The given limit can be expressed as the definite integral:
∫[0 to 1] 3x^8 dx
To express the limit as a definite integral, we can use the definition of a Riemann sum. Let's consider the function f(x) = x^8.
The given limit can be rewritten as:
lim(n→∞) Σ[i=1 to n] (3i^8 / n^9)
Now, let's express this limit as a definite integral. We can approximate the sum using equal subintervals of width Δx = 1/n. The value of i can be replaced with x = iΔx = i/n. The summation then becomes:
lim(n→∞) Σ[i=1 to n] (3(i/n)^8 / n^9)
This can be further simplified as:
lim(n→∞) (1/n) Σ[i=1 to n] (3(i/n)^8 / n)
Taking the limit as n approaches infinity, the sum can be written as:
lim(n→∞) (1/n) ∑[i=1 to n] (3(i/n)^8 / n) ≈ ∫[0 to 1] 3x^8 dx
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Complete the remainder of the
table for the given function rule:
y = -2x +9
-4 -2 0 2 4
[?] [] [] []
y 17
The complete table of values for the function rule y = -2x +9 is
x -4 -2 0 2 4
y 17 13 9 5 1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to complete the remainder of the table for the given function rule?From the question, the function rule is given as:
y = -2x +9
The table of values is given as:
x -4 -2 0 2 4
y 17
Next, we substitute the other values of x in the equation y = -2x +9
y = -2(-2) +9 = 13
y = -2(0) +9 = 9
y = -2(2) +9 = 5
y = -2(4) +9 = 1
So, the complete table of values is
-4 -2 0 2 4
y 17 13 9 5 1
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The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to construct the following boxplot. Box plot Based on this boxplot, which of the following statements is true
The interquartile range is 55.
What is interquartile range?The interquartile range is the difference between the upper quartile and the lower quartile. In example 1, the IQR = Q3 – Q1 = 87 - 52 = 35. The IQR is a very useful measurement. It is useful because it is less influenced by extreme values as it limits the range to the middle 50% of the values.
Interquartile range = higher quartile - lower quartile
Given data, 50,25,80,10
To arrange the given data in ascending order 10,25,50,80.
Now, we will find the median for the given data.
The median is obtained by first arranging the data in ascending order and applying the following rule.
If the number of observations is even, then the median is [tex]\frac{n}{2}th[/tex] term.
In given data the number of observations is '4'(even)
If the number of observations is even, then the median is [tex]\frac{4}{2} th[/tex] means 2nd term. So median for the given data is 25. It means the value of lower quartile is 25 .
Interquartile range = higher quartile - lower quartile
= 80-25
= 55
Thus, interquartile range for the given data is 55.
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The above question is not complete.
Sound the loudness of a sound l in decibels is defined by l= 10 log.r, where r is the relative intensity of the sound. a chofr director wants to determine how many members could sing while maintaining a safe level of sound, about 80 decibels. if one person has a relative intensity of 10 when singing, then how many people could sing with the same relative intensity to achieve a loudness of 80 decibels?
Around 298 people can sing together with the same relative intensity to achieve a loudness of 80 decibels.
Given Information
Loudness of sound is given as, l = 10 log₁₀r
Here, r is the relative intensity.
Relative intensity of a single person when singing = 10
Loudness to be achieved, L = 10 decibels
Calculating the Number of People
Let the number of people with relative intensity 10 singing together be n decibels, then to produce a loudness of 80 decibels, we have,
80 = 10 log₁₀(r × n)
80 = 10 log₁₀(10 × n) [∵ r = 10]
log₁₀(10 × n) = 8
10n ≈ 2980
n = 298
Therefore, 298 people, each with a relative intensity of 10 decibels can sing together to achieve a loudness of 80 decibels.
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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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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:
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]
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.
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?
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
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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Line A is perpendicular to Line B.
If the slope of Line A is
-1/7
what is the slope of Line B?
[?]
Answer:
7
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other. For example, if line A has a slope of 2, then line B, perpendicular to line A, will have a slope of -0.5.
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.
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.
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
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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what is the length of side s of the square shown below
Hello,
an other method
Pythagorean theorem :
x² + x² = 6²
2x² = 36
x² = 36/2
x² = 18
x = √18 (and not -√18 because x ≥ 0)
x = √(9 × 2)
x = √(3² × 2)
x = 3√2
Answer A
The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5 She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales Now she has 14 more books of fairy tales than encyclopedias How many picture books does she have?
Using a system of equations, it is found that she has 9 picture books.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of picture books.Variable y: Number of encyclopedias.Variable z: Number of fairy tale books.The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:
[tex]\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}[/tex]
She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:
z + 5 - 0.5y = 14.
z - 0.5y = 9
From the ratios, we have that:
[tex]y = \frac{4}{3}x, z = \frac{5}{3}x[/tex]
Hence we solve for x to find the number of picture books:
[tex]z - \frac{y}{2} = 9[/tex]
[tex]\frac{5}{3}x - \frac{2}{3}x = 9[/tex]
x = 9.
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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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What is the common difference in this
recursive definition?
common is 1 because 3-2 is 1
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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335cm rounding off to the
nearest
Answer:
nearest what?
Step-by-step explanation:
nearest tens's=340
nearest hundred's=300
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?
= {y: y is a multiple of 3, 5 < y < 10}
Answer:
Step-by-step explanation:
6 and 9
A coin is flipped, and a number cube is rolled. what is the probability of getting tails on the coin and an even number on the number cube?
The probability of getting tails on the coin and an even number on the number cube is 1/4
What are probabilities?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The sample space of a coin is:
S = {H, T}
The sample space of a die is:
S = {1, 2, 3, 4, 5, 6}
The above means that:
A coin has 2 faces, one of which is the tail.
So, we have:
P(Tail) = 1/2
A number cube has 6 numbers, 3 or which are even.
So, we have
P(Even) = 3/6
The required probability is
P = P(Tail) * P(Even)
This gives
P = 1/2 * 3/6
Evaluate
P = 1/4
Evaluate the quotient
P = 0.25
Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25
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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
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 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.
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