($20 x 150)
Amount won = $2,500 ($3,000 x 1/12 x 10/1)
Thus, the amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.
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Question Completion:How much do you expect to win?
help
11-16
please i dont understand
Answer:
see attached
Step-by-step explanation:
There are many vocabulary words and theorems associated with angles where a transversal crosses parallel lines. These are needed for the "explain your reasoning" part of the question.
Where 2 lines crossWhere one line crosses another, the angles formed are either "adjacent" (share a side and vertex), or "vertical" (share only a vertex, formed from opposite rays). In Figure 11, x° and 67° are "adjacent" angles. In Figure 12, y° and 109° are "vertical" angles.
The adjacent angles are also called a "linear pair", and their total is 180°. They are supplementary.
The vertical angles are congruent.
Where a transversal crosses parallel linesTwo sets of four angles are formed when a transversal crosses parallel lines. The relations between angles of one of those sets and angles of the other of those sets are described using several different terms:
"Alternate" angles are on opposite sides of the transversal. "Consecutive" or "same-side" angles are on the same side of the transversal. "Exterior" angles are outside the parallel lines. "Interior" angles are between the parallel lines. "Corresponding" angles are in the same relation to the point of intersection.
Alternate exterior angles (congruent): Fig. 11, x° and y°.
Alternate interior angles (congruent): Fig. 13, y° and the one marked with the right angle symbol.
Consecutive interior angles (supplementary): Fig. 12, x° and 109°; Fig. 14, x° and y°.
Consecutive exterior angles (supplementary): none shown in these figures.
Corresponding angles (congruent): Fig 14, x° and 65°; Fig. 16, x° and 130°.
The upshot of all of these relations is this:
all acute angles are congruentall obtuse angles are congruentobtuse angles are supplementary to acute anglesIf any angle is a right angle, all of them are.ApplicationThe attached table shows the values of x° and y° in the various figures. For the purpose here, we simply identified the angles as acute or obtuse, and matched values accordingly. The explanation can get as elaborate as you like. For example, ...
11. x° and y° are alternate exterior angles, so congruent. x° and 67° are a linear pair, so x° = 180° -67° = 113°.
12. x° and 109° are consecutive interior angles, so supplementary. x° = 180° -109° = 71°. y° and 109° are vertical angles, so congruent.
Point Y is the circumcenter of ΔDEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. The length of F Y is 3 x + 7 and the length of Y E is 5 x minus 3.
Find FY.
5
11
17
22
The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.
What is the Circumcenter of a Triangle?The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.
Based on the definition of the circumcenter, and Y is the circumcenter, therefore:
YE = FY
Plug in the values
5x - 3 = 3x + 7
5x - 3x = 3 + 7
2x = 10
x = 5
FY = 3x + 7 = 3(5) + 7
FY = 22 units.
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Answer:
D
Step-by-step explanation:
HELP ASAP PLS
Select the correct answer from each drop-down menu.
Quadratic function f is shown on the graph.
I don't know what the options are in the drop-down menu but the function f is symmetric around the point (4,–1) which is called the axis of symmetry. (4,–1) is the minimum of the graph.
What is the nth term of the sequence below?
2, 6, 12, 20, . . .
A. [tex]n {}^{2} \: + \: 1[/tex]
B. [tex]3n[/tex]
C. [tex]n(n \: + \: 1)[/tex]
D. [tex] {n}^{2} \: - \: 1[/tex]
Answer:
Option C
Kindly award branliest
Step-by-step explanation:
Tn = n(n + 1)
T1 = 1(1 +1) = 1(2) = 2
T2 = 2(2+1) = 2(3) =6
T3 = 3(3 + 1) = 3(4) = 12
T4 = 4(4 + 1) = 4(5) = 20
... It obeys
A taxi charges $2.50 for the first mile and $0.40 for each mile after that. The expression below shows how to find the total cost, in dollars, of a 20-mile taxi ride. 2.50 0.40 (20 minus 1)
The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.
Given a taxi charges $2.50 for the first mile and $0.40 for each mile
We are required to make an expression showing total cost and total cost of a 20 mile ride.
let the miles ride by tax be x.
Total cost of the product or service=Number of units*price of one units.
We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.
So,the expression showing looks like 2.50+0.40x.
Now to find the cost when taxi travels 20 miles, we have to put x=20,
Cost=2.50+0.40*20
=2.50+(40*20)/100
=2.50+800/100
=2.50+8
=$10.50
Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.
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7. Jeff and Stephen go to the mall. The two
boys buy a total of 15 T-shirts. Stephen gets
three less than twice as many T-shirts as Jeff.
a) Write an equation to represent the
information in the second sentence.
b) Write an equation to represent the
information in the third sentence.
c) Solve the linear system by substitution
to find the number of T-shirts each boy
bought.
d) If the T-shirts cost $8.99 each, how
much did each boy spend before taxes?
Answer:
Let j = number of shirts Jeff bought and s = the number of shirts Stephen bought.
a.) s + j = 15
b.) 2j - 3 = s
c.) Plug 2j -3 into the equation from question a.
2j -3 + j = 15
3j -3 = 15
3j = 18
j = 6
2j - 3 = s when j = 6
2(6) - 3 = s
s = 9
Jeff bought 6 shirts; Stephen bought 9 shirts.
d.) Jeff cost = 8.99(6) = $53.94
Stephen cost = 8.99(9) = $80.91
i need help with this page
11. m ∠ BCE = 25 °
m ∠BAD = 39°
12. n = 11. 5°
13. The quadrilaterals are rectangle and parallelogram. Option A and C
14. HK = 8cm
How to determine the angles11. From the figure shown, we have that;
m ∠ EBC = 27°
m ∠ ADE = 52°
To find
m ∠ BCE
Note that m ∠ ADE is alternate and equal to m∠ DEC = 52 and is also on a straight line with ∠BEC
52 + ∠BEC = 180°
∠BEC = 180 - 52° = 128°
Remember that ∠BEC, ∠ BCE and ∠ EBC are angles in a triangle which sum up to 180°
128° + ∠ BCE + 27° = 180°
∠ BCE = 180 ° - 155°
∠ BCE = 25 °
To determine m ∠BAD
65° + 76 + m ∠BAD = 180° , sum of angles in a a triangle
m ∠BAD = 180 - 141
m ∠BAD = 39°
12. Value of n is gotten by equating the two lengths
( 10n + 19) = (12n - 4)
collect like terms
10n - 12n = -4 - 19
- 2n = -23
n = -23/-2
n = 11. 5°
13. The only quadrilaterals with congruent diagonals are;
rectangleparallelogram14. To find line HK
Substract the shortest line, IJ from the longest line GL
HK = GL - IJ
HK = 15 - 7
HK = 8cm
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Someone help me please
Answer:
50
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem to find the hypotenuse. a^2+b^2 = c^2
40^2+30^2 = c^2
1600+900 = c^2
2500 = c^2
50 = c
A die is rolled twice. What is the probability of getting either a multiple of 2 on the first roll or a total of 6 for both rolls
The correct answer is 7/12.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.Let A = Getting multiple of on the first one
B = A total of for both roll
P (A U B) = P(A) + P(B) - P(A ∩ B)
[tex]\frac{18}{36} + \frac{5}{36} - \frac{2}{36} \\\\ = \frac{21}{36} \\[/tex]
[tex]\frac{7}{12}[/tex]
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What is the common difference in this
recursive definition?
common is 1 because 3-2 is 1
Sabrina finished 8/11 of her math assignment. if there are 22 problems in her assignment what fraction represents the number of problems completed over the total number of problems in the assignment ?
The fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.
According to the question,
There are 22 problems in her assignment and Sabrina finished 8/11 of her math assignment.
In order to find the fraction represents the number of problems completed over the total number of problems in the assignment.
(8/11) * (2/2) = 16/22
Hence, the fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.
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11. (04.01 MC)
Choose the system of equations that matches the following graph: (1 point)
The linear functions that match the following graph are given by:
2x + y = 0.-5x + y = -7.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The system of equations in this problem is composed by two lines.
The decaying line goes though (-2,4) and (2,-4), hence the slope is given by:
m = (-4 - 4)/(2 - (-2)) = -2
Hence:
y = -2x + b
When x = -2, y = 4, hence we find b as follows:
4 = -2(-2) + b
b = 0.
Hence:
y = -2x -> 2x + y = 0.
The increasing line goes though (1,-2) and (2,3), hence the slope is given by:
m = (3 - (-2))/(2 - 1) = 5
Hence:
y = 5x + b
When x = 1, y = -2, hence we find b as follows:
-2 = 5 + b
b = -7.
Hence:
y = 5x - 7.
-5x + y = -7.
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Write the slope-intercept equation of the line that passes through the given points (1,-7),(5,-15)
Answer:
y=-2x+5
Step-by-step explanation:
The slope is
[tex] \frac{ - 15 - ( - 7)}{5 - 1} = \frac{ - 8}{4} = - 2[/tex]
Substituting into point-slope form,
y + 7 = -2(x-1)
y + 7 = -2x + 2
y = -2x + 5
You buy 4 health bars and 3 health drinks for $10. your friend buys 6 health bars and 2 health drinks for $10.
Answer:
The bars cost 1 each and the drinks cost 2 each.
Step-by-step explanation:
Let b = bars and d = drinks
4b + 3d = 10 6b + 2d = 10
There are a few ways to solve this. If I want to eliminate the b's from both equations. I would multiple the first equation all the way through by -6 and the second equation all the way through by 4.
4b+ 3d = 10
-6(4b + 3d) =(10)-6 Multiple all the way through by -6
-24b -18d = -60 A positive multiplies by a negative is a negative
6b + 2d = 10
4(6b + 2d) = (10)4 Multiple all the way through by 4
24b + 8d = 40
Take the two bold equations from above and add them together
-24b - 18d = -60
24 b + 8d = 40
-10d = -20 Divide both sides by -10
d = 20 A negative divided by a positive is a negative.
Plug in 2o for d in either of the top two equations and get b = 1.
What is the slope of the line shown below?
(-1,-4)
(2, 2)
Answer:
2
Step-by-step explanation:
(-1,-4) (2,2)
To find the slope, use the equation y2-y1/x2-x1
2-(-4)/2-(-1) = 6/3
6/3=2
2 is the slope.
Drag the tiles to the correct boxes to complete the pairs Match each inequality to the number line that represents its solution
Answer:
x ≤ 7 => [tex]- \frac{13x}{18}[/tex] + [tex]\frac{5}{9} \geq - \frac{9}{2}[/tex]
x ≤ 8 => -[tex]\frac{x}{10}[/tex] + [tex]\frac{1}{5}[/tex] ≥ -[tex]\frac{33}{55}[/tex]
x ≤ -5 => - [tex]\frac{50x}{3}[/tex] - [tex]\frac{11}{6}[/tex] [tex]\geq[/tex] [tex]\frac{163}{2}[/tex]
x ≤ -6 => [tex]\frac{3x}{2}[/tex] + 105 ≤ 96
Step-by-step explanation:
-[tex]\frac{x}{10}[/tex] + [tex]\frac{1}{5}[/tex] ≥ -[tex]\frac{33}{55}[/tex]
[tex]\frac{1}{5}[/tex] + [tex]\frac{33}{55}[/tex] ≥ [tex]\frac{x}{10}[/tex] / *10
2 + 6 ≥ x
8 ≥ x
- [tex]\frac{50x}{3}[/tex] - [tex]\frac{11}{6}[/tex] [tex]\geq[/tex] [tex]\frac{163}{2}[/tex] / *6
- 100x - 11 ≥ 489
-500 ≥ 100x
-5 ≥ x
[tex]\frac{3x}{2}[/tex] + 105 ≤ 96
[tex]\frac{3x}{2}[/tex] ≤ 96 - 105 / * [tex]\frac{2}{3}[/tex]
x ≤ -6
[tex]- \frac{13x}{18}[/tex] + [tex]\frac{5}{9} \geq - \frac{9}{2}[/tex] /*18
-13x + 10 ≥ - 81
-13x ≥ -91 /:-13
x ≥ 7
90 pointssss!Please help! On parts a, b, and c. Thank you!
There is a 40% probability that a student PASSES their first statistics exam. Using a Binomial Distribution, if we randomly select 7 students: What is the probability that more than 5 PASS their first statistics exam
The probability that more than 5 students will pass their exam is 0.0188416.
How to find the probability?The probability that a student passes their examination = 40% = 0.4
The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam
The probability that 6 students pass their exam =
[tex]7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032[/tex]
The probability that 7 students pass their exam =
[tex]7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384[/tex]
The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384
= 0.0188416
Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.
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A plot of land has been surveyed for a new housing development with borders AB, BC, DC, and DA. The plot of land is a right trapezoid with a height of 60 feet and an opposite leg length of 65 feet.
Right trapezoid A B C D is shown. Angles A and D are right angles. Sides A B and D C are parallel. The length of A D is 60 feet and the length of B C is 65 feet.
If the measure of angle BCD is 67.4°, the measure of angle ABC is
°.
If the length of base AB is 80 feet, the length of DC is
feet.
Answer:
90 approximately because if AB is 80 then DC should be 90 because AB come before DC in letters
Answer:
112.6 degrees and 105 feet.
Step-by-step explanation:
took the assignment
Find the scale factor of TUVW to ABCD
Answer:
the scale factor is :
[tex]\frac{9}{15}[/tex]
Step-by-step explanation:
The trapezoids TUVW and ABCD are similar
and AB is the corresponding side of the side TU
Then the function that transform TUVW to ABCD is of scale factor :
[tex]= \frac{AB}{TU}[/tex]
[tex]= \frac{9}{15}[/tex]
How many times larger is the volume of a cone if the radius is doubled?
Enter only a number as your answer.
Answer:
Here's my answer
it's not number but
hope this help
A university surveyed its students on their opinions of campus housing. the following two-way table displays data for the sample of 200200200 students who responded to the survey. how many students in this sample had a negative opinion of campus housing? students gender positive opinion negative opinion neutral opinion male 404040 363636 141414 female 424242 565656 1212
Of students in the sample, 90/200 fraction of the students were male.
What is a fraction?In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.To find the fraction of male students:
Number of male students = 90
Number of female students = 110
So, total students = 90 + 110 = 200
Fraction of students who were male = male students / total students
Fraction of students who were male = 90/200
So, 90/200 fraction of the students were male.
Therefore, 90/200 fraction of the students were male.
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The question you are looking for is given here:
A university surveyed its students on their opinions of campus housing. The following two-way table displays data for the sample of
200 students responded to the survey.
If the first equation is multiplied by 3 and then the equations are added, the result is _____.
3x + y = 3
x - 3y = -2
Answer:
10x-6y-11
Step-by-step explanation:
3(3x+y) = 3(3) +×-3y=-2
9x + 3y = 9 + x -3y =-2
9x+x = -3y-3y =-2-9
10x = -6y =-11
10x-6y-11
18. A8 x 6 x 4 cm³ metallic cube is melted. Find the minimum volume of molten metal which should be added to
mould it into a cube whose edge is an integer.
(1) 20
(2) 21
(3) 23
(4) 24
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
How to estimate the minimum volume of molten metal?Volume exists as a scalar quantity representing the amount of three-dimensional space encircled by a closed surface.
The minimum volume of a shape with measured dimensions exists provided by the lowest values of the dimensions when accounting for measurement error. Maximum Volume: The maximum volume of a shape with measured dimensions exists provided by the highest values of the measurements when accounting for measurement error.
The volume of the cube [tex]= 8*6*4[/tex]
[tex]= 192 cm^3[/tex]
To create the X as the sides of the cube we should add material.
The nearest cube number to 192 exists at 216
The amount of material to be added exists
= 216 -192
[tex]= 24 cm^3[/tex]
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
Therefore, the correct answer is an option (4) 24.
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n this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
In order to determine the number of different groups of three players that are possible for Coach Bennet to select from, we would use a mathematical model referred to as combination.
Mathematically, combination is given by this mathematical equation:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of items.r is the number of times of choosing items.Substituting the given parameters into the formula, we have;
Number of groups = (⁶C₃ × ⁸C₀) + (⁶C₂ × ⁸C₁) + (⁶C₁ × ⁸C₂) + (⁶C₀ × ⁸C₃)
Number of groups = 20 + 120 + 168 + 56
Number of groups = 364 different groups.
Therefore, there are 364 different groups of three players possible for Coach Bennet to select.
In conclusion, we can infer and logically deduce that this is a combination because the order in which the players are selected isn't important.
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Complete Question:
In this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
How many different groups of three players are possible for Coach Bennet to select?
335cm rounding off to the
nearest
Answer:
nearest what?
Step-by-step explanation:
nearest tens's=340
nearest hundred's=300
A _______ group is another name for a command group
Answer:
department
Step-by-step explanation:
A "task force" group is another name for a command group.
We have,
A task force is a temporary grouping of individuals or units with a specific objective or mission.
It is typically formed to address a particular task or problem and is led by a designated commander or leader.
Task forces can be assembled from different departments or organizations to collaborate and work together towards a common goal.
Thus,
A "task force" group is another name for a command group.
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