What do domain restrictions mean for the graph of a rational function?

A possible value for the missing term of the geometric sequence 1250,__,50,.. is 250.

In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁ = ar²/ar

x/1250 = 50/x

x² = 1250 × 50

x² = 62500

x = √62500

x = 250

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Complete Question;

What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

Answer:

16

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Divide by 22.5 to find the number of sides n

n = \(\frac{360}{22.5}\) = 16

It an be concluded tat the regular polygon has 16 sides

A regular polygon is a polygon with equal angles and equal sides.

The sum of exterior angles of a regular polygon is 360°

According to the given data

One exterior angle of a regular polygon measures 22.5 °

Let us consider that the regular polygon has "n" sides

So from the exterior angle sum property of the regular polygon we can write that

\(\rm n \times 22.5\textdegree = 360 \textdegree\\ n = 360\textdegree /22.5\textdegree \\n = 16\)

So it an be concluded tat the regular polygon has 16 sides

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The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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Answer:

6h + 1

Step-by-step explanation:

number of hours: h

pay per hour: 30

pay for the hours: 30h

add sales bonus: 30h + 5

1/5 of total above: (1/5)(30h + 5) = 6h + 1

Answer: 6h + 1

The value of P(x < 5) is 0.600. The value of P(x > 8) = 0.125The value of P(6 < x < 10) is 0.375. The value of P(x < 6 or x > 10) is 0.625. The value of x is 2.154

To solve the given problems, we'll use the probability density function (PDF) f(x) = 2/x^3 for x > 1.

a) To find P(x < 5), we need to integrate the PDF from 1 to 5:

P(x < 5) = ∫[1, 5] (2/x^3) dx = [-1/2x^2] evaluated from 1 to 5 = -1/2(5)^2 - (-1/2(1)^2) = 0.600.

b) To find P(x > 8), we integrate the PDF from 8 to infinity:

P(x > 8) = ∫[8, ∞] (2/x^3) dx = [-1/2x^2] evaluated from 8 to ∞ = -1/2(∞)^2 - (-1/2(8)^2) = 0.125.

c) To find P(6 < x < 10), we integrate the PDF from 6 to 10:

P(6 < x < 10) = ∫[6, 10] (2/x^3) dx = [-1/2x^2] evaluated from 6 to 10 = -1/2(10)^2 - (-1/2(6)^2) = 0.375.

d) To find P(x < 6 or x > 10), we subtract P(6 < x < 10) from 1:

P(x < 6 or x > 10) = 1 - P(6 < x < 10) = 1 - 0.375 = 0.625.

e) To determine x such that P(X < x) = 0.75, we set up the equation and solve for x:

∫[1, x] (2/t^3) dt = 0.75. Integrating the PDF, we get [-1/t^2] evaluated from 1 to x = -1/x^2 - (-1/1^2) = -1/x^2 + 1 = 0.75. Solving for x, we find x = 2.154.

In summary, the probability calculations are as follows:

a) P(x < 5) = 0.600

b) P(x > 8) = 0.125

c) P(6 < x < 10) = 0.375

d) P(x < 6 or x > 10) = 0.625

e) x = 2.154 for P(X < x) = 0.75.

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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x > 1. Determine the following (round all of your answers to 3 decimal places):

a) P(x < 5)=

b) P(x > 8)=

c) P(6 < x < 10)=

d) P(x < 6 or x > 10)=

e) Determine x such that P(X < x) = 0.75

Answer:

Step-by-step explanation:

Answer

Option B is correct

x = 4√3

Explanation

The right angle triangle is sketched above and we will use trignometric relations to solve this.

We need the value of x,

In a right angle triangle, the side opposite the right angle is called the Hypotenuse, the side opposite the given angle (let us use 60° as the given angle) is called the Opposite and the remaining side is called the Adjacent.

For this question,

Hypotenuse = ?

Opposite = 12

Adjacent = x

Using TOA, we can say that

Tan 60° = (Opp/Adj)

tan 60° = (12/x)

Note that Tan 60° = √3

tan 60° = (12/x)

√3 = (12/x)

Cross multiply and we have

x = (12/√3)

We can then rationalize this

x = 4√3

Hope this Helps!!!

The value of the test statistic for this data set is 40.

To test whether dramas draw a larger crowd on average than comedies using the Wilcoxon rank-sum test, we need to first calculate the value of the test statistic.

The Wilcoxon rank-sum test is a non-parametric statistical test that is used to compare the means of two groups when the assumptions of the t-test are not met. It works by ranking the combined data from both groups and comparing the ranks of the observations from each group.

To calculate the value of the test statistic for this data set, we first need to combine the revenues from both drama and comedy movies and rank them in order from lowest to highest. The resulting ranks for each group would be as follows:

Revenues (millions of dollars) | Drama | Comedy

260110                                      |    1        |   5

300150                                     |    2       |   6

250200                                    |    3       |   7

270290                                    |    4       |   8

280170                                     |    5       |   9

280210                                     |    6       |   10

Next, we need to sum the ranks for each group and calculate the difference between the two sums. In this case, the sum of the ranks for the drama group is 15, and the sum of the ranks for the comedy group is 55. The difference between these two sums is 40, which is the value of the test statistic.

Therefore, the value of the test statistic for this data set is 40.

In the next step, we would use this test statistic to determine whether the data provide sufficient evidence to reject the null hypothesis that the two groups have the same mean. This would involve calculating the p-value and comparing it to the desired level of significance.

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Answer:

We can factor out a 4x from the numerator and a 2 from the denominator, which gives:

(4x(x+1)) / 2( x^2 - 1)

We can then factor the denominator further using the difference of squares formula, which gives:

(4x(x+1)) / 2(x+1)(x-1)

Simplifying this expression further, we can cancel out the (x+1) terms in the numerator and denominator, which gives:

2x / (x-1)

Therefore, 4x^2 + 4x / 2x^2 - 2 simplifies to 2x / (x-1).

The formula is true for all positive integers n.

The formula to verify that for all n ≥ 1, the sum of the squares of the first 2n positive integers is given by the formula is as follows :1² + 2² +3²+...+(2n)² =n(2n + 1)(4n+1)/ 3

To prove this formula is true for all n greater than or equal to 1, we need to use the mathematical induction method.

Base case:

Let's assume that n= 1. Then,1² + 2²=1(2(1)+1)(4(1)+1)/ 3=5/3Therefore, the formula is correct for the initial case (n=1).

Induction Hypothesis:

Suppose that the formula is true for all integers 1≤ k ≤ n. That is, 1² + 2² + 3² + ... + (2k)²= k(2k+1)(4k+1)/3.

We have to prove that this formula is true for the case n+1, i.e.1² + 2² + 3² + ... + (2n)² + [(2(n+1))]² = (n+1)[2(n+1)+1][4(n+1)+1]/3

Proof:

Now, we will prove the induction step, as follows:

(1² + 2² + 3² + ... + (2n)²)+ [(2(n+1))]²=(n+1)(2(n+1)+1)(4(n+1)+1)/3(k= n+1)

[Using Induction Hypothesis]= k(2k+1)(4k+1)/3= (n+1)[2(n+1)+1][4(n+1)+1]/3

Therefore, the formula is true for all positive integers n.

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Answer:

15, - 7, 8, - 24

Step-by-step explanation:

1

f(4) = \(\frac{1}{2}\) × 4 + 13 = 2 + 13 = 15

2

f(5) = \(\frac{3}{5}\) × 5 - 10 = 3 - 10 = - 7

3

f(- 1) = (- 1)² + 7 = 1 + 7 = 8

4

f(2) = 3(2)³ - 12(2)² = 3(8) - 12(4) = 24 - 48 = - 24

Answer:

48

Step-by-step explanation:

Adam has 2/3 of books that brett and charlie have : 2/3 of 72 wich is 48

The following is the null and alternate hypothesis:

H₀ = u = 40.1

H₁ = u < 40.1

The null hypothesis should read as follows if we want to test the assertion that the average workweek has decreased:

The claim that there is a decrease in the typical work week should be made in the alternative hypothesis. The genuine mean is smaller than 40.1 can be used to express this.

The null hypothesis should assert that the average work week has not been significantly reduced, which is the opposite of the alternative. This can be expressed mathematically as 40.1 as the genuine mean.

Therefore, The alternative and null hypothesis are then:

H₀ = u = 40.1

H₁ = u < 40.1

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Answer:

\(d \approx 12.6\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A (-4, 2)

Point B (8, 6)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

The relationship between the figure JKLM and it's image, J'K'L'M' following a dilation by a scale factor of 1 is that JKLM and J'K'L'M' have the same dimensions, and location

Scale factors are numbers that are used to multiply a quantity to scale it by a given rate.

Part A

In order to easily describe the relationship between the image J'K'L'M' and the original figure JKLM, the point J can be taken as the origin such that the image vertices are obtained by dilating the points on the original figure in their original direction relative to J using the specified scale factor.

The coordinates of the vertices of JKLM relative to J are;

J(0, 0), K(6, 0), L(6, -6), M(0, -6)

Distance of K from J = 6 - 0 = 6 units to the right of K

Therefore, using a scale factor of 1;

The distances of the vertices of square J'K'L'M' from point J are the same and in the same direction as the distances of the vertices of square JKLM from point J.

The vertices of J'K'L'M' using a scale factor of 1 are therefore located at the same coordinates as the vertices of square JKLM

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

  A = C²/(4π)

Step-by-step explanation:

You want a formula for the area of a circle, given its circumference.

Relevant relations for a circle are ...

  A = πr² . . . . . . . . A = area, r = radius

  C = 2πr . . . . . . . . C = circumference

Solving the circumference equation for r, we find ...

  r = C/(2π)

Substituting that into the area equation, we have ...

  A = π(C/(2π))²

  A = C²/(4π)

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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).

The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).

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Answer:

see below

Step-by-step explanation:

Pair 1 is a rotation since we turn figure A into figure B

Pair 2 is a reflection since we flip figure A into figure B over a horizontal line

Pair 3 is a translation since we slide figure A into figure B by moving it down

Answer:

95

Step-by-step explanation:

19 x 5 = 95

Answer:

Between 5 and 5 1/2 inches

Step-by-step explanation:

(A) the number of ways to pass out 13 cards to each of the two players is (52! / (13! × 13!)) × (39! / (26! × 13!)) (B) We can calculate probability by dividing the number of favorable outcomes by the total number of possible outcomes. (26! / (13! × 13!))²] / [(52! / (13! × 13!)) × (39! / (26! × 13!))]

A) To determine the number of ways to distribute 13 cards to each of the two players, we can use the concept of combinations. Since the order of distribution does not matter, we'll use the formula for combinations:

C(52, 13) × C(39, 13)

= (52! / (13! × (52 - 13)!)) × (39! / (13! × (39 - 13)!))

Simplifying this expression:

= (52! / (13! × 39!)) × (39! / (13! × 26!))

= (52! / (13! × 13! × 26!)) × (39! / (26! × 13!))

= (52! / (13! × 13! × 26!)) × (39! / (26! × 13!))

= (52! / (13! × 13!)) × (39! / (26! × 13!))

Therefore, the number of ways to pass out 13 cards to each of the two players is (52! / (13! × 13!)) × (39! / (26! × 13!)).
B) To calculate the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color, we need to find the favorable outcomes and divide it by the total number of possible outcomes.
The favorable outcome is when player 1 receives 13 cards of one color and player 2 receives 13 cards of the other color.
For player 1 to receive 13 red cards, there are C(26, 13) ways, and for player 2 to receive 13 black cards, there are C(26, 13) ways.

Therefore, the number of favorable outcomes is C(26, 13) ×C(26, 13).
The total number of possible outcomes is the same as the answer to part A, which is C(52, 13) × C(39, 13).
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.

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There are approximately \(6.54 \times 10^{11}\) ways to distribute 13 cards to each of the two players, and the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color is approximately 0.76%.

a. To determine the number of ways to pass out 13 cards to each of the two players, we can use the concept of combinations. We need to select 13 cards out of the total 52 cards for the first player, and then the remaining 13 cards will automatically go to the second player. The number of ways to choose 13 cards out of 52 is given by the combination formula: \(52_C_{13} = \frac{52!}{(13!(52-13)!)}\). Evaluating this expression, we find that there are approximately \(6.54 \times 10^{11}\) ways to distribute the cards.

b. The probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color depends on the specific color that each player receives. Let's consider the case where player 1 receives all red cards and player 2 receives all black cards. There are 26 red cards and 26 black cards, so the probability of player 1 receiving all red cards is given by: \(\frac{26_C_{13} \times 26_C_0}{52_C_{13}}\). Evaluating this expression, we find that the probability is approximately 0.0076, or 0.76%.

In conclusion, there are approximately \(6.54 \times 10^{11}\) ways to distribute 13 cards to each of the two players, and the probability that player 1 will receive 13 cards of one color and player 2 will receive 13 cards of the other color is approximately 0.76%.

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Answer:

  A.  0

Step-by-step explanation:

You want the discriminant of the quadratic 4x²+4x+1.

The discriminant of quadratic ax²+bx+c is ...

  d = b² -4ac

Your given expression has ...

Substituting these values into the formula for the discriminant, we get ...

  d = 4² -4(4)(1) = 16 -16 = 0

The discriminant of the polynomial is 0.

Answer:

First, you have to add 11 on both sides, so the answer is A

Rounding to the nearest whole number, the expected number of wins in a season for a team with 1394 turnovers is 38.

To find the expected number of wins in a season for a team with 1394 turnovers, we can substitute the value of x = 1394 into the regression equation:

y = 98 - 0.043x

y = 98 - 0.043 * 1394

y ≈ 98 - 59.942

y ≈ 38.058

Rounding to the nearest whole number, the expected number of wins in a season for a team with 1394 turnovers is 38.

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1. You can solve a system of equations using graphs when there are no decimals or fractions in the equations. This can allow you to almost precisely plot a graph, and determine the values of the variables.

2. You can use the substitution method when one (or both) of the equations is already solved for one of the variables.

3. Elimination is best used when the equations are written in the form Ax + B = C, and also when the coefficients are values not equal to 1.

The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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Answer:

Step-by-step explanation: