Consider the function y = g (x), where:

lim g(x) = 5 x-8

lim g (x) = -3

•g (8) = -3

Which of the following statements is true about the function when x = 8?

The function has an INFINITE discontinuity at x = 8.

The function has a REMOVABLE discontinuity at x = 8.

The function is continuous at .= 8

The function has a JUMP discontinuity at x = 8.​

Answer:

2

Step-by-step explanation:

5 ÷ 2.5 = x

x = 2

2 1/2 is also written as 2.5 in it's decimal form

Since figure B is 2.5 times bigger than Figure A, dividing the similar side length by this multiplier gives you the smaller side length of figure A

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

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The town with the greater population density is C. Town A, with about 1,027 people per square mile.

Population density is the quotient of the number of individuals (population) living in a specified location divided by the geographic size of the area, usually measured in squared miles.

Towns          Population        Squared Miles        Persons/square mile

Town A         397,546                387                      1,027 (397,546/387)

Town B         264,108                 261                      1,012 (264,108/261)

Thus, we can conclude that Town A has a greater population density than Town B.

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Answer:75

Step-by-step explanation:

Answer:

m = −2

Step-by-step explanation:

Answer:

m=-2

Step-by-step explanation:

8m+5=6m+1

8m-6m=2m

2m+5=1

1-5=-4

2m=-4

-4/2=-2

m=-2

Answer: 13 saltos en total, 6 de los saltos de 3 metros, 7 de los saltos de 2 metros

Step-by-step explanation:

Si sumas 2+3, suma 5 y 5 cabe en 32 6 veces con un resto 2. (2+3)6 +2 = 30 +2 = 32 metros.

Answer:

452.389342 cubic inches

Step-by-step explanation:

The volume of a sphere is calculated using the formula V = 4/3 pi r^3

to determine the radius, you can notice that 4 spheres take up 24 in in length. This means that the radius of 1 sphere is 24/4/2 = 3 inches.

from there we plug and play: V = 4/3 * pi * 3^3 = 113.097336 cubic inches.

Note that this is only the volume of 1 sphere, so we multiply by 4

and we get 452.389342 cubic inches

Answer:

452.4

Step-by-step explanation:

Radius of each sphere: 24/4/2=3

Formula for volume: (4pir^3)/3

Formula for 4 spheres: 4 times (4pir^3)/3

Substitute 3 for r

Answer:

10

Step-by-step explanation:

Distance formula:

d = √(x₂-x₁)²+(y₂-y₁)²

A (1,2) D (4,3)

d = √(4-1)²+(3-2)² = 3.16227766

All 4 sides of a square are equal lengths.

The equation for the area of a square:

A = a²

A = (3.16227766)² = 10

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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The value of the unknown angle x is 22 degrees.

SV is a parallel to RU.

RV is a transversal line that cut across the parallel lines SV and RU.

Therefore,

x = ∠V(alternate angles)

Alternate angles are congruent.

Hence,

∠V + 44 + 5x + 4 = 180 (sum of angles in a triangle)

x + 44 + 5x + 4 = 180

x + 5x + 48  = 180

6x + 48 = 180

6x = 180 - 48

6x = 132

divide both sides by 6

x = 132  /6

x = 22 degrees

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We have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

To prove the inequality 2^n > n^2 using induction with a basis greater than 4, we will use n=5 as the basis.

Basis: n = 5
2^5 = 32 and 5^2 = 25. Since 32 > 25, the inequality holds true for n = 5.

Now, we need to assume that the inequality holds true for an arbitrary positive integer k > 4, and then prove that it holds true for k + 1.

Assume: 2^k > k^2 for k > 4.

Prove: 2^(k + 1) > (k + 1)^2

Step 1: Multiply both sides of the assumption by 2.
2 * (2^k) > 2 * (k^2)

Step 2: Simplify the left side of the inequality.
2^(k + 1) > 2k^2

Step 3: Show that 2k^2 is greater than (k + 1)^2 for k > 4.
2k^2 > (k + 1)^2
2k^2 > k^2 + 2k + 1

Step 4: Rearrange the inequality to show that it holds true for k > 4.
k^2 - 2k - 1 > 0

Since k > 4, it is clear that k^2 - 2k - 1 > 0, as the left side increases as k increases.

Therefore, we have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

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Answer:

Step-by-step explanation:

The 1st and second option

Answer:first and second

Step-by-step explanation:

To measure out exactly 1 gallon of water we need exactly six possible number of moves.

To measure out exactly 1 gallon of water using two jugs, one with a 3-gallon capacity and one with an 5-gallon capacity, you can follow some steps

Fill the 5-gallon jug with water completely. Pour the water from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of water in the 5-gallon jug.

Empty the 3-gallon jug completely. Pour the 2 gallons of water from the 5-gallon jug into the empty 3-gallon jug.

Fill the 5-gallon jug with water again. Pour water from the 5-gallon jug into the 3-gallon jug until it is full, which will leave exactly 1 gallon of water in the 5-gallon jug.

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Answer:

17\(\frac{1}{3}\)miles

40miles

Step-by-step explanation:

Given parameters;

Distance traveled by  the car = 1\(\frac{1}{2}\)miles  = \(\frac{3}{2}\)miles

Time taken = 2\(\frac{1}{4}\)minutes  = \(\frac{9}{4}\)minutes

Unknown:

Distance covered in 26minutes and in 1hr = ?

Solution:

Speed is the rate of change of distance with time.

   Speed  = \(\frac{distance}{time taken}\)

A. Insert the parameters and find the speed;

   Speed  = \(\frac{\frac{3}{2} }{\frac{9}{4} }\) = \(\frac{3}{2}\) x \(\frac{4}{9}\) = \(\frac{2}{3}\)miles/minutes

Distance covered in 26minutes;

   Distance  = speed x time

   Distance  = \(\frac{2}{3}\) x 26  = \(\frac{52}{3}\) miles  = 17\(\frac{1}{3}\)miles

B. Distance covered in 1hr or 60minutes;

  Distance = \(\frac{2}{3}\) x 60 = 40miles

Answer:

A) i 346.5

ii 346.5

B) I 115 tickets

ii $430

iii 4.88%

C) 129

Tower Productions would need to perform approximately 128 shows each year to earn a profit of $4,128,000.

To answer the given requirements, we need to calculate the revenue and variable costs for each show, determine the number of shows needed to break even using the equation approach, calculate the number of shows needed to earn a profit of $4,128,000 using the contribution margin ratio approach, and evaluate if the profit goal is realistic.

Let's calculate each step:

Requirement 1:

Revenue per show = Average tickets sold per show * Ticket price

Revenue per show = 900 * $65 = $58,500

Variable costs per show:

Cost of programs = $9 per guest * 900 guests = $8,100

Cost of performers = Number of performers * Net pay per show

Cost of performers = 55 * $330 = $18,150

Total variable costs per show = Cost of programs + Cost of performers

Total variable costs per show = $8,100 + $18,150 = $26,250

Requirement 2:

To compute the number of shows Tower Productions must perform each year to break even, we use the equation approach:

Break-even sales in dollars = Fixed costs + Target profit

Break-even sales in dollars = $580,500 + $0 (since it's break-even)

Number of shows needed to break even = Break-even sales in dollars / Revenue per show

Number of shows needed to break even = $580,500 / $58,500 = 9.93

Therefore, Tower Productions must perform 10 shows each year to break even (rounded up to the nearest whole number).

Requirement 3:

To compute the number of shows needed each year to earn a profit of $4,128,000 using the contribution margin ratio approach:

Contribution margin ratio = (Revenue per show - Total variable costs per show) / Revenue per show

Contribution margin ratio = ($58,500 - $26,250) / $58,500 ≈ 0.552

Required sales in dollars = Target profit / Contribution margin ratio

Required sales in dollars = $4,128,000 / 0.552 ≈ $7,476,403.63

Number of shows needed to earn a profit of $4,128,000 = Required sales in dollars / Revenue per show

Number of shows needed to earn a profit of $4,128,000 = $7,476,403.63 / $58,500 ≈ 128

Therefore, Tower Productions would need to perform approximately 128 shows each year to earn a profit of $4,128,000.

Based on the given information and calculations, it is difficult to determine if the profit goal of $4,128,000 is realistic without additional context or industry benchmarks. It would require careful evaluation of various factors such as market demand, competition, and historical performance. Additionally, it would be important to consider whether the theater's capacity and scheduling constraints allow for a sufficient number of shows to achieve the desired profit.

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a) The Highest Rating is 10

b) The lowest Rating is 3

c) The rating that appears the most times is 7.

The range in statistics refers to the distribution of your data between the lowest and highest value in the distribution. It is a widely used indicator of variation. Measures of variability provide you with descriptive statistics for summarising your data set in addition to measures of central tendency.

Given Ratings:

7, 7, 4, 7, 4, 9, 3, 5, 5, 3, 6, 8, 5, 4, 8, 3, 10, 8, 7,9

a) The Highest Rating is 10

b) The lowest Rating is 3

c) The rating that appears the most times

     Ratings                     Frequency

         3                                 |||

         4                                 |||

         5                                 |||

         6                                   |

         7                                 ||||

         8                                 |||

         9                                  ||

         10                                  |

Hence, the rating 7 appears most times.

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Answer:

30 questions

Step-by-step explanation:

if you cross multiply and divide like this,

\(\frac{27}{x}= \frac{90}{100}\)

27 x 100 = 2700

2700 / 90 = 30

you'll get ; 30 !

Answer:

There are 30 total questions on the exam

Explanation:

90% = 0.9

0.9 x TOTAL = 27

27/ 0.9 = TOTAL

30 = TOTAL

Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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A value of p for which div f = 0, i.e  if f is not divergence-free, then it is possible that there is no value of p for which div f = 0.  the answer is dne ( does not exist).

The question is asking whether there is a value of p for which the divergence of a vector field f is equal to zero. The divergence of a vector field is a scalar function that measures the amount of "outwardness" of the field at a given point. In other words, it measures how much the vector field is spreading out or converging at a point.

To determine whether there is a value of p for which div f = 0, we need to consider the mathematical expression for the divergence of f. The divergence of f is given by the following formula:
div f = (∂fx/∂x) + (∂fy/∂y) + (∂fz/∂z)

where fx, fy, and fz are the x, y, and z components of the vector field f, respectively. The partial derivatives in the formula represent the rate of change of the vector field in each of the coordinate directions.

To find out whether there is a value of p for which div f = 0, we need to determine the expression for f in terms of p. Without any information about f, we cannot answer this question definitively. If we are given a specific expression for f, we can substitute it into the formula for div f and try to solve for p. If there is a value of p that satisfies the equation div f = 0, then we can say that such a value exists.

However, if we are not given any information about f, we can still make some general observations. If f is a divergence-free vector field, meaning that div f = 0 everywhere, then any value of p will satisfy the equation. This is because the divergence is identically zero, so it does not depend on the value of p.

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The coordinates of the location where the facility should be built are (7, 0).

We are given the coordinates of three cities J(5, 2), K(-7, 2) and L(-5, -8).

A television station wants to build a new broadcast facility that is equidistant from the three cities.

We need to find out the coordinates of the location where the facility should be built.

We can use the distance formula to find the distance between two points (x1, y1) and (x2, y2):d

= √[(x₂ - x₁)² + (y₂ - y₁)²]

Let (x, y) be the coordinates of the broadcast facility.

We know that the distance from the facility to city J is equal to the distance from the facility to city K, and also equal to the distance from the facility to city L.

Using the distance formula, we can write these three equations:√[(x - 5)² + (y - 2)²]

= √[(x + 7)² + (y - 2)²]  [Distance from facility to city J = distance from facility to city K]

√[(x - 5)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city J = distance from facility to city L]√[(x + 7)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city K = distance from facility to city L]

Squaring both sides of these equations, we get: (x - 5)² + (y - 2)² = (x + 7)² + (y - 2)²  ...

(1)Simplifying this equation, we get: x = -1

Similarly, (x - 5)² + (y - 2)² = (x + 5)² + (y + 8)²  ...

(2)Simplifying this equation, we get: x² + y² - 10x - 4y + 90 = 0

Similarly, (x + 7)² + (y - 2)² = (x + 5)² + (y + 8)²  ..

.(3)Simplifying this equation, we get: x² + y² - 4x - 10y - 6 = 0

Now, we need to solve equations (2) and (3) for y and x respectively.x² + y² - 10x - 4y + 90 = 0

[Equation (2)]x² + y² - 4x - 10y - 6 = 0 [Equation (3)]

Multiplying equation (2) by 10, and equation (3) by 4,

we get:10x² + 10y² - 100x - 40y + 900 = 0  ...(4)

4x² + 4y² - 16x - 40y - 24 = 0  ...

(5)Subtracting equation (5) from equation (4),

we get:6x² + 6y² - 84x + 924 = 0

Simplifying this equation by dividing both sides by 6,

we get:x² + y² - 14x + 154 = 0

Completing the square, we get:(x - 7)² + y² = 95

This is the equation of a circle with center at (7, 0) and radius √95 units.

Therefore, the coordinates of the broadcast facility are (7, 0).

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Answer:

Step-by-step explanation:

The same array can represent both multiplication and division because for multiplication you count all the dots in the array. For division you do the array backward. 81÷9= ?. For this problem you would draw out 9 dots, then adding rows you would count to 81. Once you got to 81, the amount of columns you have is your answer. So for that problem your answer is 9.

Answer:

3/6

Step-by-step explanation:

The odds of getting an odd number are 3/6

The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

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Answer:

-1/5

y=-1/5 x-8

-1/5 is the slope

Step-by-step explanation:

-1/5

Formula-    y=mx+b

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Rewrite in slope-intercept form.

Simplify the left side

Simplify each term.

Combine 1/8 and x.

x/9+5y/8=-5

Subtract x/8 from both sides of the equation.

5y/8=-5-x/8

Multiply both sides of the equation by8/5.

8/5.5y/8=8/5(-5-x/8)

Simplify both sides of the equation.

Simplify the left side.

Simplify 8/5.5y/8

y=-x/5-8

y=-1/5 x-8

Step-by-step explanation:

Given equation:

1/8x + 5/8y =-5

Now write it in standard form like ax+by+c=0

1/8x + 5/8y + 5= 0

Now,slope of line (m) = -a/b

here value of a is 1/8 and value of b is 5/8

now by formula..

-(1/8)÷(5/8) = m(slope)

-1/8 × 8/5 = m

-1/5 = m

here ia your answer

1.  T5s = (1.08x10¹³ cm * (6.96x10⁵⁰ cm² / dVenus²))0.25 2. This

discrepancy is due to the greenhouse effect on Venus, where the thick

atmosphere traps heat and causes a much higher temperature. 3. TSS =

(1.08x10¹³ cm * (6.96x10⁵⁰ cm² / (2.28x10 cm)²))0.25. 4. different from the

observed subsolar.

1. To calculate T5s for Venus, we can use the formula

T5s = (\(Vermes * (r^{2} / dVenus^2))^{0.25}\).

Plugging in the given values, we have

T5s = (1.08x10¹³ cm * (6.96x10⁵⁰ cm² / dVenus²))0.25.

2. The measured surface temperature on Venus is around 700 K, which is significantly higher than the calculated T5s.

This discrepancy is due to the greenhouse effect on Venus, where the thick atmosphere traps heat and causes a much higher temperature.

3. Using the formula TSS = (\(Vermes * (r^2 / dMars^2))^{0.25}\),

we can calculate TSS for Mars. With the given average distance of Mars from the Sun (2.28x10 cm),

we have TSS = (1.08x10^13 cm * (6.96x10⁵⁰ cm² / (2.28x10 cm)²))0.25.

4. The calculated TSS for Mars is likely to be different from the observed subsolar temperature of Martian soil (300 K).

This difference can be attributed to various factors, such as the greenhouse effect, atmospheric composition, and surface conditions.

5. The greenhouse effect on Mars and Venus has distinct impacts on their surface temperatures.

While the subsolar surface temperature on Mars is relatively pleasant, the average temperature across the planet is about 212 K, well below the freezing point of water (273 K).

In contrast, Venus experiences a much higher average temperature due to the extreme greenhouse effect, resulting in surface temperatures of around 700 K.

6. The presence of extensive polar caps of frozen water and CO2 on Mars suggests that liquid water could have existed on the planet in the past.

One possible explanation is that Mars underwent climate changes, causing the frozen water and CO2 to melt and form liquid water.

However, further research is needed to fully understand the mechanisms behind the presence of liquid water on Mars in the past.\

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Answer:

The equation of the line that passes through the given points is ;

7y = -x + 12

Step-by-step explanation:

Here, we want to get the equation of the line that passes through the given points

The general equation form

is;

y = mx + b

where m is the slope and b is the y-intercept

Now, let us substitute the x and y coordinate values of each of the points;

for (-2,2); we have

2 = -2m + b

b = 2m + 2 •••••(i)

for F;

1 = 5m + b

b = 1-5m ••••••(ii)

Equate both b

1-5m = 2m + 2

1-2 = 2m + 5m

7m = -1

m = -1/7

Recall;

b = 2m + 2

b = 2(-1/7) + 2

b = -2/7 + 2

b = (-2 + 14)/7 = 12/7

The equation of the line is thus;

y = -1/7x + 12/7

Multiply through by 7

7y = -x + 12