Express the limit as a definite integral. [Hint: Consider
f(x) = x8.]
lim n→[infinity]
n 3i8
n9
sum.gif
i = 1

The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.

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.

Learn more about the circumcenter of a triangle on:

https://brainly.com/question/8055762

#SPJ1

Answer:

D

Step-by-step explanation:

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]

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.

The linear functions that match the following graph are given by:

A linear function is modeled by:

y = mx + b

In which:

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.

More can be learned about linear function concepts at https://brainly.com/question/24808124

#SPJ1

Using a system of equations, it is found that she has 9 picture books.

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:

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.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

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

common is 1 because 3-2 is 1

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

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.

Learn more about relative intensity here:

https://brainly.com/question/28068746

#SPJ4

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:

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.

Read more on combination here: brainly.com/question/17139330

#SPJ1

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?

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

Linear equations are equations that have constant average rates of change, slope or gradient

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

Read more about linear functions at:

https://brainly.com/question/4025726

#SPJ1

Answer:

nearest what?

Step-by-step explanation:

nearest tens's=340

nearest hundred's=300

The probability that more than 5 students will pass their exam is 0.0188416.

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.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

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.

Learn more about fraction here

https://brainly.com/question/183694

#SPJ4

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.

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.

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.

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.

Learn more about expected winnings in games at https://brainly.com/question/23430366

#SPJ1

How much do you expect to win?

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

The interquartile range is 55.

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.

To learn more about  interquartile range from the given link:

https://brainly.com/question/15115336

#SPJ4

The above question is not complete.

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 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.

Two 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:

The 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.

Of students in the sample, 90/200 fraction of the students were male.

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.

Know more about fractions here:

https://brainly.com/question/1622425

#SPJ4

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.

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 15 foot ramp must make an angle 19.45° with the ground to reach the same window.

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°.

Read more on sine of angles;

https://brainly.com/question/2920412

#SPJ1

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

11. 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;

14.  To find line HK

Substract the shortest line, IJ from the longest line GL

HK = GL - IJ

HK = 15 - 7

HK = 8cm

Learn more about geometry here:

https://brainly.com/question/24375372

#SPJ1

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

Answer:

Here's my answer

it's not number but

hope this help

The probability of getting tails on the coin and an even number on the number cube is 1/4

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

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

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

Answer:

Step-by-step explanation:

6 and 9

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

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.

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.